Technical Field

[0001] Various embodiments relate generally to methods and devices for channel estimation.

Background

[0002] Various radio communication technologies may rely on channel estimation for reception and demodulation of radio signals. Numerous different channel models have been applied and may each be tailored to the particular characteristics of each radio communication technology.

[0003] Next generation or "5G" radio access technologies may target operation in mid to high GHz frequency bands, such as e.g. 30 GHz and higher. Such high frequency radio carriers may suffer from considerable path loss, which may increase approximately linearly with carrier frequency. In order to compensate for potentially severe path loss, 5G radio access technologies (in particular those using massive multiple-input multiple-output

(MIMO)) may highly directional or "sharp" analog beamforming in one or both of the transmit and receive directions.

[0004] The properties of the resulting equivalent channels composed of the physical channel and such analog beamformers may differ substantially from many existing channel models. As a result, many established channel estimation methods may yield sub-optimum

performance and thus be ill suited for next generation applications.

Brief Description of the Drawings

[0005] In the drawings, like reference characters generally refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the invention. In the following description, various embodiments of the invention are described with reference to the following drawings, in which:

FIG. 1 shows a delay-Doppler response of a channel;

FIG. 2 shows a first channel estimate for a wireless channel;

FIG. 3 shows second channel estimate for a wireless channel;

FIG. 4 shows a channel estimation circuit;

FIG. 5 shows an internal configuration of a communication device;

FIG. 6 shows a first method of performing channel estimation; and

FIG. 7 shows a second method of performing channel estimation.

Description

[0006] The following detailed description refers to the accompanying drawings that show, by way of illustration, specific details and embodiments in which the invention may be practiced.

[0007] The word "exemplary" is used herein to mean "serving as an example, instance, or illustration". Any embodiment or design described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments or designs.

[0008] The words "plural" and "multiple" in the description and the claims expressly refer to a quantity greater than one. Accordingly, any phrases explicitly invoking the

aforementioned words (e.g. "a plurality of [objects]", "multiple [objects]") referring to a quantity of objects expressly refers more than one of the said objects. The terms "group (of)", "set [of]", "collection (of)", "series (of)", "sequence (of)", "grouping (of)", etc., and the like in the description and in the claims, if any, refer to a quantity equal to or greater than one, i.e. one or more. The terms "proper subset", "reduced subset", and "lesser subset" refer to a subset of a set that is not equal to the set, i.e. a subset of a set that contains less elements than the set.

[0009] It is appreciated that any vector and/or matrix notation utilized herein is exemplary in nature and is employed solely for purposes of explanation. Accordingly, it is understood that the approaches detailed in this disclosure are not limited to being implemented solely using vectors and/or matrices, and that the associated processes and computations may be equivalently performed with respect to sets, sequences, groups, etc., of data, observations, information, signals, etc. Furthermore, it is appreciated that references to a "vector" may refer to a vector of any size or orientation, e.g. including a lxl vector (e.g. a scalar), a lxM vector (e.g. a row vector), and an Mxl vector (e.g. a column vector). Similarly, it is appreciated that references to a "matrix" may refer to matrix of any size or orientation, e.g. including a lxl matrix (e.g. a scalar), a lxM matrix (e.g. a row vector), and an Mxl matrix (e.g. a column vector).

[0010] A "circuit" as user herein is understood as any kind of logic-implementing entity, which may include special-purpose hardware or a processor executing software. A circuit may thus be an analog circuit, digital circuit, mixed-signal circuit, logic circuit, processor, microprocessor, Central Processing Unit (CPU), Graphics Processing Unit (GPU), Digital Signal Processor (DSP), Field Programmable Gate Array (FPGA), integrated circuit,

Application Specific Integrated Circuit (ASIC), etc., or any combination thereof. Any other kind of implementation of the respective functions which will be described below in further detail may also be understood as a "circuit". It is understood that any two (or more) of the circuits detailed herein may be realized as a single circuit with substantially equivalent functionality, and conversely that any single circuit detailed herein may be realized as two (or more) separate circuits with substantially equivalent functionality. Additionally, references to a "circuit" may refer to two or more circuits that collectively form a single circuit. [0011] As used herein, "memory" may be understood as a non-transitory computer-readable medium in which data or information can be stored for retrieval. References to "memory" included herein may thus be understood as referring to volatile or non-volatile memory, including random access memory (RAM), read-only memory (ROM), flash memory, solid- state storage, magnetic tape, hard disk drive, optical drive, etc., or any combination thereof. Furthermore, it is appreciated that registers, shift registers, processor registers, data buffers, etc., are also embraced herein by the term memory. It is appreciated that a single component referred to as "memory" or "a memory" may be composed of more than one different type of memory, and thus may refer to a collective component comprising one or more types of memory. It is readily understood that any single memory component may be separated into multiple collectively equivalent memory components, and vice versa. Furthermore, while memory may be depicted as separate from one or more other components (such as in the drawings), it is understood that memory may be integrated within another component, such as on a common integrated chip.

[0012] The term "base station" used in reference to an access point of a mobile

communication network may be understood as a macro base station, micro base station, Node B, evolved NodeBs (eNB), Home eNodeB, Remote Radio Head (RRH), relay point, etc. As used herein, a "cell" in the context of telecommunications may be understood as a sector served by a base station. Accordingly, a cell may be a set of geographically co-located antennas that correspond to a particular sectorization of a base station. A base station may thus serve one or more cells (or sectors), where each cell is characterized by a distinct communication channel. Furthermore, the term "cell" may be utilized to refer to any of a macrocell, microcell, femtocell, picocell, etc.

[0013] For purposes of this disclosure, radio communication technologies may be classified as one of a Short Range radio communication technology, Metropolitan Area System radio communication technology, or Cellular Wide Area radio communication technology. Short Range radio communication technologies include Bluetooth, WLAN (e.g. according to any IEEE 802.11 standard), and other similar radio communication technologies. Metropolitan Area System radio communication technologies include Worldwide Interoperability for Microwave Access (WiMax) (e.g. according to an IEEE 802.16 radio communication standard, e.g. WiMax fixed or WiMax mobile) and other similar radio communication technologies. Cellular Wide Area radio communication technologies include GSM, UMTS, LTE, LTE- Advanced (LTE-A), CDMA, WCDMA, LTE-A, General Packet Radio Service (GPRS), Enhanced Data Rates for GSM Evolution (EDGE), High Speed Packet Access (HSPA), HSPA Plus (HSPA+), and other similar radio communication technologies. Cellular Wide Area radio communication technologies also include "small cells" of such technologies, such as microcells, femtocells, and picocells. Cellular Wide Area radio communication technologies may be generally referred to herein as "cellular" communication technologies. It is understood that exemplary scenarios detailed herein are demonstrative in nature, and accordingly may be similarly applied to various other mobile communication technologies, both existing and not yet formulated, particularly in cases where such mobile communication technologies share similar features as disclosed regarding the following examples.

[0014] The term "network" as utilized herein, e.g. in reference to a communication network such as a mobile communication network, encompasses both an access section of a network (e.g. a radio access network (RAN) section) and a core section of a network (e.g. a core network section). The term "radio idle mode" or "radio idle state" used herein in reference to a mobile terminal refers to a radio control state in which the mobile terminal is not allocated at least one dedicated communication channel of a mobile communication network. The term "radio connected mode" or "radio connected state" used in reference to a mobile terminal refers to a radio control state in which the mobile terminal is allocated at least one dedicated uplink communication channel of a mobile communication network. [0015] Unless explicitly specified, the term "transmit" encompasses both direct (point-to- point) and indirect transmission (via one or more intermediary points). Similarly, the term "receive" encompasses both direct and indirect reception. The term "communicate" encompasses one or both of transmitting and receiving, i.e. unidirectional or bidirectional communication in one or both of the incoming and outgoing directions.

[0016] Terrestrial wireless communication systems may experience multipath propagation, in which transmitted radio signals may arrive at a receiver via two or more different paths. Accordingly, the receiver may receive a combined signal that is composed of contributions from each multipath, where each multipath may introduce a different complex gain, delay, and frequency shift to the originally transmitted signal.

[0017] The various time and frequency shifts may arise from time delays and Doppler shifts unique to each multipath. For example, a direct (or "line-of-sight") multipath signal may propagate along the shortest path from the transmitter the receiver, while other multipath signals may be reflected (e.g. by terrestrial objects, atmospheric/ionospheric effects, etc.) and as a result propagate along a longer path before being received at the receiver. Such differing path lengths may thus cause similarly differing times of arrival for each multipath signal that is seen as a time delay at the receiver. Each multipath signal may also arrive at the receiver at a different angle as a result of the distinct propagation paths. Accordingly, the multipath signals may each be received at moving receivers (e.g. mobile terminals) with a unique frequency shift as a result of the Doppler effect.

[0018] The channel model may thus be expressed as the sum of the contributions of each received multipath, where each multiple exhibits a unique gain, frequency shift (Doppler shift), and time delay (multipath delay). Given the constantly fluctuating nature of practical radio environments, the properties of each multipath may change over time. Accordingly, effective channel estimates may need to model wireless channels as an evolving two- dimensional function of both time and frequency. [0019] As indicated in the Background, various next generation radio access technologies may produce equivalent channels (composed of the physical channel and sharp analog beamformers) that differ considerably from channels observed in conventional radio access technologies. In particular, the equivalent channels of such 5G radio access technologies may produce channel responses that are concentrated in a low number of disjoint areas of the delay-Doppler domain. FIG. 1 shows an exemplary power-density distribution of such a channel response. As shown in FIG. 1, the channel power may be highly concentrated in several "clusters" of the channel domain, i.e. the resolvable multipath components of the channel may be concentrated in terms of delay and Doppler shift in several condensed regions. The remaining areas of the delay-Doppler spectrum of the channel response may be relatively sparse, i.e. may have few or no multipath components.

[0020] An accurate channel estimation filter may thus need to have sufficient bandwidth (in both the delay and Doppler direction) to cover the contributions of each of the resolvable multipaths in the delay-Doppler spectrum. Accordingly, such channel estimation filters may need to have a range in the delay direction in accordance with the delay spread, i.e. the difference in time between the earliest and latest arriving multipaths, and a range in the

Doppler direction in accordance with the Doppler spread, i.e. the furthest separation in

Doppler shift of the multipaths. Conventionally, a channel estimation filter may be derived that covers a continuous area of the delay-Doppler spectrum, e.g. a continuous area spanning from at least the highest Doppler shift of Cluster 1 to the lowest Doppler shift of Cluster 3 in the Doppler direction and from at least the smallest time delay in the Cluster 2 to the largest time delay in Cluster 3 as shown in the exemplary delay-Doppler response of FIG. 2.

However, there may be a high computational cost of developing such wideband filters due to the extended continuous range in both directions that such a filter must cover in order to address the delay and Doppler shift contributions of each resolvable multipath. While these computational costs may be alleviated by precomputing filter coefficients to cover a sufficient number of different possibilities of delay and Doppler spread, the memory requirements to store filter coefficients for an appropriate number of variant filters may be substantial.

Additionally, given a clustered channel power distribution as previously detailed regarding FIG. 1, such wideband filters may additionally capture high levels of noise in the sparse regions of the filter response (e.g. in the upper-left corner of the filter).

[0021] Accordingly, a channel estimator may instead apply a "composite" filter approach to develop a channel filter that concentrates its response around the cluster regions of the actual channel response as depicted in FIG. 3. Specifically, the channel estimator may utilize one or more prototype filters (e.g. 300), which may be narrowband filters that may be centered in the delay-Doppler domain. As shown in FIG. 3, a channel estimator may then identify the location of the clusters in the delay-Doppler domain of the channel response and subsequently apply a time and frequency shift to the base filter in order to separately fit the base filter around each identified cluster location, thus producing a plurality of shifted base filters each centered around an identified cluster region. The channel estimator may then weight each shifted base filter (310-330) and develop a composite filter as the superposition of each of the resulting shifted base filters. Accordingly, the channel estimator may develop a channel filter that is concentrated around the cluster regions of channel power while only requiring storage of a narrow base filter and avoiding the high computational cost of developing a wide channel filter as detailed in FIG. 2. Furthermore, due to the aforementioned concentration around the channel clusters (thus avoiding the capture of excess noise), the resulting composite filter may offer better performance in low Signal-to-Noise ratio (S R) conditions. While FIG. 3 depicts a 2D base filter for purposes of graphical illustration, as will be detailed the channel estimator may utilize separate ID prototype frequency-direction prototype filters and ID prototype time-direction filters and subsequently combine the ID filters to generate a final 2xlD filter as the composite filter. Such 2xlD filter generation may further reduce the computational burden at the channel estimator. [0022] FIG. 4 shows channel estimation circuit 400, which as will be detailed may be configured to compute a channel estimate as a composite filter formed by a superposition of weighted base filters that are shifted in one or both of the delay and Doppler directions.

Channel estimation circuit 400 may be included in a communication device such as communication device 500 shown in FIG. 5, which may be configured to transmit and receive wireless signals.

[0023] As shown in FIG. 5, communication device 500 may include antenna system 502, radio frequency (RF) transceiver 504, baseband modem 506 (including physical layer processing circuit 508 and controller 510), data source 512, memory 514, and data sink 516. Although not explicitly shown in FIG. 5, communication device 500 may include one or more additional hardware, software, and/or firmware components (such as

processors/microprocessors, controllers/microcontrollers, other specialty or generic hardware/processors/circuits, etc.), user input/output devices (display(s), keypad(s), touchscreen(s), speaker(s), external button(s), camera(s), microphone(s), etc.), peripheral device(s), memory, power supply, external device interface(s), subscriber identify module(s) (SIMs), etc. Communication device 500 may be structurally realized as an uplink or a downlink node, such as either a mobile terminal or a base station in a cellular radio network context.

[0024] In abridged operational overview, communication device 500 may transmit and receive wireless signals on one or more radio communication networks. Baseband modem 506 may direct such communication functionality of communication device 500 according to the communication protocols associated with each radio communication network, and may execute control over antenna system 502 and RF transceiver 504 in order to transmit and receive radio signals according to the formatting and scheduling parameters defined by each communication protocol. [0025] Baseband modem 506 may transmit and receive radio signals with antenna system

502, which may be a single antenna or an antenna array composed of multiple antennas and may additionally include analog antenna combination and/or beamforming circuitry. In the receive path (RX), RF transceiver 504/RX may receive analog radio frequency signals from antenna system 502 and perform analog and digital RF front-end processing on the analog radio frequency signals to produce digital baseband samples (e.g. In-Phase/Quadrature (IQ) samples) to provide to baseband modem 504. RF transceiver 504/RX may accordingly include analog and digital reception circuitry including amplifiers (e.g. a Low Noise Amplifier

(LNA), filters, RF demodulators (e.g. an RF IQ demodulator), and analog-to-digital converters (ADCs) to convert the received radio frequency signals to digital baseband samples. In the transmit path (TX), RF transceiver 504/TX may receive digital baseband samples from baseband modem 306 and perform analog and digital RF front-end processing on the digital baseband samples to produce analog radio frequency signals to provide to antenna system 502 for wireless transmission. RF transceiver 504/TX may thus include analog and digital transmission circuitry including amplifiers (e.g. a Power Amplifier (PA), filters, RF modulators (e.g. an RF IQ modulator), and digital-to-analog converters (DACs) to mix the digital baseband samples received from baseband modem 506 to produce the analog radio frequency signals for wireless transmission by antenna system 502.

[0026] As shown in FIG. 5, baseband modem 506 may include physical layer processing circuit 508, which may perform physical layer transmission and reception processing to prepare outgoing transmit data provided by controller 510 for transmission via RF transceiver

504/TX and prepare incoming received data provided by RF transceiver 504/RX for processing by controller 510. Physical layer processing circuit 508 may accordingly perform one or more of error detection, forward error correction encoding/decoding, channel coding and interleaving, physical channel modulation/demodulation, physical channel mapping, radio measurement and search, frequency and time synchronization, antenna diversity processing, power control and weighting, rate matching, retransmission processing, etc. Physical layer processing circuit 508 may be structurally realized as hardware logic, e.g. as an integrated circuit or FPGA, as software logic, e.g. as program code defining arithmetic, control, and I/O instructions stored in a non-transitory computer-readable storage medium and executed on a processor, or as a combination of hardware and software logic. Although not explicitly shown in FIG. 5, physical layer processing circuit 508 may include a control circuit such as a processor configured to control the various hardware and software processing components of physical layer processing circuit 508 in accordance with physical layer control logic defined by the communications protocol for the relevant radio access technologies.

[0027] Communication device 500 may be configured to operate according to one or more radio access technologies, which may be directed by controller 510. Controller 510 thus be responsible for controlling the radio communication components of communication device

500 (antenna system 502, RF transceiver 504, and physical layer processing circuit 508) in accordance with the communications protocol of each supported radio access technology, and accordingly may represent the data link layer (Layer 2) and network layer (Layer 3) of each supported radio access technology. Controller 510 may be structurally embodied as a protocol processor configured to execute protocol software and subsequently control the radio communication components of communication device 500 in order to transmit and receive communication signals in accordance with the corresponding protocol control logic. Although shown as a single entity in FIG. 5, controller 510 may be composed of multiple controllers, such as e.g. multiple dedicated controllers with each dedicated controller (e.g. protocol processor) corresponding to one or more of the supported radio access technologies. One or more of antenna system 502, RF transceiver 504, and physical layer processing circuit 508 may be similarly partitioned into multiple dedicated components each corresponding to one or more of the supported radio access technologies. Depending on the specifics of each such configurations and the number of supported radio access technologies, controller 510 may be configured to control the radio communication operations of communication device 500 in accordance with a master/slave RAT hierarchical or multi-SIM scheme.

[0028] Communication device 500 may further comprise data source 512, memory 514, and data sink 516, where data source 512 may include all sources of communication data above the network layer(s) of controller 510 (i.e. above Layer 3) and data sink 512 may include all destinations of communication data above the network layer(s) of controller 510 (i.e. above Layer 3). Such may include, for example, an application processor of communication device 500, which may be configured to execute various applications and/or programs of

communication device 500, such as e.g. an Operating System (OS), a User Interface (UI) for supporting user interaction with mobile terminal 300, and/or various user applications. The application processor may interface with baseband modem 506 (as data source 512/data sink 516) to transmit and receive user data such as voice data, video data, messaging data, application data, basic Internet/web access data, etc., over a the radio network connection(s) provided by baseband modem 506. Data source 512 and data sink 516 may additionally represent various user input/output devices of communication device 500, such as display(s), keypad(s), touchscreen(s), speaker(s), external button(s), camera(s), microphone(s), etc.

[0029] Memory 514 may comprise a memory component of communication device 500, such as e.g. a hard drive or another such permanent memory device. Although not explicitly depicted in FIG. 5, the various other components of communication device 500 shown in FIG. 5 may additionally each include integrated permanent and non-permanent memory

components, such as for storing software program code, buffering data, etc.

[0030] As introduced above, physical layer processing circuit 508/RX may include channel estimation circuit 400, which may be configured to obtain channel estimates based on radio signals received by communication device 500 at antenna system 502. Communication device 500 may then apply the channel estimates in any of a number of different communication contexts, including at physical layer processing circuit 508 to modulate and demodulate communication signals.

[0031] As shown in FIG. 4, channel estimation circuit 400 may include channel

preprocessing circuit 402, timing offset (TO) estimation circuit 404, frequency direction (FD) filter synthesis circuit 406, time direction (TD) filter synthesis circuit 410, and composite filter synthesis circuit 412. As will be detailed, channel estimation circuit 400 may be characterized as a communication circuit arrangement including an offset estimation circuit

(e.g. TO estimation circuit 404 and/or FO estimation circuit 408) configured to identify one or more condensed channel power regions of a channel response based on an initial channel estimate, a first filter shift circuit (e.g. FD filter synthesis circuit 406 or TD filter synthesis circuit 410) configured to apply a shift to a first prototype filter according to each of the one or more condensed channel power regions to generate one or more first shifted prototype filters, and a filter synthesis circuit (e.g. composite filter synthesis circuit 412) configured to combine the one or more first shifted prototype filters to generate a combined filter that approximates the channel response. Channel estimation circuit 400 may alternatively be characterized as a communication circuit arrangement including an offset estimation circuit

(e.g. TO estimation circuit 404 and FO estimation circuit 408) configured to evaluate an initial channel estimate of a channel to identify one or more concentrated channel power regions of a multidimensional response of the channel, a first filter shift circuit (e.g. FD filter synthesis circuit 406 or TD filter synthesis circuit 410) configured to apply a shift to a first base filter according to positions of the one or more concentrated channel power regions in a first direction of the multidimensional response to generate one or more first shifted based filters, a second filter shift circuit (e.g. FD filter synthesis circuit 406 or TD filter synthesis circuit 410) configured to apply a shift to a second base filter according to positions of the one or more concentrated channel power regions in a second direction of the multidimensional response to generate one or more second shifted base filters, and a filter synthesis circuit (e.g. composite filter synthesis circuit 412) configured to combine the one or more first shifted base filters and the one or more second shifted base filters to generate a combined filter that approximates the channel.

[0032] Referring to the previous descriptions of FIGs. 2 and 3, channel estimation circuit 400 may identify cluster regions of a target channel in the delay-Doppler domain (delay- Doppler areas that correspond to high channel power) and apply narrowband prototype filters to generate shifted and weighted prototype filters that are located in the cluster regions.

Channel estimation circuit 400 may then combine each of the weighted and shifted prototype filters to generate a composite filter to estimate the target channel, where the composite filter is concentrated around the identified cluster regions as a result of the prototype filter synthesis and accordingly may be well-suited to characterize the multipath delay-Doppler response of the wireless channel. The resulting composite filter may thus effectively avoid the capture of excessive noise (thus offering improved performance in noisy conditions) and offer a marked reduction in computational complexity over conventional channel filter generation techniques that calculate filter coefficients for filters with wideband delay-Doppler responses.

[0033] As shown in FIGs. 2 and 3, the channel response may be concentrated in a plurality of clusters, i.e. C clusters, where each of the C clusters falls on a particular area of the delay- Doppler spectrum. Each cluster may thus correspond to a number of multipath components that exhibit timing offsets τ (delays) and frequency offsets φ (Doppler shifts) that are concentrated proximate to one another to form the cluster.

[0034] Channel estimation circuit 400 may develop a channel filter H that approximates a channel response for a multi-carrier modulation scheme, such as e.g. Orthogonal Frequency

Division Multiplexing (OFDM), in which a transmitter may modulate a respective data symbol onto each of a plurality of subcarriers during each of a successive sequence of symbol periods. Given a finite number of subcarriers K and partitioning the successive sequence of symbols into blocks of L symbols, channel filter H may be expressed as K x L complex- valued matrix (i.e. H E <C ^KxL ) containing where each channel coefficient h _{k l} of H gives the complex- valued channel response at the Z-th symbol on the k-t subcarrier. As previously indicated, the delay-Doppler response of H may vary over time and frequency, and accordingly each of the multipaths of the wireless channel may produce a different contribution to each symbol depending on the time-frequency position (k, Ϊ) thereof.

[0035] Assigning P _c as the number of multipaths in the c-th cluster of the channel response, a single channel coefficient h _{k l} of H at frequency subcarrier k and symbol I may be expressed as

where _{c p} is the complex gain of the p-th mutltipath of the c-th cluster (distributed as a zero- mean complex normal distributed random variable as a~CN(0, Fk is ^tne equivalent baseband frequency at subcarrier position k, T _l is the time at symbol index I (relative to the beginning of the sampling period), and x _{c p} and q) _{c p} are the timing offset (delay) and frequency offset (Doppler shift), respectively, of the p-th mutltipath of the c-th cluster. In other words, channel coefficient h _{k l} may be the sum of the contributions of each multipath of each cluster at frequency index k and time index I.

[0036] Channel estimation circuit 400 may thus aim to obtain estimated channel coefficients h _{k l} that accurately approximate h _{k l} by generating a composite filter as the superposition of multiple shifted and weighted prototype filters, where each base filter is shifted in time and frequency to match with the location of a cluster region in the channel power response.

Channel estimation circuit 400 may thus need to identify the appropriate time and frequency shifts that correspond to the location of each cluster region in the delay-Doppler domain as well as identify the proper weight of each cluster region. Channel estimation circuit 400 may rely on noisy channel estimates as a starting point in identifying the positions and weights for each channel cluster.

[0037] As shown in FIG. 4, channel estimation circuit 400 may receive noisy reference symbols Y, which may be a vector of predefined reference symbol IQ samples obtained by physical layer processing circuit 508/RX via antenna system 502 and RF transceiver 504. Each of the noisy reference symbols of Y may multiplexed in time and frequency to certain symbol periods (a subset of the L symbols of the sampling period, i.e. multiplexed in time) and subcarriers (a subset of the K total subcarriers, i.e. multiplexed in frequency) according to a specific pattern. Channel preprocessing circuit 402 may receive multiple such noisy reference symbol vectors Y over time depending on the multiplexing pattern of the reference symbols in time and may subsequently generate a noisy channel estimate H based on one or more reference symbol vectors Y . Each of the noisy reference symbols of Y may correspond to a predefined reference symbol, and accordingly Y may correspond to a predefined reference symbol vector Y. Accordingly, channel preprocessing circuit 402 may generate H by comparing each the noisy reference symbols of each received Y to the corresponding predefined reference symbols of Y in order to determine the effect of the wireless channel and noise on Y to yield Y. For example, channel preprocessing circuit 402 may demodulate Y to obtain demodulated reference symbols Y as Y = Y ° Y ^* , where ° is the entrywise product (Hadamard product) and Y ^* is the complex conjugate of predefined reference symbols Y. As each noisy reference symbol of Y corresponds to a specific subcarrier and symbol period, the resulting elements of Y may each give a noisy sample of the channel H at a given time- frequency point. Channel preprocessing circuit 402 may then interpolate between the time- frequency positions of each noisy reference symbol of Y to obtain a noisy channel sample for each subcarrier and symbol period of H, thus obtaining the K ^■ L noisy channel samples of H. As channel preprocessing circuit 402 may continue to receive new noisy reference symbol vectors Y over time, channel preprocessing circuit 402 may generate new noisy channel estimates H over time to reflect the varying nature of the actual channel H.

[0038] Noisy channel estimate H as obtained by channel preprocessing circuit 402 may thus be expressed as

H = H + N (2) where N G€, ^KxL is independent and identically distributed complex normal noise assumed to be white over time and frequency (i.e. vec(N)~CN(0, σ ² Ι) with / as the K X L identity matrix and σ ² as the noise variance) and H is the actual channel.

[0039] Channel preprocessing circuit 402 may then provide noisy channel estimate H to composite filter synthesis circuit 412, which may utilize noisy channel estimate H to generate the final composite filter coefficients h _{k l} of estimated channel filter H following generation of the shifted and weighted base filters by FD filter synthesis circuit 406 and TD filter synthesis circuit 410. Channel preprocessing circuit 402 may additionally generate frequency- direction channel covariance matrix R _F and time-direction channel covariance matrix R _T to provide to TO estimation circuit 404 and FO estimation circuit 408, respectively. Given Equation (7), the channel H in the neighborhood of sample (k, Ϊ) may be a normal distributed random variable with i;ec(H)~C (0, i?) where R G £ ^LKxKL is the channel covariance matrix (with k = 0,1, ... , K— 1 and I = 0,1, ... , L— 1). Channel covariance matrix R may be expressed as the Kronecker product R = R ^T _T ® R _F between frequency direction channel covariance matrix R _F G £ ^KxK and time direction channel covariance matrix R _T G ⁽ C ^ixi , where R ^T _T is the transpose of R ^T _T . R _F and R _T may be expressed as c-i ¾-i c=0 p=0 (3)

[0040] Accordingly, R _F and R _T may give the covariance over the K subcarriers and L symbol periods of H, respectively. Channel preprocessing circuit 402 may thus calculate R _F and R _T by observing H over time in order to monitor the relationship of the elements of H over time and frequency. Specifically, channel preprocessing circuit 402 may calculate R _F as R _F = E [HH ^H ] (where H ^H is the Hermitian transpose of H and E [-] is the expectation operator) and calculate R _T as R _T = E [H ^H H] . Accordingly, channel preprocessing circuit 402 may observe HH ^H and H ^H H over time to obtain the respective expectations to obtain R _F and

[0041] As shown in FIG. 4, channel preprocessing circuit 402 may provide R _F and R _T to TO estimation circuit 404 and FO estimation circuit 408, respectively. TO estimation circuit 404 may then process R _F to identify the locations of the cluster regions of the delay-Doppler response of H along the delay axis (time) while FO estimation circuit 404 may process R _T to identify the locations of the cluster regions of the delay-Doppler response of H along the Doppler axis (frequency). TO estimation circuit 404 and FO estimation circuit 408 may then provide the resulting time and frequency positions to FD filter synthesis circuit 406 and TD filter synthesis circuit 410, which may each apply the identified time and frequency positions to single dimensional prototype filters to generate one or more single dimensional shifted and weighted base filters, which composite filter synthesis circuit 412 may utilize to generate the 2xlD composite channel filter H to estimate the channel. [0042] Accordingly, as opposed to directly generating a 2D filter, channel estimation circuit 402 may generate one or more ID time-direction filters at TD filter synthesis circuit 410 and one or more ID frequency-direction filters at FD filter synthesis circuit 406, where each of the one or more ID time-direction filters are placed at a respective identified cluster region of the channel response on the Doppler axis and each of the one or more ID frequency-direction filters are placed at a respective identified cluster region of the channel response on the delay axis. By superposing each of the resulting ID time-direction filters and each of the resulting ID frequency direction filters and combining the resulting ID superposed time-direction filter and resulting ID superposed frequency-direction filter, channel estimation circuit 400 may obtain a 2xlD composite filter with a channel response that is concentrated in the delay- Doppler domain around the identified cluster regions of the channel.

[0043] Accordingly, TO estimation circuit 404 may receive R _F and produce N timing offset estimates to provide to FD filter synthesis circuit 406, where each of the N timing offsets identify the location of an identified cluster region of H on the delay axis. Specifically, TO estimation circuit 404 may evaluate a range of hypothesis timing offset estimates that span the potential delay spectrum range of H in order to identify N of the hypothesis timing offset estimates that correspond to a high concentration of channel power.

[0044] TO estimation circuit 404 may select the N timing offset estimates from a set of equidistant timing offset hypotheses {t ₀ ff _, o> toff,i _> — · ^off,N _tot -i} that span the potential delay spectrum range of H, where N _tot ≥ \T _max /T _proto \ is the cardinality (i.e. total number of hypothesis timing offsets), T _proto is the bandwidth of the ID prototype frequency-direction filter w _FD _ _proto and T _max is the maximum potential timing offset range. TO estimation circuit 404 may identify the N timing offset estimates by evaluating each of the N _tot timing offset hypotheses as a potential location of prototype frequency-direction filter w _FD _ _proto at a particular point on the delay axis. [0045] As previously indicated, prototype frequency-direction filter w _FD _ _proto may be narrowband and predefined (i.e. precomputed), and accordingly may be precomputed and stored at TO estimation circuit 404. TO estimation filter 404 may either employ a single ID prototype frequency-direction filter or a set of multiple different ID prototype direction- filters, such as several ID prototype frequency-direction filters each tailored to a different operating S R value, several ID prototype frequency-direction filters having different bandwidths, etc. In a multi-filter scenario, TO estimation circuit 404 may select an

appropriate ID prototype frequency-direction filter w _FD _ _proto according to a predetermined condition, such as e.g. an observed SNR or e.g. an observation that indicates the bandwidth of one or more cluster regions of H in the frequency direction, and subsequently apply the selected prototype frequency-direction filter w _FD _ _proto in the timing offset estimation process. The ID prototype frequency-direction filter(s) may have a rectangular gain profile or another preconfigured gain profile. As the ID prototype frequency-direction filter(s) may be relatively narrowband and precomputed, TO estimation circuit 404 may be able to reduce memory requirements while avoiding the excessive computations involved in generating filter coefficients.

[0046] TO estimation filter 404 may evaluate prototype frequency-direction filter w _FD _ _proto with a timing offset hypothesis matrix T defined as

(5) where K is the length of w _FD _ _proto (and the dimension of H in frequency, i.e. the number of subcarriers K) and φ _η = 2π(η— n')f _sc where f _sc is the subcarrier separation in frequency and n' is the lowest index in the neighborhood of n. Accordingly, each column of T may correspond to one of the N _tot timing offset hypotheses where each element of each column differs according to the frequency difference between each of the K subcarriers.

[0047] In order to select the N timing offset estimates from the set of N _tot timing offset estimate hypotheses, TO estimation circuit 404 may "test" each of the N _tot timing offset estimate hypotheses by placing prototype frequency-direction filter w _FD _ _proto at each of the timing offset estimate hypotheses and calculating the channel power, i.e. the amount of channel energy plus noise, that is captured by prototype frequency-direction filter w _FD _ _proto when placed at each of the timing offset estimate hypotheses. Timing offset hypotheses that produce a high channel power may thus indicate the presence of a cluster region of H (along the frequency direction) while timing offset hypotheses that produce considerably lower channel power may indicate the absence of a cluster region of H (e.g. a sparse region of H). TO estimation circuit 404 may calculate a frequency direction channel power metric vector

PFD = diag- ^X {T ^H■ diag(w _FD _ _proto ) ^■ R _F ^■ diag{w _ _proto ) ^■ t) (6) where diag(-) maps the elements of an input vector (e.g. a column vector ) to the diagonal elements of a quadratic matrix (yielding diag(w _FD _ _proto ) of dimension K x K) and diag ^'1 ^) maps the diagonal elements of a matrix to a vector (yielding p _FD of dimension

1, i.e. a column vector).

[0048] TO estimation circuit 404 may thus produce N _ror -length power metric vector p _FD , where each element p _FDiU of p _FD indicates the channel power metric captured by w _FD _ _proto when positioned at timing offset t ₀ // _, n ^on the delay axis. TO estimation circuit 404 may then select the N largest elements of p _FD , which may accordingly be the N timing offset estimates that produce the highest channel power metric when w _FD _ _proto is positioned at the timing offset estimate on the delay axis. TO estimation circuit 404 may then provide each of the N timing offset estimates and the corresponding N power metrics to FD filter synthesis circuit 406. The number N≤ N _tot may be configurable or determined via a configurable threshold s _th . For example, TO estimation circuit 404 may select the timing offset hypotheses that produce the N largest power metrics in p _FD as the N timing offset estimates as detailed above. Alternatively, TO estimation circuit 404 may select all timing offset hypotheses that produce a power metric p _FDiU that satisfies the condition PFD,n/PFD,n _max > ^s tn (where PFD,n _max is the highest valued element of p _FD ). Alternatively, TO estimation circuit 404 may select a maximum of N _max elements of p _FD that satisfy PFD,n/PFD,n _max > ^s tn - Regardless, N may denote the total number of timing offset estimates provided by TO estimation circuit 404 to FD filter synthesis circuit 406. Furthermore, in the case which TO estimation circuit 404 has multiple precomputed prototype frequency-direction filters w _FD _ _proto available, TO estimation circuit 404 may calculate a power metric vector p _FD for multiple of the available precomputed prototype frequency-direction filters w _FD _ _proto in order to evaluate the channel power captured at each of the set of timing offset hypotheses corresponding to each prototype frequency-direction filter. As the bandwidths and/or weighting may vary for each prototype frequency-direction filter, the captured channel energy may differ across the timing offset hypotheses for each prototype frequency-direction filter (where the set of timing offset hypotheses may also differ in size and spacing depending on the bandwidth T _proto of each prototype frequency-direction filter). Accordingly, TO estimation circuit 404 may be configured to select multiple prototype frequency-direction filters w _FD _ _proto each

corresponding to a potentially differing set of timing offset estimates, where each of the selected prototype frequency-direction filters w _FD _ _proto produces a high channel power metric at the corresponding timing offset estimates. In such a multi-prototype filter scenario, FD filter synthesis circuit 406 may repeat the following operations for each selected prototype frequency-direction filter w _FD _ _proto and the corresponding timing offset estimates to produce the composite frequency-direction filter w _FD _ _comp . Such use of multiple prototype frequency- direction filters WFD-proto ^ma Y offer a tradeoff between performance and computational complexity/power usage.

[0049] FD filter synthesis circuit 406 may then apply the timing offsets and corresponding power metrics to w _FD _ _proto at FD phase shift and weighting circuits 406O-406N-I. Each FD phase shift and weighting circuit 406 _n may thus apply a phase shift to w _FD _ _proto to align WFD-proto to the corresponding time delay t ₀ // _, n (thus shifting w _FD _ _proto along the delay axis) and apply a gain to w _FD _ _proto according to p _F D,n to obtain shifted and weighted prototype filter w _FD _ _{proto n} . Specifically , each of the N FD phase shift and weighting circuits 406O-406N-I may generate a respective shifted and weighted prototype filter

WpD-proto,n ^as

W _FD -proto.n ^{~ w} FD,proto (7) where t _n is the n-th column vector of T (corresponding to t ₀ ^ _n ).

[0050] As shown in FIG. 4, FD filter synthesis circuit 406 may sum each of the N shifted and weighted prototype filters w _FD _ _{proto n} to produce composite frequency-direction filter ^w FD-comp ^as

[0051] Accordingly, FD filter synthesis circuit 406 may produce composite frequency- direction filter ^FD-comp ^as the sum of each of the N shifted and weighted prototype filters ^w FD-proto,n, where each of the N shifted and weighted prototype filters w _D _ _proto<n are shifted according to a specific timing delay corresponding to an identified position of a cluster region of the channel on the delay axis. FD filter synthesis circuit 406 may then calculate the Hermitian transpose of composite frequency-direction filter Wp _D _ _comp and provide Wp _D _ _comp to composite filter synthesis circuit 402.

[0052] FO estimation circuit 408 and TD filter synthesis circuit 410 may analogously identify M frequency offset estimates (on the Doppler axis) and subsequently generate M shifted and weighted filters WrD-proto.m from ID prototype time-direction filter w _TD _ _proto in an analogous manner. Accordingly, FO estimation circuit 408 may receive time-direction channel covariance matrix R _T from channel preprocessing circuit 402 and subsequently evaluate each of a set of M _{to t} equidistant frequency offset hypotheses

{foff,Q> foff,i>—> foff,Mtot-i] ^{t0 se} l ^ect M frequency offset estimates, where each frequency offset estimates gives an identified position of a cluster region of H on the Doppler axis. The cardinality (total number) M _{to t} of frequency offset hypotheses may be given as M _{to t} ≥

Fproto] where F _proto is the bandwidth of ID prototype time-direction filter w _TD _ _proto . FO estimation circuit 408 may evaluate each of the frequency offset hypotheses with frequency offset hypotheses matrix F defined as eifofffi o ... _e ifoff,N _tot (9) . .. _e Jfoff.N _tot - where L is the length of w _TD _ _proto (and equivalently the dimension of H in time, i.e. the number of symbol periods L) and ϋ _η = 2π(η— n')t _os gives the phase shift due to symbol separation in time with n' is the lowest index in the neighborhood of n and t _os gives the symbol period. [0053] FO estimation circuit 408 may similarly evaluate each of the frequency offset hypotheses (where the n-th column of F corresponds to the n-th frequency offset hypotheses) as the potential location of a cluster region of H on the Doppler axis. FO estimation circuit 408 may identify the M most significant frequency offset hypotheses by calculating a time- direction channel power metric vector p _TD as

PTD — diag ¹ {F ^e■ diag(w' TD-proto ) ^■ R _T ^■ diag(w' TD-proto (10)

) ^■ ')

[0054] FO estimation circuit 408 may then select the M frequency offset hypotheses that produce the most significant channel power metric as the frequency offset estimates, where M may similarly be configurable and/or dependent on a configurable threshold as detailed above regarding N in TO estimation circuit 404. FO estimation circuit 408 may thus select the M frequency offset hypotheses that capture the largest amount of channel power of H when ID prototype time-direction filter WTD-proto is positioned at the frequency offset estimate on the Doppler axis. FO estimation circuit 408 may then provide the M frequency offset estimates to TD filter synthesis circuit 410. As detailed above regarding TO estimation circuit 406, M may be configurable and/or based on a threshold value, such as e.g. a channel power metric threshold value. Similarly, FO estimation circuit 408 may evaluate multiple prototype time- direction filters WrD-proto according to a set of timing offset hypotheses for each prototype time-direction filter to obtain a channel power metric p _TD for each prototype time-direction filter. FO estimation circuit 408 may then select certain prototype time-direction filters ^w TD-proto ^an d certain corresponding timing offset estimates that produce high channel power metrics to provide to TD filter synthesis circuit 410. While detailed below for a single prototype time-direction filter w _TD _ _proto and the corresponding M frequency offset estimates, in such a multi-filter scenario TD filter synthesis circuit 410 may apply the following operation for each selected prototype time-direction filters w _TD _ _proto and the corresponding timing offset estimates to produce the composite time-direction filter w _TD _ _comp .

[0055] TD filter synthesis circuit 410 may then apply a corresponding phase shift and weighting to w _TD _ _proto at each of TD phase shift and weighting circuits 410O-410M-I according to each of the M frequency offset estimates and corresponding channel power metrics. Specifically, each of the M TD phase shift and weighting circuits 410O-410M-I may generate a respective shifted and weighted prototype filter w _TD _ _{proto m} as

wTD-proto,m ^~ JPTD.mdiag(fm w- TD-proto (1 1) where f _m is the m-th column vector of F (corresponding to / ₀ // _, m)-

[0056] As shown in FIG. 4, TD filter synthesis circuit 410 may sum each of the M shifted and weighted prototype filters w _TD _ _{proto m} to produce composite time-direction filter ^w TD-comp ^as

(12) wTD-comp ⁼ ? ^W TD-proto,m

m=0

where w _TD _ _cornp is thus a ID time-direction filter composed of each of the M shifted and weighted prototype filters w TD-proto, m -

[0057] TD filter synthesis circuit 410 may then provide WrD-comp to composite filter synthesis circuit 412, which as previously detailed may also receive noisy channel estimate H and frequency-direction composite filter Wp _D - _CO mp f ^rom channel preprocessing circuit 402 and FD filter synthesis circuit 406, respectively. [0058] Composite filter synthesis circuit 412 may then apply composite frequency-direction and time-direction filters Wp _D - _CO mp ^an d w _TD _ _comp to noisy channel estimate H by left-right multiplying H by w^ _D _ _comp and w _TD _ _comp as

¾c,i ^{= w} FD-compH ^w TD-comp ^ ⁾

to obtain the channel estimate h _{k l} for each time-frequency position (k, Ϊ) .

[0059] Accordingly, composite filter synthesis circuit 412 may combine single-direction filters WFD -COTHP ^an d w _TD - _comp to form a 2xlD combined filter and obtain a channel estimate for each time-frequency position h _{k l} of H. As channel estimation circuit 400 may obtain h _{k l} as a combination of each of the shifted and weighted frequency- and time-direction filters w _FD - _{proto iU} and w _TD - _{proto iTn} , each channel estimate h _{k l} may focus on the

contributions of the channel H that arise from multipath components with delay-Doppler characteristics in the cluster regions of the channel response.

[0060] As long as the neighborhood relation within H remains constant, i.e. relative to the indices (k, I), H may be applicable to various (k, Ϊ) indexed channel coefficients. For example, while channel estimation circuit 400 may determine H for a certain time-frequency block spanning K subcarriers and L symbol periods as detailed above, H may remain an accurate channel estimate for other K x L time-frequency blocks of different subcarriers and symbol periods, where each element h _{k l} of H may apply to the corresponding (k, Ϊ) -indexed element of the other K X L time-frequency blocks. It is further noted that H may need to be adapted for time-frequency positions near Physical Resource Block (PRB) edges. [0061] Communication device 500 may employ channel estimates h _{k l} for a number of different purposes, such as demodulation, noise estimation, channel state reporting, etc.

Accordingly, channel estimation circuit 400 may provide channel estimates h _{k l} to other components of baseband modem 506, such as e.g. to physical layer demodulation circuitry of physical layer processing circuit 508 which may subsequently apply h _{k l} to demodulate signals received by communication device 500 (including e.g. for ΜΊΜΟ applications) such as e.g. as part of a equalization filter, or e.g. to measurement circuitry of physical layer processing circuit 508 which may apply h _{k l} to obtain noise power estimates and/or signal-to- noise ratio (S R) measurements. Channel estimation circuit 400 may additionally provide channel estimates h _{k l} to controller 510, which may provide channel state reports to other communication devices. Although various different values for K and L are possible, channel estimation circuit 400 may employ values for K and L that correspond to the reference symbol spacing of Y, where (as previously detailed) the reference symbols may be distributed according to a predefined pattern. For example, channel estimation circuit 400 may employ e.g. K = 12 and L = 4, e.g. to correspond to the 12 subcarriers of a given Physical Resource Block (PRB) in LTE and the 4 symbol separation of resource symbols in time (e.g. for a Cell- specific Reference Symbol (CRS) pattern).

[0062] While the above description may focus on generation of a 2xlD composite filer from ID prototype filters, channel estimation circuit 400 may alternatively utilize 2D prototype filters to generate a 2D composite filter in an analogous manner, such as by identifying the frequency and timing offsets for the positions of each cluster region of the noisy channel estimate and shifting the 2D composite filter to the position of each identified cluster region. Such variations are also within the scope of this disclosure.

[0063] FIG. 6 shows method 600 of performing channel estimation. As shown in FIG. 6, method 600 includes obtaining an initial channel estimate (610), identifying one or more condensed channel power regions of a channel response based on the initial channel estimate (620), applying a shift to one or more prototype filters according to each of the one or more condensed channel power regions to generate one or more shifted prototype filters (630), and combining the one or more shifted prototype filters to generate a combined filter to approximate the channel response (640).

[0064] FIG. 7 shows method 700 of performing channel estimation. As shown in FIG. 7, method 700 includes obtaining an initial channel estimate of a channel (710), evaluating the initial channel estimate of the channel to identify one or more concentrated channel power regions of a multidimensional response of the channel (720), applying a shift to a first base filter according to positions of the one or more concentrated channel power regions in a first direction of the multidimensional response to generate one or more first shifted based filters (730), applying a shift to a second base filter according to positions of the one or more concentrated channel power regions in a second direction of the multidimensional response to generate one or more second shifted base filters (740), and combining the one or more first shifted base filters and the one or more second shifted base filters to generate a combined filter to approximate the channel (750).

[0065] In one or more further exemplary aspects of the disclosure, one or more of the features described above in reference to FIGS. 1-5 may be further incorporated into method 600 and/or method 700. In particular, method 600 and/or method 700 may be configured to perform further and/or alternate processes as detailed regarding channel estimation circuit 400 and/or communciation device 500.

[0066] The terms "user equipment", "UE", "mobile terminal", "user terminal", etc., may apply to any wireless communication device, including cellular phones, tablets, laptops, personal computers, wearables, multimedia playback and other handheld electronic devices, consumer/home/office/commercial appliances, vehicles, and any number of additional electronic devices capable of wireless communications. [0067] While the above descriptions and connected figures may depict electronic device components as separate elements, skilled persons will appreciate the various possibilities to combine or integrate discrete elements into a single element. Such may include combining two or more circuits for form a single circuit, mounting two or more circuits onto a common chip or chassis to form an integrated element, executing discrete software components on a common processor core, etc. Conversely, skilled persons will recognize the possibility to separate a single element into two or more discrete elements, such as splitting a single circuit into two or more separate circuits, separating a chip or chassis into discrete elements originally provided thereon, separating a software component into two or more sections and executing each on a separate processor core, etc.

[0068] It is appreciated that implementations of methods detailed herein are demonstrative in nature, and are thus understood as capable of being implemented in a corresponding device. Likewise, it is appreciated that implementations of devices detailed herein are understood as capable of being implemented as a corresponding method. It is thus understood that a device corresponding to a method detailed herein may include a one or more components configured to perform each aspect of the related method.

[0069] The following examples pertain to further aspects of this disclosure:

[0070] Example 1 is a method for performing channel estimation in mobile communication, the method including obtaining an initial channel estimate, identifying one or more condensed channel power regions of a channel response based on the initial channel estimate, applying a shift to one or more prototype filters according to each of the one or more condensed channel power regions to generate one or more shifted prototype filters, and combining the one or more shifted prototype filters to generate a combined filter to approximate the channel response.

[0071] In Example 2, the subject matter of Example 1 can optionally include wherein the initial channel estimate is a noisy channel estimate. [0072] In Example 3, the subject matter of Example 1 can optionally include wherein obtaining the initial channel estimate includes obtaining the initial channel estimate by comparing received noisy reference symbols to predefined local reference symbols.

[0073] In Example 4, the subject matter of any one of Examples 1 to 3 can optionally include wherein the channel response is a delay-Doppler multipath response.

[0074] In Example 5, the subject matter of Example 4 can optionally include wherein each element of the combined filter approximates the multipath delay-Doppler response at a specific subcarrier and a specific symbol period of a multi- sub carrier modulation scheme.

[0075] In Example 6, the subject matter of Example 4 can optionally include wherein identifying the one or more condensed channel power regions of the channel response based on the initial channel estimate includes identifying one or more frequency offsets

corresponding to positions of the one or more condensed channel power regions along a Doppler dimension of the channel response, and identifying one or more time offsets corresponding to positions of the one or more condensed channel power regions along a delay dimension of the channel response.

[0076] In Example 7, the subject matter of Example 6 can optionally include wherein the one or more prototype filters include a time-direction prototype filter, and wherein applying the shift to the one or more prototype filters according to each of the one or more condensed channel power regions to generate the one or more shifted prototype filters includes shifting the time-direction prototype filter along the Doppler dimension of the channel response according to each of the one or more frequency offsets to generate one or more first shifted prototype filters of the one or more shifted prototype filters.

[0077] In Example 8, the subject matter of Example 7 can optionally include wherein identifying the one or more frequency offsets corresponding to the positions of the one or more condensed channel power regions along the Doppler dimension of the channel response includes evaluating each of a plurality of frequency offset hypotheses to identify a subset of the plurality of frequency offset hypotheses that produce high channel power metrics as the one or more frequency offsets.

[0078] In Example 9, the subject matter of Example 8 can optionally include wherein evaluating each of the plurality of frequency offset hypotheses to identify the subset of the plurality of frequency offset hypotheses that produce high channel power metrics as the one or more frequency offsets includes calculating a channel power metric for each of the plurality of frequency offset hypotheses with the time-direction prototype filter and a time- direction covariance matrix derived from the initial channel estimate, and selecting the one or more frequency offsets from the plurality of frequency offset hypotheses based on the channel power metrics for the plurality of frequency offset hypotheses.

[0079] In Example 10, the subject matter of any one of Examples 7 to 9 can optionally include wherein shifting the time-direction prototype filter along the Doppler dimension of the channel response according to each of the one or more frequency offsets to generate the one or more first shifted prototype filters of the one or more shifted prototype filters includes for each respective frequency offset of the one or more frequency offsets, performing a phase shift along the Doppler dimension of the channel response with elements of the time- dimension prototype filter according to the respective frequency offset to generate a respective first shifted prototype filter of the one or more first shifted prototype filters.

[0080] In Example 11, the subject matter of any one of Examples 6 to 10 can optionally include wherein the one or more prototype filters include a frequency-direction prototype filter, and wherein applying the shift to the one or more prototype filters according to each of the one or more condensed channel power regions to generate the one or more shifted prototype filters includes shifting the frequency-direction prototype filter along the delay dimension of the channel response according to each of the one or more time offsets to generate one or more second shifted prototype filters of the one or more shifted prototype filters, and wherein combining the one or more shifted prototype filters to generate the combined filter to approximate the channel response includes combining the one or more first shifted prototype filters and the one or more second shifted prototype filters to generate the combined filter.

[0081] In Example 12, the subject matter of Example 11 can optionally include wherein identifying the one or more time offsets corresponding to the positions of the one or more condensed channel power regions along the delay dimension of the channel response includes evaluating each of a plurality of time offset hypotheses to identify a subset of the plurality of timing offset hypotheses that produce high channel power metrics as the one or more time offsets.

[0082] In Example 13, the subject matter of Example 12 can optionally include wherein evaluating each of the plurality of time offset hypotheses to identify the subset of the plurality of timing offset hypotheses that produce high channel power metrics as the one or more time offsets includes calculating a channel power metric for each of the plurality of timing offset hypotheses with the frequency-direction prototype filter and a frequency-direction covariance matrix derived from the initial channel estimate, and selecting the one or more time offsets from the plurality of time offset hypotheses based on the channel power metrics for the plurality of time offset hypotheses.

[0083] In Example 14, the subject matter of any one of Examples 11 to 13 can optionally include wherein shifting the frequency-direction prototype filter along the delay dimension of the channel response according to each of the one or more time offsets to generate the one or more second shifted prototype filters of the one or more shifted prototype filters includes for each respective time offset of the one or more time offsets, performing a phase shift along the delay dimension of the channel response with elements of the frequency-direction prototype filter according to the respective time offset to generate a respective second shifted prototype filter of the one or more second shifted prototype filters. [0084] In Example 15, the subject matter of any one of Examples 11 to 14 can optionally further include applying a respective gain to each of the one or more first shifted prototype filters and applying a respective gain to each of the one or more second shifted prototype filters.

[0085] In Example 16, the subject matter of Example 15 can optionally further include calculating the respective gain to apply to each of the one or more first shifted prototype filters based on the initial channel estimate and calculating the respective gain to apply to each of the one or more second shifted prototype filters based on the initial channel estimate.

[0086] In Example 17, the subject matter of any one of Examples 11 to 16 can optionally include wherein combining the one or more first shifted prototype filters and the one or more second shifted prototype filters to generate the combined filter includes combining the one or more first shifted prototype filters to generate a time-direction composite filter, combining the one or more second shifted prototype filters to generate a frequency-direction composite filter, and combining the time-direction composite filter and the frequency-direction composite filter to generate the combined filter.

[0087] In Example 18, the subject matter of Example 17 can optionally include wherein combining the time-direction composite filter and the frequency-direction composite filter to generate the combined filter includes applying the time-direction composite filter and the frequency-direction composite filter to the initial channel estimate to generate the combined filter.

[0088] In Example 19, the subject matter of Example 17 or 18 can optionally include wherein the time-direction composite filter is single dimensional, the frequency-direction composite filter is single-dimensional, and the combined filter is two-dimensional.

[0089] In Example 20, the subject matter of any one of Examples 17 to 19 can optionally include wherein the time-direction composite filter is a superposition of the one or more first shifted prototype filters and the frequency-direction composite filter is a superposition of the one or more second shifted prototype filters.

[0090] In Example 21, the subject matter of any one of Examples 17 to 20 can optionally include wherein combining the one or more first shifted prototype filters to generate the time- direction composite filter includes summing the one or more first shifted prototype filters to obtain the time-direction composite filter.

[0091] In Example 22, the subject matter of any one of Examples 17 to 21 can optionally include wherein combining the one or more second shifted prototype filters to generate the frequency-direction composite filter includes summing the one or more second shifted prototype filters to obtain the frequency-direction composite filter.

[0092] In Example 23, the subject matter of any one of Examples 1 to 22 can optionally include wherein the one or more prototype filters are single-dimensional.

[0093] In Example 24, the subject matter of any one of Examples 1 to 6 can optionally include wherein the one or more prototype filters are two-dimensional.

[0094] In Example 25, the subject matter of Example 24 can optionally include wherein applying the shift to the one or more prototype filters according to each of the one or more condensed channel power regions to generate the one or more shifted prototype filters includes applying a two-dimensional shift along a Doppler dimension and a delay dimension of the channel response to obtain the one or more shifted prototype filters.

[0095] In Example 26, the subject matter of Example 25 can optionally include wherein combining the one or more shifted prototype filters to generate the combined filter to approximate the channel response includes summing the one or more shifted prototype filters to generate the combined filter.

[0096] In Example 27, the subject matter of Example 25 or 26 can optionally include wherein the combined filter is a superposition of the one or more shifted prototype filters. [0097] In Example 28, the subject matter of any one of Examples 1 to 23 can optionally include wherein the combined filter is a 2xlD filter.

[0098] In Example 29, the subject matter of any one of Examples 1 to 28 can optionally further include receiving signal data, and demodulating the received signal with the combined filter.

[0099] In Example 30, the subject matter of any one of Examples 1 to 29 can optionally further include transmitting a channel estimate based on the combined filter.

[0100] Example 31 is a non-transitory computer readable medium storing instructions that when executed by a controller of a communication device cause the communication device to perform the method of any one of Examples 1 to 30.

[0101] Example 31 is a non-transitory computer readable medium storing instructions that when executed by a processor cause the processor to perform the method of any one of Examples 1 to 30.

[0102] Example 33 is a communication device configured to perform the method of any one of Examples 1 to 30.

[0103] Example 34 is a communication circuit arrangement configured to perform the method of any one of Examples 1 to 30.

[0104] Example 35 is a method of performing channel estimation, the method including obtaining an initial channel estimate of a channel, evaluating the initial channel estimate of the channel to identify one or more concentrated channel power regions of a multidimensional response of the channel, applying a shift to a first base filter according to positions of the one or more concentrated channel power regions in a first direction of the multidimensional response to generate one or more first shifted based filters, applying a shift to a second base filter according to positions of the one or more concentrated channel power regions in a second direction of the multidimensional response to generate one or more second shifted base filters, and combining the one or more first shifted base filters and the one or more second shifted base filters to generate a combined filter to approximate the channel.

[0105] In Example 36, the subject matter of Example 35 can optionally include wherein the initial channel estimate is a noisy channel estimate.

[0106] In Example 37, the subject matter of Example 35 or 36 can optionally include wherein obtaining the initial channel estimate of the channel includes obtaining the initial channel estimate by comparing noisy received reference symbols to local predefined reference symbols.

[0107] In Example 38, the subject matter of any one of Examples 35 to 37 can optionally include wherein the multidimensional response is a delay-Doppler multipath response.

[0108] In Example 39, the subject matter of Example 38 can optionally include wherein each element of the combined filter approximates the delay-Doppler response at a specific subcarrier and a specific symbol period of a multi-subcarrier modulation scheme.

[0109] In Example 40, the subject matter of any one of Examples 35 to 39 can optionally include wherein evaluating the initial channel estimate of the channel to identify the one or more concentrated channel power regions of the multidimensional response of the channel includes identifying one or more frequency offsets corresponding to the positions of the one or more concentrated channel power regions in the first direction of the multidimensional response, and identifying one or more time offsets corresponding to the positions of the one or more concentrated channel power regions in the second direction of the multidimensional response.

[0110] In Example 41, the subject matter of Example 40 can optionally include wherein the multidimensional response is a delay-Doppler multipath response, the first base filter is a time-direction filter, and the second base filter is a frequency-direction filter, the first direction of the multidimensional response is a Doppler direction, and the second direction of the multidimensional response is a delay direction. [0111] In Example 42, the subject matter of Example 40 or 41 can optionally include wherein identifying the one or more frequency offsets corresponding to the positions of the one or more concentrated channel power regions in the first direction of the multidimensional response includes evaluating each of a plurality of frequency offset hypotheses that correspond to high channel power of the initial channel estimate to identify a subset of the plurality of frequency offset hypotheses as the one or more frequency offsets.

[0112] In Example 43, the subject matter of Example 42 can optionally include wherein evaluating each of the plurality of frequency offset hypotheses that correspond to high channel power of the initial channel estimate to identify the subset of the plurality of frequency offset hypotheses as the one or more frequency offsets includes calculating a channel power metric for each of the plurality of frequency offset hypotheses with the first base filter and a time-direction covariance matrix derived from the initial channel estimate, and selecting the one or more frequency offsets from the plurality of frequency offset hypotheses based on the channel power metrics for the plurality of frequency offset hypotheses.

[0113] In Example 44, the subject matter of any one of Examples 41 to 43 can optionally include wherein applying the shift to the first base filter according to the positions of the one or more concentrated channel power regions in the first direction of the multidimensional response to generate the one or more first shifted base filters includes shifting the first base filter in the first direction of the multidimensional response according to each of the one or more frequency offsets to generate the one or more first shifted base filters.

[0114] In Example 45, the subject matter of Example 44 can optionally include wherein each of the one or more first shifted based filters are approximately centered at a respective frequency offset of the one or more frequency offsets.

[0115] In Example 46, the subject matter of Example 44 or 45 can optionally include wherein shifting the first base filter in the first direction of the multidimensional response according to each of the one or more frequency offsets to generate the one or more first shifted base filters includes for each respective frequency offset of the one or more frequency offsets, performing a phase shift in the first direction of the multidimensional response with elements of the first base filter according to the respective frequency offset to generate a respective first shifted base filter of the one or more first shifted base filters.

[0116] In Example 47, the subject matter of any one of Examples 40 to 46 can optionally include wherein identifying the one or more time offsets corresponding to the positions of the one or more concentrated channel power regions in the second direction of the

multidimensional response includes evaluating each of a plurality of time offset hypotheses that correspond to high channel power of the initial channel estimate to identify a subset of the plurality of time offset hypotheses as the one or more time offsets.

[0117] In Example 48, the subject matter of Example 47 can optionally include wherein evaluating each of the plurality of time offset hypotheses that correspond to high channel power of the initial channel estimate to identify the subset of the plurality of time offset hypotheses as the one or more time offsets includes calculating a channel power metric for each of the plurality of time offset hypotheses with the second base filter and a frequency- direction covariance matrix derived from the initial channel estimate, and selecting the one or more time offsets from the plurality of time offset hypotheses based on the channel power metrics for the plurality of time offset hypotheses.

[0118] In Example 49, the subject matter of any one of Examples 41 to 48 can optionally include wherein applying the shift to the second base filter according to the positions of the one or more concentrated channel power regions in the second direction of the

multidimensional response to generate the one or more second shifted base filters includes shifting the second base filter in the second direction of the multidimensional response according to each of the one or more time offsets to generate the one or more second shifted base filters. [0119] In Example 50, the subject matter of Example 49 can optionally include wherein each of the one or more second shifted based filters are approximately centered at a respective time offset of the one or more time offsets.

[0120] In Example 51, the subject matter of Example 49 or 50 can optionally include wherein shifting the second base filter in the second direction of the multidimensional response according to each of the one or more time offsets to generate the one or more second shifted base filters includes for each respective time offset of the one or more time offsets, performing a phase shift in the second direction of the multidimensional response with elements of the second base filter according to the respective time offset to generate a respective second shifted base filter of the one or more second shifted base filters.

[0121] In Example 52, the subject matter of any one of Examples 35 to 51 can optionally further include applying a respective gain to each of the one or more first shifted base filters and applying a respective gain to each of the one or more second shifted base filters.

[0122] In Example 53, the subject matter of Example 52 can optionally further include calculating the respective gain to apply to each of the one or more first shifted base filters based on the initial channel estimate and calculating the respective gain to apply to each of the one or more second shifted base filters based on the initial channel estimate.

[0123] In Example 54, the subject matter of any one of Examples 35 to 53 can optionally include wherein combining the one or more first shifted base filters and the one or more second shifted base filters to generate the combined filter to approximate the channel includes combining the one or more first shifted base filters to generate a time-direction composite filter, combining the one or more second shifted base filters to generate a frequency-direction composite filter, and combining the time-direction composite filter and the frequency- direction composite filter to generate the combined filter.

[0124] In Example 55, the subject matter of Example 54 can optionally include wherein combining the time-direction composite filter and the frequency-direction composite filter to generate the combined filter includes applying the time-direction composite filter and the frequency-direction composite filter to the initial channel estimate to generate the combined filter.

[0125] In Example 54, the subject matter of Example 54 or 55 can optionally include wherein the time-direction composite filter is single dimensional, the frequency-direction composite filter is single-dimensional, and the combined filter is two-dimensional.

[0126] In Example 57, the subject matter of any one of Examples 54 to 56 can optionally include wherein the time-direction composite filter is a superposition of the one or more first shifted base filters and the frequency-direction composite filter is a superposition of the one or more second shifted base filters.

[0127] In Example 58, the subject matter of Example 54 can optionally include wherein combining the one or more first shifted base filters to generate the time-direction composite filter includes summing the one or more first shifted base filters to obtain the time-direction composite filter, and wherein combining the one or more second shifted base filters to generate the frequency-direction composite filter includes summing the one or more second shifted base filters to obtain the frequency-direction composite filter.

[0128] In Example 59, the subject matter of any one of Examples 35 to 58 can optionally include wherein the first base filter and the second base filter are single-dimensional.

[0129] In Example 60, the subject matter of any one of Examples 35 to 59 can optionally include wherein the combined filter is a 2xlD filter.

[0130] In Example 61, the subject matter of any one of Examples 35 to 60 can optionally further include receiving signal data, and demodulating the signal data with the combined filter.

[0131] In Example 62, the subject matter of any one of Examples 35 to 61 can optionally further include transmitting a channel estimate based on the combined filter. [0132] Example 63 is a non-transitory computer readable medium storing instructions that when executed by a controller of a communication device cause the communication device to perform the method of any one of Examples 35 to 62.

[0133] Example 64 is a non-transitory computer readable medium storing instructions that when executed by a processor cause the processor to perform the method of any one of Examples 35 to 62.

[0134] Example 65 is a communication device configured to perform the method of any one of Examples 35 to 62.

[0135] Example 66 is a communication circuit arrangement configured to perform the method of any one of Examples 35 to 62.

[0136] Example 67 is a communication circuit arrangement system adapted for channel estimation in mobile communication, the system including a channel preprocessing circuit configured to obtain an initial channel estimate, an offset estimation circuit configured to identify one or more condensed channel power regions of a channel response based on the initial channel estimate, a filter shift circuit configured to apply a shift to one or more prototype filters according to each of the one or more condensed channel power regions to generate one or more shifted prototype filters, and a filter synthesis circuit configured to combine the one or more shifted prototype filters to generate a combined filter to

approximates a channel response.

[0137] In Example 68, the subject matter of Example 67 can optionally include wherein the initial channel estimate is a noisy channel estimate.

[0138] In Example 69, the subject matter of Example 67 or 68 can optionally include wherein the channel preprocessing circuit is configured to obtain the initial channel estimate by comparing received noisy reference symbols to predefined local reference symbols.

[0139] In Example 70, the subject matter of any one of Examples 67 to 69 can optionally include wherein the channel response is a delay-Doppler multipath response. [0140] In Example 71, the subject matter of Example 70 can optionally include wherein each element of the combined filter approximates the multipath delay-Doppler response at a specific subcarrier and a specific symbol period of a multi-subcarrier modulation scheme.

[0141] In Example 72, the subject matter of Example 70 or 71 can optionally include wherein the offset estimation circuit includes a frequency offset estimation circuit and a time offset estimation circuit, the frequency offset estimation circuit configured to identify one or more frequency offsets corresponding to positions of the one or more condensed channel power regions along a Doppler dimension of the channel response, and the time offset estimation circuit configured to identify one or more time offsets corresponding to positions of the one or more condensed channel power regions along a delay dimension of the channel response.

[0142] In Example 73, the subject matter of Example 72 can optionally include wherein the one or more prototype filters include a time-direction prototype filter, and wherein the filter shift circuit is configured to apply the shift to the one or more prototype filters according to each of the one or more condensed channel power regions to generate the one or more shifted prototype filters by shifting the time-direction prototype filter along the Doppler dimension of the channel response according to each of the one or more frequency offsets to generate one or more first shifted prototype filters of the one or more shifted prototype filters.

[0143] In Example 74, the subject matter of Example 73 can optionally include wherein the frequency offset estimation circuit is configured to identify the one or more frequency offsets corresponding to the positions of the one or more condensed channel power regions along the

Doppler dimension of the channel response by evaluating each of a plurality of frequency offset hypotheses to identify a subset of the plurality of frequency offset hypotheses that produce high channel power metrics as the one or more frequency offsets.

[0144] In Example 75, the subject matter of Example 74 can optionally include wherein the frequency offset estimation circuit is configured to evaluate each of the plurality of frequency offset hypotheses to identify the subset of the plurality of frequency offset hypotheses that produce high channel power metrics as the one or more frequency offsets by calculating a channel power metric for each of the plurality of frequency offset hypotheses with the time- direction prototype filter and a time-direction covariance matrix derived from the initial channel estimate, and selecting the one or more frequency offsets from the plurality of frequency offset hypotheses based on the channel power metrics for the plurality of frequency offset hypotheses.

[0145] In Example 76, the subject matter of any one of Examples 73 to 75 can optionally include wherein the filter shift circuit is configured to shift the time-direction prototype filter along the Doppler dimension of the channel response according to each of the one or more frequency offsets to generate the one or more first shifted prototype filters of the one or more shifted prototype filters by for each respective frequency offset of the one or more frequency offsets, performing a phase shift along the Doppler dimension of the channel response with elements of the time-direction prototype filter according to the respective frequency offset to generate a respective first shifted prototype filter of the one or more first shifted prototype filters.

[0146] In Example 77, the subject matter of any one of Examples 72 to 76 can optionally include wherein the one or more prototype filters include a frequency-direction prototype filter, and wherein the filter shift circuit is configured to apply the shift to the one or more prototype filters according to each of the one or more condensed channel power regions to generate the one or more shifted prototype filters by shifting the frequency-direction prototype filter along the delay dimension of the channel response according to each of the one or more time offsets to generate one or more second shifted prototype filters of the one or more shifted prototype filters, and wherein the filter synthesis circuit is configured to combine the one or more shifted prototype filters to generate the combined filter to approximate the channel response by combining the one or more first shifted prototype filters and the one or more second shifted prototype filters to generate the combined filter.

[0147] In Example 78, the subject matter of Example 77 can optionally include wherein the time offset estimation circuit is configured to identify the one or more time offsets corresponding to the positions of the one or more condensed channel power regions along the delay dimension of the channel response by evaluating each of a plurality of time offset hypotheses to identify a subset of the plurality of timing offset hypotheses that produce high channel power metrics as the one or more time offsets.

[0148] In Example 79, the subject matter of Example 78 can optionally include wherein the time offset estimation circuit is configured to evaluate each of the plurality of time offset hypotheses to identify the subset of the plurality of timing offset hypotheses that produce high channel power metrics as the one or more time offsets by calculating a channel power metric for each of the plurality of timing offset hypotheses with the frequency-direction prototype filter and a frequency-direction covariance matrix derived from the initial channel estimate, and selecting the one or more time offsets from the plurality of time offset hypotheses based on the channel power metrics for the plurality of time offset hypotheses.

[0149] In Example 80, the subject matter of any one of Examples 77 to 79 can optionally include wherein the filter shift circuit is configured to shift the frequency-direction prototype filter along the delay dimension of the channel response according to each of the one or more time offsets to generate the one or more second shifted prototype filters of the one or more shifted prototype filters by for each respective time offset of the one or more time offsets, performing a phase shift along the delay dimension of the channel response with elements of the frequency-direction prototype filter according to the respective time offset to generate a respective second shifted prototype filter of the one or more second shifted prototype filters.

[0150] In Example 81, the subject matter of any one of Examples 77 to 80 can optionally include wherein the filter shift circuit is further configured to apply a respective gain to each of the one or more first shifted prototype filters and to apply a respective gain to each of the one or more second shifted prototype filters.

[0151] In Example 82, the subject matter of Example 81 can optionally include wherein the filter shift circuit is configured to calculate the respective gain to apply to each of the one or more first shifted prototype filters based on the initial channel estimate and to calculate the respective gain to apply to each of the one or more second shifted prototype filters based on the initial channel estimate.

[0152] In Example 83, the subject matter of any one of Examples 77 to 82 can optionally include wherein the filter shift circuit is further configured to combine the one or more first shifted prototype filters to generate a time-direction composite filter and to combine the one or more second shifted prototype filters to generate a frequency-direction composite filter, and wherein the filter synthesis circuit is configured to combine the one or more first shifted prototype filters and the one or more second shifted prototype filters to generate the combined filter by combining the time-direction composite filter and the frequency-direction composite filter to generate the combined filter.

[0153] In Example 84, the subject matter of Example 83 can optionally include wherein the filter synthesis circuit is configured to combine the time-direction composite filter and the frequency-direction composite filter to generate the combined filter by applying the time- direction composite filter and the frequency-direction composite filter to the initial channel estimate to generate the combined filter.

[0154] In Example 85, the subject matter of Example 83 or 84 can optionally include wherein the time-direction composite filter is single dimensional, the frequency-direction composite filter is single-dimensional, and the combined filter is two-dimensional.

[0155] In Example 86, the subject matter of any one of Examples 83 to 85 can optionally include wherein the filter shift circuit is configured to combine the one or more first shifted prototype filters to generate the time-direction composite filter by summing the one or more first shifted prototype filters to obtain the time-direction composite filter.

[0156] In Example 87, the subject matter of any one of Examples 83 to 86 can optionally include wherein the filter shift circuit is configured to combine the one or more second shifted prototype filters to generate the frequency-direction composite filter by summing the one or more second shifted prototype filters to obtain the frequency-direction composite filter.

[0157] In Example 88, the subject matter of any one of Examples 67 to 87 can optionally include wherein the one or more prototype filters are single-dimensional.

[0158] In Example 89, the subject matter of any one of Examples 67 to 72 can optionally include wherein the one or more prototype filters are two-dimensional.

[0159] In Example 90, the subject matter of Example 89 can optionally include wherein the filter shift circuit is configured to apply the shift to the one or more prototype filters according to each of the one or more condensed channel power regions to generate the one or more shifted prototype filters by applying a two-dimensional shift along a Doppler dimension and a delay dimension of the channel response to obtain the one or more shifted prototype filters.

[0160] In Example 91, the subject matter of Example 90 can optionally include wherein the filter synthesis circuit is configured to combine the one or more shifted prototype filters to generate the combined filter to approximate the channel response by summing the one or more shifted prototype filters to generate the combined filter.

[0161] In Example 92, the subject matter of Example 90 or 91 can optionally include wherein the combined filter is a superposition of the one or more shifted prototype filters.

[0162] In Example 93, the subject matter of any one of Examples 67 to 88 can optionally include wherein the combined filter is a 2xlD filter.

[0163] In Example 94, the subject matter of any one of Examples 67 to 93 can optionally further include a demodulation circuit configured to receive signal data, and demodulate the received signal data with the combined filter. [0164] In Example 95, the subject matter of any one of Examples 67 to 94 can optionally further include a control circuit configured to transmit a channel estimate based on the combined filter.

[0165] In Example 96, the subject matter of any one of Examples 67 to 95 can optionally further include a radio transceiver and configured as a radio communication device.

[0166] Example 97 is a baseband processing circuit including the communication circuit arrangement of any one of Examples 67 to 95.

[0167] Example 98 is a communication circuit arrangement including a channel

preprocessing circuit configured to obtain an initial channel estimate of a channel, an offset estimation circuit configured to evaluate the initial channel estimate of the channel to identify one or more concentrated channel power regions of a multidimensional response of the channel, a first filter shift circuit configured to apply a shift to a first base filter according to positions of the one or more concentrated channel power regions in a first direction of the multidimensional response to generate one or more first shifted based filters, a second filter shift circuit configured to apply a shift to a second base filter according to positions of the one or more concentrated channel power regions in a second direction of the multidimensional response to generate one or more second shifted base filters, and a filter synthesis circuit configured to combine the one or more first shifted base filters and the one or more second shifted base filters to generate a combined filter to approximate the channel.

[0168] In Example 99, the subject matter of Example 98 can optionally include wherein the initial channel estimate is a noisy channel estimate.

[0169] In Example 100, the subject matter of Example 98 or 99 can optionally include wherein the channel preprocessing circuit is configured to obtain the initial channel estimate of the channel by comparing noisy received reference symbols to local predefined reference symbols. [0170] In Example 101, the subject matter of any one of Examples 98 to 100 can optionally include wherein the multidimensional response is a delay-Doppler multipath response.

[0171] In Example 102, the subject matter of Example 101 can optionally include wherein each element of the combined filter approximates the delay-Doppler response at a specific subcarrier and a specific symbol period of a multi-subcarrier modulation scheme.

[0172] In Example 103, the subject matter of any one of Examples 98 to 102 can optionally include wherein the offset estimation circuit includes a frequency offset estimation circuit and a time offset estimation circuit, the frequency offset estimation circuit configured to identify one or more frequency offsets corresponding to the positions of the one or more concentrated channel power regions in the first direction of the multidimensional response, and the time offset estimation circuit configured to identify one or more time offsets corresponding to the positions of the one or more concentrated channel power regions in the second direction of the multidimensional response.

[0173] In Example 104, the subject matter of Example 103 can optionally include wherein the wherein the multidimensional response is a delay-Doppler multipath response, the first base filter is a time-direction filter, and the second base filter is a frequency-direction filter, the first direction of the multidimensional response is a Doppler direction, and the second direction of the multidimensional response is a delay direction.

[0174] In Example 105, the subject matter of Example 103 or 104 can optionally include wherein the frequency offset estimation circuit is configured to identify the one or more frequency offsets corresponding to the positions of the one or more concentrated channel power regions in the first direction of the multidimensional response by evaluating each of a plurality of frequency offset hypotheses that correspond to high channel power of the initial channel estimate to identify a subset of the plurality of frequency offset hypotheses as the one or more frequency offsets. [0175] In Example 106, the subject matter of Example 105 can optionally include wherein the frequency offset estimation circuit is configured to evaluate each of the plurality of frequency offset hypotheses that correspond to high channel power of the initial channel estimate to identify the subset of the plurality of frequency offset hypotheses as the one or more frequency offsets by calculating a channel power metric for each of the plurality of frequency offset hypotheses with the first base filter and a time-direction covariance matrix derived from the initial channel estimate, and selecting the one or more frequency offsets from the plurality of frequency offset hypotheses based on the channel power metrics for the plurality of frequency offset hypotheses.

[0176] In Example 107, the subject matter of any one of Examples 104 to 106 can optionally include wherein the first filter shift circuit is configured to apply the shift to the first base filter according to the positions of the one or more concentrated channel power regions in the first direction of the multidimensional response to generate the one or more first shifted base filters by shifting the first base filter in the first direction of the multidimensional response according to each of the one or more frequency offsets to generate the one or more first shifted base filters.

[0177] In Example 108, the subject matter of Example 107 can optionally include wherein each of the one or more first shifted based filters are approximately centered at a respective frequency offset of the one or more frequency offsets.

[0178] In Example 109, the subject matter of Example 107 or 108 can optionally include wherein the first filter shift circuit is configured to shift the first base filter in the first direction of the multidimensional response according to each of the one or more frequency offsets to generate the one or more first shifted base filters by for each respective frequency offset of the one or more frequency offsets, performing a phase shift in the first direction of the multidimensional response with elements of the first base filter according to the respective frequency offset to generate a respective first shifted base filter of the one or more first shifted base filters.

[0179] In Example 110, the subject matter of any one of Examples 103 to 109 can optionally include wherein the time offset estimation circuit is configured to identify the one or more time offsets corresponding to the positions of the one or more concentrated channel power regions in the second direction of the multidimensional response by evaluating each of a plurality of time offset hypotheses that correspond to high channel power of the initial channel estimate to identify a subset of the plurality of time offset hypotheses as the one or more time offsets.

[0180] In Example 111, the subject matter of Example 110 can optionally include wherein the time offset estimation circuit is configured to evaluate each of the plurality of time offset hypotheses that correspond to high channel power of the initial channel estimate to identify the subset of the plurality of time offset hypotheses as the one or more time offsets by calculating a channel power metric for each of the plurality of time offset hypotheses with the second base filter and a frequency-direction covariance matrix derived from the initial channel estimate, and selecting the one or more time offsets from the plurality of time offset hypotheses based on the channel power metrics for the plurality of time offset hypotheses.

[0181] In Example 112, the subject matter of any one of Examples 104 to 111 can optionally include wherein the second filter shift circuit is configured to apply the shift to the second base filter according to the positions of the one or more concentrated channel power regions in the second direction of the multidimensional response to generate the one or more second shifted base filters by shifting the second base filter in the second direction of the multidimensional response according to each of the one or more time offsets to generate the one or more second shifted base filters. [0182] In Example 113, the subject matter of Example 112 can optionally include wherein each of the one or more second shifted based filters are approximately centered at a respective time offset of the one or more time offsets.

[0183] In Example 114, the subject matter of Example 112 or 113 can optionally include wherein the second filter shift circuit is configured to shift the second base filter in the second direction of the multidimensional response according to each of the one or more time offsets to generate the one or more second shifted base filters by for each respective time offset of the one or more time offsets, performing a phase shift in the second direction of the

multidimensional response with elements of the second base filter according to the respective time offset to generate a respective second shifted base filter of the one or more second shifted base filters.

[0184] In Example 115, the subject matter of any one of Examples 98 to 114 can optionally include wherein the first filter shift circuit is further configured to apply a respective gain to each of the one or more first shifted base filters and the second filter shift circuit is further configured to apply a respective gain to each of the one or more second shifted base filters.

[0185] In Example 116, the subject matter of Example 115 can optionally include wherein the first filter shift circuit is further configured to calculate the respective gain to apply to each of the one or more first shifted base filters based on the initial channel estimate and the second filter shift circuit is further configured to calculate the respective gain to apply to each of the one or more second shifted base filters based on the initial channel estimate.

[0186] In Example 117, the subject matter of any one of Examples 98 to 116 can optionally include wherein the first filter shift circuit is further configured to combine the one or more first shifted base filters to generate a time-direction composite filter and the second filter shift circuit is further configured to combine the one or more second shifted base filters to generate a frequency-direction composite filter, and wherein the filter synthesis circuit is configured to combine the one or more first shifted base filters and the one or more second shifted base filters to generate the combined filter to approximate the channel by combining the time- direction composite filter and the frequency-direction composite filter to generate the combined filter.

[0187] In Example 118, the subject matter of Example 117 can optionally include wherein the filter synthesis circuit is configured to combine the time-direction composite filter and the frequency-direction composite filter to generate the combined filter by applying the time- direction composite filter and the frequency-direction composite filter to the initial channel estimate to generate the combined filter.

[0188] In Example 119, the subject matter of Example 117 or 118 can optionally include wherein the first filter shift circuit is configured to combine the one or more first shifted base filters to generate the time-direction composite filter by summing the one or more first shifted base filters to obtain the time-direction composite filter, and wherein the second filter shift circuit is configured to combine the one or more second shifted base filters to generate the frequency-direction composite filter by summing the one or more second shifted base filters to obtain the frequency-direction composite filter.

[0189] In Example 120, the subject matter of any one of Examples 98 to 119 can optionally include wherein the first base filter and the second base filter are single-dimensional.

[0190] In Example 121, the subject matter of any one of Examples 98 to 120 can optionally include wherein the combined filter is a 2xlD filter.

[0191] In Example 122, the subject matter of any one of Examples 98 to 121 can optionally further include a modulation circuit configured to receive signal data, and demodulate the signal data with the combined filter.

[0192] In Example 123, the subject matter of any one of Examples 98 to 122 can optionally further include a control circuit configured to transmit a channel estimate based on the combined filter. [0193] In Example 124, the subject matter of any one of Examples 98 to 123 can optionally further include a radio transceiver and configured as a radio communication device.

[0194] Example 125 is a baseband processing circuit including the communication circuit arrangement of any one of Examples 98 to 123.

[0195] All acronyms defined in the above description additionally hold in all claims included herein.

[0196] While the invention has been particularly shown and described with reference to specific embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced.