TECHNICAL FIELD

The present disclosure relates to wireless communications, and in particular, to estimating a downlink covariance matrix using samples or a portion of the uplink covariance matrix.

BACKGROUND

The Third Generation Partnership Project (3 GPP) has developed and is developing standards for Fourth Generation (4G) (also referred to as Long Term Evolution (LTE)) and Fifth Generation (5G) (also referred to as New Radio (NR)) wireless communication systems. Such systems provide, among other features, broadband communication between network nodes, such as base stations, and mobile wireless devices (WD), as well as communication between network nodes and between WDs. Sixth Generation (6G) wireless communication systems are also under development.

Wireless communications systems employing relatively large number of antennas at the network node (e.g., base station (BS)) to serve multiple wireless devices, are known as massive Multiple-Input Multiple-Output (MIMO) systems.

They may be characterized at least in part by high spectral efficiency and high power efficiency, better spatial resolution, and less complex transceiver design. To help harness the full potential of massive MIMO systems, accurate channel state information (CSI) of the channels between the network node and wireless devices in the downlink (DL) and the uplink (UL) directions is typically required. Acquiring the UL CSI can be achieved using a channel probing technique where wireless devices send prescribed pilots to the network node. For Time Division Duplex (TDD) systems, the UL and DL channels share the same frequency band; hence, the UL CSI matches the DL CSI due to channel reciprocity. However, for Frequency Division Duplex (FDD) systems, channel reciprocity does not hold due to the wide gap between the UL and DL frequency bands; hence, UL CSI does not match DL CSI. Sending DL pilots to the wireless devices from each network node antenna and having the wireless devices feedback the channel estimates to the network node incurs huge feedback overhead that strongly deteriorates the system efficiency. Moreover, the long pilot sequences required by the large number of antennas result in training times that may exceed the channel coherence time.

The channel spatial covariance matrix plays a role in CSI acquisition. The coherence time of the channel spatial covariance matrix is longer than the channel coherence time; therefore, estimating this matrix can be performed less frequently and this reduces the training overhead. Moreover, since the propagation directions are frequency invariant for the UL and DL bands, the angular power spectrum (APS), i.e., the signal power distribution in the angular domain, is frequency invariant for UL and DL bands. The frequency invariance of the APS is exploited in several existing methods to estimate the DL spatial covariance matrix from an observation of the UL spatial covariance matrix. That is, an idea of these existing methods is to estimate the UL covariance matrix, then using this matrix: either to explicitly estimate the APS and use it to compute an estimate of the DL covariance matrix, or to apply some transformation to the UL covariance matrix estimate to get the DL covariance matrix. In the latter case, the APS frequency invariance assumption is implicitly preserved in the applied transformation. Although these methods are based on the same assumption, they have different accuracy and complexity.

For example, legacy solutions for FDD systems rely on using the covariance matrix estimated from uplink measurements without any frequency correction. This can lead to significant performance degradation when the duplex gap between uplink and downlink transmission bands is large, e.g., for LTE band 4, the uplink band is 1710-1755 MHz while the downlink band is 2110-2155 MHz, i.e., the duplex gap is 400 MHz. Existing frequency correction methods for covariance matrices in some existing methods have high complexity. For example, the algorithm in one existing method explicitly estimates the APS samples by solving a complex optimization problem and then estimates the downlink covariance from the estimated APS. The total complexity of this algorithm can be shown to be 0(gM ³ ) where M is the number of network node antennas and g » M is the number of samples in the APS estimate. The scheme in another existing method uses a truncated Fourier series expansion to represent the APS and obtains the downlink covariance matrix using a matrix multiplication operation that multiples the vectorized uplink covariance matrix by a transformation matrix. The complexity of this scheme is dominated by this matrix multiplication and is of 0(M ⁴ ).

SUMMARY

Some embodiments advantageously provide methods, systems, and apparatuses for estimating a downlink covariance matrix using samples or a portion of the uplink covariance matrix.

In one or more embodiments, massive MIMO systems with wireless devices communicating with a network node operating in FDD mode is considered. In FDD systems, unlike TDD systems, frequency separation between uplink and downlink results in a lack of channel reciprocity and consequently, different uplink/downlink channel covariance matrices. For these FDD systems, a scheme described herein provides an approximate downlink covariance matrix using only uplink covariance samples or a specific portion of the uplink covariance matrix. One or more embodiments described herein provide a method that can be implemented as a low complexity matrix multiplication using a fixed matrix that depends only on the network node array manifold and uplink/downlink frequency separation. The accuracy of some embodiments described herein advantageously increases with an increasing number of antennas at the network node. In one or more embodiments, the theoretical results were confirmed by numerical simulations.

According to one aspect, a network node is configured to communicate with a wireless device, WD, using frequency division duplex, FDD, communications. The network node includes processing circuitry configured to: determine an uplink covariance Toeplitz matrix based at least in part on measurements of signals received from the WD in an uplink frequency band on a number of antenna elements in an array of antenna elements of an antenna of the network node; determine a downlink covariance Toeplitz matrix based at least in part on a single row and column of the uplink covariance Toeplitz matrix; and apply the downlink covariance Toeplitz matrix for downlink transmissions to the WD in a downlink frequency band.

According to this aspect, in some embodiments, determining the downlink covariance Toeplitz matrix includes determining a frequency invariant angular power spectrum, APS, the APS being determined as a Fourier series, coefficients of the Fourier series being based at least in part on the single row and column of the uplink covariance Toeplitz matrix. In some embodiments, a number of coefficients in the Fourier series is based at least in part on the number of antenna elements in the array of antenna elements. In some embodiments, determining the downlink covariance Toeplitz matrix includes determining a product of a matrix of Sine functions and a vector containing elements of the single row and column of the uplink covariance Toeplitz matrix. In some embodiments, the processing circuitry is further configured to store the matrix of Sine functions, the matrix of Sine functions being independent of the signal measurements and being preoperationally computed. In some embodiments, determining the uplink covariance Toeplitz matrix includes finding a sample Toeplitz matrix that minimizes a Frobenius norm of a difference between the sample Toeplitz matrix and an uplink covariance matrix determined from the signal measurements. In some embodiments, determining the downlink covariance Toeplitz matrix includes determining a first downlink covariance Toeplitz matrix corresponding to a first dimension of a two-dimensional array of the antenna elements and determining a second downlink covariance Toeplitz matrix corresponding to the second dimension of the two-dimensional array. In some embodiments, determining the downlink covariance Toeplitz matrix includes determining a Kronecker product of the first and second downlink covariance Toeplitz matrices corresponding to the first and second dimensions of the two-dimensional array. In some embodiments, determining the downlink covariance Toeplitz matrix includes determining a polarization-independent downlink covariance Toeplitz matrix that is applied for each polarization of an array of dual polarized antenna elements of the antenna. In some embodiments, the single row and column are a first row and column, respectively, of the uplink covariance Toeplitz matrix.

According to another aspect, a method in a network node configured to communicate with a wireless device, WD, using frequency division duplex, FDD, communications, includes: determining an uplink covariance Toeplitz matrix based at least in part on measurements of signals received from the WD in an uplink frequency band on a number of antenna elements in an array of antenna elements of an antenna of the network node; determining a downlink covariance Toeplitz matrix based at least in part on a single row and column of the uplink covariance Toeplitz matrix; and applying the downlink covariance Toeplitz matrix for downlink transmissions to the WD in a downlink frequency band.

According to this aspect, in some embodiments, determining the downlink covariance Toeplitz matrix includes determining a frequency invariant angular power spectrum, APS, the APS being determined as a Fourier series, coefficients of the Fourier series being based at least in part on the single row and column of the uplink covariance Toeplitz matrix. In some embodiments, a number of coefficients in the Fourier series is based at least in part on the number of antenna elements in the array of antenna elements. In some embodiments, determining the downlink covariance Toeplitz matrix includes determining a product of a matrix of Sine functions and a vector containing elements of the single row and column of the uplink covariance Toeplitz matrix. In some embodiments, the method also includes storing the matrix of Sine functions, the matrix of Sine functions being independent of the signal measurements and being preoperationally computed. In some embodiments, determining the uplink covariance Toeplitz matrix includes finding a sample Toeplitz matrix that minimizes a Frobenius norm of a difference between the sample Toeplitz matrix and an uplink covariance matrix determined from the signal measurements. In some embodiments, determining the downlink covariance Toeplitz matrix includes determining a first downlink covariance Toeplitz matrix corresponding to a first dimension of a two-dimensional array of the antenna elements and determining a second downlink covariance Toeplitz matrix corresponding to the second dimension of the two-dimensional array. In some embodiments, determining the downlink covariance Toeplitz matrix includes determining a Kronecker product of the first and second downlink covariance Toeplitz matrices corresponding to the first and second dimensions of the two-dimensional array. In some embodiments, determining the downlink covariance Toeplitz matrix includes determining a polarization-independent downlink covariance Toeplitz matrix that is applied for each polarization of an array of dual polarized antenna elements of the antenna. In some embodiments, the single row and column are a first row and column, respectively, of the uplink covariance Toeplitz matrix. BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present embodiments, and the attendant advantages and features thereof, will be more readily understood by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein:

FIG. 1 is a schematic diagram of an example network architecture illustrating a communication system connected via an intermediate network to a host computer according to the principles in the present disclosure;

FIG. 2 is a block diagram of a host computer communicating via a network node with a wireless device over an at least partially wireless connection according to some embodiments of the present disclosure;

FIG. 3 is a flowchart illustrating example methods implemented in a communication system including a host computer, a network node and a wireless device for executing a client application at a wireless device according to some embodiments of the present disclosure;

FIG. 4 is a flowchart illustrating example methods implemented in a communication system including a host computer, a network node and a wireless device for receiving user data at a wireless device according to some embodiments of the present disclosure;

FIG. 5 is a flowchart illustrating example methods implemented in a communication system including a host computer, a network node and a wireless device for receiving user data from the wireless device at a host computer according to some embodiments of the present disclosure;

FIG. 6 is a flowchart illustrating example methods implemented in a communication system including a host computer, a network node and a wireless device for receiving user data at a host computer according to some embodiments of the present disclosure;

FIG. 7 is a flowchart of an example process in a network node according to some embodiments of the present disclosure;

FIG. 8 is a flowchart of an example process in a wireless device according to some embodiments of the present disclosure; FIG. 9 is a flowchart of another example process in a network node according to principles disclosed herein;

FIG. 10 is a diagram of the scheme/method according to some embodiments of the present disclosure; FIG. 11 is a diagram of a uniformly space dual polarized array;

FIG. 12 is a graph of relative loss in received SINR versus a for M=8 according to some embodiments of the present disclosure; and

FIG. 13 is a graph of relative loss in received SINR versus a for M=16 according to some embodiments of the present disclosure.

DETAILED DESCRIPTION

Some existing methods for estimating DL spatial covariance matrix from the observed UL covariance matrix for FDD systems suffer from high complexity that disadvantageously uses limited processing resources. One or more embodiments described herein advantageously help solve some of the problems with existing systems by, for example, using only the first row and column of the uplink covariance matrix to compute the downlink covariance matrix for FDD systems. In one or more embodiments, the Fourier series expansion of the APS may be used where only a specific portion of the uplink covariance matrix is used for computation. In the algorithm described herein only the first row and column of the uplink covariance matrix is used to compute the downlink covariance matrix. Hence the complexity of the algorithm described herein is of 0

Before describing in detail example embodiments, it is noted that the embodiments reside primarily in combinations of apparatus components and processing steps related to estimating a downlink covariance matrix using samples or a portion of the uplink covariance matrix.

Accordingly, components have been represented where appropriate by conventional symbols in the drawings, showing only those specific details that are pertinent to understanding the embodiments so as not to obscure the disclosure with details that will be readily apparent to those of ordinary skill in the art having the benefit of the description herein. Like numbers refer to like elements throughout the description. As used herein, relational terms, such as “first” and “second,” “top” and “bottom,” and the like, may be used solely to distinguish one entity or element from another entity or element without necessarily requiring or implying any physical or logical relationship or order between such entities or elements. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the concepts described herein. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes” and/or “including” when used herein, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.

In embodiments described herein, the joining term, “in communication with” and the like, may be used to indicate electrical or data communication, which may be accomplished by physical contact, induction, electromagnetic radiation, radio signaling, infrared signaling or optical signaling, for example. One having ordinary skill in the art will appreciate that multiple components may interoperate and modifications and variations are possible of achieving the electrical and data communication.

In some embodiments described herein, the term “coupled,” “connected,” and the like, may be used herein to indicate a connection, although not necessarily directly, and may include wired and/or wireless connections.

The term “network node” used herein can be any kind of network node comprised in a radio network which may further comprise any of base station (BS), radio base station, base transceiver station (BTS), base station controller (BSC), radio network controller (RNC), g Node B (gNB), evolved Node B (eNB or eNodeB), Node B, multi- standard radio (MSR) radio node such as MSR BS, multi-cell/multicast coordination entity (MCE), integrated access and backhaul (IAB) node, relay node, donor node controlling relay, radio access point (AP), transmission points, transmission nodes, Remote Radio Unit (RRU) Remote Radio Head (RRH), a core network node (e.g., mobile management entity (MME), self-organizing network (SON) node, a coordinating node, positioning node, MDT node, etc.), an external node (e.g., 3rd party node, a node external to the current network), nodes in distributed antenna system (DAS), a spectrum access system (SAS) node, an element management system (EMS), etc. The network node may also comprise test equipment. The term “radio node” used herein may be used to also denote a wireless device (WD) such as a wireless device (WD) or a radio network node.

In some embodiments, the non-limiting terms wireless device (WD) or a user equipment (UE) are used interchangeably. The WD herein can be any type of wireless device capable of communicating with a network node or another WD over radio signals, such as wireless device (WD). The WD may also be a radio communication device, target device, device to device (D2D) WD, machine type WD or WD capable of machine to machine communication (M2M), low-cost and/or low-complexity WD, a sensor equipped with WD, Tablet, mobile terminals, smart phone, laptop embedded equipped (LEE), laptop mounted equipment (LME), USB dongles, Customer Premises Equipment (CPE), an Internet of Things (IoT) device, or a Narrowband IoT (NB-IOT) device, etc.

Also, in some embodiments the generic term “radio network node” is used. It can be any kind of a radio network node which may comprise any of base station, radio base station, base transceiver station, base station controller, network controller, RNC, evolved Node B (eNB), Node B, gNB, Multi-cell/multicast Coordination Entity (MCE), IAB node, relay node, access point, radio access point, Remote Radio Unit (RRU) Remote Radio Head (RRH).

Transmitting in downlink may pertain to transmission from the network or network node to the wireless device. Transmitting in uplink may pertain to transmission from the wireless device to the network or network node. Transmitting in sidelink may pertain to (direct) transmission from one wireless device to another. Uplink, downlink and sidelink (e.g., sidelink transmission and reception) may be considered communication directions. In some variants, uplink and downlink may also be used to described wireless communication between network nodes, e.g. for wireless backhaul and/or relay communication and/or (wireless) network communication for example between base stations or similar network nodes, in particular communication terminating at such. It may be considered that backhaul and/or relay communication and/or network communication is implemented as a form of sidelink or uplink communication or similar thereto.

Note that although terminology from one particular wireless system, such as, for example, 3GPP LTE and/or New Radio (NR), may be used in this disclosure, this should not be seen as limiting the scope of the disclosure to only the aforementioned system. Other wireless systems, including without limitation Wide Band Code Division Multiple Access (WCDMA), Worldwide Interoperability for Microwave Access (WiMax), Ultra Mobile Broadband (UMB) and Global System for Mobile Communications (GSM), may also benefit from exploiting the ideas covered within this disclosure.

Note further, that functions described herein as being performed by a wireless device or a network node may be distributed over a plurality of wireless devices and/or network nodes. In other words, it is contemplated that the functions of the network node and wireless device described herein are not limited to performance by a single physical device and, in fact, can be distributed among several physical devices.

Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms used herein should be interpreted as having a meaning that is consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

Some embodiments provide estimating a downlink covariance matrix using samples or a portion of the uplink covariance matrix.

Referring now to the drawing figures, in which like elements are referred to by like reference numerals, there is shown in FIG. 1 a schematic diagram of a communication system 10, according to an embodiment, such as a 3GPP-type cellular network that may support standards such as LTE and/or NR (5G), which comprises an access network 12, such as a radio access network, and a core network 14. The access network 12 comprises a plurality of network nodes 16a, 16b, 16c (referred to collectively as network nodes 16), such as NBs, eNBs, gNBs or other types of wireless access points, each defining a corresponding coverage area 18a, 18b, 18c (referred to collectively as coverage areas 18). Each network node 16a, 16b, 16c is connectable to the core network 14 over a wired or wireless connection 20. A first wireless device (WD) 22a located in coverage area 18a is configured to wirelessly connect to, or be paged by, the corresponding network node 16a. A second WD 22b in coverage area 18b is wirelessly connectable to the corresponding network node 16b. While a plurality of WDs 22a, 22b (collectively referred to as wireless devices 22) are illustrated in this example, the disclosed embodiments are equally applicable to a situation where a sole WD is in the coverage area or where a sole WD is connecting to the corresponding network node 16. Note that although only two WDs 22 and three network nodes 16 are shown for convenience, the communication system may include many more WDs 22 and network nodes 16.

Also, it is contemplated that a WD 22 can be in simultaneous communication and/or configured to separately communicate with more than one network node 16 and more than one type of network node 16. For example, a WD 22 can have dual connectivity with a network node 16 that supports LTE and the same or a different network node 16 that supports NR. As an example, WD 22 can be in communication with an eNB for LTE/E-UTRAN and a gNB for NR/NG-RAN.

The communication system 10 may itself be connected to a host computer 24, which may be embodied in the hardware and/or software of a standalone server, a cloud-implemented server, a distributed server or as processing resources in a server farm. The host computer 24 may be under the ownership or control of a service provider, or may be operated by the service provider or on behalf of the service provider. The connections 26, 28 between the communication system 10 and the host computer 24 may extend directly from the core network 14 to the host computer 24 or may extend via an optional intermediate network 30. The intermediate network 30 may be one of, or a combination of more than one of, a public, private or hosted network. The intermediate network 30, if any, may be a backbone network or the Internet. In some embodiments, the intermediate network 30 may comprise two or more sub-networks (not shown). The communication system of FIG. 1 as a whole enables connectivity between one of the connected WDs 22a, 22b and the host computer 24. The connectivity may be described as an over-the-top (OTT) connection. The host computer 24 and the connected WDs 22a, 22b are configured to communicate data and/or signaling via the OTT connection, using the access network 12, the core network 14, any intermediate network 30 and possible further infrastructure (not shown) as intermediaries. The OTT connection may be transparent in the sense that at least some of the participating communication devices through which the OTT connection passes are unaware of routing of uplink and downlink communications. For example, a network node 16 may not or need not be informed about the past routing of an incoming downlink communication with data originating from a host computer 24 to be forwarded (e.g., handed over) to a connected WD 22a. Similarly, the network node 16 need not be aware of the future routing of an outgoing uplink communication originating from the WD 22a towards the host computer 24.

A network node 16 is configured to include an estimation unit 32 which is configured to perform one or more network node 16 functions as described herein such as with respect to estimating a downlink covariance matrix using samples or a portion of the uplink covariance matrix. More particularly, the estimation unit 32 may be configured to determine a downlink covariance Toeplitz matrix based at least in part on a single row and column of the uplink covariance Toeplitz matrix. A wireless device 22 is configured to include a signaling unit 34 which is configured to perform one or more wireless device 22 function as described herein such as with respect to a downlink covariance matrix that is estimated using samples or a portion of the uplink covariance matrix.

Example implementations, in accordance with an embodiment, of the WD 22, network node 16 and host computer 24 discussed in the preceding paragraphs will now be described with reference to FIG. 2. In a communication system 10, a host computer 24 comprises hardware (HW) 38 including a communication interface 40 configured to set up and maintain a wired or wireless connection with an interface of a different communication device of the communication system 10. The host computer 24 further comprises processing circuitry 42, which may have storage and/or processing capabilities. The processing circuitry 42 may include a processor 44 and memory 46. In particular, in addition to or instead of a processor, such as a central processing unit, and memory, the processing circuitry 42 may comprise integrated circuitry for processing and/or control, e.g., one or more processors and/or processor cores and/or FPGAs (Field Programmable Gate Array) and/or ASICs (Application Specific Integrated Circuitry) adapted to execute instructions. The processor 44 may be configured to access (e.g., write to and/or read from) memory 46, which may comprise any kind of volatile and/or nonvolatile memory, e.g., cache and/or buffer memory and/or RAM (Random Access Memory) and/or ROM (Read- Only Memory) and/or optical memory and/or EPROM (Erasable Programmable Read-Only Memory).

Processing circuitry 42 may be configured to control any of the methods and/or processes described herein and/or to cause such methods, and/or processes to be performed, e.g., by host computer 24. Processor 44 corresponds to one or more processors 44 for performing host computer 24 functions described herein. The host computer 24 includes memory 46 that is configured to store data, programmatic software code and/or other information described herein. In some embodiments, the software 48 and/or the host application 50 may include instructions that, when executed by the processor 44 and/or processing circuitry 42, causes the processor 44 and/or processing circuitry 42 to perform the processes described herein with respect to host computer 24. The instructions may be software associated with the host computer 24.

The software 48 may be executable by the processing circuitry 42. The software 48 includes a host application 50. The host application 50 may be operable to provide a service to a remote user, such as a WD 22 connecting via an OTT connection 52 terminating at the WD 22 and the host computer 24. In providing the service to the remote user, the host application 50 may provide user data which is transmitted using the OTT connection 52. The “user data” may be data and information described herein as implementing the described functionality. In one embodiment, the host computer 24 may be configured for providing control and functionality to a service provider and may be operated by the service provider or on behalf of the service provider. The processing circuitry 42 of the host computer 24 may enable the host computer 24 to observe, monitor, control, transmit to and/or receive from the network node 16 and or the wireless device 22. The processing circuitry 42 of the host computer 24 may include an information unit 54 configured to enable the service provider to provide, process, estimate, store, transmit, receive, analyze, forward, relay, etc., information related to estimating a downlink covariance matrix using samples or a portion of the uplink covariance matrix.

The communication system 10 further includes a network node 16 provided in a communication system 10 and including hardware 58 enabling it to communicate with the host computer 24 and with the WD 22. The hardware 58 may include a communication interface 60 for setting up and maintaining a wired or wireless connection with an interface of a different communication device of the communication system 10, as well as a radio interface 62 for setting up and maintaining at least a wireless connection 64 with a WD 22 located in a coverage area 18 served by the network node 16. The radio interface 62 may be formed as or may include, for example, one or more RF transmitters, one or more RF receivers, and/or one or more RF transceivers. The communication interface 60 may be configured to facilitate a connection 66 to the host computer 24. The connection 66 may be direct or it may pass through a core network 14 of the communication system 10 and/or through one or more intermediate networks 30 outside the communication system 10.

In the embodiment shown, the hardware 58 of the network node 16 further includes processing circuitry 68. The processing circuitry 68 may include a processor 70 and a memory 72. In particular, in addition to or instead of a processor, such as a central processing unit, and memory, the processing circuitry 68 may comprise integrated circuitry for processing and/or control, e.g., one or more processors and/or processor cores and/or FPGAs (Field Programmable Gate Array) and/or ASICs (Application Specific Integrated Circuitry) adapted to execute instructions. The processor 70 may be configured to access (e.g., write to and/or read from) the memory 72, which may comprise any kind of volatile and/or nonvolatile memory, e.g., cache and/or buffer memory and/or RAM (Random Access Memory) and/or

ROM (Read-Only Memory) and/or optical memory and/or EPROM (Erasable Programmable Read-Only Memory).

Thus, the network node 16 further has software 74 stored internally in, for example, memory 72, or stored in external memory (e.g., database, storage array, network storage device, etc.) accessible by the network node 16 via an external connection. The software 74 may be executable by the processing circuitry 68. The processing circuitry 68 may be configured to control any of the methods and/or processes described herein and/or to cause such methods, and/or processes to be performed, e.g., by network node 16. Processor 70 corresponds to one or more processors 70 for performing network node 16 functions described herein. The memory 72 is configured to store data, programmatic software code and/or other information described herein. In some embodiments, the software 74 may include instructions that, when executed by the processor 70 and/or processing circuitry 68, causes the processor 70 and/or processing circuitry 68 to perform the processes described herein with respect to network node 16. For example, processing circuitry 68 of the network node 16 may include estimation unit 32 configured to perform one or more network node 16 functions as described herein such as with respect to estimating a downlink covariance matrix using samples or a portion of the uplink covariance matrix.

The communication system 10 further includes the WD 22 already referred to. The WD 22 may have hardware 80 that may include a radio interface 82 configured to set up and maintain a wireless connection 64 with a network node 16 serving a coverage area 18 in which the WD 22 is currently located. The radio interface 82 may be formed as or may include, for example, one or more RF transmitters, one or more RF receivers, and/or one or more RF transceivers.

The hardware 80 of the WD 22 further includes processing circuitry 84. The processing circuitry 84 may include a processor 86 and memory 88. In particular, in addition to or instead of a processor, such as a central processing unit, and memory, the processing circuitry 84 may comprise integrated circuitry for processing and/or control, e.g., one or more processors and/or processor cores and/or FPGAs (Field Programmable Gate Array) and/or ASICs (Application Specific Integrated Circuitry) adapted to execute instructions. The processor 86 may be configured to access (e.g., write to and/or read from) memory 88, which may comprise any kind of volatile and/or nonvolatile memory, e.g., cache and/or buffer memory and/or RAM (Random Access Memory) and/or ROM (Read-Only Memory) and/or optical memory and/or EPROM (Erasable Programmable Read-Only Memory).

Thus, the WD 22 may further comprise software 90, which is stored in, for example, memory 88 at the WD 22, or stored in external memory (e.g., database, storage array, network storage device, etc.) accessible by the WD 22. The software 90 may be executable by the processing circuitry 84. The software 90 may include a client application 92. The client application 92 may be operable to provide a service to a human or non-human user via the WD 22, with the support of the host computer 24. In the host computer 24, an executing host application 50 may communicate with the executing client application 92 via the OTT connection 52 terminating at the WD 22 and the host computer 24. In providing the service to the user, the client application 92 may receive request data from the host application 50 and provide user data in response to the request data. The OTT connection 52 may transfer both the request data and the user data. The client application 92 may interact with the user to generate the user data that it provides.

The processing circuitry 84 may be configured to control any of the methods and/or processes described herein and/or to cause such methods, and/or processes to be performed, e.g., by WD 22. The processor 86 corresponds to one or more processors 86 for performing WD 22 functions described herein. The WD 22 includes memory 88 that is configured to store data, programmatic software code and/or other information described herein. In some embodiments, the software 90 and/or the client application 92 may include instructions that, when executed by the processor 86 and/or processing circuitry 84, causes the processor 86 and/or processing circuitry 84 to perform the processes described herein with respect to WD 22. For example, the processing circuitry 84 of the wireless device 22 may include a signaling unit 34 configured to perform one or more wireless device 22 function as described herein such as with respect to estimating a downlink covariance matrix using samples or a portion of the uplink covariance matrix.

In some embodiments, the inner workings of the network node 16, WD 22, and host computer 24 may be as shown in FIG. 2 and independently, the surrounding network topology may be that of FIG. 1.

In FIG. 2, the OTT connection 52 has been drawn abstractly to illustrate the communication between the host computer 24 and the wireless device 22 via the network node 16, without explicit reference to any intermediary devices and the precise routing of messages via these devices. Network infrastructure may determine the routing, which it may be configured to hide from the WD 22 or from the service provider operating the host computer 24, or both. While the OTT connection 52 is active, the network infrastructure may further take decisions by which it dynamically changes the routing (e.g., on the basis of load balancing consideration or reconfiguration of the network).

The wireless connection 64 between the WD 22 and the network node 16 is in accordance with the teachings of the embodiments described throughout this disclosure. One or more of the various embodiments improve the performance of OTT services provided to the WD 22 using the OTT connection 52, in which the wireless connection 64 may form the last segment. More precisely, the teachings of some of these embodiments may improve the data rate, latency, and/or power consumption and thereby provide benefits such as reduced user waiting time, relaxed restriction on file size, better responsiveness, extended battery lifetime, etc.

In some embodiments, a measurement procedure may be provided for the purpose of monitoring data rate, latency and other factors on which the one or more embodiments improve. There may further be an optional network functionality for reconfiguring the OTT connection 52 between the host computer 24 and WD 22, in response to variations in the measurement results. The measurement procedure and/or the network functionality for reconfiguring the OTT connection 52 may be implemented in the software 48 of the host computer 24 or in the software 90 of the WD 22, or both. In embodiments, sensors (not shown) may be deployed in or in association with communication devices through which the OTT connection 52 passes; the sensors may participate in the measurement procedure by supplying values of the monitored quantities exemplified above, or supplying values of other physical quantities from which software 48, 90 may compute or estimate the monitored quantities. The reconfiguring of the OTT connection 52 may include message format, retransmission settings, preferred routing etc.; the reconfiguring need not affect the network node 16, and it may be unknown or imperceptible to the network node 16. Some such procedures and functionalities may be known and practiced in the art. In certain embodiments, measurements may involve proprietary WD signaling facilitating the host computer’s 24 measurements of throughput, propagation times, latency and the like. In some embodiments, the measurements may be implemented in that the software 48, 90 causes messages to be transmitted, in particular empty or ‘dummy’ messages, using the OTT connection 52 while it monitors propagation times, errors, etc.

Thus, in some embodiments, the host computer 24 includes processing circuitry 42 configured to provide user data and a communication interface 40 that is configured to forward the user data to a cellular network for transmission to the WD 22. In some embodiments, the cellular network also includes the network node 16 with a radio interface 62. In some embodiments, the network node 16 is configured to, and/or the network node’s 16 processing circuitry 68 is configured to perform the functions and/or methods described herein for preparing/initiating/maintaining/supporting/ending a transmission to the WD 22, and/or preparing/terminating/maintaining/supporting/ending in receipt of a transmission from the WD 22.

In some embodiments, the host computer 24 includes processing circuitry 42 and a communication interface 40 that is configured to a communication interface 40 configured to receive user data originating from a transmission from a WD 22 to a network node 16. In some embodiments, the WD 22 is configured to, and/or comprises a radio interface 82 and/or processing circuitry 84 configured to perform the functions and/or methods described herein for preparing/initiating/maintaining/supporting/ending a transmission to the network node 16, and/or preparing/terminating/maintaining/supporting/ending in receipt of a transmission from the network node 16.

Although FIGS. 1 and 2 show various “units” such as estimation unit 32, and signaling unit 34 as being within a respective processor, it is contemplated that these units may be implemented such that a portion of the unit is stored in a corresponding memory within the processing circuitry. In other words, the units may be implemented in hardware or in a combination of hardware and software within the processing circuitry.

FIG. 3 is a flowchart illustrating an example method implemented in a communication system, such as, for example, the communication system of FIGS. 1 and 2, in accordance with one embodiment. The communication system may include a host computer 24, a network node 16 and a WD 22, which may be those described with reference to FIG. 2. In a first step of the method, the host computer 24 provides user data (Block S100). In an optional substep of the first step, the host computer 24 provides the user data by executing a host application, such as, for example, the host application 50 (Block S102). In a second step, the host computer 24 initiates a transmission carrying the user data to the WD 22 (Block S104). In an optional third step, the network node 16 transmits to the WD 22 the user data which was carried in the transmission that the host computer 24 initiated, in accordance with the teachings of the embodiments described throughout this disclosure (Block S106). In an optional fourth step, the WD 22 executes a client application, such as, for example, the client application 92, associated with the host application 50 executed by the host computer 24 (Block s 108).

FIG. 4 is a flowchart illustrating an example method implemented in a communication system, such as, for example, the communication system of FIG. 1, in accordance with one embodiment. The communication system may include a host computer 24, a network node 16 and a WD 22, which may be those described with reference to FIGS. 1 and 2. In a first step of the method, the host computer 24 provides user data (Block SI 10). In an optional substep (not shown) the host computer 24 provides the user data by executing a host application, such as, for example, the host application 50. In a second step, the host computer 24 initiates a transmission carrying the user data to the WD 22 (Block SI 12). The transmission may pass via the network node 16, in accordance with the teachings of the embodiments described throughout this disclosure. In an optional third step, the WD 22 receives the user data carried in the transmission (Block S 114).

FIG. 5 is a flowchart illustrating an example method implemented in a communication system, such as, for example, the communication system of FIG. 1, in accordance with one embodiment. The communication system may include a host computer 24, a network node 16 and a WD 22, which may be those described with reference to FIGS. 1 and 2. In an optional first step of the method, the WD 22 receives input data provided by the host computer 24 (Block S 116). In an optional substep of the first step, the WD 22 executes the client application 92, which provides the user data in reaction to the received input data provided by the host computer 24 (Block SI 18). Additionally or alternatively, in an optional second step, the WD 22 provides user data (Block S120). In an optional substep of the second step, the WD provides the user data by executing a client application, such as, for example, client application 92 (Block S122). In providing the user data, the executed client application 92 may further consider user input received from the user. Regardless of the specific manner in which the user data was provided, the WD 22 may initiate, in an optional third substep, transmission of the user data to the host computer 24 (Block S124). In a fourth step of the method, the host computer 24 receives the user data transmitted from the WD 22, in accordance with the teachings of the embodiments described throughout this disclosure (Block S126).

FIG. 6 is a flowchart illustrating an example method implemented in a communication system, such as, for example, the communication system of FIG. 1, in accordance with one embodiment. The communication system may include a host computer 24, a network node 16 and a WD 22, which may be those described with reference to FIGS. 1 and 2. In an optional first step of the method, in accordance with the teachings of the embodiments described throughout this disclosure, the network node 16 receives user data from the WD 22 (Block S128). In an optional second step, the network node 16 initiates transmission of the received user data to the host computer 24 (Block S130). In a third step, the host computer 24 receives the user data carried in the transmission initiated by the network node 16 (Block S132).

FIG. 7 is a flowchart of an example process in a network node 16 according to some embodiments of the present disclosure. One or more blocks described herein may be performed by one or more elements of network node 16 such as by one or more of processing circuitry 68 (including the estimation unit 32), processor 70, radio interface 62 and/or communication interface 60. Network node 16 is configured to estimate (Block S134) a downlink covariance matrix associated with a downlink channel based at least on only a portion of an uplink covariance matrix associated with an uplink channel where the downlink channel lacks channel reciprocity with the uplink channel, as described herein. Network node 16 is further configured to perform (Block S136) at least one action based at least on the downlink covariance matrix, as described herein.

According to one or more embodiments, the portion of the uplink covariance matrix corresponds to a first row and first column of the uplink covariance matrix. According to one or more embodiments, the estimating of the downlink covariance matrix includes computing a downlink covariance vector based at least on the first row and first column of the uplink covariance matrix, and constructing a Toeplitz downlink covariance matrix based at least on the computing downlink covariance vector. According to one or more embodiments, the processing circuitry is configured to perform uplink measurements based on at least one uplink signal from the wireless device, and determine the uplink covariance matrix based at least on the uplink measurements. According to one or more embodiments, the at least one action includes performing downlink transmission based at least on the estimated downlink covariance matrix. FIG. 8 is a flowchart of an example process in a wireless device 22 according to some embodiments of the present disclosure. One or more blocks described herein may be performed by one or more elements of wireless device 22 such as by one or more of processing circuitry 84 (including the signaling unit 34), processor 86, radio interface 82 and/or communication interface 60. Wireless device 22 is configured to receive (Block S 138) a downlink transmission that is based on an estimate downlink covariance matrix associated with a downlink channel where the estimated downlink covariance matrix is based at least on only a portion of an uplink covariance matrix associated with an uplink channel, and the downlink channel lacks channel reciprocity with the uplink channel, as described herein. Wireless device 22 is further configured to process (Block S 140) the downlink transmission.

According to one or more embodiments, the portion of the uplink covariance matrix corresponds to a first row and first column of the uplink covariance matrix. According to one or more embodiments, the processing circuitry is further configured to cause transmission of at least one uplink signal to the network node for performing uplink measurements where the uplink covariance matrix is based at least on the uplink measurements.

FIG. 9 is a flowchart of another example process in a network node 16 according to some embodiments of the present disclosure. One or more blocks described herein may be performed by one or more elements of network node 16 such as by one or more of processing circuitry 68 (including the estimation unit 32), processor 70, radio interface 62 and/or communication interface 60. Network node 16 is configured to determine an uplink covariance Toeplitz matrix based at least in part on measurements of signals received from the WD in an uplink frequency band on a number of antenna elements in an array of antenna elements of an antenna of the network node (Block S142). The process also includes determining a downlink covariance Toeplitz matrix based at least in part on a single row and column of the uplink covariance Toeplitz matrix (Block S 144). The process further includes applying the downlink covariance Toeplitz matrix for downlink transmissions to the WD in a downlink frequency band (Block S146).

In some embodiments, determining the downlink covariance Toeplitz matrix includes determining a frequency invariant angular power spectrum, APS, the APS being determined as a Fourier series, coefficients of the Fourier series being based at least in part on the single row and column of the uplink covariance Toeplitz matrix. In some embodiments, a number of coefficients in the Fourier series is based at least in part on the number of antenna elements in the array of antenna elements. In some embodiments, determining the downlink covariance Toeplitz matrix includes determining a product of a matrix of Sine functions and a vector containing elements of the single row and column of the uplink covariance Toeplitz matrix. In some embodiments, the method also includes storing the matrix of Sine functions, the matrix of Sine functions being independent of the signal measurements and being preoperationally computed. In some embodiments, determining the uplink covariance Toeplitz matrix includes finding a sample Toeplitz matrix that minimizes a Frobenius norm of a difference between the sample Toeplitz matrix and an uplink covariance matrix determined from the signal measurements. In some embodiments, determining the downlink covariance Toeplitz matrix includes determining a first downlink covariance Toeplitz matrix corresponding to a first dimension of a two-dimensional array of the antenna elements and determining a second downlink covariance Toeplitz matrix corresponding to the second dimension of the two-dimensional array. In some embodiments, determining the downlink covariance Toeplitz matrix includes determining a Kronecker product of the first and second downlink covariance Toeplitz matrices corresponding to the first and second dimensions of the two- dimensional array. In some embodiments, determining the downlink covariance

Toeplitz matrix includes determining a polarization-independent downlink covariance Toeplitz matrix that is applied for each polarization of an array of dual polarized antenna elements of the antenna. In some embodiments, the single row and column are a first row and column, respectively, of the uplink covariance Toeplitz matrix.

Having generally described arrangements for estimating a downlink covariance matrix using samples or a portion of the uplink covariance matrix, details for these arrangements, functions and processes are provided as follows, and which may be implemented by the network node 16, wireless device 22 and/or host computer 24.

Some embodiments provide estimating a downlink covariance matrix using samples or a portion of the uplink covariance matrix. Some functionality described below with respect to network node 16 may be performed by network node 16 such as via processing circuitry 68, processor 70, estimation unit 32, radio interface 62, etc. Some functionality described below with respect to wireless device 22 may be performed by wireless device 22 such as via processing circuitry 84, processor 86, signaling unit 34, radio interface 82, etc.

System Model

A MIMO channel between a network node 16 and a single antenna wireless device 22 is considered. It is assumed that the network node 16 is equipped with an M-antenna uniform linear array (ULA) with M » 1. The transmission relies on a FDD system in which the uplink transmission, from wireless device 22 to network node 16, occurs over the frequency interval while the downlink transmission occurs on the frequency interval • A narrow-band transmission is considered, i.e., . Therefore, the entire uplink and downlink frequency intervals can be each seen as a single frequency, f _u and f _d , respectively.

A wide sense stationary (WSS) uncorrelated scattering channel model is considered in which the channel vectors evolve in time according to a WSS process. In this model, samples of time-variant channel vector fi(t) at intervals of channel coherence time T _c , i.e., h[n] = h(nT _c ), constitute a zero-mean WSS circularly - symmetric Gaussian process that is white in the time domain and correlated in the spatial domain. The spatial uplink and downlink covariance matrices are respectively given by: wherein q is the angle of arrival (AoA) and r(q) is the APS and ()^ denotes the Hermitian transpose.

Moreover, a _M (0) and CL _d (&) denote the uplink and downlink steering vectors, respectively, and for a ULA are given by: where d is the antenna spacing in the ULA, A _u and l ₁ are uplink and downlink wavelengths, respectively, given by A where c ₀ denotes the speed of light.

Using the above channel covariance matrices and steering vectors, it can be shown that channel covariance matrices are Hermitian, semi-definite and Toeplitz. Therefore, each covariance matrix can be constructed from its first column. This property will be used in the covariance matrix approximation method described herein.

It is assumed that the APS, p(θ), is frequency invariant and unknown while steering vectors a _u (θ) and α _d (&) are frequency variant and known. Therefore, in an FDD system, covariance matrices R _u and R _d are different but effectively related to each other. This property is used to approximate the downlink channel covariance matrix R _d given the uplink channel covariance matrix R _u .

Downlink Channel Covariance Matrix Approximation Process/Method In this section, a method to approximate the downlink covariance matrix R _d using the Fourier series expansion is provided. The method may be performed by network node 16. More precisely, first, the elements of the first row and column of R _u are used to obtain an implicit approximation of APS which is used to obtain an approximate downlink covariance matrix. Further, a direct transform from uplink covariance matrix to downlink covariance matrix is described. FIG. 10 is a diagram of a downlink covariance estimation algorithm that may be implemented by network node 16. The network node 16 may compute (Block S148) a covariance matrix based at least on channel estimates and a noise variance estimate. Network node 16 gets/determines (Block S150) a Toeplitz covariance (e.g., uplink Toeplitz covariance matrix) based at least on the computed covariance matrix referred to in Block S148. Network node 16 extracts (Block S152) a first row and first column of the Toeplitz covariance and constructs * » . Network node 16 computes (Block S154) downlink covariance vectors, as described herein. Network node 16 constructs (Block S156) a Toeplitz downlink covariance matrix which may correspond to the downlink covariance matrix.

Implicit Approximation of APS

In this section, an approximate APS is implicitly calculated by obtaining a different form of the integral that computes the uplink covariance matrix. This can be achieved by using the expression for the steering vectors of a uniform linear array

(ULA) to obtain the pqr-th entry of a _M (q)a _M (q)^ which is equal to where p = 0, ... , (M — 1) and q = 0, ... , (M — 1). Hence, it can be shown that the pq- th entry of R _u is equal to

Similarly, for the downlink: p, q = 0, ...,M - 1

Using the above expression for [R _u ] _pq , the m-th entry of the first column of matrix R _u is given while the m-th entry of the first row of where m = 0, (M — 1). Using the equations of the first row and first column, a scalar is defined where m = p — q, and it is shown that it is given by:

A Fourier series of a periodic function /(x) with period T is given by: where and {a _fc } are the Fourier series coefficients.

Comparing the above expression for with that for a _k , it can be seen that i.e., the entries of the first column and the first row of R _u , can be interpreted as Fourier series coefficients of p'(θ) with k

- and considering the fact that k is an integer yields where y is a natural number.

Now using the above expression for the Fourier expansion of a periodic function /(x), an approximation of r' (Q) can be written as:

This approximation shows that r'(q ) is reconstructed by its Fourier series coefficients, up to M — 2 harmonics. The term corresponding to k = 0 is the DC component, the term corresponding to k = 1 represents the fundamental frequency and the terms corresponding to m = 2, ... , M — 1 represent the next M — 2 harmonics. Therefore, as the number of antennas of, for example, network node 16 increases, more harmonics are used, and a more accurate approximation will result. However, it is noted that if Ρ (θ) contains some discontinuities, the reconstructed r'(θ) oscillates at these positions due to Gibbs Phenomenon. In particular, the height of overshooting or undershooting does not depend on the number of harmonics while the duration of the oscillations decreases with the number of harmonics. Despite this fact, simulation results illustrate that the scheme described herein outperforms existing scheme(s) at high M even for APS containing discontinuities. An approximation of Downlink Channel Covariance Matrix

Now, r'(q ) is employed to approximate downlink channel covariance matrix R _d . For a ULA, using the above expression for the steering vectors, it is shown that the channel covariance matrices are positive semi-definite, Hermitian and Toeplitz. That is, each covariance matrix can be constructed by network node 16 using only the first column. For a ULA with antenna spacing d and uplink wavelength _u and given uplink channel covariance matrix R _u , the m-th entry of the first column of R _d , denoted by [R _d ] _{m i} , is given by: m = 0, ...,M — 1 where In particular, for m = 0, ...,M — l.

The above results can be rewritten in a matrix format which shows a direct transformation from uplink channel covariance matrix to the downlink one. In particular: where contains the first row and first column entries of R _u and is given by: and the matrix Φ contains samples of the sine function and is given by:

The transfer matrix Φ given depends on the number of antennas in the ULA and downlink-uplink frequency ratio Therefore, this matrix can be computed offline, in advance of operation. Note that the dimension of the matrix F is given by M X 2 M — 1, and hence, the complexity of computing

Given the first column of the estimated downlink covariance matrix, [R_d ]_(:1), the full covariance matrix R_d can be acquired by exploiting the Hermitian symmetry and Toeplitz properties of the covariance matrix. The downlink single layer precoder can be computed as the principal eigenvector of the estimated downlink covariance matrix.

Uplink Channel Covariance Matrix Sample Computation

So far, it has been assumed that the uplink channel covariance matrix is available. In practice, uplink covariance matrix samples can be computed at the network node 16 by a limited number of noisy uplink channel vectors. More precisely, transmitting pilots at the wireless device 22, the noisy channel vector received at the network node 16 during the 1-th coherence time is given by y ₁ = h1 + n _I , wherein h _\ is the channel vector and n ₁ is Gaussian noise vector with zero mean and covariance matrix Let Ldenote the number of available samples of y _\ . Using y _\ 1 = 1, ... , L, the covariance matrix sample can be computed by: given It is noted that this is Hermitian but not necessarily Toeplitz which is a factor in the scheme described herein.

To overcome this, the computed uplink covariance matrix sample may be projected to the cone of Toeplitz positive semi-definite matrices by using the following convex optimization problem: wherein T ₊ denotes the set of positive semi-definite Toeplitz M X M matrices and ||. I | denotes the Frobenius norm of a matrix. This projected uplink covariance R _u ' can be used in the scheme described herein instead of actual R _u .

Note that the above optimization problem can be efficiently solved where the constraint X E T ₊ corresponds to a set of linear constraints on the elements of X. Extension to two Dimensional arrays

Next, a network node 16 employing a 2-dimensional polarized array as shown in FIG. 11 is considered. Let M _v and M _H denote the number of rows and columns of the 2-dimensional antenna array, respectively, i.e., the total number of antenna elements is given by 2 M _V M _H . The M _{v X} M _{H X} 2 multi-dimensional matrix H(t) is defined such that the (m, n, p ) element of H(t) is the coefficient of the channel associated with the antenna element in row m, column n and polarization p at time instant t where m = and p = 0, 1. Furthermore, the

2 M _V M _{H X} 1 full channel vector is denoted as: where (. ) ^r denotes the transpose operator, and hp(t) is the M _V M _{H X} 1 vector containing the coefficients of the channel associated with the antennas with polarization p, and h(p)(t) can be obtained by applying the vectorization operator (that stacks the columns of a 2-dimensional matrix on top of each other) to the two- dimensional sub-matrix of H(t ) associated with polarization p.

Due to the similarity of the covariance matrices of channel associated with each set of polarized antennas, the following holds: where E{. } denotes the statistical expectation operator, the covariance per polarization denoted by the M _V M _H X M _V M _H matrix R^ may be estimated. Furthermore, it is known that the covariance matrix of the channel vector associated with a 2- dimensional array can be approximated as the Kronecker product of the horizontal and vertical covariance matrices. Hence, the following: where O denotes the Kronecker product operator, R _H is the M _H X M _H covariance matrix in the horizontal direction and R _v is the M _v X M _v covariance matrix in the vertical direction. Hence, the downlink covariance approximation algorithm described herein can be applied separately in both directions and the per-polarization downlink covariance matrix R(p) can be estimated from the Kronecker product of the two matrices. In particular, the input measurement set for the vertical direction uses the columns of the matrix H(t ) as its input measurement set where 2 M _H samples are available from each full channel vector measurement. Similarly, the horizontal covariance estimation algorithm uses the rows of H(t ) as its input measurements and 2 M _v samples are available from each full channel vector measurement.

The single user (SU)-MIMO precoders for each wireless device 22 can be constructed using the dominant eigen vectors of its tracked covariance matrix. For the polarized antenna array shown in FIG. 11, the rank r SU-MIMO precoder can be obtained by co-phasing the eigen vectors of the covariance matrix per polarization. For example, the rank 2 SU-MIMO precoder is given by: where f ₀ is the co-phasing factor and v ₀ is the dominant eigen vector of the estimated per-polarization downlink covariance matrix R(p) Note that a fixed or random co-phasing factor can be used by the network node 16.

The dominant eigen vector of the covariance matrix v ₀ can be directly obtained from the estimated horizontal and vertical eigen vectors as: are the dominant eigen vectors of the estimated horizontal and vertical covariance matrices, respectively.

Numerical Simulations

In this section, the performance of the scheme described herein is compared with an existing scheme. A baseline is considered where there is no downlink covariance matrix estimation and the noisy uplink covariance is used directly as the estimated downlink covariance matrix. The performance metric used in the simulations is the relative loss in the downlink received signal-to-interference-plus- noise-ratio (SINR) ratio which can be measured by where v is the principal eigenvector of the downlink covariance of the tested method, R _d is the actual downlink covariance matrix (not the estimated one) and is the largest eigenvalue of the actual downlink covariance matrix. More precisely, the metric shows the relative loss in the received SINR at the wireless device 22 using a precoder composed of the principal eigenvector of the estimated downlink covariance matrix and the received SINR using the principal eigenvector of the exact downlink covariance matrix.

The case of smooth APS is considered. In this case, based on the geometry- based stochastic channel model (GSCM), a model for APS is used in which r(q ) is simulated as a summation of some Gaussian distributions given by: wherein, P is drawn uniformly random from {1,2, ... ,5},/ _p (0) denotes a Gaussian distribution with mean q _r uniformly drawn from and standard deviation^ uniformly drawn from [3°, 5°]. Moreover, {w _p } are drawn uniformly random from [0,1] and normalized such that It is noted that, in this model, P denotes the number of clusters of scatterers, are the cluster powers, are clusters mean AoAs and denote angular spreads.

It is assumed that a noisy version of the uplink channel covariance matrix is available at network node 16. In particular, network node 16 has access to uplink covariance samples through 1000 noisy channel estimates. To obtain a noisy channel vector at network node 16, the APS is used to generate the actual uplink covariance matrix R _u and then the actual channel vector is computed as

1, ..., L, wherein Ίn1 is a Gaussian random vector with zero mean and identity covariance matrix. Afterwards, a noisy version of h _\ is assumed to be available at network node 16 and used for computing the estimated uplink covariance matrix.

FIG. 12 illustrates the relative loss in the received SINR, that is evaluated versus the uplink and downlink frequency gap, i.e., for M = 8. The scheme described herein and the existing scheme have very close performance. The simulation results for M = 16 are illustrated in FIG. 13. FIG. 13 illustrates that the scheme described herein outperforms the existing scheme. For instance, at a = 1.2 the scheme described herein yields a relative SINR loss of about 0.3 X 10 ^-3 compared to 7 X 10 ^-3 yielded by the existing scheme.

Comparing the results provided in FIGS. 12 and 13, it can be seen that increasing the number of antennas at the ULA improves the simulation results for the methods described herein. Therefore, the simulation results confirm the analytical findings indicating that a higher number of antennas, i.e., higher number of harmonics, yields better implicit estimation of APS and hence better downlink channel covariance matrix estimation.

Therefore, one or more embodiments described herein provide for estimating the downlink covariance matrix from uplink channel estimates in FDD systems with low computational complexity. Further, significant performance improvement in received downlink SINR is shown through simulations compared to a baseline legacy scheme where the uplink covariance matrix is used for downlink precoding.

Further, one or more embodiments described herein provide an algorithm that may be used for FDD systems where the network node 16 employs a uniform linear array to approximate the downlink covariance matrix using only uplink covariance samples. The method can be implemented as a low complexity matrix multiplication using a fixed matrix that depends only on the array manifold and uplink/downlink frequency separation.

The downlink covariance estimation algorithm may be extended to the case of uniform two-dimensional polarized arrays by estimating the downlink covariance matrix in the vertical and horizontal directions separately and merging the covariance matrices and/or the eigen vectors of the two directions to estimate the full-dimension covariance matrix and/or the downlink precoding vectors.

Some embodiments may include one or more of the following:

Embodiment A1. A network node configured communicate with a wireless device (WD), the network node configured to, and/or comprising a radio interface and/or comprising processing circuitry configured to: estimate a downlink covariance matrix associated with a downlink channel based at least on only a portion of an uplink covariance matrix associated with an uplink channel, the downlink channel lacking channel reciprocity with the uplink channel; and perform at least one action based at least on the downlink covariance matrix.

Embodiment A2. The network node of Embodiment Al, wherein the portion of the uplink covariance matrix corresponds to a first row and first column of the uplink covariance matrix.

Embodiment A3. The network node of any one of Embodiments A1-A2, wherein the estimating of the downlink covariance matrix includes: computing a downlink covariance vector based at least on the first row and first column of the uplink covariance matrix; and constructing a Toeplitz downlink covariance matrix based at least on the computing downlink covariance vector. Embodiment A4. The network node of any one of Embodiments A1-A3, wherein the processing circuitry is configured to: perform uplink measurements based on at least one uplink signal from the wireless device; and determine the uplink covariance matrix based at least on the uplink measurements.

Embodiment A5. The network node of any one of Embodiments A1-A4, wherein the at least one action includes performing downlink transmission based at least on the estimated downlink covariance matrix.

Embodiment Bl. A method implemented in a network node that is configured to communicate with a wireless device, the method comprising: estimating a downlink covariance matrix associated with a downlink channel based at least on only a portion of an uplink covariance matrix associated with an uplink channel, the downlink channel lacking channel reciprocity with the uplink channel; and performing at least one action based at least on the downlink covariance matrix.

Embodiment B2. The method of Embodiment B 1, wherein the portion of the uplink covariance matrix corresponds to a first row and first column of the uplink covariance matrix.

Embodiment B3. The method of any one of Embodiments B 1-B2, wherein the estimating of the downlink covariance matrix includes: computing a downlink covariance vector based at least on the first row and first column of the uplink covariance matrix; and constructing a Toeplitz downlink covariance matrix based at least on the computing downlink covariance vector.

Embodiment B4. The network node of any one of Embodiments B 1-B3, wherein the processing circuitry is configured to: perform uplink measurements based on at least one uplink signal from the wireless device; and determine the uplink covariance matrix based at least on the uplink measurements. Embodiment B5. The network node of any one of Embodiments B 1-B4, wherein the at least one action includes performing downlink transmission based at least on the estimated downlink covariance matrix.

Embodiment Cl. A wireless device (WD) configured to communicate with a network node, the WD configured to, and/or comprising a radio interface and/or processing circuitry configured to: receive a downlink transmission that is based on an estimate downlink covariance matrix associated with a downlink channel, the estimated downlink covariance matrix being based at least on only a portion of an uplink covariance matrix associated with an uplink channel, the downlink channel lacking channel reciprocity with the uplink channel; and process the downlink transmission.

Embodiment C2. The WD of Embodiment Cl, wherein the portion of the uplink covariance matrix corresponds to a first row and first column of the uplink covariance matrix.

Embodiment C3. The WD of any one of Embodiments C1-C2, wherein the processing circuitry is further configured to cause transmission of at least one uplink signal to the network node for performing uplink measurements, the uplink covariance matrix being based at least on the uplink measurements.

Embodiment Dl. A method implemented in a wireless device that is configured to communicate with a network node, the method comprising: receiving a downlink transmission that is based on an estimate downlink covariance matrix associated with a downlink channel, the estimated downlink covariance matrix being based at least on only a portion of an uplink covariance matrix associated with an uplink channel, the downlink channel lacking channel reciprocity with the uplink channel; and processing the downlink transmission.

Embodiment D2. The method of Embodiment Dl, wherein the portion of the uplink covariance matrix corresponds to a first row and first column of the uplink covariance matrix.

Embodiment D3. The method of any one of Embodiments D1-D2, further comprising causing transmission of at least one uplink signal to the network node for performing uplink measurements, the uplink covariance matrix being based at least on the uplink measurements.

As will be appreciated by one of skill in the art, the concepts described herein may be embodied as a method, data processing system, computer program product and/or computer storage media storing an executable computer program. Accordingly, the concepts described herein may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects all generally referred to herein as a “circuit” or “module.” Any process, step, action and/or functionality described herein may be performed by, and/or associated to, a corresponding module, which may be implemented in software and/or firmware and/or hardware. Furthermore, the disclosure may take the form of a computer program product on a tangible computer usable storage medium having computer program code embodied in the medium that can be executed by a computer. Any suitable tangible computer readable medium may be utilized including hard disks, CD-ROMs, electronic storage devices, optical storage devices, or magnetic storage devices.

Some embodiments are described herein with reference to flowchart illustrations and/or block diagrams of methods, systems and computer program products. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer (to thereby create a special purpose computer), special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer readable memory or storage medium that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instruction means which implement the function/act specified in the flowchart and/or block diagram block or blocks.

The computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

It is to be understood that the functions/acts noted in the blocks may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Although some of the diagrams include arrows on communication paths to show a primary direction of communication, it is to be understood that communication may occur in the opposite direction to the depicted arrows.

Computer program code for carrying out operations of the concepts described herein may be written in an object oriented programming language such as Python, Java® or C++. However, the computer program code for carrying out operations of the disclosure may also be written in conventional procedural programming languages, such as the "C" programming language. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer. In the latter scenario, the remote computer may be connected to the user's computer through a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).

Many different embodiments have been disclosed herein, in connection with the above description and the drawings. It will be understood that it would be unduly repetitious and obfuscating to literally describe and illustrate every combination and subcombination of these embodiments. Accordingly, all embodiments can be combined in any way and/or combination, and the present specification, including the drawings, shall be construed to constitute a complete written description of all combinations and subcombinations of the embodiments described herein, and of the manner and process of making and using them, and shall support claims to any such combination or subcombination.

Abbreviations that may be used in the preceding description include: Abbreviation Explanation

AoA Angle of Arrival

APS Angular Power Spectrum

BS Base Station

CSI Channel State Information DL Downlink

FDD Frequency Division Duplex

MIMO Multiple-Input Multiple- Output

SU Single User

TDD Time Division Duplex UF Uplink

UFA Uniform Finear Array

WSS Wide Sense Stationary

It will be appreciated by persons skilled in the art that the embodiments described herein are not limited to what has been particularly shown and described herein above. In addition, unless mention was made above to the contrary, it should be noted that all of the accompanying drawings are not to scale. A variety of modifications and variations are possible in light of the above teachings without departing from the scope of the following claims.