DETECTION FOR WIRELESS COMMUNICATION Related Applications

This application claims the benefit of United States Provisional Application Serial No.

61/883,605 filed September 27, 2013, entitled "COMPLEX-DOMAIN CHANNEL-ADAPTIVE LATTICE REDUCTION AIDED MIMO DETECTION FOR WIRELESS COMMUNICATION," which application is incorporated herein by reference in its entirety.

Technical Field

Embodiments described herein generally relate to multiple-input, multiple-output (MIMO) systems and particularly to MIMO detectors.

Background

Modern wireless systems, such as, for example, mobile broadband systems, may employ multiple-input, multiple- output (MIMO) schemes to increase spectral efficiency and data rates. Various wireless communication standards allow MIMO schemes. For example, 802.11η provides for a 4x4 system (e.g., 4 access point antennas and 4 station antennas.) As another example, 802.1 lac provides for an 8x4 system (e.g., 8 access point antennas and 4 station antennas.) Still, as another example, 3GPP LTE Advanced release 10 provides an 8x8 system (e.g., 8 access point antennas and 8 station antennas.)

In general, MIMO schemes provide that a data stream is de-multiplexed into multiple streams (e.g., one for each transmit antenna) transmitted through a channel, and received by a receiver using multiple antennas. For example, a data stream may be de-multiplexed into multiple data streams. Each of these multiple data streams may be modulated using different symbols and then transmitted to the receiver. As will be appreciated, the use of multiple transmit channels allows the MIMO system to increase the data rates achievable in the transmission spectrum. At the receiver, then, these transmitted data streams must be combined and the original signal estimated. MIMO systems include a MIMO detector at the receiver, which combines the transmitted data streams and estimates the original signal. A variety of different techniques and algorithms for MIMO detection have been proposed. Some of the proposed techniques and algorithms provide a minimum bit error rate (e.g., Maximum Likelihood (ML) detection, Sphere Decoder (SD) detection, lattice reduction (LR)-aided detection, or the like.) However, these techniques are computationally expensive to implement and are often impractical as the number of antennas increases. For example, ML detection complexity grows exponentially as the number of antennas grows. As such, ML detection is impractical for larger MIMO systems. SD detection has prohibitively large area and power requirements necessary for implementation. Furthermore, SD detection may not reach an optimal solution within necessary time constraints. Although LR-aided detectors may achieve the same diversity as an ML detector, LR-aided detectors exhibit some performance loss compared to ML detectors. Furthermore, LR-aided detectors require a complex enumeration of a search space that involves an unconstrained expansion of nodes of the search space. While a particular MIMO detection algorithm may be suitable for transmission channels having high signal to noise ration (SNR), the particular MIMO detection algorithms may not be suitable for transmission channels having a low SNR. Likewise, MIMO detection algorithm suitable for transmission channels having a low SNR may not be suitable for transmission channels having a high SNR. Thus, there is a need for a MIMO detector that can support multiple standards (e.g., provide for large numbers of transmit and receive antennas) without necessitating impractical area and power requirements to implement. Additionally, there is a need for a MIMO detector that is suitable for high SNR transmission channels as well as low SNR transmission channels.

Furthermore, there is a need for a reduced complexity LR-aided MIMO detector.

Brief Description of the Drawings

FIG. 1 illustrates an example of a MIMO system according to an embodiment.

FIG. 2 illustrates a portion of the MIMO system according to an embodiment. FIG. 3 illustrates an example LR-aided MIMO detector according to an embodiment.

FIGS. 4A-4D illustrate an example two-dimensional search space and an on-demand expansion of nodes of the two-dimensional search space.

FIGS. 5-6 illustrate examples of logic flows for LR-aided MIMO detection according to an embodiment. FIG. 7 illustrates an embodiment of a storage medium. FIG. 8 illustrates a device according to an embodiment. Detailed Description

Examples are generally directed to lattice reduction (LR)-aided multiple-input, multiple output (MEVIO) detectors for use in MEVIO systems. These LR-aided MIMO detectors may be included with or implemented by receivers in communication components (e.g., access points, mobile devices, cells, or the like) that may be configured to operate in accordance with various wireless network standards. These wireless network standards may include standards promulgated by the Institute of Electrical Engineers (IEEE). These wireless network standards may include Ethernet wireless standards (including progenies and variants) associated with the IEEE 802.11-2012. For example, some examples may be implemented for operation with the 802.1 In and/or the

802.1 lac Standards. Additionally, these wireless network standards may include standards promulgated by 3 rd Generation Partnership Project (3GPP). These wireless network standards may include Ethernet wireless standards (including progenies and variants) associated with the 3GPP LTE Standard. For example, some examples may be implemented for operation with the 3GPP LTE- Advanced release 10 Standard.

According to some examples, a reduced complexity LR-aided MIMO detector that is adaptive to varying channel conditions may be provided in a MEVIO receiver. The MIMO receiver may determine a plurality of estimated signals based on a complex enumeration of a two-dimensional search space, where a search radius limits the complex enumeration. The complex enumeration includes an on-demand expansion of nodes of the two-dimensional search space, where the number of nodes expanded is limited by a node expansion parameter. For example, received signals may be extended into a search vector and translated into a two-dimensional search space based on a lattice reduction process. The LR-aided MIMO detector may be configured to apply a complex K-best enumeration process of the two-dimensional search space where a number of nodes in the two-dimensional search space are expanded. K and the number of nodes that are expanded may be varied based on channel conditions to provide a balance between energy efficiency (e.g., power consumption of the LR-aided MIMO detector) and bit error rate. For example, the value of K and the number of nodes that are expanded may be dynamically adjusted based on a channel quality index, desired bit error rate (BER) targets, and/or a signal-to- noise (SNR) ratio of the channel. Limiting the number of nodes that are expanded provides a reduction in the complexity of the LR-aided MIMO detection process.

FIG. 1 is a block diagram illustrating an example MEVIO system 1000. In some examples, as shown in FIG. 1, the MIMO system 1000 includes a MEVIO transmitter 100 and a MIMO receiver 200. As can be seen, the MIMO transmitter 100 and the MEVIO receiver 200 each include a number of antennas. For example, the MIMO transmitter 100 includes transmit (Tx) antennas 118-1 to 118-N while the MIMO receiver 200 includes receive (Rx) antennas 218-1 to

218-M. The transmitter 100 is configured to transmit signals 11-1 to 11-N to the receiver 200 using the wireless channel 10. It is to be appreciated, that the number of Tx antennas 118 and Rx antennas 218 may vary depending upon the implementation and/or the standard with which the system 1000 is designed to operate. Additionally, in some examples, the number of Tx antennas 118 may be the same as the number of Rx antennas 218. With some examples, the number of Tx antennas 118 may be different that the number of Rx antennas 218. Furthermore, it is to be appreciated, that although the system 1000 is described having a transmitter (e.g, the transmitter 100) and a receiver (e.g., the receiver 200), each of the transmitter and receiver may be configured to both transmit and receive signals. Said differently, although not illustrated, the transmitter 100 may include circuitry configured to both transmit and receive signals using the wireless channel 10. Similarly, although not illustrated, the receiver 200 may include circuitry configured to both receive and transmit signals using the wireless channel 10.

In some examples, the transmitter 100 and/or the receiver 200 may be components in a wireless system, such as, for example, access points, base stations, cells, mobile devices, or the like. As a particularly illustrative example, the transmitter 100 may be an access point (e.g., macro cell, small cell, base station, or the like) in a mobile broadband network, such as, for example, a mobile broadband network operating in compliance with at least one or more wireless communication standards (e.g., 802.11η, 802.1 lac, 3GPP LTE- Advanced release 10, or the like) while the receiver 200 may be a mobile device (e.g., smartphone, tablet, laptop, wireless access point, or the like) in the mobile broadband network.

Turning more specifically to FIG. 1, at the transmitter 100, input data 110 is processed by transmitter circuitry 120 to transmit the input data 110 to the receiver 200 using the Tx antennas 118-1 to 118-N in compliance with a MIMO scheme. More specifically, the input data 110 may be transmitted to the receiver 200 as signals 11-1 to 11-N using the wireless channel 10. It is to be appreciated that a variety of different techniques are known for transmitting data according to a MIMO scheme. In general, however, the transmitter circuitry 120 may be configured to de- multiplex the input data 110 into multiple data streams. For example, the input data 110 may be de-multiplexed into N data streams (e.g., one for each of the Tx antennas 118-1 to 118-N.) In some examples, the input data 110 may be coded (e.g., based upon a standard, or the like.) The transmitter circuitry 120 may additionally be configured to modulate the de-multiplexed data streams. For example, the de-multiplexed data streams may be modulated using different constellation sets of quadrature amplitude modulation (QAM) symbols. The transmitter circuitry 120 may additionally be configured to transmit the de-multiplexed and modulated data streams to the receiver using the Tx antennas 118-1 to 118-N. It is important to note, that the input data 110 may represent any of a variety of types of data that may be conveyed through wireless channel 10. Furthermore, the input data 110 may be generated by the transmitter 100 or may be generated elsewhere. Furthermore, the input data 110 may be retrieved from storage (not shown), such as, for example, a computer readable storage media. It is to be appreciated, that the signals 11-1 to 11-N may correspond to symbols (e.g., encoded symbols, or the like). Said differently, the signals 11-1 to 11-N may each be a symbol or a stream of symbols that are transmitted from the transmitter 100 to the receiver 200. At the receiver 200, output data 210 is determined from the signals 11-1 to 11-N by an LR-aided MIMO detection process. Said differently, the signals transmitted by the transmitter 100 are estimated by the receiver 200 based on the received signals and an LR-aided MIMO detection process. As will be appreciated, the signals 11-1 to 11-N may correspond to one or more symbols. During transmission, the order of the symbols or the symbols themselves may be changed due to effects of the channel 10. The receiver then determines an estimate for what the original symbols and their order were. Although care is taken herein to distinguish between signals, symbols, transmitted signals, received signals, estimated signals, etc., it is to be appreciated, that the desired meaning is to be understood from the context in which each phrase is used. In some instances, these phrases may be used interchangeably and sometimes may inadvertently be used interchangeably. Additionally, the reference numerals 11-1 to 11-N are used to designate the signals in the system generally and may correspond to transmitted signals, received signals, estimated signals, or the like. Examples are not limited in this context.

The signals 11-1 to 11-N are received at the Rx antennas 218-1 to 218-M and processed by the receiver circuitry 220. More specifically, output data 210 may be generated by the receiver circuitry 220 from the received signals 11-1 to 11-N. In some examples, the receiver circuitry 220 may apply various baseband processing (e.g., frequency offset compensation,

synchronization, equalization, or the like) to the signals 11-1 to 11-N. Additionally, the receiver circuitry 220 may apply an LR-aided MIMO detection process to the signals 11-1 to 11-N. In various examples, the receiver circuitry extends the signals 11-1 to 11-N into search vectors and translates the search vectors into a two-dimensional search space based on a lattice reduction process.

The receiver circuitry applies a complex K-best process to search the two-dimensional search space and determine estimates for the received signals. In general, the receiver circuitry 220 may implement a complex K-best search of the two-dimensional search space where the search includes expanding nodes of the two-dimensional search space based on an on-demand expansion process limited by a node expansion parameter. In implementing the complex K-best process, the receiver circuitry may dynamically change the value of K and the node expansion parameter. For example, the value of K and the node expansion parameter may be dynamically adjusted based on channel estimation feedback using a channel quality indicator (CQI) 230. When the CQI 230 indicates good channel conditions, the value of K and the node expansion parameter may be reduced. When the CQI 230 indicates poor channel conditions, the value of K and the node expansion parameter may be increased. Additionally, the value of K and the node expansion parameter may be dynamically adjusted based on the signal-to-noise (SNR) ratio of the wireless channel 10. For example, where the SNR of the wireless channel 10 is high, the value of K and the node expansion parameter may be reduced. Where the SNR of the wireless channel 10 is low, the value of K and the node expansion parameter may be increased.

Additionally, the value of K and the node expansion parameter may be dynamically adjusted based on a desired BER target. Said differently, the value of K and the node expansion parameter may be dynamically adjusted based on an acceptable BER. For example, for a high acceptable BER, the value of K and the node expansion parameter may be reduced. For a low acceptable BER, the value of K and the node expansion parameter may be increased.

It is important to note, that the CQI 230 may be generated by the receiver 200 or may be generated elsewhere in the system 1000. Furthermore, a variety of different techniques for measuring and/or quantifying channel quality are known. For example, some standards (e.g.,

3GPP LTE) provide for the receiver to generate the CQI as a 4-bit value and transmit the CQI to the transmitter for the transmitter to adapt the modulation scheme based on the current channel conditions. The CQI 230 may correspond to this 4-bit value. Examples are, however, not limited in this context. Accordingly, the system 1000 provides a MIMO receiver that may be adaptable to a variety of different wireless channel conditions and/or operable with a variety of communication standards. In particular, the receiver may provide for a reduction in the complexity associated with performing LR-aided MIMO detection while maintaining acceptable levels of BER and/or quality of service across a variety of channel conditions.

FIG. 2 is a block diagram for the receiver 200. Although the receiver 200 shown in FIG. 2 has a limited number of elements in a certain topology or configuration, it may be appreciated that the receiver 200 may include more or less elements in alternate configurations as desired for a given implementation. The receiver 200 may include a computer and/or firmware implemented apparatus having circuitry 220 arranged to execute one or more components 222-a. It is noted that "a" and "b" and "c" and similar designators as used herein are intended to be variables representing any positive integer. Thus, for example, if an implementation sets a value for a = 4, then a complete set of components 222-a may include modules 222-1, 222-2, 222-3 or 222-4. The examples are not limited in this context.

According to some examples, the receiver 200 may be included in a receiver (e.g., access point, cell, mobile device, or the like) in a MIMO system. The receiver and the MIMO system may be capable of operating in compliance with one or more wireless technologies such as those described herein. For example, a receiver as shown in FIG. 2 may be arranged or configured to wirelessly receive multiple signals using multiple antennas and detect the transmitted signals using a LR-aided MIMO detector. It is noted, that although the receiver 200 is discussed in conjunction with the MIMO system of FIG. 1, the examples are not limited in this context.

In some examples, as shown in FIG. 2, receiver 200 includes the circuitry 220 (e.g., as shown in FIG. 1.) The circuitry 220 may be generally arranged to execute one or more components 222-a. Circuitry 220 can be any of various commercially available processors, including without limitation an AMD® Athlon®, Duron® and Opteron® processors; ARM® application, embedded and secure processors; IBM® and Motorola® DragonBall® and PowerPC® processors; IBM and Sony® Cell processors; Qualcomm® Snapdragon®; Intel® Celeron®, Core (2) Duo®, Core i3, Core i5, Core i7, Itanium®, Pentium®, Xeon®, Atom® and XScale® processors; and similar processors. Dual microprocessors, multi-core processors, and other multi-processor architectures may also be employed as circuitry 220. According to some examples circuitry 220 may also be an application specific integrated circuit (ASIC) and components 222-a may be implemented as hardware elements of the ASIC. According to some examples circuitry 220 may also be a field programmable gate array (FPGA) and components 222-fl may be implemented as hardware elements of the FPGA.

According to some examples, the receiver 200 may include a baseband processor 222-1. The circuitry 220 may execute the baseband processor 222-1 to receive a plurality of signals transmitted through a wireless channel using a plurality of receiving antennas. For example, the circuitry 220 may execute the baseband processor 222-1 to receive the signals 11-1 to 11-N using Rx antennas 218-1 to 218-M. With some examples, the signals 11-1 to 11-N may be encoded using different sets of symbols (e.g., ASK, APSK, FSK, PSK, QAM, 16-QAM, 64- QAM, 256-QAM, or the like). It is to be appreciated, that although not shown in this figure for simplicity, the signals 11-1 to 11-N may be processed (e.g., down converted from RF to baseband, or the like) between being received by the Rx antennas 218-1 to 218-M and processed by the baseband processor 222-1.

Additionally, the circuitry 220 may execute the baseband processor 222-1 to perform one or more baseband processing operations of the received signals 11-1 to 11-N. For example, the baseband processor 222-1 may apply frequency offset compensation, synchronization, and/or equalization to the received signals 11-1 to 11-N.

In some examples, the apparatus 200 may include an LR-aided MIMO detector 222-2. The circuitry 220 may execute the MIMO detector 222-2 to determine a plurality of estimated signals corresponding to the plurality of received signals. Said differently, the MIMO detector 222-2 may estimate the transmitted signals 11-1 to 11-N. More specifically, the MIMO detector 222-2 may estimate the symbols corresponding to the signals 11-1 to 11-N. As will be appreciated, the signals 11-1 to 11-N will be subject to noise, interference, or other errors due to being transmitted through the wireless channel 10. As such, the MIMO detector 222-2 determines an estimate for these signals. In general, the MIMO detector 222-2 is configured to implement an LR-aided MIMO detection process and determine the estimated signals based on a search radius and a node expansion parameter, where the search radius and/or the node expansion parameter are dynamically adjusted. For example, the MIMO detector 222-2 may implement a complex K- best search of a two-dimensional search space generated from a lattice reduction process where the search includes expanding nodes of the two-dimensional search space based on an on- demand expansion process limited by a node expansion parameter, with the value of K and the value of the node expansion parameter being dynamically adjustable based on channel conditions (e.g., the CQI 230.)

According to some examples, the apparatus 200 may include a complex enumeration tuner 222- 3. The circuitry 220 may execute the complex enumeration tuner 222-3 to dynamically adjust the search radius and/or the node expansion parameter. More specifically, the complex enumeration tuner 222-3 may dynamically generate a search radius 240 (SR) and a node expansion parameter 250 (NEP) for use by the MIMO detector 222-2 in applying the complex K-best expansion. For example, the complex enumeration tuner 222-3 may dynamically adjust the value of K and the node expansion parameter used by the MIMO detector 222-2 to estimate the transmitted signals. With some examples, the complex enumeration tuner 222-3 may determine an optimal value of K and the node expansion parameter based on the CQI 230 (e.g., using a lookup table, a function, fuzzy-logic, or the like.) The complex enumeration tuner 222-3 may then generate the search radius 204 and the node expansion parameter 250 using the determined optimal value of K and the node expansion parameter.

With some examples, the maximum search radius and node expansion parameter implementable by the LR-aided MIMO detector 222-2 may be determined based on a worst-case possible channel condition estimate for the wireless channel 10. Subsequently, during operation, the search radius and the node expansion parameter may be dynamically adjusted between the maximum value and a minimum value (e.g., 1, or the like). In addition, the complex enumeration tuner 222-3 may dynamically adjust the search radius and the node expansion parameter based on user feedback, BER targets, or the like. Said differently, the value of K and the value of the node expansion parameter may be adjusted (e.g., increased or decreased) in order to achieve acceptable BERs or in order to improve a user experience. As such, power consumption of the LR-aided MIMO detector 222-2 may be balanced between achieving an acceptable level of BER and increasing energy efficiency and throughput (e.g., time to perform MIMO detection.) Furthermore, the complexity associated with performing MIMO detection may be reduced. With some example, the maximum value of the search radius may be 4. In some examples, the maximum value of the node expansion parameter may be 4.

According to some examples, the apparatus 200 may include a MIMO decoder 222-4. The circuitry 220 may execute the MIMO decoder 222-4 to decode the estimated signals based on the encoding scheme. For example, if the transmitter 100 encoded the signals using different constellation sets of 16-QAM symbols, the MIMO decoder 222-4 may decode the estimated signals using the same constellation sets of 16-QAM symbols. Additionally the MIMO decoder 222-4 may multiplex the decoded signals to generate the output signal 210.

FIG. 3 illustrates a block diagram of an example LR-aided MIMO detector 300. With some examples, the LR-aided MIMO detector 300 may be implemented as the LR-aided MIMO detector 222-2 of the receiver 200 described above. Prior to describing the LR-aided MIMO detector 300, it is worthy to note that a MIMO system with N transmit antennas and M receive antennas, operating in a symmetric X-QAM scheme, with log ₂ X bits per symbol may be modeled by the following equation: y = Hs + v, where s = [Si^ _, ■■■ _< ¾] , (βϊ ε S) is the N-dimensional complex information symbol vector transmitted. The set δ is the constellation set of the QAM symbols, and y = [y _lt y ₂ , ... , }¾] ^Γ is the M-dimensional complex information symbol vector received. The equivalent baseband model of the Rayleigh fading channel between the transmitter and the receiver is described by a complex valued N x M channel matrix H. The vector v = [v _lt v ₂ , ... , v _M ] ^T represents the M- dimensional complex zero-mean Gaussian noise vector with variance σ ² .

Since the MIMO system is modeled using complex signals (e.g., the signals include both real and imaginary components,) a complex K-best process results in a single 2-dimensional search. In some examples, the search may begin with the N ^th layer. For each n ^th layer, the MIMO detector 300 may derive the K best partial candidates [s^" ⁾ , s ₂ ⁽ - ⁿ - ⁾ , ... , s _fe ^], where partial candidate represents the i ^th path through the search tree from the root node to the level n, and is given by [s^^, s^^,■■■ , ^s i,N^] - The error at each step is measured by the partial Euclidian distance (PED), which represents the accrued error at a given level of the search tree, for a given path through the search tree. As will be appreciated, the K candidates at level n represent the K partial candidates with the minimum PED among all the children of the K candidates of the (n+1 level, wherein the distance is calculated using the following equation:

Where R _{j k} are components of the NxN upper triangular matrix R such that H = QR, where Q is an (N + M) x N orthonormal matrix.

Turning now more specifically to FIG. 3, the LR-aided MIMO detector 300 includes a signal extender 310, a complex K-best enumerator 320, and a postprocessor 330. The signal extender 310 may include logic and/or features to determine a two-dimensional search space

corresponding to the signal 11-1 to 11-N by extending the signals 11-1 to 11-N into a plurality of extended search vectors. For example, the signal extender 310 may extend the signals 11-1 to 11-N based on a minimum-mean square error (MMSE) extension process. By extending the signal 11-1 to 11-N based on an MMSE extension process, the MIMO detection may effectively incorporate information about the transmission quality. The signal extender 310 may also include logic and/or features to translate the plurality of extended search vectors into the two- dimensional search space based on a lattice reduction process. As will be appreciated, lattice reduction changes the basis of the plurality of extended search vectors from an original basis to an extended basis. Furthermore, it is to be appreciated, that a variety of techniques for implementing MMSE extension and lattice reduction may be implemented. Examples are not limited in this context.

The complex K-best enumerator 320 may include logic and/or features to apply a complex K- best enumeration of the two-dimensional search space based on a search radius, where nodes of the two-dimensional search spaces are enumerated based on an on-demand enumeration process limited by a node extension parameter. As described above, the complex enumeration tuner 222- 3 may generate the search radius 240 (e.g., K) and the node extension parameter 250. The complex K-best enumerator 320 may use these dynamically adjustable values in applying the complex K-best process to the two-dimensional search space.

In general, the complex K-best enumerator 320 determines a number of potential candidate estimates for each of the N levels of the search tree. The number of potential candidates determined at each n ^th level corresponds to (e.g., equals) the search radius and is sometimes referred to herein as the "k" potential candidates. It is to be appreciated, that the complex K-best enumerator 320 may implement a variety of techniques for determining the k potential candidates. For example, the complex K-best enumerator 320 may determine the k potential candidates from their PED as described above.

As will be appreciated, the k potential candidates at level n represent the k potential candidates with the minimum PED among all the children of the k candidates of the (n+1 level In order to determine the k potential candidates at a particular level, the nodes of the two- dimensional search space for the (n+l) ^st level (e.g., the children) are expanded. The complex K- best enumerator expands the nodes for a two-dimensional search space based on an on-demand expansion process. The on-demand expansion process proceeds to expand nodes in decreasing error (e.g., PED) order. With some examples, the on-demand expansion determines a first node based on the received signal being estimated, applies a real Schnorr-Euchner (SE) expansion starting with the first node, expands one or more additional nodes based on an imaginary SE expansion. With some examples, the first node is determined by rounding the real and imaginary portion of the received signal to determine a closest estimated symbol. As such, potential candidates may be determined without expanding all the children of each candidate, thereby reducing the complexity of MEVIO detection.

For example, FIGS. 4A - 4D illustrate an example on-demand expansion of a two-dimensional search space 400 having nodes 410-1 to 410-16. Said differently, these figures illustrate an example on-demand expansion of the two-dimensional search space 400 for a one of the "k" candidates corresponding to the complex K-best enumeration. It is to be appreciated, that the example shown in these figures is shown in a simplified manner. For example, the number of nodes 410 is shown at a quantity to facilitate understanding and is not intended to be limiting.

Furthermore, it is to be appreciated that this represents a single expansion for 1 level of the search tree. As will be appreciated, a number of two-dimensional search spaces are typically expanded to determine the estimated signals. For example, for a signal from an 8x8 MIMO system, 8 two-dimensional search spaces may be expanded to determine an estimate for the signals in this system.

In general, FIGS. 4A - 4D depicts the two-dimensional search space 400 having 16 symbols 410-1 to 410-16 (e.g., possibly corresponding to a 16-QAM encoded signal, or the like.) The symbols 410 have both a real and imaginary components, as depicted by the real axis 402 and the imaginary axis 404. It is important to note, that the nodes 410 are not all labeled in each figure. Instead, all nodes 410-1 to 410-16 are labeled in FIG. 4A while in FIGS. 4B - 4D, only those nodes that are expanded and/or selected as a candidate (e.g., identified as having the lowest PED) are labeled. Turning more specifically to FIG. 4A, a first symbol of the symbols 410 is selected. For example, a portion 420 of the received signals 11-1 to 11-N (e.g., corresponding to the transmission of one symbol) is rounded to the nearest symbol 410. More specifically, the real and imaginary component of the portion 420 is rounded to the nearest symbol 410. As depicted, the portion 420 is rounded to the symbol 410-6. As such, for this example, the first symbol is the symbol 410-6.

Turning now to FIG. 4B, a number of nodes are expanded, starting from the first symbol. Said differently, a number of the nodes 410 are expanded starting from the symbol 410-6 (e.g., the nearest symbol to the signal being estimated.) With some examples, a real SE expansion

(indicated by dashed rectangle 430) is applied to the nodes of the two-dimensional search space 400, starting from the first node. With this example, the real SE expansion 430 expands node 410-6 to node 410-7, node 410-7 to node 410-5, and node 410-5 to node 410-8. In some examples, real SE expansion may include fixing the imaginary component of the nodes to cause the expansion to proceed along a row of the two-dimensional search space 400 (e.g., the row indicated by dashed rectangle 430.) It is important to note, that this example shows 3 nodes (e.g., 410-5, 410-7, and 410-8) being expanded from the first node. As discussed herein, the number of expanded nodes is limited by the node expansion parameter, which may be larger or smaller than 3. As such, although this example depicts the entire row being expanded, this is not intended to be limiting. Furthermore, the node expansion parameter may be dynamically adjusted based on channel conditions.

Accordingly, this example is not intended to be limiting based on the number of nodes indicated as being expanded, but is instead shown at a quantity to facilitate understanding. The expanded nodes are added to the list of potential candidates (e.g., indicated by the slashed lines through the nodes 410) for the symbol being estimated.

Turning now to FIG. 4C, the best of the expanded nodes (e.g., based on the PED, or the like) is selected and imaginary SE expansion is applied to expand one additional node. For example, of the candidate nodes 410-5 to 410-8, FIG. 4C depicts the node 410-6 as being selected as a potential candidate (e.g., indicated by crisscrossed lines through the node.) Additionally, the node 410-10 is expanded from this selected candidate node (e.g., 410-6) based on an imaginary SE expansion process. As depicted, the imaginary SE expansion process expands the node 410-6 (e.g., the selected node) to the node 410-10. In some examples, imaginary SE expansion may include fixing the real component of the nodes to cause the expansion to proceed along one of the columns of the two-dimensional search space (e.g., along the imaginary axis 404.) Turning now to FIG. 4D, the best of the expanded nodes (e.g., based on the PED, or the like) is selected and imaginary SE expansion is again applied to expand one additional node. For example, of the candidate nodes 410-5 to 410-8, and 410-10, FIG. 4D depicts the node 410-10 as being selected as a potential candidate (e.g., indicated by crisscrossed lines through the node.) Additionally, the node 410-2 is expanded from the accepted potential candidate node (e.g., 410- 10) based on an additional imaginary SE expansion process.

FIGS. 5 - 6 illustrate examples of logic flows 500 and 600, respectively. The logic flows 500 and/or 600 may be representative of some or all of the operations executed by one or more logic, features, or devices described herein, such as the receiver 200, circuitry 220, and/or the LR-aided MIMO detector 300. In particular, a receiver may implement the logic flows 500 and/or 600 in a MIMO system to detect MIMO signals. For example, the baseband processor 222-1, the LR- aided MIMO detector 222-2, the complex enumeration tuner 222-3, and/or the channel decoder 222-4 may implement the logic flows 500 and/or 600.

Turning now more specifically to FIG. 5, in the logic flow 500, at block 502, a receiver in a MIMO system may receive a plurality of signals transmitted through a wireless channel by a plurality of antennas. For example, the receiver 200 in the MIMO system 1000 may receive the signals 11-1 to 11-N transmitted through the wireless channel 10 using the antennas 218-1 to 218-M. More specifically, the baseband processor 222-1 may receive the signals 11-1 to 11-N. At block 504, the plurality of received signals may be extended into search vectors where the search vectors correspond to a two-dimensional search space. For example, the receiver 200 may extend the received signals into search vectors. More specifically, the LR-aided MEVIO detector 222-2 may extend the received signal into search vectors (e.g., based on an MMSE process, or the like) and translate the search vectors to a two-dimensional search space using lattice reduction.

At block 506, a quality corresponding to the wireless channel may be determined. For example, the receiver 200 may determine the CQI 230.

At block 508, a search radius and a node expansion parameter based on the quality may be determined. For example, the receiver 200 may determine a search radius (e.g., value of K, or the like) and a node expansion parameter based on the CQI 230. More specifically, the complex enumeration tuner 222-3 may determine the search radius 240 and the node expansion parameter 250 based on the CQI 230.

At block 510, a plurality of estimated signals corresponding to the transmitted signals may be determined based on a complex enumeration and an on-demand expansion of the two- dimensional search space, the complex enumeration limited by the search radius and the on- demand expansion limited by the node expansion parameter. For example, the receiver 200 (or more specifically, the LR-aided MIMO detector 222-2) may determine the estimated signals by applying a complex enumeration and on-demand expansion of the two-dimensional search space. Turning now to FIG. 6, a receiver (e.g., the receiver 200) may implement the logic flow 600 to apply a complex K-best enumeration and on-demand expansion of a two-dimensional search space to perform LR-aided MIMO detection as described herein. With some examples, the logic flow 600 may correspond to block 510 (or a portion of block 510) of the logic flow 500.

Examples, however, are not limited in the context. At block 602, k potential candidates for estimating a received signal are determined. For examples, a K-best enumeration process may be applied to determine the k potential candidates, where k is the search radius. With some examples, the LR-aided MIMO detector 222-2 may determine the k potential candidates. More particularly, starting at a first level of the search tree (e.g., the lattice reduced search tree,) the LR-aided MEVIO detector 222-2 may determine k potential candidates based on a K-best process.

At block 604, for each of the k potential candidates determined at block 602, a number of nodes of the two-dimensional search space (e.g., the space 400 described above) are expanded based on an on-demand expansion limited by the node expansion parameter. For example, the LR-aided

MIMO detector 222-2 may determine a first node in the two-dimensional search space by rounding the real and imaginary portion of a portion of the received signal to a nearest symbol. A number of nodes may be expanded from the first node based on a real SE expansion. At block 606, the expanded node with the lowest PED may be selected and the list of potential candidates updates based on the selected nodes PED. For examples, the LR-aided MIMO detector 222-2 may select the node with the lowest PED and update the potential candidates based on this selected node.

At decision 608, it is determined if k nodes have been taken. If k nodes have not been taken, the process returns to block 606, where another node is selected (e.g., the node with the k ^th lowest PED, or the like) and the potential candidates updated. If k nodes have been taken, the logic flow 600 continues to decision 610.

At decision 610, it is determined that all levels of the search tree have been enumerated based on the complex K-best enumeration. If all levels have not been enumerated, the logic flow 600 returns to block 602 and another level (e.g., the n+1) is enumerated. If all levels have been enumerated, the logic flow continues to block 612.

At block 612, the k-best potential candidates are output. For example, the LR-aided MIMO detector 222-2 may output the k-best potential candidates.

FIG. 7 illustrates an embodiment of a storage medium 700. The storage medium 700 may comprise an article of manufacture. In some examples, the storage medium 700 may include any non-transitory computer readable medium or machine readable medium, such as an optical, magnetic or semiconductor storage. The storage medium 700 may store various types of computer executable instructions, such as instructions to implement logic flow 500 and/or 600. Examples of a computer readable or machine readable storage medium may include any tangible media capable of storing electronic data, including volatile memory or non- volatile memory, removable or non-removable memory, erasable or non-erasable memory, writeable or re- writeable memory, and so forth. Examples of computer executable instructions may include any suitable type of code, such as source code, compiled code, interpreted code, executable code, static code, dynamic code, object-oriented code, visual code, and the like. The examples are not limited in this context.

FIG. 8 illustrates an embodiment of a device 2000. In some examples, device 2000 may be configured or arranged for wireless communications in a wireless MIMO system such as the MIMO system 1000 shown in FIG. 1. In some examples, the receiver 200 may be implemented in the device 2000. For example, the device 2000 may implement the receiver 200 as apparatus

2200. Additionally, the device 2000 may implement storage medium 700 and/or a logic circuit

2600. The logic circuit 2600 may include physical circuits to perform operations described for the apparatus 2200, storage medium 700, and/or logic flow 600. As shown in FIG. 8, device

2000 may include a radio interface 2110, baseband circuitry 2120, and computing platform 2130, although examples are not limited to this configuration.

The device 2000 may implement some or all of the structure and/or operations for the apparatus 2200, the storage medium 700 and/or the logic circuit 2600 in a single computing entity, such as entirely within a single device. The embodiments are not limited in this context.

Radio interface 2110 may include a component or combination of components adapted for transmitting and/or receiving single carrier or multi-carrier modulated signals (e.g., including complementary code keying (CCK) and/or orthogonal frequency division multiplexing (OFDM) symbols and/or single carrier frequency division multiplexing (SC-FDM symbols) although the embodiments are not limited to any specific over-the-air interface or modulation scheme. Radio interface 2110 may include, for example, a receiver 2112, a transmitter 2116 and/or a frequency synthesizer 2114. Radio interface 2110 may include bias controls, a crystal oscillator and antennas 2118-1 to 2118-f. In another embodiment, radio interface 2110 may use external voltage-controlled oscillators (VCOs), surface acoustic wave filters, intermediate frequency (IF) filters and/or RF filters, as desired. Due to the variety of potential RF interface designs an expansive description thereof is omitted.

Baseband circuitry 2120 may communicate with radio interface 2110 to process receive and/or transmit signals and may include, an analog-to-digital converter 2122 and/or a digital-to-analog converter 2124 for use in processing receive/transmit signals (e.g., up converting, down converting, filtering, sampling or the like.) Further, baseband circuitry 2120 may include a baseband or physical layer (PHY) processing circuit 2126 for PHY link layer processing of respective receive/transmit signals. Baseband circuitry 2120 may include, for example, a processing circuit 2128 for medium access control (MAC)/data link layer processing. Baseband circuitry 2120 may include a memory controller 2132 for communicating with MAC processing circuit 2128 and/or a computing platform 2130, for example, via one or more interfaces 2134.

In some examples, the MAC 2128 may be configured to include and/or perform the structures and/or methods described herein. Said differently, the MAC 21128 may be configured to include the LR-aided MIMO detector 222-2 (e.g., embodied as apparatus 2200). As another example, the MAC 2128 may be configured to include the storage medium 700. As another example, the

MAC 2128 may be configured to implement logic circuit 500 and/or 600 (e.g., embodied as logic circuit 2600.) As another example, the MAC 2128 may access the computing platform

2130 to implement and/or perform the structure and/or methods described herein. In some embodiments, PHY processing circuit 2126 may include a frame construction and/or detection module, in combination with additional circuitry such as a buffer memory, to construct and/or deconstruct communication frames (e.g., containing subframes). Alternatively or in addition, MAC processing circuit 2128 may share processing for certain of these functions or perform these processes independent of PHY processing circuit 2126. In some embodiments, MAC and PHY processing may be integrated into a single circuit.

Computing platform 2130 may provide computing functionality for device 2000. As shown, computing platform 2130 may include a processing component 2140. In addition to, or alternatively of, baseband circuitry 2120 of device 2000 may execute processing operations or logic for the apparatus 2200, storage medium 700, and logic circuit 2600 using the processing component 2130. Processing component 2140 (and/or PHY 2126 and/or MAC 2128) may comprise various hardware elements, software elements, or a combination of both. Examples of hardware elements may include devices, logic devices, components, processors,

microprocessors, circuits, processor circuits, circuit elements (e.g., transistors, resistors, capacitors, inductors, and so forth), integrated circuits, application specific integrated circuits (ASIC), programmable logic devices (PLD), digital signal processors (DSP), field programmable gate array (FPGA), memory units, logic gates, registers, semiconductor device, chips, microchips, chip sets, and so forth. Examples of software elements may include software components, programs, applications, computer programs, application programs, system programs, software development programs, machine programs, operating system software, middleware, firmware, software modules, routines, subroutines, functions, methods, procedures, software interfaces, application program interfaces (API), instruction sets, computing code, computer code, code segments, computer code segments, words, values, symbols, or any combination thereof. Determining whether an example is implemented using hardware elements and/or software elements may vary in accordance with any number of factors, such as desired computational rate, power levels, heat tolerances, processing cycle budget, input data rates, output data rates, memory resources, data bus speeds and other design or performance constraints, as desired for a given example. Computing platform 2130 may further include other platform components 2150. Other platform components 2150 include common computing elements, such as one or more processors, multi- core processors, co-processors, memory units, chipsets, controllers, peripherals, interfaces, oscillators, timing devices, video cards, audio cards, multimedia input/output (I/O) components (e.g., digital displays), power supplies, and so forth. Examples of memory units may include without limitation various types of computer readable and machine readable storage media in the form of one or more higher speed memory units, such as read-only memory (ROM), random- access memory (RAM), dynamic RAM (DRAM), Double-Data-Rate DRAM (DDR AM), synchronous DRAM (SDRAM), static RAM (SRAM), programmable ROM (PROM), erasable programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, polymer memory such as ferroelectric polymer memory, ovonic memory, phase change or ferroelectric memory, silicon-oxide-nitride-oxide-silicon (SONOS) memory, magnetic or optical cards, an array of devices such as Redundant Array of Independent Disks (RAID) drives, solid state memory devices (e.g., USB memory, solid state drives (SSD) and any other type of storage media suitable for storing information.

Computing platform 2130 may further include a network interface 2160. In some examples, network interface 2160 may include logic and/or features to support network interfaces operated in compliance with one or more wireless broadband technologies such as those described in one or more standards associated with IEEE 802.11 such as IEEE 802.11η, 802.15, etc., or with a technical specification such as WFA Hotspot 2.0, or with various other wireless standards and/or technologies such as, for example, 3GPP, WiMAX, WiGIG, or the like.

Device 2000 may be part of a source or destination node in a MIMO system and may be included in various types of computing devices to include, but not limited to, user equipment, a computer, a personal computer (PC), a desktop computer, a laptop computer, a notebook computer, a netbook computer, a tablet computer, an ultra-book computer, a smart phone, embedded electronics, a gaming console, a server, a server array or server farm, a web server, a network server, an Internet server, a work station, a mini-computer, a main frame computer, a supercomputer, a network appliance, a web appliance, a distributed computing system, multiprocessor systems, processor-based systems, wearable computing device or combination thereof. Accordingly, functions and/or specific configurations of device 2000 described herein; may be included or omitted in various embodiments of device 2000, as suitably desired. In some embodiments, device 2000 may be configured to be compatible with protocols and frequencies associated with IEEE 802.11 Standards or Specification and/or 3GPP Standards or Specifications for MIMO systems, although the examples are not limited in this respect. The components and features of device 2000 may be implemented using any combination of discrete circuitry, application specific integrated circuits (ASICs), logic gates and/or single chip architectures. Further, the features of device 2000 may be implemented using microcontrollers, programmable logic arrays and/or microprocessors or any combination of the foregoing where suitably appropriate. It is noted that hardware, firmware and/or software elements may be collectively or individually referred to herein as "logic" or "circuit."

It should be appreciated that the exemplary device 2000 shown in the block diagram of FIG. 8 may represent one functionally descriptive example of many potential implementations.

Accordingly, division, omission or inclusion of block functions depicted in the accompanying figures does not infer that the hardware components, circuits, software and/or elements for implementing these functions would be necessarily be divided, omitted, or included in embodiments.

Some examples may be described using the expression "in one example" or "an example" along with their derivatives. These terms mean that a particular feature, structure, or characteristic described in connection with the example is included in at least one example. The appearances of the phrase "in one example" in various places in the specification are not necessarily all referring to the same example.

Some examples may be described using the expression "coupled", "connected", or "capable of being coupled" along with their derivatives. These terms are not necessarily intended as synonyms for each other. For example, descriptions using the terms "connected" and/or

"coupled" may indicate that two or more elements are in direct physical or electrical contact with each other. The term "coupled," however, may also mean that two or more elements are not in direct contact with each other, but yet still co-operate or interact with each other.

What has been described above includes examples of the disclosed architecture. It is, of course, not possible to describe every conceivable combination of components and/or methodologies, but one of ordinary skill in the art may recognize that many further combinations and permutations are possible. Accordingly, the novel architecture is intended to embrace all such alterations, modifications and variations that fall within the spirit and scope of the appended claims. The detailed disclosure now turns to providing examples that pertain to further embodiments. The examples provided below are not intended to be limiting.

Example 1 : An apparatus for a wireless receiver. The apparatus including circuitry, an lattice reduction (LR)-aided multiple-input multiple-output (MIMO) detector for execution by the circuitry to determine a set of estimated signals that corresponds to a set of signals received over a wireless channel by multiple antennas, the LR-aided MIMO detector to determine the set of estimated signals based on a complex enumeration and an on-demand expansion of a two- dimensional search space, the complex enumeration associated with a search radius and the on- demand expansion associated with a node expansion parameter, and a complex enumeration tuner for execution by the circuitry to dynamically modify the search radius and the node expansion parameter based on a quality measurement of the wireless channel.

Example 2: The apparatus of example 1, the complex enumeration tuner to decrease the search radius when the quality measurement increases, decrease the node expansion parameter when the quality measurement increases, or decrease both the search radius and the node expansion parameter when the quality measurement increases.

Example 3: The apparatus of example 1, the complex enumeration tuner to increase the search radius when the quality measurement decreases, increase the node expansion parameter when the quality measurement decreases, or increase both the search radius and the node expansion parameter when the quality measurement decreases. Example 4: The apparatus of example 1, the complex enumeration tuner to dynamically modify the search radius between a minimum and a maximum value.

Example 5: The apparatus of example 3, wherein the minimum value is 1 and the maximum value is 4.

Example 6: The apparatus of example 1, the LR-aided MIMO detector to include a complex K- best enumerator to determine the set of estimated signals based on a complex K-best

enumeration process, wherein the search radius corresponds to the value of K in the K-best enumeration process.

Example 7: The apparatus of example 6, wherein the set of received signals corresponds to a set of transmitted signals encoded using a constellation set of symbols, the MIMO detector to determine a set of potential candidates for estimating at least a portion of each of the received signals, each of the potential candidates indicating an estimate for a symbol, the symbol corresponding to the symbol with which the transmitted signal is encoded.

Example 8: The apparatus of example 7, the two-dimensional search space including a plurality of nodes, the complex K-best enumerator to determine the plurality of potential candidates based on the on-demand expansion, the on-demand expansion including expanding ones of the plurality of nodes for each of the potential candidates.

Example 9: The apparatus of example 8, the complex K-best enumerator to expand a select number of nodes from a first node based on a real Schnorr-Euchner (SE) expansion, select one of the expanded nodes as a potential candidate, and expand another node based on an imaginary SE expansion.

Example 10: The apparatus of example 9, the complex K-best enumerator to determine the first node based on rounding the real and imaginary component of the portion of the received signal to the nearest symbol. Example 11: The apparatus of example 10, the complex K-best enumerator to select the one of the expanded nodes as the potential candidate based on a partial Euclidian distance.

Example 12: The apparatus of any of examples 1 to 11, the MEVIO detector including a signal extender to determine the two-dimensional search space by extending the received signals into a set of extended search vectors based on a minimum-mean square error extension process. Example 13: The apparatus of example 12, the signal extender to translate the extended search vectors into the two-dimensional search space based on a lattice reduction process, the lattice reduction process to change the basis of the extended search vectors from an original basis to an extended basis.

Example 14: The apparatus of example 13, wherein the set of potential candidates correspond to the set of extended search vectors in the extended basis, the LR-aided MIMO detector including a post search processor to translate the plurality of potential candidates from the extended basis to the original basis.

Example 15: The apparatus of example 14, the post search processor to selected a one of the potential candidates in the original basis as the estimated symbol based on a partial Euclidian distance.

Example 16: The apparatus of any of examples 1 to 11 or 13 to 15, further comprising a baseband processor for execution by the circuitry to receive the plurality of signals.

Example 17: The apparatus of example 16, the baseband processor to perform one or more baseband processing operations on the plurality of received signals. Example 18. The apparatus of example 17, the one or more baseband processing operations selected from the group consisting of: frequency offset compensation, synchronization, and equalization.

Example 19: The apparatus of any of examples 1 to 11 or 13 to 15, further comprising a MIMO decoder to determine an output signal from the estimated signals.

Example 20: The apparatus of example 19, the MIMO decoder to decode the estimated signals based on an encoding scheme.

Example 21: The apparatus of example 20, the encoding scheme selected from the group consisting of ASK, APSK, FSK, PSK, QAM, 16-QAM, 64-QAM, and 256-QAM. Example 22: A method implemented by a receiver in a MIMO system. The method including receiving a set of signals transmitted through a wireless channel by multiple antennas, extending the received signals into a set of search vectors, the search vectors corresponding to a two- dimensional search space, determining a quality measurement corresponding to the wireless channel, determining a search radius based on the quality, and determining, for each of the plurality of transmitted signals, an estimated signal corresponding to the transmitted signal based on a complex enumeration and an on-demand expansion of the two-dimensional search space, the complex enumeration associated with a search radius and the on-demand expansion associated with by a node expansion parameter.

Example 23: The method of example 22, decreasing the search radius when the quality measurement increases, decreasing the node expansion parameter when the quality measurement increases, or decreasing both the search radius and the node expansion parameter when the quality measurement increases.

Example 24: The method of example 22, increasing the search radius when the quality measurement decreases, increasing the node expansion parameter when the quality measurement decreases, or increasing both the search radius and the node expansion parameter when the quality measurement decreases.

Example 25: The method of example 22, dynamically modifying the search radius between a minimum and a maximum value.

Example 26: The method of example 25, wherein the minimum value is 1 and the maximum value is 4. Example 27: The method of example 22, further comprising dynamically modifying the node expansion parameter.

Example 28: The method of example 22, determining the set of estimated signals based on a complex K-best enumeration process, wherein the search radius corresponds to the value of K in the K-best enumeration process.

Example 29: The method of example 28, wherein the transmitted signals are encoded using a constellation set of symbols, determining a set of potential candidates for estimating at least a portion of each of the received signals, each of the potential candidates indicating an estimate for a symbol, the symbol corresponding to the symbol with which the received signal is encoded. Example 30: The method of example 29, the two-dimensional search space including a plurality of nodes, determining the set of potential candidates based on the on-demand expansion, the on- demand expansion including expanding ones of the plurality of nodes for each of the potential candidates.

Example 31: The method of example 30, expanding a selected number of nodes from a first node based on a real Schnorr-Euchner (SE) expansion, select one of the expanded nodes as a potential candidate, and expand another node based on an imaginary SE expansion.

Example 32: The method of example 31, determining the first node based on rounding the real and imaginary component of the portion of the received signal to the nearest symbol.

Example 33: The method of example 32, selecting the one of the expanded nodes as the potential candidate based on a partial Euclidian distance.

Example 34: The method of any of examples 22 to 33, extending the plurality of received signals into a set of extended search vectors based on a minimum-mean square error extension process.

Example 35: The method of example 34, translating the extended search vectors into the two- dimensional search space based on a lattice reduction process, the lattice reduction process to change the basis of the extended search vectors from an original basis to an extended basis.

Example 36: The method of example 35, wherein the potential candidates correspond to the potential search vectors in the extended basis, translating the potential candidates from the extended basis to the original basis. Example 37: The method of example 36, selecting a one of the potential candidates in the original basis as the estimated symbol based on a partial Euclidian distance.

Example 38: The method of any of examples 22 to 33 or 35 to 37, performing one or more baseband processing operations on the plurality of received signals. Example 39: The method of example 38, the one or more baseband processing operations selected from the group consisting of: frequency offset compensation, synchronization, and equalization.

Example 40. The method of any of examples 22 to 33 or 35 to 37, determining an output signal from the plurality of estimated signals. Example 41: The method of example 40, decoding the plurality of estimated signals based on an encoding scheme.

Example 42: The method of example 41, the encoding scheme selected from the group consisting of ASK, APSK, FSK, PSK, QAM, 16-QAM, 64-QAM, and 256-QAM.

Example 43: An apparatus comprising means to perform the method of any of examples 22 to 42.

Example 44: At least one machine readable medium comprising a plurality of instructions that in response to being executed on a receiver in a multiple-input multiple- output (MIMO) communication system cause the receiver to perform the method of any of examples 22 to 42.