Patent Publication Number: US-7720166-B2

Title: System, method and device of decoding spatially multiplexed signals

Description:
BACKGROUND OF THE INVENTION 
   A wireless communication system may include a first station able to communicate with a second station over a communication channel. In a spatial multiplexing communication system the first station may include a transmitter to transmit parallel streams representing a message via a plurality of transmit antennas (N TX &gt;1). The second station may include a receiver to receive a plurality of symbols corresponding to the transmitted streams via a plurality of receive antennas (N RX ≧N TX ). 
   The receiver may include an equalizer to decode the received symbols, which may be a mixture of the transmitted symbols, into metrics (LLRs). The receiver may also include a Maximum Likelihood Sequence Estimation (MLSE) decoder, e.g., a turbo decoder or a viterbi decoder, to determine an estimation of the message based on the metrics. 
   The equalizer may determine the metrics based on a Maximum Likelihood Decoding (MLD) algorithm, which may include scanning all constellation points of all the N Tx , transmit antennas. Accordingly, the MLD algorithm may have a complexity of M N     Tx   , wherein M denotes a constellation size implemented by the transmitter. For example, if N TX =2, and M=64, then the MLD algorithm may have a complexity of 4096. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The subject matter regarded as the invention is particularly pointed out and distinctly claimed in the concluding portion of the specification. The invention, however, both as to organization and method of operation, together with objects, features and advantages thereof, may best be understood by reference to the following detailed description when read with the accompanied drawings in which: 
       FIG. 1  is a schematic illustration of a wireless communication system in accordance with some demonstrative embodiments of the present invention; 
       FIG. 2  is a schematic illustration of a decoder in accordance with one demonstrative embodiment of the invention; 
       FIG. 3  is a schematic flow-chart illustration of a method of decoding received signals in accordance with some demonstrative embodiments of the invention; 
       FIG. 4  is a schematic illustration of a decoder in accordance with another demonstrative embodiment of the invention; 
       FIG. 5  is a schematic illustration of a decoder in accordance with yet another demonstrative embodiment of the invention; and 
       FIG. 6  is a schematic flow-chart illustration of a method of determining metric values in accordance with some demonstrative embodiments of the invention. 
   

   It will be appreciated that for simplicity and clarity of illustration, elements shown in the drawings have not necessarily been drawn accurately or to scale. For example, the dimensions of some of the elements may be exaggerated relative to other elements for clarity or several physical components included in one functional block or element. Further, where considered appropriate, reference numerals may be repeated among the drawings to indicate corresponding or analogous elements. Moreover, some of the blocks depicted in the drawings may be combined into a single function. 
   DETAILED DESCRIPTION OF THE INVENTION 
   In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be understood by those of ordinary skill in the art that the present invention may be practiced without these specific details. In other instances, well-known methods, procedures, components and circuits may not have been described in detail so as not to obscure the present invention. 
   Although embodiments of the invention are not limited in this regard, discussions utilizing terms such as, for example, “processing,” “computing,” “calculating,” “determining,” “establishing”, “analyzing”, “checking”, or the like, may refer to operation(s) and/or process(es) of a computer, a computing platform, a computing system, or other electronic computing device, that manipulate and/or transform data represented as physical (e.g., electronic) quantities within the computer&#39;s registers and/or memories into other data similarly represented as physical quantities within the computer&#39;s registers and/or memories or other information storage medium that may store instructions to perform operations and/or processes. 
   Although embodiments of the invention are not limited in this regard, the terms “plurality” and “a plurality” as used herein may include, for example, “multiple” or “two or more”. The terms “plurality” or “a plurality” may be used throughout the specification to describe two or more components, devices, elements, parameters, or the like. For example, “a plurality of signals” may include two or more signals. 
   Some embodiments of the invention may be implemented, for example, using a machine-readable medium or article which may store an instruction or a set of instructions that, if executed by a machine (for example, by a processor and/or by other suitable machines), cause the machine to perform a method and/or operations in accordance with embodiments of the invention. Such a machine may include, for example, any suitable processing platform, computing platform, computing device, processing device, computing system, processing system, computer, processor, or the like, and may be implemented using any suitable combination of hardware and/or software. The machine-readable medium or article may include, for example, any suitable type of memory unit memory device, memory article, memory medium, storage device, storage article, storage medium and/or storage unit, for example, memory, removable or non-removable media, erasable or non-erasable media, writeable or re-writeable media, digital or analog media, hard disk, floppy disk, Compact Disk Read Only Memory (CD-ROM), Compact Disk Recordable (CD-R), Compact Disk Rewriteable (CD-RW), optical disk, magnetic media, various types of Digital Versatile Disks (DVDs), a tape, a cassette, or the like. The instructions may include any suitable type of code, for example, source code, compiled code, interpreted code, executable code, static code, dynamic code, or the like, and may be implemented using any suitable high-level, low-level, object-oriented, visual, compiled and/or interpreted programming language, e.g., C, C++, Java, BASIC, Pascal, Fortran, Cobol, assembly language, machine code, or the like. 
   It should be understood that the present invention may be used in a variety of applications. Although the present invention is not limited in this respect, the circuits and techniques disclosed herein may be used in many apparatuses such as units of a wireless communication system, for example, a Wireless Local Area Network (WLAN) system, a Wireless Metropolitan Area Network (WMAN) communication system, and/or in any other unit and/or device. Units of a communication system intended to be included within the scope of the present invention include, by way of example only, modems, Mobile Units (MU), Access Points (AP), wireless transmitters/receivers, and the like. 
   Types of WLAN and/or WMAN communication systems intended to be within the scope of the present invention include, although are not limited to, WLAN and/or WMAN communication systems as described by “IEEE-Std 802.16, 2004 Edition, Air Interface for Fixed Broadband Wireless Access Systems” standard (“the 802.16 standard”), and more particularly in “IEEE-Std 802.16e, 2005 Edition, Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands”, and the like. 
   Although the scope of the present invention is not limited in this respect, the circuits and techniques disclosed herein may also be used in units of wireless communication systems, digital communication systems, satellite communication systems and the like. 
   Devices, systems and methods incorporating aspects of embodiments of the invention are also suitable for computer communication network applications, for example, intranet and Internet applications. Embodiments of the invention may be implemented in conjunction with hardware and/or software adapted to interact with a computer communication network, for example, a LAN, wide area network (WAN), or a global communication network, for example, the Internet. 
   Part of the discussion herein may relate, for exemplary purposes, to receiving and/or decoding a signal. However, embodiments of the invention are not limited in this regard, and may include, for example, receiving and/or decoding a symbol, a block, a data portion, a packet, a data sequence, a frame, a data signal, a preamble, a signal field, a content, an item, a message, a protection frame, a transmission or the like. 
   Reference is made to  FIG. 1 , which schematically illustrates a wireless communication system  100  in accordance with some demonstrative embodiments of the present invention. 
   According to some demonstrative embodiments of the invention, communication system  100  may include a WLAN/WMAN system. System  100  may include a first communication device  102  able to communicate with a second communication device  104  over a communication channel  106 . For example, device  102  and/or device  104  may include a station, e.g., in accordance with the 802.16 standard. 
   According to some demonstrative embodiments of the invention, device  102  may include N Tx  antennas  110 , and/or device  104  may include N Rx  antennas  112  to transmit and/or receive symbols, e.g., over channel  106 , wherein N Rx ≧N Tx ≧2. Although the scope of the present invention is not limited in this respect, types of antennae that may be used for antennas  110  and/or  112  may include but are not limited to internal antenna, dipole antenna, omni-directional antenna, a monopole antenna, an end fed antenna, a circularly polarized antenna, a micro-strip antenna, a diversity antenna and the like. 
   According to some demonstrative embodiments of the invention, communication device  102  may include a transmitter  108  to transmit a spatially-multiplexed transmission by transmitting set of N TX  signals via N TX  antennas  110 , respectively, e.g., as is known in the art. In one example, transmitter  108  may perform horizontal encoding to encode the transmission, for example, by using N TX  Forward Error Correction (FEC) encoders to generate the set of N TX  transmitted signals, respectively, e.g., as is known in the art. In another example, transmitter  108  may perform vertical encoding to encode the transmission, for example, by generating the set of N TX  transmitted signals based on an output of a single FEC encoder. 
   According to some demonstrative embodiments of the invention, one or more of the transmitted signals may include one or more Orthogonal Frequency Division Multiple Access (OFDMA) symbols modulated over one or more subcarriers, e.g., as is known in the art. For example, a signal of the transmitted signals may include a plurality of Quadrature Amplitude Modulation (QAM) symbols modulated over a plurality of subcarriers, as is known in the art. The QAM symbols may include, for example, symbols selected from a constellation of a size M (the “M-ary constellation”), as is known in the art. For example, the QAM symbols may include 2-QAM symbols, Quadrature Phase Shift Key (QPSK) symbols, 8-QAM symbols, 16-QAM symbols, 64-QAM symbols, and/or any other suitable symbols, e.g., as are known in the art. 
   According to some demonstrative embodiments of the invention, communication device  102  may use a subcarrier permutation for communicating with device  104 . The permutation may include, for example, a predefined set of subcarriers, e.g., selected from a plurality of available subcarriers. Communication device  102  may use one or more other permutations for communicating with one or more other devices, e.g., as is known in the art. 
   According to some demonstrative embodiments of the invention, communication device  104  may include a receiver  114  to receive signals over channel  106 . For example, receiver  114  may receive a set of N Rx  time-domain signals via N Rx  antennas  112 , respectively. The received signals may include symbols modulated over the subcarrier permutation of device  104 , e.g., as is known in the art. The N Rx  received signals may include symbols corresponding, for example, to symbols of the signals transmitted by transmitter  108 . 
   According to some demonstrative embodiments of the invention, receiver  114  may include a front end  116  and/or a transformer  118 , e.g., as are known in the art. Front end  116  may include any suitable front end module to convert the time-domain signals received from antennas  112  into time-domain signals  117  of a format suitable for transformer  118 , as known in the art. Transformer  118  transform signals  117  into a plurality of frequency-domain signals, e.g., including signals  124  and  126 . Transformer  118  may include, for example, a Fast Fourier Transformation (FFT) module, e.g., as is known in the art. 
   According to some demonstrative embodiments of the invention, receiver  114  may also include a channel estimator  122  to generate, based on the frequency-domain signals provided by transformer  118 , a plurality of signals  136  representing a plurality of channel estimations of the plurality of subcarriers, respectively, e.g., as is known in the art. For example, a channel corresponding to a subcarrier of the plurality of subcarriers may be represented, for example, by a channel matrix, denoted H, e.g., a N RX ·N TX  matrix s is known in the art. 
   According to some demonstrative embodiments of the invention, receiver  114  may also include a decoder  120  to decode the received signals and to generate signals  166  representing an estimation of the signals transmitted by device  102 , e.g., as described in detail below. In some demonstrative embodiments of the invention, decoder  120  may be able to perform “hard-decoding” of the received signals, e.g., as described below with reference to  FIGS. 2 ,  3 , and/or  4 . In another demonstrative embodiment of the invention, decoder  120  may be able to perform “soft-decoding” of the received signals, e.g., as described below with reference to  FIGS. 5  and/or  6 . However, the invention is not limited in this respect, and in other embodiments of the invention decoder  120  may be able to perform any suitable decoding operation, e.g., including one or more “soft-decoding” operations, “hard-decoding” operations, any other decoding operations, and/or any combination thereof. 
   According to some demonstrative embodiments of the invention, decoder  120  may include a hypothesis generator  193  to determine at least one hypothetical value of a selected signal of the set of N Tx  transmitted signals based on at least one respective set of hypothetical values assigned to a subset of the set of the N Tx  transmitted signals, respectively, e.g., as described in detail below. In some demonstrative embodiments of the invention, decoder  120  may determine signals  166  based on the at least one hypothetical value of the selected signal, and/or the at least one set of hypothetical values, e.g., as described in detail below. 
   According to some embodiments, receiver  114  and/or transmitter  108  may be implemented, for example, using separate and/or integrated units, for example, using a transmitter-receiver or transceiver. 
   The set of signals received by receiver  114  over a subcarrier of the subcarrier permutation of device  104 , may be represented, for example, as follows:
 
   y =H s + v     (1)
 
wherein  y  denotes a [N Rx x1] vector representing the N Rx  respective signals received over N Rx  antennas  112 , respectively;  s  denotes a [N Tx x1] vector including N Tx  symbols of an M-ary constellation transmitted via N Tx  antennas  110 , respectively; and  v  denotes a [N Rx x1] vector representing noise, e.g., Independently and Identically Distributed (IID) noise.
 
   A set of estimated values of  s , denoted ŝ, may be determined, for example, by the following Maximum Likelihood (ML) solution of Equation 1: 
                     s   _     ^     =             arg   ⁢   max     ⁢               s   ∈   S       ⁢           ⁢     Pr   ⁡     (       y   _     ❘     s   _       )         =     arg   ⁢           ⁢       min     s   ∈   S       ⁢              y   _     -     H   ⁢     s   _              2                   (   2   )               
wherein S denotes a group of combinations of M constellation points over N Tx  antennas  110 ; and wherein the notation ∥w∥ 2  denotes a L 2  norm operation applied to the parameter w, i.e., ∥w∥ 2 ≡w*w. However, it will be appreciated by those of ordinary skill in the art that the solution of Equation 2 may require, for example, scanning M N     Tx    hypothesis values of  s .
 
   According to some demonstrative embodiments of the invention, a set of hypothetical values may be assigned to a selected subset of the N Tx  transmitted signals, including a number of signals smaller than N Tx ; and a hypothetical value of at least one selected signal of the N Tx  transmitted signals, e.g., a signal not included in the selected subset of signals, may be determined based on the set of assigned hypothetical values. For example, a set of N Tx−1  hypothetical values, denoted  s   R , may be assigned to a selected subset including N Tx−1  signals of the N Tx  transmitted signals, respectively. A hypothetical value of the selected signal, denoted ŝ 1 ( s   R ), may be determined, for example, based on the set S R , e.g., as described below. 
   It will be appreciated by those of ordinary skill in the art that a ML Sequence Estimation (MLSE), denoted s′, of a single encoded stream of symbols, denoted s, transmitted from a single antenna and received by one or more antennas may be implemented by a combination of a Maximal Ratio Combiner (MRC) followed by a MLSE decoder. If the encoded stream includes symbols selected from a discrete constellation, the MLSE decoder may be implemented by a slicer, as is known in the art. For example, the estimation of s′ may be determined as follows: 
                         ⁢             s   ′     =           arg   ⁢   min       s   ∈   Q       ⁢            y   -     h   ·   s            2       =           ⁢           arg   ⁢   min       s   ∈   Q       ⁡     (            y        2     -     2   ·     Re   ⁡     [     y   ·     h   *     ·     s   *       ]         +            h        2     ·          s        2         )       =                   =     arg   ⁢           ⁢       min     s   ∈   Q       ⁢     [       (       h   *     ⁢   h     )     ·                  (       h   *     ⁢   h     )       -   1       ⁢     h   *     ⁢   y     -     s   ⁢          2     ⁢       +          y        2       -         (       h   *     ⁢   h     )       -   1       ⁢              h   *     ⁢   y          2         ]         =                           =         arg   ⁢   min       s   ∈   Q       ⁢                (       h   *     ⁢   h     )       -   1       ·     h   *     ·   y     -     s   ⁢          2     ⁢     =     slice   ⁢           ⁢     (         (       h   *     ·   h     )       -   1       ·     h   *     ·   y     )         ⁢                                     (   3   )               
wherein y denotes a received stream corresponding to the stream s, h denotes a channel between the transmitting antenna and the receiving antennas, and Q denotes a predefined group of constellation points.
 
   It will also be appreciated by those of ordinary skill in the art that a ML estimation of first and second parameters, denoted θ1 and θ2, respectively, may be performed by determining a ML estimation of θ2 for a given value of θ1, and determining the value of θ1 which may maximize the ML estimation of θ2, for example, as follows: 
                       max     (       θ   ⁢           ⁢   1     ,     θ   ⁢           ⁢   2       )       ⁢     (     L   ⁡     (       θ   ⁢           ⁢   1     ,     θ   ⁢           ⁢   2       )       )       =       max     θ   ⁢           ⁢   1       ⁢     ⌊       max     θ   ⁢           ⁢   2       ⁢     (     L   ⁡     (       θ   ⁢           ⁢   1     ,     θ   ⁢           ⁢   2       )       )       ⌋         ⁢                   (   4   )               
wherein L(θ1, θ2) denotes a log-likelihood of the received signal as a function of the parameters θ1 and θ2.
 
   According to some demonstrative embodiments of the invention, the value of ŝ 1 ( s   R ) corresponding to the set of hypothetical values  s   R  may be determined by applying a predefined function to the set of hypothetical values  s   R , the received signals  y , and/or the channel estimation H, e.g., as described below. 
   According to some demonstrative embodiments of the invention, the ML estimation of the values of s corresponding to the values  y  may be equivalent to deter mining a ML estimation of ŝ 1 ( s   R ) based on the set of assigned values  s   R ; and determining the values of  s   R  which may maximize the log-likelihood of  y  for ŝ 1 ( s   R ), e.g., as follows: 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
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   According to some demonstrative embodiments of the invention, a hypothetical value, denoted x, of a contribution of the hypothetical value ŝ 1 ( s   R ) to the received signal  y  may be determined, for example, by subtracting a contribution of the set of hypothetical values  s   R  from the received signal  y . For example, the value x may be determined as follows:
 
 x= y −H   R   · s     R   (6)
 
wherein H R  denotes one or more portions, e.g., columns, of the matrix H corresponding to the selected subset of signals.
 
   According to some demonstrative embodiments of the invention, the value of ŝ 1 ( s   R ) may be determined by applying a MRC operation to the value of x, and applying a slicing operation to the result of the MRC operation. For example, the value of ŝ 1 ( s   R ) may be determined based on the following equation, which may be derived by substituting y with x, and h with H 1  in Equation 3:
 
 ŝ   1 (   s     R )=slice [( H   1   *H   1 ) −1   H   1 *(   y −H   R     s     R )]  (7)
 
wherein H 1  denotes a portion, e.g., a column, of the matrix H corresponding to the selected signal.
 
   According to some demonstrative embodiments of the invention, hypothesis generator  193  may determine the value ŝ 1 ( s   R ) according to Equation 7. 
   According to some demonstrative embodiments of the invention, decoder  120  may assign a plurality of sets of hypothetical values  s   R  to the selected subset of signals, and hypothesis generator  193  may generate a plurality of hypothetical values ŝ 1 ( s   R ) of the selected signal based on the plurality of sets of hypothetical values, respectively, e.g., as described below. Decoder  120  may also determine a plurality of vectors  s  including the plurality of sets of hypothetical values  s   R , respectively; and the plurality of hypothetical values ŝ 1 ( s   R ), respectively. Decoder  120  may select one of the plurality vectors  s  (“the selected vector  s ”) based on any suitable criteria, e.g., as described below. Decoder  120  may generate signals  166  corresponding to the selected vector  s . 
   According to some demonstrative embodiments of the invention, decoder  120  may select the vector  s  based on a plurality of distance values, e.g., Euclidian distances, corresponding to the received signals  y , the plurality of hypothetical values ŝ 1 ( s   R ), and/or the plurality of sets of hypothetical values  s   R , respectively. For example, decoder  120  may determine a plurality of distance values, denoted d   s     2 , corresponding to the plurality vectors  s , respectively, e.g., as follows:
 
 d     s     2   =∥ y −H s ∥   2   =∥ y −H   R   s   R   −H   1   s   1 ∥ 2   (8)
 
   According to some demonstrative embodiments of the invention, may decoder  120  select the vector  s  such that the selected vector  s  results in a minimal distance value, e.g., according to Equation 8, compared, for example, to the distance values resulting from other vectors, e.g., as described below. 
   Reference is now made to  FIG. 2 , which schematically illustrates a decoder  200  in accordance with one demonstrative embodiment of the invention. Although the invention is not limited in this respect, decoder  200  may perform the functionality of decoder  120  ( FIG. 1 ). Although the invention is not limited in this respect, decoder  200  may be implemented, for example, to perform “hard-decoding” of the signals  y . 
   According to some demonstrative embodiments of the invention, decoder  200  may generate an output  213  including  s  values representing the transmitted signals, e.g., based on input  201  including received signals  y , and/or input  203  including the channel matrix H, as described in detail below. 
   According to some demonstrative embodiments of the invention, decoder  200  may include a counter  202 , a hypothesis generator  204 , a distance estimator  212 , and/or a selector, as are described in detail below. 
   According to some demonstrative embodiments of the invention, counter  202  may include any suitable counter to assign one or more sets of hypothetical values  s   R  to the subset of N Tx  transmitted signals, e.g., as described below. Hypothesis generator  204  may include any suitable generator to generate the hypothetical value ŝ 1 ( s   R ) corresponding to the set of hypothetical values  s   R , e.g., in accordance with Equation 7. Although the invention is not limited in this respect, hypothesis generator  204  may include, for example, a subtractor  206  to generate the hypothetical value x, e.g., according to Equation 6; a combiner  208  to apply a MRC operation to the hypothetical value x; and/or a slicer  210  to apply a slicing operation to an output  209  of combiner  208 . Combiner  208  may include any suitable MRC combiner, e.g., as is known in the art. Slicer  210  may include any suitable slicer, e.g., a QAM slicer as is known in the art. Distance estimator  212  may include any suitable estimator to estimate a distance value resulting from the set of hypothetical values  s   R , and the hypothetical value ŝ 1 ( s   R ), e.g., according to Equation 8. Selector  210  may include any suitable selector to select the vector  s  by applying any suitable criteria to distance values determined by estimator  212 , e.g., as described below. Although the invention is not limited in this respect, the  s  values of output  209  may substantially be equal to the values ŝ, e.g., according to Equation 2. 
   Some demonstrative embodiments of the invention are described herein in the context of a subtractor, e.g., subtractor  206 , a combiner, e.g., combiner  208 , and/or a slicer, e.g., slicer  210  being separate units of a hypothesis generator, e.g., generator  204 ; and/or a hypothesis generator, e.g., generator  204 , a counter, e.g., counter  202 , a distance estimator, e.g., estimator  212 , and/or a selector, e.g., selector  214 , being separate parts of a decoder, e.g., decoder  204 . However, it will be appreciated by those skilled in the art that, according to other embodiments of the invention, the decoder, counter, hypothesis generator, subtractor, combiner, slicer, distance estimator, and/or selector may be implemented in any other suitable configuration and/or arrangement, e.g., as described below with reference to  FIG. 4 . 
   Reference is also made to  FIG. 3 , which schematically illustrates a method of decoding received signals corresponding to a set of N Tx  transmitted signals in accordance with some demonstrative embodiments of the invention. Although the invention is not limited in this respect, one or more operations of the method of  FIG. 3  may be implemented by decoder  200 , and/or hypothesis generator  204 . 
   As indicated at block  302 , the method may include assigning a set of one or more hypothetical values to a subset including one or more signals of the set of N Tx  transmitted signals, respectively. For example, counter  202  may assign one or more hypothetical values  s   R  to one or more of the N Tx  transmitted signals, respectively, e.g., as described above. 
   As indicated at block  304 , the method may also include determining a hypothetical value of a selected signal of the N Tx  transmitted signals based on the set of assigned hypothetical values. For example, hypothesis generator  204  may determine the value of ŝ 1 ( s   R ), e.g., based on Equation 7. 
   According to some demonstrative embodiments of the invention, determining the hypothetical value of the selected signal may include determining the hypothetical value x based on the hypothetical values  s   R  and the received signals  y , for example, according to Equation 6, as indicated at block  306 ; applying a MRC operation to the hypothetical value x, e.g., as indicated at block  308 ; and/or applying a slicing operation to a result of applying the MRC operation, e.g., as indicated at block  310 . 
   According to some demonstrative embodiments of the invention, a hypothesis set of values, denoted  s , representing a hypothesis of the N Tx  transmitted signals may include the set of hypothetical values  s   R  and the hypothetical value ŝ 1 ( s   R ). 
   As indicated at block  312 , the method may also include determining a distance value corresponding to the hypothesis set  s . For example, estimator  212  may determine the distance value d   s     2 , e.g., according to Equation 8. 
   According to some demonstrative embodiments of the invention, as indicated at block  314 , the method may also include repeating the operations of blocks  302 ,  304 , and/or  312  to determine a plurality of distance values corresponding to a plurality of hypothesis sets including a plurality of the sets of the values  s   R  representing a plurality of available constellation combinations of the subset of the N Tx  signals, respectively, and a respective plurality of the values ŝ 1 ( s   R ). For example, counter  202  may assign M N     Tx−1    sets of  s   R  values corresponding to M N     Tx−1    constellation combinations of N Tx−1  signals, e.g., if the subset of transmitted signals includes N Tx−1  signals of the N Tx  transmitted signals, as described above. Accordingly, generator  204  may generate M N     Tx−1    hypothetical values ŝ 1 ( s   R ) corresponding to the M N     Tx−1    sets; and/or estimator  212  may determine M N     Tx−1    distance values corresponding to M N     Tx−1    hypothesis sets  s , respectively, e.g., as described above. 
   As indicated at block  316 , the method may also include selecting one of the M N     Tx−1    hypothesis sets based on any suitable criteria For example, selector  214  may select the set  s  resulting in a minimal distance value compared to the distance values resulting from other hypothesis sets, e.g., as described above. 
   Some demonstrative embodiments of the invention, e.g., as described above with reference to  FIGS. 2  and/or  3 , relate to applying the MRC operation one or more times to one or more of the sets of hypothetical values  s   R , respectively, e.g., after determining the hypothetical value x and before applying the slicing operation. However, according to other demonstrative embodiments of the invention, the MRC operation may be performed, e.g., once, for example, before assigning the hypothetical values  s   R  to the selected subset of transmitted signals, e.g., as described below. 
   According to some demonstrative embodiments of the invention, N Tx  antennas  110  ( FIG. 1 ) may include-two antennas. Accordingly, the N Tx  transmitted signals may include two transmitted signals; the set of one or more hypothetical values  s   R  assigned to the subset of the two signals may include a value, denoted s 0 , assigned to a first signal of the two transmitted signals; the selected signal may include a second signal, denoted s 1 , of the two transmitted signals; the channel matrix H may include a N Rx x2 matrix having first and second columns, denoted  h   0  and  h   1 , respectively, corresponding to the first and second transmitted signals, respectively. A hypothetical value of the second signal, denoted ŝ 1 (s 0 ) may be determined, for example, as follows:
 
 ŝ   1 ( s   0 )=slice [(   h     1   * h     1 ) −1     h     1 *(   y − h     0   s   0 )]  (9)
 
   The distance value corresponding to the hypothesis set  s  including the values s 1  and s 0  may be determined, for example, as follows:
 
 d     s     2   =∥ y −H s ∥   2   =∥ y − h     0   s   0   − h     1   s   1 ∥ 2   (10)
 
   According to some demonstrative embodiments of the invention, the following values may be determined, e.g., before assigning the hypothetical value s 0 :
 
   a   *=(   h     1   * h     1 ) −1     h     1 *  (11)
 
Δ z=− a *· h     0 ·Δ  (12)
 
wherein Δ denotes a constellation spacing, e.g., Δ=2, as is known in the art. The following variables may be defined:
 
   b     x,y   = y − h     0   ·s   0   (13)
 
 z   x,y =(   h     1   * h     1 ) −1     h     1 *(   y − h     0   s   0 )=   a *· b     x,y   (14)
 
   According to some demonstrative embodiments of the invention, the values of s 0  and/or s 1  may be determined according to the following pseudo-code algorithm: 
   
     
       
         
             
           
             
                 
             
             
               Algorithm 1 
             
             
                 
             
           
          
             
                 
             
          
         
         
             
             
          
             
                 
               Define c(x,y) as the constellation points 
             
             
                 
               initialize b:b 0,0  = y − h 0  · c(0,0) (complex vector) 
             
             
                 
               initialize z: z 0,0  = a* · b 0,0  (complex number) 
             
             
                 
               for x=0 to m−1 // m=sqrt(M) 
             
             
                 
               { 
             
             
                 
                for y=0 to m−1 
             
             
                 
                { 
             
             
                 
                s 1  = slice(z x,y ) 
             
             
                 
                d x,y   2  = ||b x,y  − h 1 s 1 || 2   
             
             
                 
                b x,y+1  = b x,y  − j · h 0  · Δ 
             
             
                 
                z x,y+1  = z x,y  + j · Δz 
             
             
                 
                } 
             
             
                 
                b x+1,0  = b x,0  − h 0  · Δ 
             
             
                 
                z x+1,y  = z x,y  + Δz 
             
             
                 
               } 
             
             
                 
               select s 0 , s 1  corresponding to minimal d x,y   
             
             
                 
                 
             
          
         
       
     
   
   Algorithm 1 may be expressed in various languages, circuits or firmware structures, and/or may be implemented by any suitable software, hardware, and/or firmware, e.g., as described below. 
   Reference is made to  FIG. 4 , which schematically illustrates a decoder  400  in accordance with another demonstrative embodiment of the invention. Although the invention is not limited in this respect, decoder  400  may perform the functionality of decoder  120  ( FIG. 1 ). Although the invention is not limited in this respect, decoder  400  may perform one or more operations of Algorithm 1, e.g., as described below. 
   According to some demonstrative embodiments of the invention, decoder  400  may generate, for example, an output  448  including selected values of s 0  and/or s 1 , based on the received signals  y , the channel estimation  h   0 , and/or the channel estimation  h   1 , e.g., as described below. 
   According to some demonstrative embodiments of the invention, decoder  400  may include, for example, a preprocessor  402  to determine the value of Δz, a first initial value, denoted z 0 , and/or a second initial value, denoted b 0 . For example, preprocessor  402  may determine the values z 0  and/or b 0  as follows:
 
 b   0   = y − h     0   ·c   00   (15)
 
 z   0 =(   h     1   * h     1 ) −1     h     1   *· b     0   (16)
 
   Preprocessor  402  may include, for example, a first combiner  404  to determine the value Δz, e.g., by applying a MRC operation to the channel estimation  h   0  using the channel estimation  h   1 , e.g., according to Equation 12; a subtractor  408  to subtract the channel estimation  h   0  from signals  y , e.g., according to Equation 15; and/or a second combiner  406  to apply a MRC operation to the value b 0  using the channel estimation  h   1 , e.g., according to Equation 16. 
   According to some demonstrative embodiments of the invention, decoder  400  may also include a first counter  422  to propagate the value of z x,y  by Δ, e.g., for each column of the QAM constellation. For example, counter  422  may propagate the value of z x,y  as follows:
 
 z   x+1,y   =z   x,y   +Δz   (17)
 
   According to some demonstrative embodiments of the invention, decoder  400  may also include a second counter  424  to propagate the value of z x,y  by j·Δz, e.g., within a column of the QAM constellation. For example, counter  424  may propagate the value of z x,y  as follows:
 
 z   x,y+1   =z   x,y   +j·Δz   (18)
 
   Accordingly, an output  426  of counter  424  may include the value of z x,y,  for example, according to Equation 14. 
   According to some demonstrative embodiments of the invention, decoder  400  may also include a slicer  428 , e.g., a QAM slicer, to apply a slicing operation to output  426 , e.g., according to Equation 9. Accordingly, an output  430  of slicer  428  may include the hypothetical value ŝ 1 (s 0 ). 
   According to some demonstrative embodiments of the invention, decoder  400  may also include a third counter  434  to propagate the value of  b   x,y  by  h   0 ·Δ, e.g., for each column of the QAM constellation. For example, counter  434  may propagate the value of  b   x,y  as follows:
 
   b     x+1,0   = b     x,0   − h     0 ·Δ  (19)
 
   According to some demonstrative embodiments of the invention, decoder  400  may also include a fourth counter  436  to propagate the value of  b   x,y  by h 0 ·jΔ, e.g., within a column of the QAM constellation. For example, counter  436  may propagate the value of  b   x,y  as follows:
 
   b     x,y+1   = b     x,y   −j· h     0 ·Δ  (20)
 
   Accordingly, an output  438  of counter  436  may include the value of  b   x,y , for example, according to Equation 13. 
   According to some demonstrative embodiments of the invention, decoder  400  may also include a subtractor  432  to determine a hypothetical contribution value, denoted  e , based on the hypothetical value ŝ 1 (s 0 ), and/or the value  b   x,y . For example, subtractor  432  may determine  e  as follows:
 
   e = b     x,y   − h     1   ŝ   1 ( s   0 )  (21)
 
   According to some demonstrative embodiments of the invention, decoder  400  may also include a distance estimator  442  to determine the distance value d   s   , e.g., based on the value  e . For example, estimator  442  may generate an output  444  corresponding to the value d   s   as follows:
 
 d     s     ≈∥ e ∥   (22)
 
   According to some demonstrative embodiments of the invention, decoder  400  may also include a selector  446  to maintain a plurality of the distance values d   s   corresponding to a plurality of hypothesis sets  s  including the different constellation values of s 0  and s 1 ; and to select one of the values of s 0  and a corresponding one of the values of s 1 , by applying any suitable criteria to the distance values d   s   . For example, selector  446  may select the values of s 0  and s 1  corresponding to a minimal distance value. 
   Some demonstrative embodiments of the invention may refer to decoding a transmission including two spatial streams transmitted by N Tx =2 transmission antennas, e.g., as described above with reference to  FIG. 4 . However, it will be appreciated by those of ordinary skill in the art that other embodiments of the invention may include decoding a transmission including any other suitable number of spatial streams transmitted by any suitable number, e.g., N Tx &gt;2, of transmission antennas. For example, decoder  400  may be modified to decode transmissions of N Tx &gt;2 transmission antennas. 
   Some demonstrative embodiments of the invention are described above with reference to a decoder, e.g., decoder  200  ( FIG. 2 ) and/or decoder  400  ( FIG. 4 ), able to determine a selected set of values  s  based on the plurality of sets of hypothetical values s R  and the plurality of respective values ŝ 1 (s R ). However, some embodiments of the invention may relate to a decoder able to determine, additionally or alternatively, any other suitable value, e.g., one or more metric values, based on one or more sets of hypothetical values s R , and/or one or more values ŝ 1 (s R ), respectively, e.g., as described below. 
   Reference is now made to  FIG. 5 , which schematically illustrates a decoder  500  in accordance with yet another demonstrative embodiment of the invention. Although the invention is not limited in this respect, decoder  500  may perform the functionality of decoder  120  ( FIG. 1 ). 
   According to some demonstrative embodiments of the invention, decoder  500  may include, for example, a metric generator  502  to determine a set of metric values  512 , e.g., including one or more Log-Likelihood-Ratio (LLR) values, based on the received signals  y , and the channel matrix H, e.g., as described below. Decoder  500  may also include a metric decoder  510  to determine values  514  representing the N Tx  transmitted signals, e.g., based on values  512 . Metric decoder  510  may include any suitable decoder, for example, a FEC decoder, e.g., a Viterbi decoder as is known in the art. 
   A signal of the set of N Rx  received signals  y  may be represented by a predefined number of bits, e.g., log 2 (M) bits, as is known in the art. 
   According to some demonstrative embodiments of the invention, metric generator  502  may generate one or more of values  512  based on the plurality of hypothetical values s 1 , and/or the plurality of sets of hypothetical values s R , e.g., as described below. 
   According to some demonstrative embodiments of the invention, metric generator  502  may determine a LLR value, denoted LLR i (n), corresponding to an i-th bit of an n-th signal of the N Tx  transmitted signals, wherein i=1 . . . log 2 (M), for example, as follows: 
                     LLR   i     ⁡     (   n   )       =         min         s   R     ∈     Z     i   ,   n     +           s   1     =         s   ^     1     ⁡     (     s   R     )             ⁢     (     d   s   2     )       -       min         s   R     ∈     Z     i   ,   n     -           s   1     =         s   ^     1     ⁡     (     s   R     )             ⁢     (     d   s   2     )                 (   23   )               
wherein Z +   i,n  denotes a set of symbol vectors of constellation points wherein the i-th bit of the n-th signal has a first value, e.g., one; Z −   i,n  denotes a set of symbol vectors of constellation points wherein the i-th bit of the n-th signal has a second value, e.g., zero; and wherein n relates to the selected subset of the transmitted signals. For example, n may be in the range of n=2 . . . N Tx , e.g., if the selected subset does not include the first signal of the N Tx  transmitted signals.
 
   According to some demonstrative embodiments of the invention, metric generator  502  may determine a plurality of LLR values corresponding to the plurality of signals of a first selected subset excluding the selected signal s 1 , e.g., according to Equation 23. Accordingly, metric generator  502  may perform M N     Tx−1    hypotheses to determine LLR values corresponding to the first selected subset of the transmitted signals. Metric generator  502  may also determine LLR values corresponding to a second selected subset of the transmitted signals including the selected signal s 1 . For example, metric generator  502  may determine the LLR values according to Equation 23, wherein n relates to the second subset, e.g., n=1 . . . u−1 u+1 . . . N Tx , wherein u is selected such that the second subset includes signal s 1 . Accordingly, metric generator  502  may perform M N     Tx−1    additional hypotheses to determine LLR values corresponding to the second subset of the transmitted signals. Thus, metric generator  502  may perform, for example, 2M N     Tx−1    hypotheses to determine values  512 . 
   According to some demonstrative embodiments of the invention, metric generator  502  may include a distance estimator  504  to determine a plurality of distance values  505  corresponding to the plurality of sets of hypothetical values s R , respectively, e.g., according to Equation 10. Distance estimator  504  may include, for example, preprocessor  402 , counter  422 , counter  424 , counter  434 , counter  436 , slicer  428 , subtractor  432 , and/or distance estimator  442 , as are described above with reference to  FIG. 4 . Distance estimator may include any other suitable estimator, e.g., including counter  202 , hypothesis generator  204 , and/or estimator  212 , as are described above with reference to  FIG. 2 . 
   According to some demonstrative embodiments of the invention, metric generator  502  may also include a collector  506  to collect a plurality of minimal distance values, denoted d min   (p) [k], corresponding to a k-th bit, wherein p=0,1. For example, collector  506  may generate an output  507  including the following minimal distance values:
 
 d   min   (0)   [k ]=min( d     s     | s   :bit k= 0)
 
 d   min   (1)   [k ]=min( d     s     | s   :bit k= 1)  (24)
 
   According to some demonstrative embodiments of the invention, metric generator  502  may also include a LLR calculator  508  to generate values  512 . For example, calculator  508  may generate a LLR value, denoted LLR[k], corresponding to the k-th bit, e.g., as follows:
 
LLR[ k]=d   min   (0)   [k]   2   −d   min   (1)   [k]   2   (25)
 
   Reference is also made to  FIG. 6 , which schematically illustrates a method of determining metric values in accordance with some demonstrative embodiments of the invention. Although the invention is not limited in this respect, one or more operations of the method of  FIG. 6  may be performed by metric generator  502 , e.g., to determine one or more of metrics  512 . 
   As indicated at block  601 , the method may include selecting a first subset of the N Tx  transmitted signals, e.g., which does not include at least one selected signal of the transmitted signals. For example, metric generator  502  may select the first subset, e.g., as described above. 
   As indicated at block  602 , the method may include assigning a set of one or more hypothetical values to the selected subset. For example, estimator  504  may assign one or more hypothetical values  s   R  to one or more of the N Tx  transmitted signals, respectively, e.g., as described above. 
   As indicated at block  604 , the method may also include determining a hypothetical value of the selected signal based on the set of assigned hypothetical values. For example, estimator  504  may determine the value of ŝ 1 ( s   R ), e.g., based on Equation 7. 
   As indicated at block  606 , the method may also include determining a distance value corresponding to the values s R  and/or ŝ 1 ( s   R ). For example, estimator  504  may determine the distance value d   s     2 , e.g., according to Equation 8 or 10. 
   As indicated at block  608 , the method may include repeating the operations of blocks  602 ,  604 , and/or  606  to determine a plurality of distance values corresponding to a plurality of hypothesis sets including a plurality of the sets of the values  s   R  representing a plurality of available constellation combinations of the selected subset, respectively, and a respective plurality of the values ŝ 1 ( s   R ), e.g., as described above with reference to  FIG. 3 . 
   As indicated at block  610 , the method may also include determining the values d min   (p) [k]. For example, collector  506  may generate output  507  according to Equation 24. 
   As indicated at block  612 , the method may also include determining one or more metrics corresponding to the signals of the selected subset. For example, calculator  508  may determine one or more of values  512 , e.g., according to Equation 25. 
   As indicated at block  614 , the method may also include selecting a second subset of the transmitted signals, e.g., not including the selected signal; and repeating the operations of blocks  602 ,  604 ,  606 ,  608 ,  610 ,  612  and/or  614  to determine one or more metrics corresponding to the selected signal. For example, metric generator  502  may select the second subset, e.g., as described above. 
   Some demonstrative embodiments of the invention are described above with reference to a metric generator, e.g., generator  502 , able to determine values  512  by calculating a first set of LLR values corresponding to bits of the first subset of the transmitted signals, which may not include the selected signal; and calculating a second set of LLR values corresponding to bits of the second subset of the transmitted signals including the selected signal, e.g., according to Equation 23. However, it will be appreciated by those of ordinary skill in the art that according to other embodiments of the invention the metric generator may determine one or more of the LLR values by applying any other suitable algorithm or operation to one or more hypothetical values s 1 , which may be determined based on one or more respective sets of hypothetical values s R , e.g., as described below. 
   According to another demonstrative embodiment of the invention, the selected signal may be selected from the N Tx  transmitted signals based on the values of the channel matrix H. For example, the selected signal may include an m-th signal, denoted s m , of the N Tx  signals, which may correspond to an m-th column of the matrix H, denoted  h   m . The value of m may be determined, for example, as follows: 
   
     
       
         
           
             
               
                 m 
                 = 
                 
                   
                     argmax 
                     m 
                   
                   ⁢ 
                   
                     
                        
                       
                         
                           h 
                           _ 
                         
                         m 
                       
                        
                     
                     2 
                   
                 
               
             
             
               
                 ( 
                 26 
                 ) 
               
             
           
         
       
     
   
   A plurality of hypothetical values, denoted Ŝ m ( s   R ) corresponding to the selected signal may be determined, for example, based on a plurality of sets of hypothetical values  s   R  assigned to the subset of N Tx−1  transmitted signals excluding the selected signal, e.g., as follows:
 
 ŝ   m (   s     R )=slice [( h   m   *h   m ) −1   h   m *(   y −H   R     s     R )]  (27)
 
   The following set of symbols may be defined:
 
 Z ′={(   s     R   ,ŝ   m )|   s     R   εY,ŝ   m (   s     R )=slice [( h   m   *h   m ) −1   h   m *(   y −H   R     s     R )]}  (28)
 
   The LLR value may be determined as follows: 
                     LLR   i     ⁡     (   n   )       =         min       s   _     ∈       Z   ′       i   ,   n     +         ⁢     (     d   s   2     )       -       min       s   _     ∈       Z   ′       i   ,   n     -         ⁢     (     d   s   2     )                 (   29   )               
wherein the distance values d s  may be determined, for example, according to Equation 8; and wherein n=1 . . . N Tx . If Z 1+   i,n  is an empty set, then the corresponding distance value d s  may be calculated over a larger set, e.g., the set
 
                   s   _     ∈         ⋃       log   2     ⁢   M         i   =   1       ⁢       Z     i   ,   n       ′   +       .                               
If the set
 
                     ⋃       log   2     ⁢   M         i   =   1       ⁢     Z     i   ,   n       ′   +                               
is empty, then the distance value may be calculated over the entire set Z′. If Z 1−   i,n  is an empty set, then the corresponding distance value may be calculated over a larger set, e.g., the set
 
                   ⁢             s   _     ∈         ⋃       log   2     ⁢   M         i   =   1       ⁢       Z     i   ,   n       ′   -       .                                 
If the set
 
               ⋃       log   2     ⁢   M         i   =   1       ⁢     Z     i   ,   n     -           
is empty, then the distance value may be calculated over the entire set Z′.
 
   According to yet another demonstrative embodiment of the invention, one or more LLR values corresponding to the received signals  y  may be determined by applying one or more zero-forcing (ZF) equalizing operations to the received signals  y , e.g., according to the following Algorithm:
         1. Apply ZF equalizer to the signals  y  to determine an equalized set:
             r =(H H H) −1  H H   y , wherein H H  denotes a complex conjugate transpose applied to the matrix H.   
           2. Repeat the following operations for j=1 . . . N TX  times:
           a. Calculate post-ZF SINR for k-th data stream:   
               

   
     
       
         
           
             SINR 
             k 
           
           = 
           
             SNR 
             
               
                 [ 
                 
                   
                     ( 
                     
                       
                         H 
                         H 
                       
                       ⁢ 
                       H 
                     
                     ) 
                   
                   
                     - 
                     1 
                   
                 
                 ] 
               
               kk 
             
           
         
       
     
       
       
         
           
             
               b. Select m-th signal from the N Tx  transmitted signals corresponding to the maximum SINR: 
             
           
         
       
     
  
   
     
       
         
           
             m 
             j 
           
           = 
           
             
               argmax 
               m 
             
             ⁢ 
             
               
                 SINR 
                 m 
               
               . 
             
           
         
       
     
       
       
         
           
             
               c. Define: Q j =set of G constellation points closet to the m j -th ZF output  r (m j ), wherein G is predetermined number. Large G may increase performance. 
               d. For each s m     j   εQ j , subtract contribution due to s m     j   , e.g.,  y = y −h m     j   s m     j   . Define the channel matrix: H=└h 1  . . . h m     j     −1  0 h m     j     +1  . . . h N     TX   ┘ 
               e. Apply ZF equalizer to  y . 
             
           
           3. Z=set of symbol vectors of N TX  signals Z={(s m     1   , . . . s m     NTX   )}. The size of Z is G N     TX     −1 . 
           4. Determine LLR for i-th bit of n-th signal: 
         
       
     
  
   
     
       
         
           
             
               LLR 
               i 
             
             ⁡ 
             
               ( 
               n 
               ) 
             
           
           = 
           
             
               
                 min 
                 
                   
                     s 
                     _ 
                   
                   ∈ 
                   
                     Z 
                     
                       i 
                       , 
                       n 
                     
                     + 
                   
                 
               
               ⁢ 
               
                 ( 
                 
                   d 
                   s 
                   2 
                 
                 ) 
               
             
             - 
             
               
                 min 
                 
                   
                     s 
                     _ 
                   
                   ∈ 
                   
                     Z 
                     
                       i 
                       , 
                       n 
                     
                     - 
                   
                 
               
               ⁢ 
               
                 
                   ( 
                   
                     d 
                     s 
                     2 
                   
                   ) 
                 
                 . 
               
             
           
         
       
     
       
       
         
           5. If Z i,n   +  or Z i,n   −  are empty sets, then calculate LLR over a larger set, e.g., as described above. 
         
       
     
  
   Algorithm 2 
   Embodiments of the present invention may be implemented by software, by hardware, or by any combination of software and/or hardware as may be suitable for specific applications or in accordance with specific design requirements. Embodiments of the present invention may include units and sub-units, which may be separate of each other or combined together, in whole or in part, and may be implemented using specific, multi-purpose or general processors, or devices as are known in the art. Some embodiments of the present invention may include buffers, registers, storage units and/or memory units, for temporary or long-term storage of data and/or in order to facilitate the operation of a specific embodiment. 
   While certain features of the invention have been illustrated and described herein, many modifications, substitutions, changes, and equivalents may occur to those of ordinary skill in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.