Abstract:
A wireless receiver detects signals generated with a multiple-input, multiple-output (MIMO) transmitter. The receiver applies maximum-likelihood detection (MLD) for soft-output signal detection, where an MLD exhaustive search across all candidate vectors is performed recursively by computing and accumulating the differences between, for example, the Euclidean metrics of consecutive candidate tests. Difference terms used for the accumulation are also calculated recursively. An ordering of candidates, such as by a triangular-waveform shaped ordering, is employed such that only one candidate variable is changed between any two consecutive candidate evaluations, leading to a reduced set of computations.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to communication systems, and, in particular, to data detection employing a multiple-input, multiple-output demapper. 
   2. Description of the Related Art 
   Reliable and efficient transmission of information signals over imperfect communication channels is essential for wireless communication systems. One method of transmission is multiple-input, multiple-output (MIMO) transmission. For MIMO transmission, a transmitter sends separate signals on two or more transmit antennas, the separately transmitted signals are combined as they pass through the channel, and the receiver receives the combined signals on each of one or more receive antennas. The receiver detects and demodulates each of the transmitted signals and processes the received signals to extract the information. 
   One successful approach to achieving reliable transmission is multi-carrier modulation (MCM). MCM is a modulation technique that might employ several transmit antennas at the transmitter. The principle of MCM is to divide a communication channel into a number of sub-carriers (also called tones or bins), with each sub-carrier independently modulated. Information is modulated onto a tone by varying the tone&#39;s phase, amplitude, or both. 
   Orthogonal frequency division multiplexing (OFDM) is a form of MCM in which tone spacing is selected such that each tone is orthogonal to all other tones over the given symbol interval. OFDM wireless local area network (wireless LAN or WLAN) systems are typically designed to conform to either a contention-based wireless medium access standard such as IEEE 802.11 or a scheduled time-division duplex (TDD) wireless medium access standard such as European Telecommunications Standards Institute (ETSI) HIPERLAN/2. In a WLAN system conforming to a contention-based standard, OFDM stations compete for access to the wireless medium using “fair contention” medium-sharing mechanisms specified in the standard. In contrast, medium access in a scheduled TDD-conforming WLAN system is controlled by a single designated station, which schedules medium access for all other transceivers. 
   IEEE Standard 802.11 and its extensions 802.11a/b/g specify the physical layers and medium access control procedures for OFDM WLAN systems. For example, an 802.11a-compliant system operates in the 5-GHz radio-frequency band and provides data communication capabilities of 6, 9, 12, 18, 24, 36, 48, and 54 Mbit/s. The system uses 52 tones (numbered from −26 to 26, excluding 0) that are modulated using binary or quadrature phase shift keying (BPSK/QPSK), 16-quadrature amplitude modulation (16-QAM), or 64-QAM. In addition, the system employs forward error correction (convolutional) coding with a coding rate of 1/2, 2/3, or 3/4. 
   In a MIMO wireless transmission, the signals that simultaneously arrive at each receive antenna are a mix of the signals coming from each of the various transmit antennas. Therefore, typical single-antenna demodulation (e.g., soft-slicing) techniques are not applicable, and MIMO demodulators (“demappers”) are employed instead. Generally, a MIMO demapper generates, based on the signals coming from the various receive antennas, “soft decisions” (or “soft bits”) for all bits modulated onto carriers of each transmit antenna. These soft bits are further processed to generate final “hard decisions” for the encoded data bits, for example, in a transmitted packet. Due to the random mutual cross-talk of transmit streams in the wireless MIMO channel, MIMO demapping can exhibit irregular performance. However, the performance of subsequent processing steps at the receiver (e.g., decoding) depends heavily on the quality of these initial soft-bit estimates. Consequently, a maximum degree of reliability in the demapping process is desired. Prior art MIMO demappers either sacrifice reliability or are relatively complex to implement. 
   One group of prior art MIMO demappers employs Zero-Forcing (ZF) or Minimum Mean Squared Error (MMSE) techniques to separate the various transmit streams from one another at the receiver. Separation is accomplished by applying sets of pre-processing (combining) weights to the signals of the various receive antennas, one set per transmit stream. Then, each resulting signal stream is demapped using single antenna stream techniques. 
   While the approach of these MIMO demappers is relatively simple to implement, suppression of mutual cross-talk between the separated signal streams might lead to noise-enhancement. In noise-enhancement, the effective Signal-to-Noise Ratio (SNR) in the various reconstructed signal streams might be relatively low depending on the properties of the wireless channel, leading to significant degradation in the generation of soft bits. 
   Another group of prior art MIMO demappers employs maximum-likelihood detection (MLD). For MLD, a search is performed in which ideal receive signals are constructed based on candidate transmit signals and the (known) MIMO transmission channel. An error metric (such as the minimum squared Euclidean distance) between the actual receive signals and the various constructed ideal receive signals is used to find the best candidate for soft-bits of a particular separated signal stream. Variations of this method might be applied to each bit encoded in the signals under consideration, and the corresponding desired soft-bits extracted from the various Euclidean distance terms. In the so-called “exhaustive search” variation of MLD, all possible candidates are considered. Other methods, such as spherically constrained decoding, reduce the size of the search by testing only a certain subset of all possible candidates. 
   However, the complexity of the search process is typically prohibitive for high-data-rate systems. For the example of 2-dimensional MIMO modulation using 64-QAM, the receiver&#39;s MIMO demapper evaluates 4096 candidate metrics, and a brute-force computation of each metric includes approximately 20 multiplication operations and 20 additions. Moreover, for systems employing OFDM, the brute-force computation is performed for each OFDM subcarrier. While the number of candidate metrics may be reduced by, for example, spherically constrained decoding, a very complex process might be required in practice to identify the relevant candidates. Moreover, when the number of candidate metrics is reduced, ensuring that the true candidate is actually found is difficult. Another disadvantage is that the spherically constrained search is performed separately per soft bit. 
   SUMMARY OF THE INVENTION 
   In accordance with embodiments of the present invention, a wireless receiver detects signals coming from the multiple transmitters (or transmit antennas) of a multiple-input, multiple-output (MIMO) system. The receiver applies maximum-likelihood detection (MLD) for soft-output signal detection, where an MLD exhaustive search across all candidate vectors is performed recursively by computing and accumulating the differences between, for example, the Euclidean metrics of consecutive candidate tests. Difference terms used for the accumulation are also calculated recursively. An ordering of candidates, such as by a triangular-shaped (waveform) ordering, is employed such that only one candidate variable is changed between any two consecutive candidate evaluations, leading to a reduced set of computations. 
   In accordance with an exemplary embodiment of the present invention, a data pattern is detected from a plurality of received signals. A sequence is provided of scan values derived from a sequence of count values, each scan value selecting one of a set of candidates in a varying pattern. For each of the sequence of count values, a difference term between a current metric value and a previous metric value is generated based on a set of coefficients for a received symbol. For each of a sequence of count values, the difference term is combined with one or more previous difference terms to provide one of a set of metric values. Based on the set of metric values corresponding to the sequence of scan values, soft-output values corresponding to the data pattern are generated. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Other aspects, features, and advantages of the present invention will become more fully apparent from the following detailed description, the appended claims, and the accompanying drawings in which: 
       FIG. 1  shows a multiple-input, multiple-output (MIMO) receiver operating in accordance with exemplary embodiments of the present invention; 
       FIG. 2  shows an exemplary 64-QAM encoding constellation as may be processed with the receiver of  FIG. 1 ; 
       FIG. 3  shows an exemplary implementation for a MIMO demapper as might be employed for the MIMO detector of  FIG. 1 ; 
       FIG. 4  shows an exemplary implementation for the mapper of  FIG. 3 ; 
       FIG. 5  shows an exemplary candidate variable scan for the exemplary implementation of  FIG. 4 ; and 
       FIG. 6  shows an exemplary implementation for the difference term generator of  FIG. 3 ; and 
       FIG. 7  shows an exemplary implementation for the comparator of  FIG. 3 . 
   

   DETAILED DESCRIPTION 
     FIG. 1  shows a multiple-input, multiple-output (MIMO) receiver  100  operating in accordance with exemplary embodiments of the present invention. Receiver  100  comprises N r  receive chains  190 ( 1 ) through  190 (Nr), where Nr is a positive. Typically, a MIMO receiver comprises two or more receive chains, where each receive chain might operate in a similar manner. 
   Receive chain  190 ( 1 ) comprises antenna  101 , radio front end (RFE)  102 , channel selection filter (CSF)  103 , programmable gain amplifier (PGA)  104 , and sampler  105 . Antenna  101  detects a signal from, for example, a wireless communication channel, where the signal might comprise two or more antenna signals generated by a MIMO transmitter. RFE  102  receives the signal from antenna  101 , band filters and gain adjusts the antenna signal, and demodulates the antenna signal to base-band (BB) or near-BB. 
   CSF  103  filters the signal from RFE  102  so as to pass the desired information channel. For example, CSF  103  might be configured to operate for a WLAN according to the IEEE 802.11a/g standards for orthogonal frequency division multiplex (OFDM). For such configuration, CSF  103  has a bandwidth of approximately 20 MHz. PGA  104  adjusts the signal from CSF  103  to be within the range supported by sampler  105 . Sampler  105  periodically time-samples the signal from PGA  104 . 
   The outputs of all Nr receive chains  109 ( 1 ) through  109 (Nr) are monitored by MIMO detector  106  to detect the data from the received signal. The signal from detectors  106  is applied to processor  107  for subsequent processing and decoding. While processor  107  is shown in  FIG. 1  as a single element, as would be apparent to one skilled in the art, the various processing of detected (e.g., encoded) data from MIMO detector  106  might be accomplished with two or more different processors. 
   The exemplary embodiment of the present invention is described herein with respect to a MIMO system employing quadrature amplitude modulation (QAM) encoding of data, though the present invention is not so limited. One skilled in the art might extend the teachings herein to other MIMO systems using other forms of encoding of data into transmit symbols. For the exemplary embodiment herein, the MIMO system employs a transmitter with N t =2 transmit antennas, each employing a 64-QAM encoding of data into transmit symbols.  FIG. 2  shows an exemplary 64-QAM encoding constellation. 
   MIMO detector  106  implements a MIMO demapping with soft-output maximum likelihood detection (SO MLD) in accordance with an exemplary embodiment of the present invention. For ease of understanding, the following gives a background of SO MLD for MIMO demapping. MIMO formulation of a log-likelihood approximation for SO MLD generates a soft-bit L(b k ) as follows in equation (1): 
                   L   ⁡     (     b   k     )       =         min       x   ⁢     ❘     ⁢     b   k       =   0       ⁢            r   -   Hx          2       -       min       x   ⁢     ❘     ⁢     b   k       =   1       ⁢            r   -   Hx          2                 (   1   )               
where L(b k ) is the soft-bit for the kth bit, k=0,1, . . . , K−1, coded into the MIMO-QAM symbol. For N t =2 and 64-QAM encoding, K=12, since (2 subcarriers)(6 bits per symbol)=12 bits are decoded per MIMO-OFDM subcarrier. The vector r is an N r -dimensional receive vector, and matrix H is the (N r XN t )-dimensional MIMO channel matrix (characterizing the narrowband MIMO transmission wireless channel impulse response or transfer function), which might be estimated by the receiver through decoding of known preamble data. The transmit vector x is the N t -dimensional candidate transmit vector which is a direction function ƒ(•) (e.g., QAM mapping) of the set of all bits b={b k } modulated into it, as defined by equation (2):
   x =ƒ( b )= x ( b )  (2) 
The receive vector r represents the signal received from the transmission medium that corresponds to the transmit vector x true  passed through the channel with transfer function H and corrupted with additive noise n. Thus, the receive vector r is as defined in equation (3):
   r=Hx   true   +n   (3) 
where each complex element in the vector x true  corresponds to one constellation point of  FIG. 1 . For the 64-QAM modulation of  FIG. 2 , Gray coding is employed that specifies that any two adjacent points only differ by one bit. A MIMO demapper evaluating equation (1) for each soft-bit attempts to find candidate vectors x for which the metric (squared Euclidean distance) term y as defined in equation (4):
   y ( x )= y ( x ( b ))=∥ r−Hx ( b )∥ 2 .  (4) 
is minimum.
 
   Computation of each term y(x) for the candidate x(b) requires a large number of complex multiplication operations and additions. Consequently, in accordance with embodiments of the present invention, each term y(x) is computed recursively using a doubly-recursive method with a candidate scanning order to reduce the overall number of computations. 
     FIG. 3  shows an exemplary implementation for a MIMO demapper as might be employed for MIMO detector  106  of  FIG. 1 . MIMO demapper  300  comprises coefficient calculator (coeff-calc)  301 , difference term generator (DTG)  302 , counter  303 , mapper  304 , comparator unit  305 , accumulator  308 , and controller  309 . Controller  309  might be employed to coordinate processing implemented by the various elements of  FIG. 3 . 
   For each clock cycle i, i=0 . . . 4095, one of 64 2 =4096 candidate vectors is evaluated for the exemplary embodiment. Counter  303  is employed to provide the clock cycle to DTG  302  and mapper  304 . Counter  303  might be implemented as a 12-bit binary counter for 64-QAM. 
   Coeff-calc  301  computes various coefficients based on the input signals r and the MIMO channel matrix H, as described subsequently. These coefficients for i) r represent the received signal symbols (in-phase and quadrature phase) components for each receive antenna and ii) the estimated channel impulse response H measured and/or estimated separately by the receiver. 
   DTG  302  recursively pre-calculates a difference term based on the coefficients generated by coefficient calculator  301 , where the difference term corresponds to the metric difference d[i] between two consecutive candidates. DTG  302  recursively pre-calculates the difference term based on the clock cycle i provided as the count value from counter  303 . DTG  302  provides the difference term to accumulator  308 . 
   Accumulator  308  generates the Euclidean distance variable y of, for example, equation (4). With y[i] previously generated, y[i+1] is generated by accumulator  308  as y[i+1]=y[i]+d[i]. Accumulator  308  is implemented as register  306  and combiner  307 . For each clock cycle i, the difference term d[i] is added, by combiner  307 , to the previously calculated value of y in register  306 . 
   In a 2-dimensional QAM-MIMO system, there are four candidate variables (A 1 , B 1 , A 2 , B 2 ): one real component and one imaginary component for each transmit antenna dimension. Following the 64-QAM constellation of  FIG. 2 , each one of these candidate variables (A 1 , B 1 , A 2 , B 2 ) takes one of the signal alphabet values {−7, −5, −3, −1, 1, 3, 5, 7}. When, in the candidate scanning process, one of these variables is changed in the overall expression for y, the metric y is updated according to this change. This variable change corresponds to selecting one of the difference terms generated by DTG  302 , as described subsequently, and forwarding the selected difference term to accumulator  308 . With every change of one of the candidate variables, the difference variable itself is updated. 
   Comparator unit  305 , in the course of the whole candidate scan, determines the minimum y values for each of the two possible values (0,1) of each bit, by comparing the current y value for the current value of candidate variables under consideration with the previous minimum of y. At the end of the process, comparator unit  305  provides the differences between these two possible values (0,1) to subsequent processing (not shown in  FIG. 3 ) as the desired SO MLD soft-bits (L(b k ) values). 
   Mapper  304  generates values to scan four candidate variables (A 1 , B 1 , A 2 , B 2 ) in a specific order based on the 12-bit binary counter from counter  303 . The sequence of counter values (e.g., 12-bit values) from counter  303  are transformed into Gray-coded values following a “triangular waveform” shaped scanning sequence by mapper  304 . Starting at its minimum value of −7, each of the four candidate variables (A 1 , B 1 , A 2 , B 2 ) undergoes the triangular waveform scan by comparator  305 . For the triangular waveform scan, each successive variable is scanned at a lower rate than the previous variable (e.g., A 1  is scanned faster than B 1 , B 1  is scanned faster than A 2 , and A 2  is scanned faster than B 2 ). Thus, whenever a certain variable has reached the top or bottom of the number range (+7 or −7), the next high-level variable is updated before the next upward or downward slope is started. 
   Operation of the exemplary MIMO demapper of  FIG. 3  is now described.  FIG. 4  shows an exemplary implementation for mapper  304  of  FIG. 3  to generate bit values b 0 -b 11  for the candidate variables. Latches C 0 -C 11  contain corresponding bit values for the count from counter  303 . Elements labeled “XOR” perform an exclusive logic OR on the identified input bits. The triangular waveform scan employs segments of three bits, where each 3-bit segment corresponds to one of the candidate variables (A 1 , B 1 , A 2 , B 2 ). The 3-bit segment counts from 0 to 7 and then from 7 to 0 to point to the various elements of the signal alphabet {−7, −5,−3,−1,1,3,5,7}. For each 3-bit segment from counter  303  (i.e., C 0 -C 2 , C 3 -C 5 , C 6 -C 8 , and C 9 -C 11 ), the up-count is 000, 001, 010, 011, 100, 101, 110, 111, and for the down-count these values are inverted. Up/down counting by 3-bit segments is accomplished via XOR block  401  which XOR&#39;s each bit in a 3-bit block with a next higher level bit. 
   The bit values t 0 -t 11  of the up/down count of each 3-bit segment might not necessarily correspond to the bit values b 1 -b 11  of the encoded and modulated symbol. For the described Gray-coded QAM symbol signal alphabet {−7, −5,−3,−1,1,3,5,7} as employed in IEEE 802.11g/a OFDM systems, the corresponding binary representation is defined as [000, 100, 110, 010, 011, 111, 101, 001]. Consequently, XOR block  402  is employed to translate the bit values t 0 -t 11  of the up/down count into bit values b 1 -b 11  of the signal alphabet. 
     FIG. 5  shows an exemplary candidate variable scan for the exemplary implementation of  FIG. 4 . As shown in  FIG. 5 , each of the four candidate variables (A 1 , B 1 , A 2 , B 2 ) undergoes a “triangular waveform” shaped scan by counter  303  and mapper  304 , where variable B 1  is scanned 8 times more slowly than A 1 , A 2  is scanned 8 times more slowly than B 1 , and B 2  is scanned 8 times more slowly than A 2 . 
   Coeff-calc  301  and DTG  302 , at any given clock cycle i, provide a difference term to accumulator  308 , as described previously, where the difference term corresponds to the metric difference d[i] between two consecutive candidates. Derivation of the coefficients and updating the difference term is now described. The vector-matrix notation of equation (4) is reduced and the result separated into various weights and coefficients. At initialization (i=0), the following variables da 1 , db 1 , da 2 , and db 2  are calculated as in equations (5a) through (5d):
 
 da 1 =Δy   A1 =2 w   1 −24 w   5 −14 w   9 −14 w   10   (5a)
 
 db 1 =Δy   B1 =2 w   2 −24 w   6 −14 w   11 −14 w   12   (5b)
 
 da 2 =Δy   A2 =2 w   3 −24 w   7 −14 w   9 +14 w   11   (5c)
 
 db 2 =Δy   B2 =2 w   4 −24 w   8 −14 w   10 −14 w   12   (5d)
 
The weight coefficients w 1  through w 12  are as given in equations (6), (7), (8), and (9):
 
                         ⁢       w   5     =       w   6     =     (       h     I   ,   11     2     +     h     Q   ,   11     2     +     h     I   ,   21     2     +     h     Q   ,   21     2       )                 (   6   )                       ⁢       w   7     =       w   8     =     (       h     I   ,   12     2     +     h     Q   ,   12     2     +     h     I   ,   22     2     +     h     Q   ,   22     2       )                 (   7   )                 (           w   9               w   10           )     =       (           w   12               -     w   11             )     =       [               +   2     ⁢     h     I   ,   12         +     2   ⁢     h     Q   ,   12         +     2   ⁢     h     I   ,   21         +     2   ⁢     h     Q   ,   21                         -   2     ⁢     h     Q   ,   12         +     2   ⁢     h     I   ,   12         +     2   ⁢     h     Q   ,   21         -     2   ⁢     h     I   ,   21                 ]     ·     (           h     I   ,   11                 h     Q   ,   11                 h     I   ,   22                 h     Q   ,   22             )                 (   8   )                       ⁢       (           w   1               w   2               w   3               w   4           )     =       [             -   2     ⁢     h     I   ,   11                 -   2     ⁢     h     Q   ,   11                 -   2     ⁢     h     I   ,   21                 -   2     ⁢     h     Q   ,   21                     +   2     ⁢     h     Q   ,   11                 -   2     ⁢     h     I   ,   11                 +   2     ⁢     h     Q   ,   21                 -   2     ⁢     h     I   ,   21                     -   2     ⁢     h     I   ,   12                 -   2     ⁢     h     Q   ,   12                 -   2     ⁢     h     I   ,   22                 -   2     ⁢     h     Q   ,   22                     +   2     ⁢     h     Q   ,   12                 -   2     ⁢     h     I   ,   12                 +   2     ⁢     h     Q   ,   22                 -   2     ⁢     h     I   ,   22               ]     ⁢     (           r     I   ,   1                 r     Q   ,   1                 r     I   ,   2                 r     Q   ,   2             )                 (   9   )               
where h (.)  are channel impulse response coefficients, r (.)  are receive signal coefficients, and subscripts I and Q represent the in-phase and quadrature-phase component values, respectively.
 
   For each clock cycle i, where i=0, . . . , 4095, the update of variables da 1 , db 1 , da 2 , and db 2  is given by the following pseudo-code: 
               100             If   ⁢           ⁢     mod   (       i   +   1     ,   512     )       =   0     ,   then             da   ⁢           ⁢   1     =         -   da     ⁢           ⁢   1     +     4   ⁢     w   10                   101             elseif   ⁢           ⁢     mod   (       i   +   8     ,   512     )       =   0     ,   then             db   ⁢           ⁢   1     =         -   db     ⁢           ⁢   1     +     4   ⁢     w   12                   102             elseif   ⁢           ⁢     mod   (       i   +   64     ,   512     )       =   0     ,   then             da   ⁢           ⁢   2     =       -   da     ⁢           ⁢   2               103             elseif   ⁢           ⁢     mod   (     i   ,   512     )       =   0     ,   then             db   ⁢           ⁢   2     =       db   ⁢           ⁢   2     +     8   ⁢     w   8                   104             elseif   ⁢           ⁢     mod   (       i   +   1     ,   64     )       =   0     ,   then             da   ⁢           ⁢   1     =         -   da     ⁢           ⁢   1     +     4   ⁢         w   9     ⁡     (     -   1     )              i   /   512                          105             elseif   ⁢           ⁢     mod   (       i   +   8     ,   64     )       =   0     ,   then             db   ⁢           ⁢   1     =         -   db     ⁢           ⁢   1     -     4   ⁢         w   11     ⁡     (     -   1     )                i   /   64          +          i   /   512                            106             elseif   ⁢           ⁢     mod   (     i   ,   64     )       =   0     ,   then             da   ⁢           ⁢   2     =       da   ⁢           ⁢   2     +     28   ⁢         w   11     ⁡     (     -   1     )                i   /   64          +          i   /   512                            107             elseif   ⁢           ⁢     mod   (       i   +   1     ,   8     )       =   0     ,   then             da   ⁢           ⁢   1     =       -   da     ⁢           ⁢   1               108             elseif   ⁢           ⁢     mod   (     i   ,   8     )       =   0     ,   then             db   ⁢           ⁢   1     =       db   ⁢           ⁢   1     +     8   ⁢     w   6                   109       else           da   ⁢           ⁢   1     =       da   ⁢           ⁢   1     +     8   ⁢     w   5                     
where the function “mod(b,m)” means b modulo m.
 
   Coeff-calc  301  generates values w1 through w12 based on the input vector r and channel impulse response matrix H. To simplify operation, coefficient calculator  301  then computes difference term coefficients e 0  through e 5 . The difference term coefficients e 0  through e 5  are generated as in equations (10) through (15):
 
e0=8w 6 =8w 5   (10)
 
e1=4w 10 =−4w 11   (11)
 
e2=4w 12 =4w 9   (12)
 
e3=8w 8    (13)
 
 e 4=8 w   7 +28 w   11   (14)
 
 e 5=8 w   7 −28 w   11   (15)
 
   DTG  302  updates the difference da 1 , db 1 , da 2 , and db 2  using difference term coefficients e 0  through e 5  based on a logic implementation for the above pseudo-code.  FIG. 6  shows an exemplary logic implementation for DTG  302  of  FIG. 3 . Latches  601 ( 1 ) through  601 ( 6 ) store difference term coefficients e 0  through e 5 , respectively, from coeff-calc  301  (latched in through enable signals e_en[ 1 ] through e_en[ 5 ]). Mux  602  provides one of difference term coefficients e 0  through e 5  in accordance with signal e_sel. The various signals of  FIG. 6  are generated by a controller (not shown in  FIG. 6 ) implementing the tests of the above pseudo-code. 
   The signal e_inv is a control signal to invert the input difference term coefficient value of inverter  603 , d_inv is a control signal to invert the difference term value of inverter  604 , e_zero is a control signal to mask the input difference term coefficient value in mask logic  605 , and d_zero is a control signal to mask the difference term value in mask logic  606 . The signal d_sel is a signal employed to select, as the output of mux  609 , one of the difference terms da 1 , db 1 , da 2 , and db 2  stored in latches  608 ( 1 ) through  608 ( 4 ), respectively (latched in through enable signals d_en[ 1 ] through d_en[ 3 ]). The select signal d_sel is generated by a controller (not shown in  FIG. 6 ) implementing the following tests: 
   
     
       
         
           
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   Combiner  607  adds the values generated by mask logic  606  and  605 . 
     FIG. 7  shows an exemplary implementation  700  for comparator  305  of  FIG. 3  that generates soft-bit values L 0  through L 11  in accordance with equation (1). For y[i], a distance metric is generated for both the corresponding bit being a 1 or a 0, and the minimum value selected. The minimum search is accomplished by storing the current minimum value and comparing the new candidate&#39;s Euclidean distance term to this stored minimum value. For each cycle i, twelve soft-bit values L 0  through L 11  are generated by corresponding minima blocks  710 ( 0 ) through  710 ( 11 ). 
   For the kth soft-bit b k , minima block  710 ( k ) comprises minimum calculator (min-calc) block  701 ( k ), flip-flops  702 ( k ) and  703 ( k ), multiplexer (mux)  704 ( k ), and combiner  705 ( k ). Min-calc block  701 ( k ) compares the current value of y[i] with the previous minimum value from mux  704 ( k ), and selects the smaller value. The output of min-calc-block  701 ( k ) is stored in flip-flops  702 ( k ) and  703 ( k ). Flip-flop  702 ( k ) stores the minimum value if b k  is a logic 1 and flip-flop  703 ( k ) stores the minimum value if b k  is a logic 0. The soft-bit value L(b k ) is calculated by combiner  705 ( k ) as the difference between the minimum value if b k  is a logic 1 and the minimum value if b k  is a logic 0. 
   A multiple-branch wireless receiver operating in accordance with one or more embodiments of the present invention may provide one or more of the following advantages. MIMO mapping employing the SO MLD method described herein reduces the complexity and power consumption of circuits generating candidate transmit vectors, while maintaining a relatively rapid computation and high probability of detection of the receiver. 
   While certain functions of blocks of the exemplary embodiments of the present invention have been described with respect to processes of circuits, the present invention is not so limited. As would be apparent to one skilled in the art, various functions of circuit elements may also be implemented in the digital domain as processing steps in a software program. Such software may be employed in, for example, a digital signal processor, micro-controller or general purpose computer. 
   The present invention can be embodied in the form of methods and apparatuses for practicing those methods. The present invention can also be embodied in the form of program code embodied in tangible media, such as floppy diskettes, CD-ROMs, hard drives, or any other machine-readable storage medium, wherein, when the program code is loaded into and executed by a machine, such as a computer, the machine becomes an apparatus for practicing the invention. The present invention can also be embodied in the form of program code, for example, whether stored in a storage medium, loaded into and/or executed by a machine, or transmitted over some transmission medium, such as over electrical wiring or cabling, through fiber optics, or via electromagnetic radiation, wherein, when the program code is loaded into and executed by a machine, such as a computer, the machine becomes an apparatus for practicing the invention. When implemented on a general-purpose processor, the program code segments combine with the processor to provide a unique device that operates analogously to specific logic circuits. 
   It will be further understood that various changes in the details, materials, and arrangements of the parts which have been described and illustrated in order to explain the nature of this invention may be made by those skilled in the art without departing from the principle and scope of the invention as expressed in the following claims.