Low-complexity detection and decoding for receiver in communication system

The detection and decoding with reduced complexity of the receiver in a communication system

This application claims priority to provisional U.S. Patent Application №60 / 738 159, entitled "Iterative detection and decoding SYSTEMS reduced complexity multiple input multiple output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM)", filed November 18 2005, assigned to the present applicant and incorporated herein by reference.

BACKGROUND

TECHNICAL FIELD

The present disclosure relates generally to communication, and more particularly to techniques for performing detection (detection) and decoding at a receiver in a communication system.

BACKGROUND

A communication system with multiple-input multiple-output (MIMO) employs multiple (T) transmit antennas at a transmitter and multiple (R) receive antennas at a receiver for data transmission. MIMO channel, formed by the T transmit antennas and R receive antennas may be decomposed into M spatial channels, where M≤min {T, R}. M spatial channels may be used to transmit data in a manner to achieve higher overall throughput and / or greater reliability.

The transmitter may encode and transmit M data streams in parallel through the T transmit antennas. The receiver obtains R received symbol streams via the R receive antennas, performs MIMO detection for the separation of the M data streams and decodes the detected symbol stream to recover the transmitted data streams. For optimal performance, the receiver would have to evaluate a number of hypotheses for all possible sequences of data bits that can be transmitted, based on all information available at the receiver. Such an exhaustive search is computationally intensive and too difficult for many applications.

Therefore, there is a need in the art for techniques perform detection and decoding with reduced complexity in achieving good performance.

Essence izobrereniya

There are described methods of performing detection and decoding with reduced complexity in achieving good performance. These techniques are embodied in various detection schemes described below, with reduced complexity.

In one design, detection with reduced complexity receiver obtains R received symbol streams are for M data streams transmitted by the transmitter performs receiver spatial processing (or spatial matched filtering) on ​​the received symbols to obtain detected symbols, performs computation of log-likelihood ratios (LLR) independently for each of D "best" data streams and performs the calculation of the logarithmic likelihood ratio (LLR) together MD remaining data streams, where in general M> D≥1, and M> 1. D best data streams may be selected based on the signal-to-noise-and-interference ratio (SNR) and / or other criteria. In another design, detection with reduced complexity receiver performs calculation log likelihood ratio (LLR) independently for each of the D best data streams, performs the calculation of the logarithmic likelihood ratio (LLR) together MD remaining data streams and reduces the number of considered hypotheses for joint calculation log likelihood ratio (LLR) by performing a search of appropriate hypotheses using sphere detection list, Monte Carlo Markov Chain or any other search techniques.

For both detection schemes dimension decreases from M to MD by performing computing log likelihood ratio (LLR) for each flow to D best data streams. Reduction of the dimension can significantly reduce the number of hypotheses considered for the joint calculation of a log likelihood ratio (LLR) for the MD remaining data streams. The number of hypotheses may be further reduced by performing the search of suitable hypotheses. These detection schemes can be used for (1) a single pass of a receiver that performs detection and decoding once, and (2) the iterative receiver that performs iterative detection and decoding. These and other detection schemes are described in detail below.

Below, various aspects and embodiments of the invention are described in more detail.

BRIEF DESCRIPTION OF DRAWINGS

The features and nature of the present invention will become more apparent from the detailed description set forth below when taken in conjunction with the drawings in which all similar reference characters refer to similar elements.

1 shows a block diagram of a transmitter and a receiver.

2 shows a block diagram of a data transmission processor and a spatial transmission processor at the transmitter.

3 shows a block diagram of a receive spatial processor and an RX data processor for one pass receiver.

4 shows a block diagram of a spatial processor and a receive data processor for receiving the iterative receiver.

5 shows a block diagram of a circuit for detecting of reduced dimensionality.

6 shows a device for detection scheme with reduced dimensionality.

7 shows exemplary search trees for the detection sphere list.

8 shows a block diagram of a circuit for detecting a reduced order.

9 shows a device for detection scheme order reduced.

Detailed description

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

The techniques described herein detection and decoding can be used for various communication systems in which multiple data streams are transmitted in parallel through a communication channel. For example, these techniques may be used for a system with multiple-input multiple-output (MIMO) with one frequency subband, for a MIMO system with multiple subbands for a system with multiple access, code-division multiplexing (CDMA), for a system with multiple access, frequency division channels (FDMA), for a system with multiple access with time division (TDMA), and so on. Several subbands may be obtained by using an orthogonal frequency division multiplexing (OFDM), Multiple Access FDMA single carrier (SC-FDMA), or some other modulation techniques. Techniques for OFDM and SC-FDMA divide the entire system bandwidth into multiple (L) orthogonal subbands, which are also called subcarriers, tones, and so on. Each subband is related to a subcarrier that may be independently modulated with data. In general, modulation symbols are sent in the frequency domain with OFDM method and in the time domain using a technique SC-FDMA. For clarity, much of the description below relates to a MIMO system, which uses the OFDM technique.

1 shows a block diagram of an embodiment of a transmitter 110 and a receiver 150 in a MIMO system 100. Transmitter 110 is equipped with multiple (T) antennas, and receiver 150 is equipped with multiple (R) antennas. To transmit the downlink (or forward link), transmitter 110 may be part of a base station, an access point, Node B, and so on, and may contain some or all the functionality of, a base station, an access point, Node B, and so on. Receiver 150 may be part of a mobile station, user terminal, user equipment, etc., and may contain some or all the functionality of a mobile station, user terminal, user equipment, and so on. For transmission on the uplink (or reverse link), transmitter 110 may be part of a mobile station, user terminal, user equipment, and so on, and receiver 150 may be part of a base station, an access point, Node B, and so on.

At transmitter 110, a TX data processor 120 receives traffic data from a data source 112 and processes (e.g., formats, encodes, interleaves, and converts the characters) traffic data to generate data symbols, which are modulation symbols for traffic data. Transmit spatial processor 130 multiplexes the data symbols with pilot symbols, which are modulation symbols for pilot. The control signal is a transmission that is known a priori by both the transmitter and the receiver and may also be called a training signal, the reference signal, a preamble, a pilot signal, and so on. Transmit spatial processor 130 performs transmitter spatial processing, and provides T streams of transmit symbols to T transmitter elements 132a-132t (TMTR). Each transmitter unit 132 processes (e.g., modulates using OFDM techniques, converts to analog, filters, amplifies, and frequency upconverts) its transmit symbol stream and generates a modulated signal. T modulated signals from transmitter elements 132a-132t are transmitted respectively from the antennas 134a-134t.

At receiver 150, R antennas 152a-152r receive the T modulated signals, and each antenna 152 provides a received signal to a respective receiving element 154 (RCVR). Each receiving element 154 processes its received signal in a manner which is complementary to the processing performed by the transmission element 132 to obtain received symbols, provides received symbols for traffic data spatial processor 160, and outputs reception received symbols for pilot processor 194 of the channel. Channel processor 194 estimates the response of the MIMO channel from transmitter 110 to receiver 150 based on the received symbols for pilot (and possibly the received symbols for traffic data) and provides channel estimates spatial processor 160 reception. Receive spatial processor 160 performs detection on the received symbols for traffic data with the channel estimates and provides soft decisions, which may be represented by log-likelihood ratios (LLR), as described below. RX data processor 170 also processes (e.g., deinterleaves and decodes) the soft decisions and outputs decoded data to the data receiver 172. The detection and decoding may be performed with a single pass through the processors 160 and 170 or iteratively between processors 160 and 170.

Receiver 150 may send feedback information to the transmitter 110 to assist in managing the transmission of data to a receiver 150. The feedback information may indicate the particular transmission mode to use for transmission, a particular rate or packet format to be used for each data stream, an acknowledgment ( ACK) and / or negative acknowledgment (NAK) for packets decoded by receiver 150, channel condition information, and so on, or any combination thereof. The feedback information is processed (e.g., encoded, interleaved, and symbol mapping), the processor 180 signaling transmission multiplexed with pilot symbols and spatially processed by the spatial processor 182 transmit and further processed by transmitter elements 154a-154r, to generate R modulated signals, which are transmitted via antennas 152a-152r.

In the transmitter 110, the R modulated signals are received by antennas 134a-134t, processed by a receiving elements 132a-132t, spatially processed by a spatial processor 136 receiving and then processed (e.g., deinterleaves and decodes) the processor 138 signaling reception to recover the feedback information . Controller / processor 140 controls data transmission to the receiver 150 based on the received feedback information. Channel processor 144 may estimate the response of the MIMO channel from receiver 150 to transmitter 110 and may receive the spatial mapping matrix used by the spatial processor 130 transmission.

Controllers / processors 140 and 190 control the operations of the transmitter 110 and receiver 150, respectively. Blocks 142 and memory 192 store data and program codes for transmitter 110 and receiver 150, respectively.

2 shows a block diagram of an embodiment of TX data processor 120 and transmit spatial processor 130 at transmitter 110. For this embodiment, all data streams use a common coding scheme, and for each data stream can use a separate coding rate and a separate modulation scheme. For clarity, the following description assumes that M data streams are sent on M spatial channels.

The processor 120 of the transmission data encoder 220 encodes traffic data in accordance with a coding scheme and generates code bits. The coding scheme may include a convolutional code, a Turbo code, a parity with a low density (LDPC) code of cyclic redundancy check (CRC), code block, and so on, or a combination thereof. The demultiplexer 222 demultiplexes (or parses) the code bits into M streams and provides the M code bit streams M sets of processing units. Each set includes a perforation 224, a channel interleaving unit 226 and symbol mapper 228. Each block 224, if necessary perforation punctures (or deletes) the code bits to achieve a code rate selected for its stream and provides code bits corresponding left block interleaver 226 channel. Each block interleaver 226 interleaves the channel (or reorders) its code bits based on an interleaving scheme and provides interleaved bits to a corresponding symbol mapper 228. The interleaving may be performed separately for each data stream (as shown in Figure 2) or with some or all data streams (not shown in Figure 2).

Each symbol mapper 228 converts its interleaved bits according to the modulation scheme selected for its stream and provides the data symbol stream {sm}. Conversion into m symbols for the flow may be achieved by (1) grouping sets of bits to form Qm values, comprised of Qm bits, Qm≥1, and (2) mapping each value comprised of Qm bits, one of the points in the signal constellation for the selected modulation scheme. Each transformed signal point is a complex value and corresponds to the data symbol. Symbol mapping may be based on conversion using the Gray code conversion or without the use of a Gray code. When converting a Gray code using neighboring points in the signal constellation (in both the horizontal and vertical directions) differ by only one bit position Qm. Convert using Gray code reduces the number of errors for more likely error events, which correspond to the transformation of the received symbol to a location near the correct location when only one coded bit has been detected by mistake. When converting a Gray code without using neighboring points may differ by more than one bit position. Transformation without the use of a Gray code can lead to a greater independence between the coded bits and may improve the performance of the iterative detection and decoding.

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The transmit spatial processor 130 receives the multiplexer 230 M streams of data symbols from symbol mapper 228a-228m and converts the data symbols and pilot symbols to the proper subbands in each symbol period. Matrix multiplier 232 multiplies the data symbols and / or pilot symbols for each subband Z spatial mapping matrix and provides transmit symbols for that subband. Different spatial mapping matrix may be used for different transmission modes and different spatial mapping matrix may be used for different subbands for some transmission modes, as described below.

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2 shows an embodiment, wherein for the M data streams can be used and a common coding scheme is selected code rates and modulation schemes. Other code rates can be achieved for the M data streams using different perforation patterns for these streams. In another embodiment, for all data streams using a common coding scheme, and the total coding rate for the M data streams are selected modulation scheme used. In another embodiment for all M data streams using a common coding scheme, common coding rate and a common modulation scheme. In yet another embodiment, each data stream is processed based on coding and modulation scheme selected for that data stream. In general, for the M data streams can be used by the same or different encoding scheme, the same or different code rate and the same or different modulation schemes. In addition, the same or different encoding scheme, the same or different code rate and the same or different modulation schemes may be used across the subbands.

Transmitter 110 typically encodes each packet separately. In an embodiment, the M data streams are coded together, so that one packet can be sent across multiple (e.g., all M) spatial channels. In another embodiment, the M data streams is independently encoded, so that each packet has been sent on one spatial channel. In yet another embodiment, some data streams are jointly encoded, while other data streams are coded independently.

For clarity, the following description assumes that spatial channel on each send one data stream. The terms "data stream" and "surround channel", thus, are interchangeable for much of the description below. The number of data streams may be configurable and may be selected based on channel conditions and / or other factors. For clarity, the following description assumes that M spatial channels of the M data streams sent.

3 shows a block diagram of spatial processor 160a receive processor 170a and RX data for one pass of the receiver. Processors 160a and 170a are an embodiment of the processors 160 and 170, respectively, at receiver 150 in Figure 1. For this embodiment, the processors 160a and 170a perform detection and decoding with a single pass through each of the processors 160a and 170a.

The spatial processor 160a receive the matrix computing unit 308, a spatial filter receives the channel estimates from channel processor 194 and outputs a spatial filter matrix based on the channel estimation and spatial mapping matrices used by the transmitter 110 as described below. MIMO detector 310 obtains received symbols from the R receive elements 154a-154r, the channel estimates from channel processor 194 and the spatial filter matrix on the element 308. The detector 310 performs MIMO detection, as described below, and provides soft decisions for K K bit codes M data symbols sent on each subband in each symbol period used for data transmission. It represents a soft decision value, consisting of several bits, which are estimates of the transmitted coded bits. Soft decisions can be represented as a logarithmic likelihood ratio (LLR) and may be called the external log likelihood ratio (LLR). If M data symbols sent on one subband in one symbol period, then K may be computed as where Qm - the number of code bits used to form a data symbol for stream m. If for all M data streams using the same modulation scheme, then K may be calculated as K = M ∙ Q, where Q - the number of code bits for each data symbol.

<IMG>

The RX data processor 170a blocks 316a-316m taking channel deinterleaving external log likelihood ratios (LLR) for the M data streams. Each block deinterleaver 316 deinterleaves the channel external log-likelihood ratios (LLR) for their flow method is complementary to the interleaving performed channel interleaving unit 226 for that stream. The multiplexer 318 multiplexes (maps or serialized) logarithmic likelihood ratio (LLR) with deinterleaved by units 316a-316m channel deinterleaving. The decoder 320 decodes the log likelihood ratios (LLR) to deinterleaving and outputs the decoded data. The following describes in detail the detection and decoding.

4 shows a block diagram of spatial processor 160b receive processor 170b and RX data for the iterative receiver. The processors 160b and 170b are another embodiment of the processors 160 and 170 respectively at the receiver 150. For this embodiment, the processors 160b and 170b perform iterative detection and decoding.

The spatial processor 160b receiving unit 408 outputs the spatial filter matrix based on the channel estimation and spatial mapping matrices used by the transmitter 110. The MIMO detector 410 obtains received symbols from the R receive elements 154a-154r, the channel estimates from channel processor 194, spatial filter matrix from block 408 and a priori log likelihood ratios (LLR) from the decoder 420. The a priori LLRs are denoted as La (bk) and represent the a priori information from the decoder 420. The MIMO detector 410 performs detection as described below, and provides K log-likelihood ratios (LLR) detector K code bits to M data symbols sent on each subband in each symbol period used for data transmission. Logarithmic Likelihood Ratio (LLR) detector is denoted as L (bk). K adders 412a-412k subtracting the a priori log likelihood ratios (LLR) of the log-likelihood ratios (LLR) detector and output the external log likelihood ratios (LLR), which is designated as Le (bk). External logarithmic likelihood ratio (LLR) are external or new information from the MIMO detector 410 to decoder 420.

<img file="00000005.tif" he="5" wi="81" img-format="tif" img-content="undefined" />

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Spatial processor 160b and receiving the reception data processor 170b may perform any number of iterations. In an embodiment, the processors 160b and 170b operate a predetermined number of iterations (e.g., 4, 6, 8 or more iterations). In another embodiment, the processors 160b and 170b perform one iteration, then checks whether the packet is decoded and / or sufficient high reliability decoder and perform another iteration if the packet is decoded incorrectly, or if the decoder reliability index is low. Error detection may be achieved using cyclic redundancy check (CRC) and / or any other code for error detection. The processors 160b and 170b can thus perform a fixed number or a variable number of iterations, iterations until a maximum number of iterations. Iterative detection and decoding is described in detail.

The received symbols at receiver 150 may be expressed as:

&lt;IMG&gt;

for l = 1, ..., L,

Equation (1)

where - the vector dimension MCH1 with M data symbols sent on subband l;

&lt;IMG&gt;

- Spatial mapping matrix dimension TCHM used by transmitter 110 for subband l;

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- MIMO channel response matrix for subband RCHT dimension l;

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- The actual MIMO channel response matrix of dimension RCHM for subband l;

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- RCH1 dimension vector with R received symbols for subband l;

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- The vector dimension RCH1 noise for subband l.

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It can be assumed that the noise is additive white Gaussian noise (AWGN) vector with zero mean and covariance matrix where - the variance of the noise, and I - identity matrix. The actual MIMO channel response includes the actual MIMO channel response matrix and the spatial mapping used by the transmitter 110.

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<img file="00000018.tif" he="12" wi="44" img-format="tif" img-content="undefined" />

In an embodiment, the detector MIMO (e.g., detector 310 or 410 MIMO) performs detection separately for each subband based on the received symbols and channel estimates for that subband and, if available, a priori log-likelihood ratios (LLR) for the data symbols sent in that subband. In another embodiment, the MIMO detector performs detection jointly for multiple subbands. A decoder (e.g., decoder 320, or 420) performs decoding on the sequence of log-likelihood ratios (LLR) for a packet that can be transmitted in one or multiple subbands. For clarity in the following description l subband index will be omitted.

The package can be divided into several blocks and each block contains K code bits. K code bits for each block may be mapped to M data symbols as follows:

Equation (2)

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wherein - the vector with M data symbols;

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- Vector K code bits for one block;

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<img file="00000021.tif" he="11" wi="41" img-format="tif" img-content="undefined" />

bm, q, for m = 1, ..., M and q = 1, ..., Qm - with bit sequence number q bm vector;

bk, for k = 1, ..., K - code bit with the serial number k in the vector b.

There is a one-to-one mapping between a given bit vector b, and the corresponding data vector s. In general, the value of Q may be the same or different for the M data symbols sent on a given subband, and the value of K may be the same or different for the L subbands.

The optimal receiver for a transmission scheme, which is shown in equation (1) is a receiver with the sequence of the maximum likelihood (ML), which performs detection and decoding for the entire package together. This optimum receiver would joint decisions on all the bits in the data packet using the knowledge of the correlation coding scheme introduced by blocks subbands and OFDM symbols for the packet. The optimum receiver would have carried out an exhaustive search of all possible sequences of bits of data that can be transferred to the package to find the sequence that most likely was transmitted. This was the optimum receiver would be too complicated.

<img file="00000024.tif" he="23" wi="101" img-format="tif" img-content="undefined" />

In an embodiment, the detector is a MIMO detector with maximum a posteriori probability algorithm (MAP), which minimizes the probability of error for each code bit and soft decision outputs for each code bit. Detector with MAP algorithm produces soft solutions in the form of a posteriori probability (APP), which are often expressed as a log-likelihood ratio (LLR). Logarithmic ratio L (bk) likelihood (LLR) detector for the code bit bk may be expressed as:

&lt;IMG&gt;

for k = 1, ..., K,

Equation (3)

wherein - the probability that the code bit bk equals 1 for a given received vector y; and

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- The probability that the code bit bk is -1 for a given received vector y.

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Log likelihood ratio (LLR) detector may be divided into two parts as follows:

L (bk) = La (bk) + Le (bk),

Equation (4)

where La (bk) - a priori log likelihood ratio (LLR) for the coded bits bk, issued decoder or possibly other sources detector MIMO, and Le (bk) - external log likelihood ratio (LLR) for the coded bits bk, issued detector MIMO decoder. The a priori log likelihood ratio (LLR) for the coded bits bk may be expressed as:

&lt;IMG&gt;

Equation (5)

wherein - the probability that the code bit bk equals 1;

&lt;IMG&gt;

- The probability that the code bit bk equals -1.

<img file="00000048.tif" he="6" wi="41" img-format="tif" img-content="undefined" />

MAP algorithm detector may be a detector with algorithm log-MAP, algorithm detector with max-log-MAP algorithm or MAP detector of any other type. The external log likelihood ratio (LLR) detector with algorithm log-MAP, which is called the log likelihood ratio (LLR) algorithm log-MAP, can be calculated as:

&lt;IMG&gt;

Equation (6)

where - vectors which theoretically have been transferred;

&lt;IMG&gt;

&lt;IMG&gt;

- A vector with all code bits in the exception vector code bit bk,

&lt;IMG&gt;

&lt;IMG&gt;

- A vector with a priori log likelihood ratio (LLR) for all code bits in the vector;

&lt;IMG&gt;

&lt;IMG&gt;

is a function of the value of Euclidean distance;

&lt;IMG&gt;

"T" denotes the transpose.

Equation (6) shows one statement for the external log likelihood ratio (LLR) detector with algorithm log-MAP. The external log likelihood ratio (LLR) can also be expressed in other species. The receiver generally sends a matrix that is an estimate of the channel response matrix real MIMO, and uses the matrix in calculating the log likelihood ratio (LLR). For ease of description, it is assumed that no channel estimation error, ie.

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&lt;IMG&gt;

&lt;IMG&gt;

&lt;IMG&gt;

Equation (6) is evaluated for each code bit in the transmitted bit vector. For each code bit bk considered hypothetical 2K bit vectors for all possible sequences of code bits {b1 ​​... bk} (or all possible combinations of values ​​of code bits) that may be transmitted for the vector 2K-1 have hypothesized bit vectors bk = + 1 and other 2K-1 have hypothesized bit vectors bk = -1. Each hypothetical bit vector has a corresponding hypothetical data vector. The expression inside amount is calculated for each hypothesized bit vector to obtain a result for that bit vector. Results for 2K-1 hypothesized bit vectors bk = + 1 are summed to obtain the total result for the numerator. Results for 2K-1 hypothesized bit vectors bk = -1 are added together to get the full result for the denominator. Log likelihood ratio (LLR) with a logarithmic maximum a posteriori probability (log-MAP) for the coded bits bk is equal to the natural logarithm (ln) of the total result for the numerator divided by the total result for the denominator.

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<img file="00000081.tif" he="14" wi="38" img-format="tif" img-content="undefined" />

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<img file="00000083.tif" he="13" wi="115" img-format="jpg" img-content="undefined" /><img file="00000084.tif" he="11" wi="69" img-format="jpg" img-content="undefined" /><img file="00000085.tif" he="11" wi="58" img-format="jpg" img-content="undefined" />

Approximation algorithm for max-log-MAP in the equation (7) replaces the summation in equation (6) for the operation max {}. Only a small degradation in performance is usually obtained from the use of the approximation algorithm for the max-log-MAP. Also other approximations may be used a log likelihood ratio (LLR) algorithm log-MAP.

Detector with algorithm log-MAP in equation (6) and the detector with the algorithm max-log-MAP in equation (7) perform joint decisions on the received symbol vector and calculate the external log likelihood ratios (LLR) for the code bits within those accepted symbols. To calculate the external log likelihood ratios (LLR) optimally, each detector MAP algorithm performs an exhaustive search of all possible combinations of data symbols which can be transmitted to the vector. This exhaustive search is computationally intensive and can be extremely difficult for many applications. The computational complexity of a log likelihood ratio (LLR) is the exponential of the number of bits (K) in the transmitted bit vector and detector algorithm log-MAP, and detector algorithm max-log-MAP. In particular, both detector MAP algorithm considering 2K hypotheses for each code bit bk. The following describes the different detection scheme with reduced complexity.

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To reduce computational complexity, the receiver may perform receiver spatial processing (or spatial matched filtering) on ​​the received symbols to obtain detected symbols and then may perform the calculation of the logarithmic likelihood ratio (LLR) independently for each detected symbol. The detected symbols are estimates of the data symbols transmitted by the transmitter. The receiver may perform receiver spatial processing based on the handling procedure zero-forcing (ZF), minimum mean square error method (MMSE), maximum ratio combining method (MRC) or some other technique. The spatial filter matrix may be derived based on techniques ZF, MMSE or MRC follows:

<img file="00000094.tif" he="12" wi="41" img-format="tif" img-content="undefined" />

&lt;IMG&gt;

Equation (9)

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<img file="00000098.tif" he="20" wi="73" img-format="tif" img-content="undefined" />

&lt;IMG&gt;

Where

<img file="00000099.tif" he="7" wi="44" img-format="tif" img-content="undefined" />

&lt;IMG&gt;

and - the spatial filter matrix for MCHR dimension methods ZF, MMSE and MRC, respectively;

<img file="00000100.tif" he="33" wi="110" img-format="tif" img-content="undefined" />

&lt;IMG&gt;

<img file="00000101.tif" he="10" wi="26" img-format="tif" img-content="undefined" />

Receiver spatial processing may be expressed as:

Equation (11)

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where the matrix can be equal to, or;

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&lt;IMG&gt;

&lt;IMG&gt;

&lt;IMG&gt;

- The vector dimension MCH1 detected symbols and evaluation of vector data.

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<img file="00000118.tif" he="19" wi="121" img-format="tif" img-content="undefined" />

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Equation (12)

&lt;IMG&gt;

where - the element with serial number m of the vector;

&lt;IMG&gt;

&lt;IMG&gt;

- Hypothetical symbol data transmitted symbol sm data;

&lt;IMG&gt;

- A vector with all code bits for the data symbol sm exception code bit bm, q;

&lt;IMG&gt;

- A vector with a priori log likelihood ratio (LLR) for all code bits in the vector;

&lt;IMG&gt;

&lt;IMG&gt;

- External log likelihood ratio (LLR) for the code bits bm, q.

&lt;IMG&gt;

Equation (12) is estimated for each code bit in each transmitted bit vector for m = 1, ..., M. Each code bit bm, q vector addresses in the bit 2Qm hypothesized bit vectors for all possible sequences of code bits that can be transmitted for the vector. Each hypothetical bit vector has a corresponding hypothetical data symbol. Expression in operation max {} is calculated for each hypothesized bit vector to produce a result for this vector. Results for hypothesized bit vectors bm, q = + 1 used in the first operation max {}. Results for hypothesized bit vectors bm, q = -1 used in the second operation max {}.

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<img file="00000133.tif" he="7" wi="43" img-format="tif" img-content="undefined" />

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The complexity of receiver spatial processing by a linear number of data streams (M) and does not depend on the size of the signal constellation. Calculation external log-likelihood ratios (LLR) for each stream reduces the number of hypotheses to evaluate with 2M ∙ Q to M ∙ 2Q, suggesting that for all M data streams using the same modulation scheme. Calculation of log likelihood ratio (LLR) for each stream can significantly reduce the computational complexity, but can lead to degraded performance at higher than desired.

In one aspect, the receiver performs receiver spatial processing on the received symbols to obtain detected symbols, performs computation of a log likelihood ratio (LLR) independently for each of the D best detected symbols and performs the calculation of the logarithmic likelihood ratio (LLR) together MD remaining detected symbols, where M &gt; D≥1. D best detected symbols may be for D data streams with the highest signal to noise ratio (SNR), to D data streams with the smallest spread of the signal to noise ratio (SNR), to D data streams with the most robust coding and so on. This scheme is called a detection circuit detecting a reduced dimensionality and can be used for a single pass of the receiver shown in Figure 3, and an iterative receiver shown in Figure 4.

The receiver may perform receiver spatial processing on the R received symbols to obtain D best detected symbols (instead of all M detected symbol). Reduced spatial filter matrix DCHR dimension can be obtained based on the reduced channel response matrix. The matrix has a dimension of R × D and D includes columns corresponding D best detected symbols. The spatial processing reception for D best detected symbols is less complex computationally.

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