An embodiment of the invention relates notably to a method for transmitting a sequence of symbols through at least a channel in a wireless communication system, the sequence of symbols comprising at least a first, a second, a third and a fourth symbols, the value of each symbol belonging to at least a signal constellation, the method comprising at least the steps of:                forming a coding matrix with said sequence of symbols, each component of the coding matrix being a linear combination of two symbols among the first, the second, the third and the fourth symbols,        transmitting a first and a second components of a first column of the coding matrix through respectively a first and a second transmit antennas at a first time slot,        transmitting a first and a second components of a second column of the coding matrix through respectively the first and the second transmit antennas at a second time slot.        
Multiple antenna techniques commonly known as MIMO (Multi-Input Multi-Output) have become very popular for wireless applications. Such techniques have been included for example in the technical specifications recently developed for wireless local area networks and metropolitan area networks. MIMO techniques may be used to provide spatial diversity and enhance robustness to signal fading, or to provide spatial multiplexing and increase throughput on the wireless channel, or to provide both.
In MIMO systems, transmitter Tx, as well as receiver Rx are equipped with multiple antennas. In the MIMO system illustrated in FIG. 1, the transmitter Tx and the receiver Rx are both equipped, for example, with respectively a first and a second transmit antennas, Tx1 and Tx2, and a first and a second receive antennas, Rx1 and Rx2.
Among the numerous solutions proposed in the literature for MIMO profiles for the downlink channel (from a base station to mobile users), the IEEE 802.16-2005 specifications (IEEE being the acronym for Institute of Electrical and Electronics Engineer) proposes a full-rate and full-diversity space-time code (STC) of dimension 2×2 described by a matrix C defined as:
      C    =                  1                              1            +                          r              2                                          ⁡              [                                                                              s                  1                                +                                  j                  ⁢                                                                          ⁢                                      rs                    4                                                                                                                        rs                  2                                +                                  s                  3                                                                                                                          s                  2                                -                                  rs                  3                                                                                                      j                  ⁢                                                                          ⁢                                      rs                    1                                                  +                                  s                  4                                                                    ]              ,          ⁢            where      ⁢                          ⁢      r        =                            -          1                +                  5                    2        ,s1, s2, s3, s4 are respectively a first, a second, a third and a fourth symbols.
At the transmitter side, using the space-time code described by the matrix C in the MIMO system for transmitting an input signal S formed with a plurality of symbols mapped in at least a signal constellation (for example 16-QAM signal constellation or 64-QAM signal constellation, QAM being the acronym for Quadrature Amplitude Modulation), consists in:                grouping the symbols four by four to form quadruplets of symbols to be transmitted,        selecting a quadruplet of symbol (s1,s2,s3,s4) to be transmitted, and forming the matrix C with this quadruplet of symbols, and        transmitting the first and the second column of said matrix C respectively at a first and a second time slots (corresponding to a given symbol period) through the first and the second transmit antennas Tx1, Tx2.        
At the receiver side, to estimate the incoming signal, the receiver evaluates the maximum likelihood function for all quadruplets of symbols (s1,s2,s3,s4) of the signal constellation and selects the one which minimizes this function. The maximum likelihood function used to evaluate the quadruplets of symbols is actually the squared Euclidean distance between the received noisy signal and the noiseless signal corresponding to that quadruplet.
Even if the matrix C is a space-time code which leads to a spatial diversity of order four, a potential problem of this space-time code is its inherent complexity. Indeed, for a signal constellation with M points, M being a positive integer, the optimum receiver hence involves the computation of M4 Euclidean distances and selects the quadruplet of symbols minimizing this distance. The receiver complexity is therefore proportional to 164=65536 for a 16-QAM signal constellation, and to 644=16777216 for a 64-QAM signal constellation. This may be prohibitive in practical applications, and, therefore, one may need to resort to suboptimum receivers which degrade performance.