Max-log receiver for multiple-input multiple-output (MIMO) systems

1. A method comprising the steps of:

i) listing out all possibilities for a first symbol of a two stream signal;

ii) determining a second symbol of the two stream signal for each said first symbol listed out,

iii) evaluating a metric for each said first symbol and second symbol pair,

iv) listing out all possibilities for second symbol,

v) determining a first symbol for each choice of said second symbol listed out,

vi) evaluating a metric for each said second symbol and first symbol pair,

vii) determining an exact max-log likelihood ratio for each bit using the metrics, and

viii) decoding codeword(s) in the two stream signal using the determined exact max-log likelihood ratios for all bits.

2. The method of claim 1 , wherein said first symbol is designated symbol- 1 and said second symbol is designated symbol- 2 .

3. The method of claim 2 , wherein maximum max-log likelihood ratios for 2 Log(M) bits in said two stream signal is obtained with O(M) complexity when symbol- 1 and symbol- 2 belong to a constellation of cardinality M, said complexity related to evaluating the metrics of 2M hypotheses O(M) denoting that the said complexity scales linearly in M.

4. The method of claim 3 , wherein further reduction in said complexity can be achieved by avoiding the redundant computation in the two modified QR decompositions_H=∥h 2 ∥ 2 UL,H=∥h 1 ∥ 2 VR, where the matrix H represents the channel with h 1 and h 2 denoting its first and second columns, respectively, U and V are scaled semi-unitary matrices and L, R are square lower and upper triangular matrices, respectively.

5. The method of claim 2 wherein the metric for x 1,j which is the j th possibility for symbol- 1 is defined by Q(x i,j )=|z 1 −L 11 x 1,j | 2 +min x 2 |z 2 −L 21 x 1,j −x 2 | 2 wherein z 1 and z 2 are obtained by linearly transforming the vector of received observations, L 11 and L 21 are elements of a lower triangular matrix obtained using a modified QR decomposition; defining q 1j =z 2 −L 21 x 1,j and expressing Q(x 1,j ) as Q(x 1,j )=|z 1 −L 11 x 1,j | 2 +min x 2 R |q 1j R −x 2 R | 2 +min x 2 1 |q 1j I −x 2 I | 2 , with q 1j R ,q 1j I denoting the real and imaginary parts of q 1j , respectively, and both x 2 R ,x 2 I belonging to a common real-valued constellation, the two minimizations for computing Q(x 1,j ) being done in parallel using simple slicing (rounding) operations each with a complexity independent of the cardinality of the said real-valued constellation.

6. The method of claim 1 , wherein said metric for x 2,j which is the j th possibility for symbol- 2 is based on Q(x 2,j )=|w 2 −R 22 x 2,j | 2 +min x 1 |W 1 −R 12 x 2,j −x 1 | 2 ; wherein w 1 and w 2 are obtained by linearly transforming the vector of received observations, R 12 and R 22 are elements of an upper triangular matrix obtained using a modified QR decomposition; defining q 2j =w 1 −R 12 x 2,j and expressing Q(x 2,j ) as Q(x 2,j )=|w 2 −R 22 x 2,j | 2 +min x 1 R |q 2j R −x 1 R |+min x 1 I |q 2j I −x 1 I | 2 , with q 2j R ,q 2j I denoting the real and imaginary parts of q 2j , respectively and both x 1 R , x 1 I belonging to a real-valued constellation, the two minimizations for computing Q(x 2,j ) being done in parallel using simple slicing operations, thereby efficiently determining all {Q(x 2,j )} j=1 M .

7. A method comprising the steps of:

i) using the method in claim 1 to decode the two codewords associated with the two streams

ii) conducting a redundancy check on the two decoded codewords

iii) In case the cyclic redundancy check of only one codeword is true, re-encoding, modulating and subtracting that codeword from the received signal to obtain a single stream signal,

iv) listing out all possibilities for the remaining symbol in the single stream signal,

v) evaluating a metric for each possibility of the remaining symbol,

vi) determining the max-log likelihood ratios for all bits using the metrics,

vii) decoding the remaining codeword in the single stream signal using the determined max-log likelihood ratios for all bits.