Complexity Reduction Schemes for Gibbs Sampling MIMO Detection with Maximum Ratio Combining

In this paper, complexity reduction schemes for Gibbs sampling multi-input multi-output (MIMO) detection with maximum ratio combining are proposed. In a conventional Gibbs sampling MIMO detection algorithm, the Gibbs sampling is directly applied to a received signal. Thus, a squared Euclid distance between the received signal vector and a candidate symbol vector is calculated as a metric and it requires (2 × No. of received antennas) multiplication operations. On the other hand, in a proposed algorithm, each candidate symbol is updated with a metric calculated by two multiplication operations. However, after each iteration, another metric is also need to be calculated to select the best candidate symbol vector. To reduce the number of multiplication operations, a summation and subtraction metric (SSM) is applied. Furthermore, as an initial transmitsymbol vector, a zero vector is applied in the conventional and proposed Gibbs sampling MIMO detection algorithms since the receiver can avoid to calculate the pseudo inverse of a channel matrix. The bit error rate performance and the complexities of these schemes are compared with that of QR decomposition with M-algorithm (QRM)-maximum likelihood detection (MLD). Numerical results obtained through computer simulation show that the proposed Gibbs sampling MIMO detection algorithm is less complex when the numbers of transmit signals and received antennas are more than 32x32.