The expected complexity of sphere decoding algorithm in spatial correlated MIMO channels

The sphere decoding (SD) algorithm is widely considered to be an efficient approach to obtain maximum likelihood (ML) performance in MIMO detection. At present, almost all of the research about the SD algorithm is based on the assumption of independent and identically distributed channel coefficients. However, the channel coefficients are often correlated in practice, which cause the complexity of the SD algorithm to vary. In this paper, we give a theoretical analysis of the complexity of Fincke and Pohst´s (FP) SD algorithm in spatial correlated MIMO channels; the exact expression of the expected complexity is derived. We present simulation results obtained from this expression to show the effect of spatial correlation on the complexity of the algorithm, for different signal-to-noise ratios (SNR) and level of spatial correlations.