Low‐Complexity Gaussian Detection for MIMO Systems

For single‐carrier transmission over delay‐spread multi‐input multi‐output (MIMO) channels, the computational complexity of the receiver is often considered as a bottleneck with respect to (w.r.t.) practical implementations. Multi‐antenna interference (MAI) together with intersymbol interference (ISI) provides fundamental challenges for efficient and reliable data detection. In this paper, we carry out a systematic study on the interference structure of MIMO‐ISI channels, and sequentially deduce three different Gaussian approximations to simplify the calculation of the global likelihood function. Using factor graphs as a general framework and applying the Gaussian approximation, three low‐complexity iterative detection algorithms are derived, and their performances are compared by means of Monte Carlo simulations. After a careful inspection of their merits and demerits, we propose a graph‐based iterative Gaussian detector (GIGD) for severely delay‐spread MIMO channels. The GIGD is characterized by a strictly linear computational complexity w.r.t. the effective channel memory length, the number of transmit antennas, and the number of receive antennas. When the channel has a sparse ISI structure, the complexity of the GIGD is strictly proportional to the number of nonzero channel taps. Finally, the GIGD provides a near‐optimum performance in terms of the bit error rate (BER) for repetition encoded MIMO systems.