In this paper, belief propagation (BP) multi-input multi-output (MIMO) detection with maximum ratio combining (MRC) and minimum mean square error (MMSE) pre-cancellation is proposed for overload MIMO. The proposed scheme applies MRC before MMSE pre-cancellation. The BP MIMO detection with MMSE pre-cancellation leads to a reduction in diversity gain due to the decreased number of connections between variable nodes and observation nodes in a factor graph. MRC increases the diversity gain and contributes to improve bit error rate (BER) performance. Numerical results obtained through computer simulation show that the BERs of the proposed BP MIMO detection with MRC and MMSE pre-cancellation yields bit error rates (BERs) that are approximately 0.5dB better than those of conventional BP MIMO detection with MMSE pre-cancellation at a BER of 10-3.

In this paper, two-stage BP detection is proposed for overloaded MIMO. The proposal combines BP with the MMSE pre-cancellation algorithm followed by normal BP detection. In overloaded MIMO systems, the loops in a factor graph degrade the demodulation performance of BP detection. MMSE pre-cancellation reduces the number of connections or coefficient values in the factor graph which improves the convergence characteristics of posteriori probabilities. Numerical results obtained through computer simulation show that the BERs of the proposed two-stage BP detection outperforms the conventional BP with MMSE pre-cancellation in a low bit energy range when the MMSE block size is four and the number of MMSE blocks is one. When the pre-cancellation is applied for complexity reduction, the proposed scheme reduces multiplication operations and summation operations by the same factor of 0.7 though the amount of the performance improvement to the conventional scheme is limited.

In this paper, the application of minimum mean square error (MMSE) pre-cancellation prior to belief propagation (BP) is proposed as a detection scheme for overloaded multiple-input multiple-output (MIMO) systems. In overloaded MIMO systems, the loops in the factor graph degrade the demodulation performance of BP. Therefore, the proposed scheme applies MMSE pre-cancellation prior to BP and reduces the number of loops. Furthermore, it is applied to the selected transmit and receive nodes so that the condition number of an inverse matrix in the MMSE weight matrix is minimized to suppress the residual interference and the noise after MMSE pre-cancellation. Numerical results obtained through computer simulation show that the proposed scheme achieves better bit error rate (BER) performance than BP without MMSE pre-cancellation. The proposed scheme improves the BER performance by 2.9-5.6dB at a BER of 5.0×10-3 compared with conventional BP. Numerical results also show that MMSE pre-cancellation reduces the complexity of BP by a factor of 896 in terms of the number of multiplication operations.