Soft-output MMSE MIMO detector under different channel estimation models

This study considers the effect of channel estimation error (CEE) on the soft-output bit log-likelihood ratio (LLR) in a multiple-input–multiple-output detection system which the source sends their quadrature amplitude modulation to the detector through Rayleigh fading channels. The new expressions of LLR with maximum-likelihood CE for deterministic channel model and minimum mean square error (MMSE) CE for random channel model are obtained separately for linear MMSE receiver using known pilot-symbol-aided CE. Meanwhile, the optimal power allocation between training and data transmissions for these two different LLR expressions, which attends to get the maximum ratio of signal and interference plus noise ratio, are obtained under the total transmitting power constraints. Numerical results show that the power allocation ratio sets to be ∼0.5 is optimal for two new different LLRs at the same total power and system noise. Moreover, the derived LLR expressions match the simulation result and outperform the conventional system without the consideration of CEE and optimal power allocation. Meanwhile, the system performance is better than the existing research with the consideration of CE.