Iterative computation of FIR MIMO MMSE-DFE with flexible complexity-performance tradeoff

In recent years, single-carrier (SC) communication for intersymbol interference (ISI) channels has enjoyed a revived interest. Its principal advantage over the multi-carrier scheme is its lower peak-to-average power ratio (PAPR). In this paper, we propose a new fast iterative algorithm to obtain the optimal finite impulse response (FIR) minimum-mean-square-error decision feedback equalizer (MMSE-DFE) for multiple-input multiple-output (MIMO) SC communication systems over ISI channels based on the QR decomposition of an augmented Toeplitz channel matrix. The proposed algorithm is not only computationally efficient but also very frugal in its memory usage. The algorithm applies to MIMO systems with any number of transmitting and receiving antennas, either balanced or unbalanced. The iterative nature of the proposed algorithm enables a flexible choice of $N_f , the length of the feedforward filter (FFF), which leads to a controllable trade-off between complexity and performance. A conversion from time-domain equalization (TDE) to a hybrid DFE (HDFE) can be used to achieve lower complexity when $N _f becomes large. Complexity analysis suggests a significant improvement over the prior art of TDE.