Asymptotically optimal low-complexity SC-FDE with noise prediction in data-like improper-complex interference

Abstract

In this paper, single-carrier (SC) block transmission of improper-complex data symbols is considered over a multiple-input multiple-output (MIMO) frequency-selective channel with data-like cochannel interference (CCI). To exploit the cyclostationarity and impropriety of the desired and the interfering signals, an equalizer is designed that oversamples the received signal and then processes the sampled block by using widely-linear (WL) feedforward (FF) and noise-predicting feedback (NP-FB) filters. For the given equalizer structure, the minimum mean-squared error (MMSE)-optimal WL FF and NP-FB filters have high computational complexity due to the augmented correlation matrix of the data-like CCI in the received signal. Motivated by the asymptotic property of the correlation matrix, we approximate in the frequency domain the matrix by a block matrix with diagonal blocks. This leads to the low-complexity WL design of a frequency-domain FF filter and a causally noise-predicting FB filter. It is shown that this MIMO SC frequency-domain equalizer with noise prediction is asymptotically optimal in the sense that the average mean-squared error converges to that of the MMSE-optimal equalizer as the block length tends to infinity. Numerical results show that the proposed equalizer performs well even with a moderate block length.