Asymptotically optimal low-complexity SC-FDE in data-like co-channel interference

In this paper, the design of a low-complexity linear equalizer is considered for single-carrier (SC) block transmission in the presence of inter-symbol interference (ISI) and data-like co-channel interference (CCI). Unlike the linear minimum mean-squared error (LMMSE) frequency-domain equalizer (FDE) designed to suppress ISI only, the LMMSE FDE suffers from high computational complexity due to the CCI component in the signal correlation matrix. Motivated by the fact that the double Fourier transform of the autocorrelation function of a wide-sense cyclostationary process consists of impulse fences with equal spacing, a low-complexity FDE is proposed that approximates the frequency-domain correlation matrix of the CCI plus noise by a block matrix with diagonal blocks. It is shown that the proposed FDE is asymptotically optimal in the sense that the average mean-squared error (MSE) converges to that of the LMMSE FDE as the block length tends to infinity. It is also shown that the proposed FDE is more numerically stable than the LMMSE FDE when the receive filter is matched to the transmit filter and its output is over-sampled to better capture the cyclostationarity of the CCI. Discussions and numerical results include SC block transmission systems with unique word instead of cyclic prefix, and systems with multiple receive antennas.