A Low-Complexity Widely-Linear MMSE Equalizer for DFT-Spread OFDM With Frequency-Domain Spectrum Shaping

In this paper, we consider the minimum mean-squared error (MMSE) equalization for uplink multi-user multiple-input multiple-output communications. In particular, the transmitters adopt discrete-Fourier transform (DFT)-spread orthogonal frequency-division multiplexing (OFDM) to send
$\pi /2$
-PAM or square-QAM symbols, possibly with frequency-domain spectrum shaping (FDSS). It is well known that, in such cases with improper-complex symbols, widely-linear (WL) equalizers can improve performance over linear equalizers, but at the cost of sometimes drastically increased computational complexity. To overcome this, we exploit the spectral correlation in the received signal induced by the impropriety from
$\pi /2$
-PAM symbols and the cyclostationarity from the FDSS. The key differences from conventional high-complexity structures are to represent all the symbols as equivalent PAM symbols that are subsequently
$\pi /2$
-modulated, and to factor the effective channel into the
$\pi /2$
-modulator, the DFT-spreader, and a partial channel defined in the frequency domain. These representation and factoring enable us to design a low-complexity structure of the WL-MMSE equalizer that performs the signal processing mostly in the frequency domain and involves only sparse and structured matrices. Numerical results show that the proposed structure achieves significantly lower complexity than the conventional structures and that it greatly outperforms the linear MMSE equalizer with a similar complexity.