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Single-carrier systems using frequency-domain equalization (SC-FDE) systems were proposed to overcome the low robustness to carrier frequency offset (CFO) and high peak-to-average-power ratio (PAPR) inherent to regular orthogonal frequency-division multiplexing (OFDM) systems. Usually, linear minimum mean square error (MMSE) equalization is used to compensate the channel effect, since maximum likelihood (ML) detection is computationally impractical. However, if the transmitted signal comes from an improper constellation, widely linear processing can be used to take advantage of all the available second-order statistics from this transmitted signal, obtaining this way a performance gain when compared to the strictly linear case. In this paper, a SC-FDE system employing widely linear MMSE equalization is proposed in its regular and decision-feedback (DFE) versions. A SC-FDE system employing widely linear MMSE Tomlinson-Harashima precoding (THP) and equalization is also proposed. With Tomlinson-Harashima precoding, the error propagation problem observed in systems using a decision-feedback equalizer vanishes, because the feedback processing is done at the transmitter. Simulation results show that together with the error performance gain, these systems have lower sensibility to the feedback filter length in systems using decision-feedback equalizers. In Tomlinson-Harashima precoded systems, the performance gain is observed even with channel estimation/channel state information errors.

Widely linear MMSE precoding and equalization techniques for SC-FDE systems