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

Abstract

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.

On the effect of channel estimation errors in SC-FDE systems using widely linear iterative equalization

“…with A 1 1 being then the regular non-iterative widely linear MMSE equalizer [9]. The feedback filter is also switched off due to the lack of previous decisions.…”

“…Widely linear (WL) processing [5], [6], [7] was proposed to take advantage of this impropriety, by processing the signal together with its conjugate version to obtain a more precise estimate. Widely linear processing applied to SC-FDE systems has been investigated in [8], [9]; it was seen that WL processing improves the error performance of these systems. In [10] a WL SC-FDE system with iterative equalization was proposed.…”

Widely Linear Equalization for IQ Imbalance and Skew Compensation in Optical Coherent Receivers

“…A comprehensive overview on this topic can be found in reference [9]. Examples of application of complex-valued WL equalization techniques can be found in the following references [10]- [13]. This paper is divided as follows: in section II, a formal description of the connection between linear real-valued and widely linear complex-valued transformations is presented.…”

Widely linear SC-FDE systems for underwater acoustic communication: Experimental results

“…However, since the equalizer is dealing with a signal from an improper constellation (which has non-zero pseudoautocorrelation), it can employ widely linear processing to use all the second-order statistics made available by the received signal and improve its performance. In order to do that, the original version of the received signal in the frequency domain r together with its conjugate version r * is processed by a widely linear equalizer R W L , expressed as [11] …”

“…In order to do that, the received signal must be processed together with its conjugate version. WL processing has been used in SC-FDE systems in [10], [11], [12]. It was seen that widely linear equalizers have better error performance than linear ones, due to their full usage of the available second order statistics, i.e., the autocorrelation together with the pseudoautocorrelation.…”