New Insights Into Widely Linear MMSE Receivers for Communication Networks Using Data-Like Rectilinear or Quasi-Rectilinear Signals

Widely linear (WL) processing has been of great interest these last two decades for multi-user (MUI) interference mitigation in radiocommunications networks using rectilinear (R) or quasi-rectilinear (QR) signals in particular. Despite numerous papers on the subject, this topic remains of interest for several current and future applications which use R or QR signals, described hereafter. In this context, using a continuous time approach, it is shown in this paper the sub-optimality of most of the WL MMSE receivers of the literature, which are implemented at the symbol rate after a matched filtering operation to the pulse shaping filter, and the necessity to know the MUI channels, always cumbersome in practice, to implement the optimal WL MMSE receiver. Then, the main challenge addressed in the paper is to propose new WL MMSE receivers able to implement the optimal one without requiring the MUI channels knowledge. For this purpose, two new WL MMSE receivers, a two-input one and a three-input one, are proposed and analyzed in this paper for R and QR signals corrupted by data-like MUI. The two-input and three-input receivers are shown to be quasi-optimal respectively for R signals using Square Root Raised Cosine (SRRC) filters with a low roll-off and for R and QR signals whatever the pulse shaping filter, showing in particular the non-equivalence of R and QR signals for WL MMSE receivers. These two new receivers open new perspectives for the implementation of the optimal WL MMSE receiver in the presence of data-like MUI from the only knowledge of the SOI channel.