Widely linear (WL) processing has raised up a great interest since nearly three decades for multiuser (MUI) interference mitigation in radiocommunications networks using rectilinear (R) or quasi-rectilinear (QR) signals in particular. This topic remains of interest for many current applications using R or QR signals such as anti-collisions in Radio Frequency Identification (RFID) or satellite-AIS systems, grant free massive access in NB-IOT networks, multipaths mitigation in the Control and Non Payload Communications (CNPC) link of Unmanned Aerial Vehicle (UAV) or FBMC-OQAM networks. Most of WL receivers currently available for MUI mitigation are WL MMSE receivers implemented at the symbol rate after a matched filtering operation to the pulse shaping filter. These WL receivers have thus a particular structure constraint which prevents them from exploiting the cyclostationarity of the data-like MUI and which makes them suboptimal within the WL MMSE receivers. For this reason, two alternative WL MMSE receivers, without any structure constraint and exploiting or not the cyclostationarity of the MUI have been computed and analyzed in the companion paper [2]. The first one is the optimal one, which requires the a priori knowledge or estimation of the MUI channels, which may be cumbersome in practice. The second one does not require the a priori knowledge of the MUI channels, is quasi-optimal for R signals and small bandwidth but remains suboptimal otherwise. In this context, to improve the performance of the latter receiver while keeping its advantages, the purpose of this paper is to propose, for both R and QR signals, a new WL MMSE receiver, called three-input WL FRESH MMSE receiver, and to analyze, both analytically and by computer simulations, its performance. This new receiver is shown to be quasi-optimal in most situations and open new perspective for implementation optimization of WL MMSE receivers and for the implementation of the optimal receiver from the only knowledge of the SOI channel.