Optimal Array Receiver for Synchronization of a Bpsk Signal Corrupted by Non Circular Interferences

The synchronization problem in the presence of interferences has been strongly studied these last two decades, mainly to mitigate the multiple access interferences from other users in DS/CDMA systems. Most of the available receivers are very specific of the CDMA context and only some scarce receivers may also be used in other contexts such as F/TDMA systems. However, these receivers assume implicitly or explicitly circular interferences and become sub-optimal for non circular (or improper) interferences, characteristic in particular of radiocommunications networks using rectilinear (or monodimensional) modulations such as BPSK modulation. For this reason, the purpose of this paper is to introduce and to analyse the performance of the optimal array receiver for synchronization of BPSK signals corrupted by non circular interferences. This receiver implements an optimal, in a least square sense, widely linear filtering of the data, mainly considered up to now for demodulation purposes of BPSK signals, followed by a correlation operation. Extensions to MSK and GMSK signals are presented elsewhere