Second-Order Optimal Array Receivers for Synchronization of BPSK, MSK, and GMSK Signals Corrupted by Noncircular Interferences

The synchronization and/or time acquisition 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. Among the available receivers, only some scarce receivers may also be used in other contexts such as F/TDMA systems. However, these receivers assume implicitly or explicitly circular (or proper) interferences and become suboptimal for noncircular (or improper) interferences. Such interferences are characteristic in particular of radio communication networks using either rectilinear (or monodimensional) modulations such as BPSK modulation or modulation becoming quasirectilinear after a preprocessing such as MSK, GMSK, or OQAM modulations. For this reason, the purpose of this paper is to introduce and to analyze the performance of second-order optimal array receivers for synchronization and/or time acquisition of BPSK, MSK, and GMSK signals corrupted by noncircular interferences. For given performances and in the presence of rectilinear signal and interferences, the proposed receiver allows a reduction of the number of sensors by a factor at least equal to two.