New insights into optimal widely linear array receivers for the demodulation of BPSK, MSK, and GMSK signals corrupted by noncircular interferences-application to SAIC

For nonstationary observations, potentially second-order (SO) noncircular, the SO optimal complex filters are time variant and, under some conditions of noncircularity, widely linear (WL). For more than a decade, there has been an increasing interest in optimal WL filters in radiocommunications contexts involving rectilinear signals such as binary phase-shift keying (BPSK) signals. In particular, it has been pointed out that single antenna interference cancellation (SAIC) may be performed by such filters in the context of BPSK cellular networks. Recently, it has been shown that, by a simple algebraic operation of demodulation on the baseband signal, the minimum shift keying (MSK) and Gaussian MSK (GMSK) modulations can be made to approximately correspond to a BPSK modulation, allowing the application of the SAIC concept to the GSM cellular network at the mobile level, being currently studied for standardization, and offering significant improvements of the network's capacity. Despite the increasing interest in optimal WL filters in rectilinear or quasi-rectilinear contexts, many questions about their behavior and their performance have still arisen. The purpose of this paper is to gain insight into the behavior, properties, and performance of optimal WL array receivers, and thus of the SAIC technology, for the demodulation of BPSK, MSK, and GMSK signals corrupted by noncircular interferences.