Exact SER and BER Analysis on Jointly Optimal Maximum Likelihood Detection of Two QPSK Signals With Phase Offset

Abstract

Analysis on the exact error rate of jointly optimal (JO) maximum likelihood (ML) multiuser detection is limited in the existing literature owing to its high computational complexity. In this paper, the JO ML detection of two quadrature phase-shift keying (QPSK) signals with an arbitrary relative phase offset is investigated. Exact, analytical symbol error rate (SER) and bit error rate (BER) formulas are derived for two users with no less than 3 dB power difference between them. Closed-form union bounds on the user SER and BER with an arbitrary phase offset and an arbitrary user power ratio are also given as a simpler approach to acquire the asymptotic error rate performance. Furthermore, insights on the potentials and properties of the JO ML detector regarding its error rate behaviors for each user are revealed through comparisons with the successive interference cancellation receiver. The accuracies of the obtained formulas are demonstrated through simulation. The results show the error rates for the two-user QPSK case no longer follow the classic knowledge on the error rate behaviors in the single signal detection. In addition, the performance and dB penalty employing different modulation types are also compared and discussed.