On the likelihood-based approach to modulation classification

In this paper, likelihood-based algorithms are explored for linear digital modulation classification. Hybrid likelihood ratio test (HLRT)- and quasi HLRT (QHLRT)- based algorithms are examined, with signal amplitude, phase, and noise power as unknown parameters. The algorithm complexity is first investigated, and findings show that the HLRT suffers from very high complexity, whereas the QHLRT provides a reasonable solution. An upper bound on the performance of QHLRT-based algorithms, which employ unbiased and normally distributed non-data aided estimates of the unknown parameters, is proposed. This is referred to as the QHLRT-Upper Bound (QHLRT-UB). Classification of binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) signals is presented as a case study. The Cramer-Rao Lower Bounds (CRBs) of non-data aided joint estimates of signal amplitude and phase, and noise power are derived for BPSK and QPSK signals, and further employed to obtain the QHLRT-UB. An upper bound on classification performance of any likelihood-based algorithms is also introduced. Method-of-moments (MoM) estimates of the unknown parameters are investigated and used to develop the QHLRT-based algorithm. Classification performance of this algorithm is compared with the upper bounds, as well as with the quasi Log-Likelihood Ratio (qLLR) and fourth-order cumulant based algorithms.