On performance bounds for joint parameter estimation and modulation classification

In this paper we investigate bounds on performance of joint parameter estimation and modulation classification. The Cramer-Rao Lower Bounds (CRLBs) of non-data aided joint estimates of signal amplitude and phase, and noise power are derived for binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) signals. In addition, an upper bound on performance of Quasi Hybrid Likelihood Ratio Test (QHLRT)-based modulation classifiers is proposed, for the case when unbiased and normally-distributed non-data aided estimates of unknown parameters are available. Results for this upper bound are presented for BPSK and QPSK classification, with signal amplitude and phase, and noise power as unknown parameters.