On the Miller-Chang lower bound for NDA carrier phase estimation

In this letter, we derive a new Miller-Chang lower bound (MCB) for the variance of unbiased non-data-aided (NDA) carrier phase estimates obtained from a block of N samples of a linearly modulated pulse-amplitude modulation or quadrature-amplitude modulation information signal, transmitted through an additive white Gaussian noise channel. This bound is tighter than the corresponding Crame´r-Rao lower bound (CRB) for data-aided or continuous-wave carrier phase estimation (CW-CRB), particularly when N is small. For some given N and sufficiently high signal-to-noise ratios, the MCB is tighter than the corresponding true NDA CRB. The main limitation of this new MCB is that its application is restricted to carrier phase estimators which are unbiased for all possible values of the received symbol sequence.