Joint Data Detection and Frequency/Phase Estimation at Low Signal-to-Noise Ratio

The problem of joint data detection and frequency/phase estimation is considered in this work. The traditional belief regarding exact generalized-likelihood-based joint detection and estimation is that its complexity is exponential in the sequence length N . This belief is justified due to the memory imposed on the transmitted sequence by the lack of knowledge of the auxiliary channel parameters at the receiver. In this paper, we show that the exact solution can be performed with O(N4) worst-case combinatorial complexity regardless of the operating signal-to-noise ratio. The concepts used in the proof of the polynomial-complexity result are also utilized to evaluate tight performance bounds on the exact and a family of approximate algorithms for joint data detection and phase or frequency/phase estimation.