Lower bounds on error performance for BPSK and QPSK systems with imperfect carrier phase recovery

Lower bounds on the error probability for BPSK and QPSK systems are presented when the detection process is corrupted by a noisy phase reference. These bounds are derived from the application of Jensen´s inequality to convex functions and from the utilization of the moment space bounding technique. A set of improved lower bounds using Jensen´s inequality is also derived. We provide explicit relationships between the derived bounds and the average power losses in the studied signals caused by the imperfect detection process. These averages have simple expressions and can be used in system designs to provide lower bounds on the detection loss