Phase and frequency estimation for PSK packets: bounds and algorithms

New Cramer-Rao lower bounds (CRBs) are derived for the estimation of phase offset, and frequency offset, from a block of random BPSK or QPSK symbols at low signal-to-noise (SNR) ratios. These bounds are compared to existing bounds which apply to the unmodulated carrier (or to known PSK symbols), and to the performance of some estimation algorithms.