Modified CRLB on the modulation parameters of a PSK signal

PSK is a common modulation format in digital communications. The estimation of modulation parameters is necessary for emitter interception in support of numerous military applications. This paper develops the Cramer-Rao lower bound (CRLB) for the modulation parameters of a PSK signal. The modulation parameters considered are the carrier frequency, the symbol time and the signal amplitude. The results show that the CRLBs for the modulation parameters are the same for M-ary PSK signals when M>2. The CRLBs between BPSK and M-ary PSK with M>2 are very close, although they are not exactly identical. The effect of pulse shaping on the CRLB of modulation parameters are also investigated.