Modified CRLB on the modulation parameters of OQPSK signal and MSK signal

When the characteristics of a digitally modulated signal are unknown, the estimation of its modulation parameters is indispensable for many digital communication applications. It is therefore very useful to establish a lower bound on the parameter estimation accuracy of a modulated signal. This paper presents the modified Cramer-Rao lower bound (MCRLB) for the modulation parameters of an offset quadrature phase shift keying (OQPSK) signal and that of a minimum shift keying (MSK) signal embedded in additive white Gaussian noise (AWGN). The modulation parameters considered are the carrier frequency f_c, the carrier phase θ_c, the signal amplitude A and the symbol time T_s. The MCRLB is dependent on the observation time, the modulation parameters and the pulse shaping function. The MCRLB is evaluated with the raised cosine and lowpass pulse shaping functions. When the roll-off factor of the raised cosine filter increases, the MCRLBs of the four parameters increase, regardless of whatever the modulation type is. In addition, the MCRLB on the T_s of a MSK signal is 3 dB lower than that of an OQPSK signal. When the bandwidth of the lowpass filter increases, the MCRLBs on f_c, θ_c and A of an OQPSK signal increases, but the MCRLB on the T_s of an OQPSK signal decreases. On the other hand, the MCRLBs on the modulation parameters of the a MSK signal all increase