Wiener’s loop filter for PLL-based carrier recovery with OQPSK and MSK

Carrier recovery for offset QPSK (OQPSK) and minimum shift keying (MSK) based on phase-lock loop (PLL) is considered in the paper. The concern of the paper is the optimization of the loop filter of the PLL. The optimization is worked out in the light of Wiener's theory taking into account the phase noise affecting the incoming carrier, the AWGN channel, and the self-noise produced by the phase detector that is commonly used for OQPSK and MSK. Delay in the loop, which may affect the numerical implementation of the phase-lock loop, is also considered in the paper. Closed-form expressions for the loop filter and for the mean-square error are given for the case where the phase noise is characterized as a first-order process.