Error Performance of DDPSK Receiver in the Presence of Composite Fading

We investigate the justification for implementing double differential phase-shift keying (DDPSK) instead of differential phase-shift keying (DPSK) in the presence of carrier frequency offset (CFO) over wireless channels affected by thermal noise, multipath fading, and shadowing. When shadowed multipath fading is modeled using the Fisher-Snedecor F distribution, we present the probability density function (PDF) of the received composite signal phase in the form of the Fourier series and derive novel analytical expressions for its Fourier coefficients. Furthermore, we present analytical expressions for the symbol error probability (SEP) in detection of DDPSK and DPSK signals over such shadowed fading channels. These expressions are derived in the form of infinite series followed by the appropriate proof of convergence. We determine the necessary number of terms to achieve a given accuracy. Derived expressions allow us to illustrate the superiority of DDPSK compared to DPSK in the presence of CFO. We analyze the applicability of DDPSK across various values of normalized CFO, multipath fading depth, and shadowing severity, considering different modulation orders. Our key conclusion is that DDPSK outperforms DPSK when CFO values are higher. Additionally, as the modulation order increases, CFO has a stronger impact on SEP degradation in DPSK detection. Notably, at higher CFO values, DDPSK superiority becomes evident even at lower signal-to-noise ratio levels.