Asymptotic noisy reference losses of subcarrier BPSK and QPSK systems in lognormal fading

We study bit-error rate performance of subcarrier binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK) systems with carrier phase error (CPE) in log-normal turbulence channels. The CPE is modeled as a Tikhonov random variable. We quantify the CPE induced asymptotic noisy reference losses using an auxiliary random variable method. Both approximate and exact calculations of the asymptotic noisy reference loss for a subcarrier BPSK system over the lognormal channel are analytically shown to be 0 dB. This suggests that a subcarrier BPSK system is robust to CPE in lognormal fading when the signal-to-noise ratio is sufficiently large. A closed-form exact asymptotic noise reference loss expression for a subcarrier QPSK system is also presented, and such performance metric can be used to assess the robustness of the system to CPE.