Performance Analysis of M-DPSK Modulation over Fast-Hoyt Fading Channels under Non-Isotropic Scattering Conditions

In this paper, we analyze the symbol error probability (SEP) performance of M-ary differential phase shift keying (M-DPSK) modulation schemes over frequency-flat fast-varying Hoyt multipath fading channels. Assuming general non-isotropic scattering conditions, we first derive a finite-range integral expression for the probability density function (PDF) of the phase difference between two non-isotropic Hoyt vectors perturbed by additive white Gaussian noise (AWGN). Based upon the theory of M-DPSK modulation and the obtained PDF formula, the SEP of M-DPSK and its corresponding asymptotic behavior in non-isotropic fast-Hoyt fading channels are derived. Specifically, a double semi-finite range integral expression for the corresponding SEP is investigated. A closed-form expression for the SEP and bit error probability (BEP) of M-DPSK and DPSK, respectively, over non-isotropic frequency-flat fast-Rayleigh fading channels is also deduced. Moreover, the obtained SEP and BEP expressions are fully validated by reducing them to already known results corresponding to the special cases like isotropic Hoyt and isotropic Rayleigh fading channels. By considering a mobile-to-mobile (M2M) non-isotropic Hoyt scattering model, we finally validate the obtained expressions for the PDF and SEP by means of computer simulations.