Average SEP for M‐ary CPSK with noisy phase reference in Nakagami fading and Gaussian noise

Abstract

SUMMARYAnalytic expressions for the symbol-error probabilities of M-ary coherent phase shift keying (M-CPSK) detection with an imperfect local carrier reference phase in Nakagami-m fading and additive Gaussian noise are derived. Both the Tikhonov probability density function (PDF) and the uniform PDF of the carrier phase error are considered. We based our analyses on a newly derived expression for the Fourier coefficients of the PDF of the composite phase of the received signal impaired by Nakagami-m fading and additive Gaussian noise. We present a comparison of the results based on the Tikhonov PDF with those based on the uniform PDF in order to show substantial performance differences between these two-phase noise models.

On the Effect of Imperfect Reference Signal Phase Recovery on Performance of PSK System Influenced by TWDP Fading

“…However, in order to realize coherent detection, it is necessary to regenerate the phase of the reference carrier. The reference carrier phase can be extracted using a phase-locked loop (PLL) [ 2 , 3 , 4 , 5 , 6 ]. The regenerated phase should follow the random signal phase fluctuations generated due to multipath propagation.…”

“…The difference between these two phases is called the phase error or phase noise. This phase error is a random process and is known to lead to the significant degradation of the system performance [ 2 , 3 , 4 , 5 , 6 ].…”

“…[ 2 ]. When multipath fading follows Nakagami- m distribution, its influence on error probability in conjunction with phase noise is considered in [ 3 ], while shadowed multipath fading is analyzed in a similar scenario in [ 4 ].The influence of the phase noise on the error probability when multipath fading is modeled by Nakagami- m distribution was considered in [ 3 ], while the effect of imperfect reference signal extraction on the error probability over a shadowed multipath fading was analyzed in [ 4 ]. Smadi and Prabhu in [ 5 ] presented a novel treatment in estimating the effect of phase noise on error performance of binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) with equal gain combined under Rayleigh, Rician and Nakagami- m fading environment.…”

“…Both ways for reference signal phase recovery over TWDP channel are open problems. For illustrative purposes, we are focusing on reference signal recovery from the pilot signal, where the loop bandwidth is much lesser than the channel bandwidth [ 3 , 4 , 5 ]. The signal phase at the voltage-controlled oscillator (VCO) output does not perfectly follow the phase of the signal being detected.…”

“…Generally, a stochastic difference exists between the incoming signal phase and the signal phase at the VCO output. The phase noise is modeled by Tikhonov distribution according to [ 2 , 3 , 4 , 5 , 6 ]. Our goal in this paper is to determine the impact of phase noise on the BER performance and mutual information [ 15 , 16 ] when multilevel phase-shift keying (PSK) signal is transmitted over a TWDP channel.…”