Performance of single and dual-polarized optically preamplified M-ary PPM systems with finite extinction ratios over FSO fading channels

Abstract

M-ary pulse position modulation (PPM) systems have been considered in free-space optical (FSO) communications, optical fiber links, and passive optical networks. In this paper, we study the error performance of direct-detection optically preamplified M-ary PPM systems over slowly fading FSO channels. The study considers the combined effects on the probability of bit error, Pb, of channel fading with a given scintillation index, σp2, the transmitter finite extinction ratio, r, and the preamplifier spontaneous emission (ASE) noise. We provide results for both single and dual-polarized systems with symbol sizes M∈{2,4,…,1024} at Pb=10−4 and Pb=10−9. The fading models considered in this study are the exponential, log-normal, and gamma–gamma channels. For single-polarized systems with infinite extinction ratios, we provide closed-form expressions for the bit error probabilities for the three channel models. For the dual-polarized systems we compute them numerically. The results indicate that gamma–gamma fading imposes a more severe penalty than the log-normal case. In this study, the power penalty at Pb=10−9 ranges between 1.8 and 14dB for the log-normal channel, whereas it ranges between 2.2 and 30.7dB for the gamma–gamma channel. The study also demonstrates that the power penalty due to the combined effects of transmitter finite r and channel fading is the sum of the penalty due to fading alone and the penalty due to a finite r alone, and that the power penalty for dual-polarized systems is about 0.4dB larger than single-polarized ones.