Power series based gamma–gamma fading MIMO/FSO link analysis with atmospheric turbulence and pointing errors

In this article, we analyze the bit error rate (BER) performance of the multiple-input multiple-output (MIMO) based free-space optical (FSO) link by adopting Gamma–Gamma (GG) distribution with atmospheric turbulences (ATs) and pointing errors (PEs). By expanding the GG distribution, the complexity is high due to Meijer-G function with MIMO. To reduce the complexity, we proposed a mathematically tractable power series based probability density function of the GG fading with PEs and ATs. Based on the proposed power series PDF, the exact BER is derived, allowing to analyze the BER performance for single-input single-output (SISO), Single Input Multiple Output (SIMO) and extended to MIMO link for three combining schemes with M-ary Phase Shift Keying (M-PSK). The derived BER expression also helps to derive the Asymptotic Bit Error Rate (ABER), diversity gain, combining gain and cross-validated for SISO, SIMO and MIMO/FSO links. The effect of PEs over the performance of the FSO link is analyzed and observed that PEs degrades the BER and gain of the FSO link rapidly. The deduced MRC provides high SNR gain at-least 3.5 dB over EGC and 8 dB gain over SC for negligible PEs ξ = 11.23 at BER 10−6 and for BER 10−3, the SNR gain for MRC over EGC is 1.5 dB and approximately above 3 dB over SC for severe PEs ξ = 1.23. The proposed power series based PDF offers high gain and power efficiency of the MIMO/FSO link over SISO and SIMO link. This article identifies the crucial factors affecting the FSO link and helps in mitigating them to design an optimal system and opens for wide range of applications like fifth-generation (5G) networks, smart city applications etc.