This study introduces the design and simulation of an M-ary multi-hop system with multiple-input single-output (MISO) configurations (notably, using optical receiver diversity) for free space optical (FSO) communication employing a coherent Gaussian optical beam as the source. In this approach, N-spatial modulation (N-SM) is integrated with L-pulse-position modulation (L-PPM) along with transmit diversity (M × 1 MISO), enhancing the efficiency of spatial modulation-driven FSO networks. Particularly, the application of MISO techniques significantly lowers the bit-error rate (BER) in turbulent conditions for a FSO system employing 2-SM/4-PPM in a 2 × 1 MISO setup, achieving a substantial improvement compared to systems using 4-SM/4-PPM without MISO. Specifically, the 2-SM/4-PPM FSO system with 2 × 1 MISO supports a data rate of 2.5 Gbps at a BER of \({10}^{-{9}}\) , with an output power of 7.5 dBm across a 11 km transmission span. In scenarios of strong turbulence (with a refractive index structure constant of \({\text{C}}_{\text{n}}^{2}={10}^{-{13}}{\text{m}}^{-{2}/{3}}\) , a 4-PPM FSO system facilitated by two relays shows a BER of \({10}^{-{9}}\) , demonstrating notable advancements over traditional on–off keying (OOK) FSO systems, which typically show a BER of \({10}^{-{4}}\) . This performance boost results from using serial relaying and M-ary multi-hop PPM, mitigating atmospheric turbulence and misalignment fading and thus extending the effective transmission range of FSO systems. Incorporating hybrid OOK/M-ary differential PPM (DPPM) methods also shows significant improvements of about 4 dB, 6 dB, and 8 dB in optical signal-to-noise ratio (OSNR) compared to the 3-DPPM, 4-DPPM, and 5-DPPM setups under the same turbulence conditions in the FSO network. These numerical findings highlight that integrating multi-hop transmission with receiver diversity presents an effective strategy for reducing the impacts of atmospheric turbulence and misalignment errors. Furthermore, the study displays considerable enhancements in BER and signal-to-noise ratio (SNR) for both multi-hop MISO and multi-hop single-input single-output (SISO) FSO systems applying M-QAM, significantly outperforming existing systems with different modulation techniques at the target BER of \({10}^{-{12}}\) . Specifically, SNR improvements of 20.89 dB and 24.78 dB were achieved for multi-hop MISO and multi-hop SISO systems using an 8-PPM scheme, while adopting 8-QAM modulation led to gains of 4.937 dB and 8.975 dB for the respective systems. In summary, multi-hop MISO systems notably surpass the performance of multi-hop SISO configurations by 4.038 dB and 3.89 dB for 8-QAM and 8-PPM respectively, A detailed comparison is drawn between Dual DPPM and an optically preamplified OOK-NRZ FSO communication system using a FSO link employing the multi-channel beamforming (MCB) technique for both systems. As per the BER utilizing MCB, it is observed that DPPM provides approximately a 10–11 dB enhancement in sensitivity compared to the OOK-NRZ FSO system in stable atmospheric conditions without turbulence according to reference proving their efficiency in handling spectral efficiency on par with competing systems. The results reveal that a high channel capacity of 20 bits per second per hertz (bits/s/Hz) is attained under weak turbulence at turbulence strength \({\text{C}}_{\text{n}}^{2}={1}\times {10}^{-{15}}{\text{m}}^{-{2}/{3}}\) for the 3 × 1 MISO configuration with 4-SM/4-SPPM. In comparison, under moderate turbulence with at \({\text{C}}_{\text{n}}^{2}={1}\times {10}^{-{14}}{\text{m}}^{-{2}/{3}}\) , the 3 × 1 MISO setup with 4-SM/4-SPPM achieves a capacity of 18 bits/s/Hz, and under strong turbulence, it reaches 16.2 bits/s/Hz at at \({\text{C}}_{\text{n}}^{2}={1}\times {10}^{-{13}}{\text{m}}^{-{2}/{3}}\) . We evaluate the average spectral efficiency (ASE) in bits per second per Hertz concerning channel capacity relative to the average transmitted optical power under strong turbulence, with and without pointing errors (PEs) of the beam divergence angle. The findings suggest that integrating spatial coherence diversity and M-ary MISO PPM/SPPM adaptive modulation in coherent OWC can enhance ASE values (bits/s/Hz). The ASE values of 53 bits/s/Hz and 37 bits/s/Hz are noted at an average transmitted power of 10 dBm for a 10 cm aperture diameter, without and with PEs in the coherent OWC-FSO M-ary MISO PPM/SPPM technique.
