This paper analyses and enhances the performance of moment generating function (MGF) techniques, in particular, Chernoff bound (CB) and modified Chernoff bound (MCB). Also, we improve the M-ary digital pulse-position modulation (M-ary DPPM) systems performance of a wavelength division multiplexing (WDM) based on the passive optical network (PON) free-space optical (FSO) communications in the presence of the atmospheric turbulence (AT), amplified spontaneous emission (ASE) noise, and interchannel crosstalk (ICC). This is a technology that can have extended leverage, higher data rates, power-efficient, and is considered an ideal option for the provision of bandwidth for potential access networks. The MCB exceeds the Gaussian approximation at high gain (G = 30) and gives the tightest bound upon the bit-error-rate (BER) compared to the CB at a low gain (G = 8). In the absence of AT and at a data rate of 2.5 Gbps on the 1550 nm wavelength, DPPM scheme with coding level (M) of 2 provide about 2.9 dB improvement in average power over at a BER of \({\text{10}}^{-\text{9}}\)compared with an equivalent on-off keying (OOK) non-return-to-zero (NRZ) in the WDM-PON/FSO system. The sensitivity of M-ary DPPM modulation remains improved over OOK even though the ICC is present. The lower power penalty (PP) is predicted to be approximately 0.2-3.0 dB in WDM-FSO systems for low coding (M) 2. At a target BER of \({\text{10}}^{-\text{12}}\), the hybrid OOK-NRZ/M-ary DPPM offers about 4-8 dB optical signal-to-noise-ratio improvements over M-DPPM of the ST for the WDM-FSO link. Finally, the use of the M-ary DPPM and the optical relaying amplification technique is a powerful treatment for mitigating the impacts of ASE noise, AT, and ICC.