## 1 Introduction  
Pulse position modulation (PPM) and digital PPM (DPPM) and systems are modulation schemes that can perform great performance in free-space optical (FSO) transmission links [1; 2]. This format is used in a variety of applications, including FSO links, hybrid fibers, optical wireless communication (OWC), subsequent FSO systems, satellite-to-satellite systems, atmospheric turbulence (AT), interchannel crosstalk (ICC), and indoor wireless channels [1; 2; 3]. The modulation of DPPM improves power efficiency and does not require monitoring of decision-making circuit thresholds [4; 5]. Many experiments on the hybrid fiber/FSO (HFFSO) systems and the OWC have been carried out [5; 6; 7; 8; 9]. Previous researches have demonstrated that the DPPM and PPM schemes outperform on-off keying (OOK) in terms of sensitivity and power efficiency for the HFFSO link. The M-pulse amplitude and position modulation (M-PAPM) for both pulse amplitude modulation (PAM) and PPM modulation have been investigated and studied for optical fiber (OF) communications [5; 6; 7; 8]. M-PAPM can provide high efficiency and sensitivity in the FSO communication; because the dispersion is free [1; 5; 8]. Because of the increased bandwidth requirement for higher data rates, OF, AT, OWC and indoor networks [8; 9; 10; 11; 12; 13; 14; 15] have been proposed to multiplex the wavelength division multiplexing (WDM) technique and dense WDM (DWDM) systems. The WDM technique could also be used in the HFFSO, OWC, and hybrid OF/multiple networks. For example, the proposed approach designs a high-performance system and bandwidth optimization solution with long-range potential, higher bit rates, high-speed technology, and enhanced data protection for WDM passive optical networks (WDM-PON) [8; 9; 13; 16]. The WDM application has been presented in both OF and FSO systems [8; 9; 17; 18; 19; 20; 21]. A suitable technique for representing amplified spontaneous emission noise (ASE) in an FSO transmission link is the moment generating function (MGF), although we have upper limits at the bit-error-rate (BER) using the updated techniques of Chernoff bound (CB), Gaussian approximating (GA), and modified Chernoff bound (MCB) [5; 8; 9; 22; 23; 24; 25]. Both the FSO and OF systems have been presented using WDM technology [8; 9; 17; 18; 19; 20; 21]. The moment generating function (MGF) represents a suitable technique for finding the amplified spontaneous emission (ASE) noise in an FSO transmission link [2; 9; 17]. Using the modified Chernoff bound (MCB) technique, Gaussian approximations (GA), and Chernoff bound (CB), we obtain upper bounds on the bit error rate (BER) [5; 8; 9; 22; 23; 24; 25]. To reduce the AT impact, approaches are proposed including compensation for the mitigation techniques and adaptive optics (AO) focused on digital signal processing [22]. We highlight the main contributions, including: (1) we use the M-ary DPPM-M-PAPM modulation to deliver additional bits to improve the efficiency; (2) we add the AO to minimize the ICC interferences and enhance the reliability performances; (3) we achieve adequate BER results with a lower complexity; (4) we extract the theoretical BER expressions and provide simulation results for M-DPPM-M-PAPM modulation schemes in the WDM-PON/HFFSO scenarios; (5) the hybrid OOK/M-ary DPPM-M-n-PAPM and the AO are offered to boost the performance and system efficiency in receivers of WDM-HFFSO systems through the OOK non-return-to-zero (OOK-NRZ) modulation; and (6) we improve the power penalty (PP) performance and the system efficiency for the WDM-HFFSO systems, optical-wireless and fiber-optic communication systems. In this work, we enhance the hybrid OOK/DPPM-M-PAPM techniques and improve the signal-to-noise-ratios (SNRs) of the HFFSO systems under the AT effects, ICC, and ASE. In this work, we enhance the hybrid OOK/DPPM-M-PAPM systems and improve the signal-to-noise-ratios (SNRs) of the HFFSO under the AT, ICC, and ASE effects. We develop the proposed model in the [9; 17].