## 1 Introduction
The desire for multi-level signaling formats such as Duobinary and PAM have been preferred to their advantages in terms of simpler transmitter and receiver structure for HS-PONs. Therefore, they have become a key solution to provide a higher line rate and improve the bandwidth utilization, capacity, and spectral effectiveness [2; 13; 17; 18; 19]. However, they are also more sensitive to driver linearity and have higher sensitivity requirements, which impose additional restrictions and may limit the system's reach. Coexistence with 10G PON technologies and reuse the deployed optical distribution network (ODN) are among the main challenges for upgrading to new generation PON systems. Technically, it requires that the optical budget (OPB), which determines the maximum tolerable optical loss between an optical line terminal (OLT) and an optical network unit (ONU), must be compliant to E1 or E2 class. However, with increased signal baudrates, impairments from both the transceivers and the fiber-link imposed constraints to fulfill the OPB requirement. Firstly, with a larger bandwidth, the receiver sensitivity can be degraded from a higher thermal noise level. Moreover, the bandwidth limitation from the optical and electrical components and the chromatic dispersion (CD) from the optical fiber channel induce more severe inter-symbol interference (ISI) [20; 21]. Mitigation techniques from both the optical and the digital domain can be used to maintain or even to improve the OPB level to enable a higher splitting ratio for an ODN, at a higher cost per customer provided equipment (CPE) [22; 23; 24; 25]. Firstly, optical amplifications can be performed to compensate for the sensitivity degradation, either with a praseodymium doped fiber amplifier (PDFA) as a booster in the OLT, or with a semiconductor optical amplifier (SOA) as a pre-amplifier in the ONU. The optical power budget of 35 dB is demonstrated in [10; 23], where both such optical amplifiers are used for the 25 Gbps PAM-4 downstream transmission. Although they achieve a higher optical power budget, the PDFA provides more than 10 dB gain. Furthermore, the attribution of digital post-equalization is not discussed. Digital equalization techniques, such as linear feed-forward (FF) equalizer or decision feedback (FB) equalizer, can help to overcome the transceiver and link induced ISI. Thus, they deserve the place in future PONs with spectral efficient modulation formats [10; 22]. Such a study is performed in [22], where the advantages of electrical duobinary (EDB) schemes and signal post-equalization are discussed for the bandwidth-limited PON. Their results of optical back-to-back sensitivity as a function of the receiver's bandwidth show that (i) the EDB outperforms the conventional NRZ irrespective to the receiver's bandwidth, (ii) the EDB transmission is more dispersion tolerant as compared to the NRZ, and (iii) the NRZ seems unfeasible for the C-band operation, and, thus, the EDB or a multilevel format should be used. Although the extensive comparison between the EDB and the NRZ alternatives is made, the optical power budget considerations remain outside the scope. This article aims to bridge the knowledge gap by countifying the gain that digital signal post-equalization has on the optical power budget in IM/DD PONs with NRZ-OOK, EDB, PAM-4, and PAM-8 formats. In this research, we consider a PON architecture based on point-to-multipoint passive optical power splitting in the ODN and focus on the downstream transmission at net-rates above 25 Gbps over a single wavelength in the C-band. Furthermore, as we limit the receiver's bandwidth to 8 GHz, we investigate whether components intended for the 10G operation can be used for 25+ Gbps operation. This enables the full compatibility with XG(S)-PON and 10G-EPON and leads to smooth migration of customers to higher net-rates in a cost-effective way.