  In this paper, we propose an analytical model to estimate the signal-to-noise
ratio (SNR) at the output of an adaptive equalizer in intensity modulation and
direct detection (IMDD) optical transmission systems affected by shot noise,
thermal noise, relative intensity noise (RIN), chromatic dispersion (CD) and
bandwidth limitations. We develop the model as an extension of a previously
presented one, and then we test its accuracy by sweeping the main parameters of
a 4-PAM-based communication system such as RIN coefficient, extinction ratio,
CD coefficient and equalizer memory. Our findings show a remarkable agreement
between time-domain simulations and analytical results, with SNR discrepancies
below 0.1 dB in most cases, for both feed-forward and decision-feedback
equalization. We consider that the proposed model is a powerful tool for the
numerical design of strongly band-limited IMDD systems using receiver
equalization, as it happens in most of modern and future M-PAM solutions for
short reach and access systems.
