1 Introduction

A previous article [1] defined four fundamental parameters, $\rho_0$, $\rho_+$, $\Delta$, and $\beta_0$ that are sufficient to determine the capacity of $M$-PPM on a soft-decision optical channel. Loosely speaking, these parameters describe the slot SNR, the ``excess'' SNR arising from different variances in signaling and nonsignaling slots, the ``skewness'' of the Webb distribution, and the closeness of the signal to the Gaussian distribution.

The Free-space Optical Communication Analysis Software (FOCAS) [2] used by NASA to determine optical link budgets uses seventy-nine physical parameters, including: laser, relay optics, telescope, and pointing parameters of the transmitter; modulation and coding formats of the signal; noise sources and atmospheric parameters; and telescope, relay optics, detector, and amplifier parameters of the receiver. These physical parameters affect capacity through their effects on the four fundamental parameters. In order to evaluate the sensitivity of capacity with respect to any given physical parameters, we explore more deeply the relationship between fundamental and physical parameters. For a full description of the physical parameters, see, e.g., [2,3,4]. The physical parameters we consider in this paper are:

• Laser and Modulator Parameters. Laser and modulator parameters include the optical frequency $\nu$, the width of the pulse slot $T_s$, the required deadtime between pulses $T_d$, the modulation extinction ratio $\alpha_{er}$, and the order $M$ of the $M$-ary Pulse Position Modulation (PPM) signal.

• Detector Parameters. Avalanche PhotoDiode (APD) detector parameters include the quantum efficiency $\eta$, excess noise factor $F$, gain $G$, noise temperature $T$, load resistance $R_L$, bulk leakage current $I_b$, and surface leakage current $I_s$.

• Channel Parameters. Channel parameters include the mean number of background photons incident on the detector $\bar n_b$, and the mean number of pulse-induced photons incident on the detector $\bar n_s$.

Some other parameters can be expressed in terms of those above, but will not be used explicitly in this article. For example, the ionization ratio $k_{\mbox{\small\em eff}}$ is related to $F$ and $G$ by $F=k_{\mbox{\small\em eff}} G+(2-1/G)(1-k_{\mbox{\small\em eff}})$, the noise equivalent one-sided bandwidth $B$ is set equal to ${1\over 2T_s}$, and the optical frequency $\nu$ only matters in how it affects $\bar n_b$ and $\bar n_s$. The dead time $T_d$ has no bearing on capacity expressed in bits per channel use. However, $T_d$ is very relevant for the total throughput, in bits per second. (The slot width $T_s$ is relevant to the capacity expressed in bits per channel use, because the level of thermal noise per slot depends on $T_s$.) And for most lasers $\alpha_{er}$ has a negligible effect, being on the order of $10^6$. Hence, in the remainder of the paper, $\nu$, $T_d$, and $\alpha_{er}$ will be ignored.