## 1 Introduction
The strength and velocity of such parameter variations in a typical low-Earth orbit (LEO) to ground FSO scenario (\(\sim\)500 km circular orbit) can be estimated as follows [25; 33]:  
* Received signal power changes due to distance variations via orbital movement from a 5\({}^{\circ}\) elevation to zenith of \(\sim\)12 dB. This change happens in minutes;
* Additional signal power variation is introduced by an increased atmospheric attenuation at low elevations, adding up to \(\sim\)6 dB of loss when close to the horizon, depending on OGS location;
* Background light, in daytime, near to the horizon is stronger than at zenith by up to \(\sim\)10 dB, with a variation speed similar to those in the atmospheric attenuation changes;
* Received power scintillations (due to atmospheric IRT) and pointing fading (caused by finite beam direction control) adds another \(\sim\)6 dB or more, on the timescale of milliseconds;
* Furthermore, the fast angular movement of a LEO satellite across the sky (up to more than 1\({}^{\circ}\)/s) will lead to additional fading from unwanted miss-pointing. Data RFE performance can be determined by its required average energy-per-bit to achieve a given electrical signal quality, stated as, e.g., in SNR, Q-factor, or bit error ratio (BER). Here, a typical value for InGaAs-APD-RFEs operating within a near 1550 nm wavelength is around 500 photons per bit (Ppb) for BER = \(10^{-9}\) and better. Overviews of practically achieved RFE sensitivities can be found in [34] on p. 330 and in [35] (Table 3). An even higher sensitivity has been reported by an alternative APD semiconductor material, HgCdTe, and commercial devices for FSO communication applications might soon be demonstrated [36; 37]. In a typical high-speed optical receiver setup, the light-sensitive photodiode generates primary photoelectrons when illuminated by background or signal light power. The reverse biasing of the diode with \(U_{R}\) causes an E-field that accelerates the primary photoelectrons, which, when colliding with other electrons, excite secondary and possibly ternary signal electrons. This electron avalanche acts as an internal diode amplification of the photocurrent, which is then converted into a voltage signal via transimpedance, \(R_{\text{T}I}\), filtered according to its required signal bandwidth, and its binary is decided by a limiting circuit when data reception takes place (see Figure 1). The RFE features a variable \(U_{R}\) that is adjusted according to APD temperature (monitored by a temperature sensor, \(S_{Temp}\)), total APD current, as monitored by \(I_{APD}\), optical received power, \(P_{Rx}\), (cannot be monitored directly without an extra power sensor), and the electrical signal amplitude, as monitored via the received signal strength indicator, RSSI. The Rx filter bandwidth, \(B\), is adjusted to a 3 dB cutoff at roughly half the data rate, \(r\). To eliminate the influence of electronic offsets, AC coupling is introduced before the limiter. The latter's threshold voltage, \(U_{T\eta r}\), is also optimized via RSSI according to the asymmetric noise distributions of the APD-RFE. The system performance can finally be evaluated via a bit error ratio tester. For an RFE with a variable bandwidth/data rate, it would be most beneficial in terms of sensitivity to adapt the feedback resistance, \(R_{T\eta}\), to the required bandwidth. However, this is not feasible with practical high-speed (>1 Gbps) systems employing integrated circuits with a fixed feedback structure. Thus, the reduction of noise through the spectral filtering by the Rx filter offers only a part of the possible SNR optimization in a variable data rate RFE. The remainder of this document is organized as follows. Section 2 summarizes the basic relationships between the photodetectors and APD performance modelling.