Old Program Director’s Course—Module 2—Teaching and evaluating for the six core competencies

Abstract

In the free-space optical (FSO) links, atmospheric turbulence and pointing errors lead to scintillation in the received signal. Due to its ease of implementation, intensity modulation with direct detection (IM/DD) based on ON–OFF-keying(OOK) is a popular signaling scheme in these systems. For long-haul FSO links, avalanche photo diodes (APDs) are commonly used, which provide an internal gain in photo-detection, allowing larger transmission ranges, as compared with PIN photo-detector (PD) counterparts. Since optimal OOK detection at the receiver requires the knowledge of the instantaneous channel fading coefficient, channel estimation is an important task that can considerably impact the link performance. In this paper, we investigate the channel estimation issue when using an APD at the receiver. Here, optimal signal detection is quite more delicate than in the case of using a PIN PD. In fact, given that APD-based receivers are usually shot-noise limited, the receiver noise will have a different distribution depending on whether the transmitted bit is ‘0’ or ‘1’, and moreover, its statistics are further affected by the scintillation. To deal with this, we first consider minimum mean-square-error (MMSE), maximum a posteriori probability (MAP) and maximum likelihood (ML) channel estimation over an observation window encompassing several consecutive received OOK symbols. Due to the high computational complexity of these methods, in a second step, we propose an ML channel estimator based on the expectation–maximization (EM) algorithm which has a low implementation complexity, making it suitable for high data-rate FSO communications. Numerical results show that for a sufficiently large observation window, by using the proposed EM channel estimator, we can achieve bit error rate performance very close to that with perfect channel state information. We also derive the Cramer–Rao lower bound (CRLB) of MSE of estimation errors and show that for a large enough observation window, this CRLB can be adequately tight.