Free-space Optical MIMO Transmission with APD Receivers

In this paper we present numerical results via both Chernofi bounding and Monte Carlo simulation illustrating the diversity advantage of optical MIMO, as well as the impact of APD receivers versus ideal photon counting treatments on system performance. We model the detector output as a Gaussian random variable and derive the maximum likelihood (ML) rule for Q-ary PPM, with the main focus on the 2-PPM case. Results show that full diversity is achieved in a Rayleigh fading environment under the assumption of independent channel path gains. The Chernofi bound is exponentially tight and within 1.5 dB for all nonfading cases and the 2x2 Rayleigh fading case. Free-space optical (optical wireless) communication can deliver reliable broadband last mile connectivity that features unlicensed operation, rapid and inexpensive setup of terminals, excellent data security, and highly directive beams that minimize interference among users. Such links must be lineof-sight of course, and typically span a few kilometers at most. One distance-limiting factor is scintillation, i.e. fading of the received optical fleld caused by atmospheric turbulence from inhomogeneities in air’s index of refraction. This presents a signiflcant penalty in some situations over a link analysis performed in vacuum. Desire to mitigate such fading efiects has generated studies of multiple co-located lasers and photodetectors that can improve system performance in a manner similar to their RF MIMO counterparts [4], [7]. Since lasers are normally on/ofi modulated and detection is noncoherent (direct), we have focused upon Q-ary pulse position modulation as an energye‐cient transmission method. We assume here that all lasers repeat the same signal (so-called ‘repetition coding’) so the scheme difiers from traditional MIMO systems in this respect. Our earlier work [10] has treated ideal photon-counting receivers for difiering fading scenarios with and without background radiation. We have shown that full transmitter diversity is obtained with repetition PPM, so that with Rayleigh fading, for example, the symbol error probability has a slope of iMN versus optical energy per bit, PTb, when displayed in log-log format. In this work, we shift the receiver model to a more realistic one: each receiver uses an avalanche photodiode (APD) following any optical collecting lens. The primary reason for adopting APDs is that the detector can more closely approach the optical shot-noise limit. In this regime, optical shot noise dominates over the electrical noise in the system giving 1 This work was supported in part by NSF Grant CCR-0208763. the best possible error performance relative to the theoretical quantum limit. However, APDs themselves are noisy in that the number of secondary photoelectrons (PEs) produced for each primary PE is a random variable, adding an excess noise to the process over what one would achieve with an ideal optical amplifler with the same gain. These efiects have earlier been studied by Conradi [2] and McIntyre [6], Webb [9], and later by Davidson and Sun [3] who assessed the accuracy of a Gaussian model for the relevant random variables in the PPM case. In these earlier works, optical fading was not considered nor was the case of multiple transmitters and multiple receivers. We endeavored to cover both of these scenarios in this paper.