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On the capacity of free-space optical intensity channels. (Sur la capacité des canaux d'intensité optique en espace libre)

Free-space optical intensity (FSOI) communication systems are widely used in short-range communication such as the infrared communication between electronic handheld devices. The transmitter in these systems modulates on the intensity of optical signals emitted by light emitting diodes (LEDs) or laser diodes (LDs), and the receiver measures incoming optical intensities by means of photodetectors. Inputs are nonnegative because they represent intensities. Moreover, they are typically subject to both peak- and average-power constraints, where the peak-power constraint is mainly due to technical limitations of the used components, whereas the average-power constraint is imposed by battery limitations and safety considerations. As a first approximation, the noise in such systems can be assumed to be Gaussian and independent of the transmitted signal. This thesis focuses on the fundamental limits of FSOI communication systems, more precisely on their capacity. The major aim of our work is to study the capacity of a general multiple-input multiple-output (MIMO) FSOI channel under a per-input-antenna peak-power constraint and a total average-power constraint over all input antennas. We present several capacity results on the scenario when there are more transmit than receive antennas, i.e., nT > nR > 1. In this scenario, different input vectors can yield identical distributions at the output, when they result in the same image vector under multiplication by the channel matrix. We first determine the minimum-energy input vectors that attain each of these image vectors. It sets at each instant in time a subset of nT − nR antennas to zero or to full power, and uses only the remaining nR antennas for signaling. Based on this, we derive an equivalent capacity expression in terms of the image vector, which helps to decompose the original channel into a set of almost parallel channels. Each of the parallel channels is an amplitude-constrained nR⇥nR MIMO channel, with a linear power constraint, for which bounds on the capacity are known. With this decomposition, we establish new upper bounds by using a duality-based upper-bounding technique, and lower bounds by using the Entropy Power Inequality (EPI). The derived upper and lower bounds match when the signal-to-noise ratio (SNR) tends to infinity, establishing the high-SNR asymptotic capacity. At low SNR, it is known that the capacity slope is determined by the maximum trace of of the covariance matrix of the image vector. We found a characterization to this maximum trace that is computationally easier to evaluate than previous forms.