On the Capacity of MISO Optical Intensity Channels With Per-Antenna Intensity Constraints

Abstract

This paper investigates the capacity of general multiple-input single-output (MISO) optical intensity channels (OICs) under per-antenna peak- and average-intensity constraints. We first consider the MISO equal-cost constrained OIC (EC-OIC), where, apart from the peak-intensity constraint, average intensities of inputs are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">equal to</i> arbitrarily preassigned constants. The second model of our interest is the MISO bounded-cost constrained OIC (BC-OIC), where, as compared with the EC-OIC, average intensities of inputs are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">no larger than</i> arbitrarily preassigned constants. By leveraging tools from quantile functions, stop-loss transform and convex ordering of nonnegative random variables, we prove two decomposition theorems for bounded and nonnegative random variables, based on which we equivalently transform both the EC-OIC and the BC-OIC into respective single-input single-output channels under a peak-intensity and several stop-loss mean constraints. Capacity lower and upper bounds for both channels are established, based on which the asymptotic capacity at high and low signal-to-noise-ratio are determined.