High-SNR Capacity of MIMO Optical Intensity Channels: A Sphere-Packing Perspective

Abstract

This letter investigates the capacity for the multiple-input multiple-output (MIMO) optical intensity channels in the high signal-to-noise ratio (SNR) regime from a sphere-packing (SP) perspective. In such a channel, the inputs represent optical intensities, hence are nonnegative. Considering the peak- and average-power constraints for the inputs, the high-SNR capacity can be expressed in terms of the volume of an image signal space through an SP argument. When the number of transmit antennas <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n_{\mathrm{T}} $ </tex-math></inline-formula> and receive antennas <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n_{\mathrm{R}} $ </tex-math></inline-formula> satisfies <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n_{\mathrm{T}} \leq n_{\mathrm{R}} $ </tex-math></inline-formula> , the image-space volume is derived in terms of singular values of the channel matrix. While for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n_{\mathrm{T}} &gt; n_{\mathrm{R}} $ </tex-math></inline-formula> , the image-space volume is derived by decomposing the image space into multiple non-overlapping subpolytopes, whose volumes can be conveniently calculated.