Capacity of Multiple-Input Multiple-Output Wireless Channels under Finite-Size Alphabet Constraints

Prof. Aleksandar Kavcic

Havard University

Friday, May 23rd, 3:00 PM, ENS 127

Abstract

The capacity of the power-constrained multiple-input multiple-output (MIMO) wireless channels has been known since the late 1990's. When the channel is the flat quasi-static Rayleigh fading channel, a Gaussian process, independent over all antennas and signal dimensions, achieves the capacity. In practice, however, for practical reasons, we cannot transmit such a source, but have to constrain ourselves to finite-size alphabets. We develop a numerical procedure that determines the capacity and capacity-achieving distributions under a finite-size alphabet constraint. This procedure is an adaptation of the well-known Blahut-Arimoto algorithm, which we cast as an expectation-maximization procedure in order to handle the possibility of having continuous random variables at the channel output. For a general input alphabet, the numerical method can be extremely computationally intensive. For this reason, we search for 'simple' finite-size constellations. It turns out that the familiar quadrature amplitude modulation (QAM) constellations are extremely attractive because the capacity-achieving distribution factors into independent distribution across all antennas and all signal dimensions. First, this eases the computation of the capacity because we can now optimize only one signal dimension for a single antenna. Second, we can construct capacity-achieving codes independent across all antennas. These are contrasted to some well-known space-time block codes, which fall short of achieving the capacity. We give examples of such capacity-achieving codes, which we construct as trellis codes. When concatenated with outer low-density parity-check codes, they can approach the capacities of wireless channels using the message-passing iterative decoder. Numerous examples are given throughout the talk.

A list of Wireless Networking and Communications Seminars is available at from the ECE department Web pages under "Seminars". The Web address for the Wireless Networking and Communications Seminars is http://signal.ece.utexas.edu/seminars