Distance Hardening in Large MIMO Systems

Asymptotic analysis plays an important role in the performance evaluation and technology design of large multiple-input multiple-output (MIMO) systems. This paper investigates an asymptotic property of large MIMO systems, called distance hardening. It involves distance metrics defined in terms of many factors, such as the channel matrix and the difference matrix of two arbitrary transmitted codewords. The asymptotic property is revealed by the use of the Chernoff bounding method and expressed in an analogous way to the well-known channel hardening. More specifically, we first derive Chernoff bounds on the tail probabilities of distance metrics, in which we are interested. Then, we formulate the asymptotic property based on a generalized definition of the hardening phenomena by referring to a formal definition of the channel hardening. The distance hardening is shown to have implications for space-time code design, MIMO detection, and millimeter wave MIMO systems. Numerical simulations are conducted to verify our theoretical development.