Low SNR Capacity of Noncoherent Fading Channels

TL;DR

This paper investigates the capacity limits of noncoherent Rayleigh fading channels at low SNR, providing asymptotic capacity results for various MIMO and SISO configurations under different power constraints.

Contribution

It derives the asymptotic capacity of noncoherent fading channels at low SNR, including new results for MIMO channels with individual power constraints and SISO channels with delay spread.

Findings

Asymptotic capacity for MIMO with sum power constraints identified

Asymptotic capacity for MIMO with individual power constraints derived for transmit separable channels

Results extended to SISO channels with delay spread

Abstract

Discrete-time Rayleigh fading single-input single-output (SISO) and multiple-input multiple-output (MIMO) channels are considered, with no channel state information at the transmitter or the receiver. The fading is assumed to be stationary and correlated in time, but independent from antenna to antenna. Peak-power and average-power constraints are imposed on the transmit antennas. For MIMO channels, these constraints are either imposed on the sum over antennas, or on each individual antenna. For SISO channels and MIMO channels with sum power constraints, the asymptotic capacity as the peak signal-to-noise ratio tends to zero is identified; for MIMO channels with individual power constraints, this asymptotic capacity is obtained for a class of channels called transmit separable channels. The results for MIMO channels with individual power constraints are carried over to SISO channels with delay spread (i.e. frequency selective fading).