Discrete-time Rayleigh fading single-input single-output (SISO) and multiple-input multipleoutput (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 goes 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). channel capacity, correlated fading, frequency selective fading, low SNR, MIMO I. INTRODUCTION In this paper we present results on the capacity of discrete-time Rayleigh fading singleinput single-output (SISO) and multiple-input multiple-output (MIMO) channels. We assume a noncoherent model where no channel state information is available at the transmitter or the receiver. The fadings are assumed to be stationary processes correlated in time but, for MIMO channels, independent for distinct input/output antenna pairs. A hard peak-power constraint, in addition to an average-power constraint, is imposed on the input signals. For MIMO channels we consider two types of constraints: under one the peak and average power constraints are imposed on each of the signals transmitted by the different antennas separately, and under the other the constraints are on the sum of the powers in the different signals. We focus on channel capacity at low signal-to-noise ratio (SNR), but we also derive upper bounds that are valid for any SNR. We also consider SISO channels with delay spread (i.e., frequency selective) fading where the fading is modeled by a finite number of taps. The fading processes corresponding to the different taps are assumed to be independent across taps, and allowed, within each tap, to be correlated in time. The capacity of fading channels at low SNR was studied in [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] . The main motivation for our present work has been to understand the capacity of communication over wideband channels. Work of Kennedy [8], Jacobs [7] , Telatar and Tse [15] , and Durisi et al. [5] demonstrate that the capacity of such channels, in the wideband limit, is the same as for
The low-SNR capacity of single-input singleoutput and multiple-input multiple-output non-coherent fading channels with peak and average February 24, 2015 DRAFT power constraints is studied in REF .
Low SNR Capacity of Noncoherent Fading Channels
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