The Noncoherent Rician Fading Channel -- Part I : Structure of the Capacity-Achieving Input

Transmission of information over a discrete-time memoryless Rician fading channel is considered where neither the receiver nor the transmitter knows the fading coefficients. First the structure of the capacity-achieving input signals is investigated when the input is constrained to have limited peakedness by imposing either a fourth moment or a peak constraint. When the input is subject to second and fourth moment limitations, it is shown that the capacity-achieving input amplitude distribution is discrete with a finite number of mass points in the low-power regime. A similar discrete structure for the optimal amplitude is proven over the entire SNR range when there is only a peak power constraint. The Rician fading with phase-noise channel model, where there is phase uncertainty in the specular component, is analyzed. For this model it is shown that, with only an average power constraint, the capacity-achieving input amplitude is discrete with a finite number of levels. For the classical average power limited Rician fading channel, it is proven that the optimal input amplitude distribution has bounded support.Comment: To appear in the IEEE Transactions on Wireless Communication

Low SNR Capacity of Noncoherent Fading Channels

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).Comment: submitted to IEEE I

On the Capacity of the Wiener Phase-Noise Channel: Bounds and Capacity Achieving Distributions

In this paper, the capacity of the additive white Gaussian noise (AWGN) channel, affected by time-varying Wiener phase noise is investigated. Tight upper and lower bounds on the capacity of this channel are developed. The upper bound is obtained by using the duality approach, and considering a specific distribution over the output of the channel. In order to lower-bound the capacity, first a family of capacity-achieving input distributions is found by solving a functional optimization of the channel mutual information. Then, lower bounds on the capacity are obtained by drawing samples from the proposed distributions through Monte-Carlo simulations. The proposed capacity-achieving input distributions are circularly symmetric, non-Gaussian, and the input amplitudes are correlated over time. The evaluated capacity bounds are tight for a wide range of signal-to-noise-ratio (SNR) values, and thus they can be used to quantify the capacity. Specifically, the bounds follow the well-known AWGN capacity curve at low SNR, while at high SNR, they coincide with the high-SNR capacity result available in the literature for the phase-noise channel.Comment: IEEE Transactions on Communications, 201

On the Capacity-Achieving Input of Channels with Phase Quantization

Several information-theoretic studies on channels with output quantization have identified the capacity-achieving input distributions for different fading channels with 1-bit in-phase and quadrature (I/Q) output quantization. But can analytical results on the capacity-achieving input also be obtained for multi-bit quantization? We answer the question in the affirmative by considering multi-bit phase quantization. We first consider a complex Gaussian channel with $b$-bit phase-quantized output and prove that the capacity-achieving distribution is a rotated $2^b$-phase shift keying (PSK). The analysis is then extended to multiple fading scenarios. We show that the optimality of rotated $2^b$-PSK continues to hold under noncoherent fast fading Rician channels with $b$-bit phase quantization when line-of-sight (LoS) is present. When channel state information (CSI) is available at the receiver, we identify $\frac{2\pi}{2^b}$-symmetry and constant amplitude as the necessary and sufficient conditions for the ergodic capacity-achieving input distribution; which a $2^b$-PSK satisfies. Finally, an optimum power control scheme is presented which achieves ergodic capacity when CSI is also available at the transmitter.Comment: Submitted to IEEE Transactions on Information Theor

Information Theory of underspread WSSUS channels

The chapter focuses on the ultimate limit on the rate of reliable communication through Rayleigh-fading channels that satisfy the wide-sense stationary (WSS) and uncorrelated scattering (US) assumptions and are underspread. Therefore, the natural setting is an information-theoretic one, and the performance metric is channel capacity. The family of Rayleigh-fading underspread WSSUS channels constitutes a good model for real-world wireless channels: their stochastic properties, like amplitude and phase distributions match channel measurement results. The Rayleigh-fading and the WSSUS assumptions imply that the stochastic properties of the channel are fully described by a two-dimensional power spectral density (PSD) function, often referred to as scattering function. The underspread assumption implies that the scattering function is highly concentrated in the delay-Doppler plane. Two important aspects need to be accounted for by a model that aims at being realistic: neither the transmitter nor the receiver knows the realization of the channel; and the peak power of the transmit signal is limited. Based on these two aspects the chapter provides an information-theoretic analysis of Rayleigh-fading underspread WSSUS channels in the noncoherent setting, under the additional assumption that the transmit signal is peak-constrained