Capacity of The Discrete-Time Non-Coherent Memoryless Gaussian Channels at Low SNR

We address the capacity of a discrete-time memoryless Gaussian channel, where the channel state information (CSI) is neither available at the transmitter nor at the receiver. The optimal capacity-achieving input distribution at low signal-to-noise ratio (SNR) is precisely characterized, and the exact capacity of a non-coherent channel is derived. The derived relations allow to better understanding the capacity of non-coherent channels at low SNR. Then, we compute the non-coherence penalty and give a more precise characterization of the sub-linear term in SNR. Finally, in order to get more insight on how the optimal input varies with SNR, upper and lower bounds on the non-zero mass point location of the capacity-achieving input are given.Comment: 5 pages and 4 figures. To appear in Proceeding of International Symposium on Information Theory (ISIT 2008

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

A Queueing Characterization of Information Transmission over Block Fading Rayleigh Channels in the Low SNR

Unlike the AWGN (additive white gaussian noise) channel, fading channels suffer from random channel gains besides the additive Gaussian noise. As a result, the instantaneous channel capacity varies randomly along time, which makes it insufficient to characterize the transmission capability of a fading channel using data rate only. In this paper, the transmission capability of a buffer-aided block Rayleigh fading channel is examined by a constant rate input data stream, and reflected by several parameters such as the average queue length, stationary queue length distribution, packet delay and overflow probability. Both infinite-buffer model and finite-buffer model are considered. Taking advantage of the memoryless property of the service provided by the channel in each block in the the low SNR (signal-to-noise ratio) regime, the information transmission over the channel is formulated as a \textit{discrete time discrete state} $D/G/1$ queueing problem. The obtained results show that block fading channels are unable to support a data rate close to their ergodic capacity, no matter how long the buffer is, even seen from the application layer. For the finite-buffer model, the overflow probability is derived with explicit expression, and is shown to decrease exponentially when buffer size is increased, even when the buffer size is very small.Comment: 29 pages, 11 figures. More details on the proof of Theorem 1 and proposition 1 can be found in "Queueing analysis for block fading Rayleigh channels in the low SNR regime ", IEEE WCSP 2013.It has been published by IEEE Trans. on Veh. Technol. in Feb. 201

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

Capacity per Unit Energy of Fading Channels with a Peak Constraint

A discrete-time single-user scalar channel with temporally correlated Rayleigh fading is analyzed. There is no side information at the transmitter or the receiver. A simple expression is given for the capacity per unit energy, in the presence of a peak constraint. The simple formula of Verdu for capacity per unit cost is adapted to a channel with memory, and is used in the proof. In addition to bounding the capacity of a channel with correlated fading, the result gives some insight into the relationship between the correlation in the fading process and the channel capacity. The results are extended to a channel with side information, showing that the capacity per unit energy is one nat per Joule, independently of the peak power constraint. A continuous-time version of the model is also considered. The capacity per unit energy subject to a peak constraint (but no bandwidth constraint) is given by an expression similar to that for discrete time, and is evaluated for Gauss-Markov and Clarke fading channels.Comment: Journal version of paper presented in ISIT 2003 - now accepted for publication in IEEE Transactions on Information Theor