On the capacity of multiple-antenna systems and parallel Gaussian channels with amplitude-limited inputs

We propose upper and lower bounds on the capacity of multiple-input multiple-output (MIMO) systems with amplitude-limited inputs. The results are derived by considering an equivalent channel via singular value decomposition, and by enlarging and reducing the corresponding feasible region of the channel input vector, for the upper and lower bounds, respectively. We analytically characterize the asymptotic behavior of the derived bounds for high and low noise levels, and study the gap between them. We also consider parallel Gaussian channels with peak and average power-constrained inputs. For such channels, the capacity-achieving distribution has been reported in the literature to be discrete, which can be computed using numerical optimization techniques. However, there is no closed-form expression and finding the capacity-achieving distribution is computationally tedious. With this motivation, we derive approximate expressions for the capacity at low and high noise variance levels. We illustrate our findings on both MIMO channels and parallel Gaussian channels via several numerical examples. © 1972-2012 IEEE

Capacity bounds for MIMO microwave backhaul links affected by phase noise

We present bounds and a closed-form high-SNR expression for the capacity of multiple-antenna systems affected by Wiener phase noise. Our results are developed for the scenario where a single oscillator drives all the radio-frequency circuitries at each transceiver (common oscillator setup), the input signal is subject to a peak-power constraint, and the channel matrix is deterministic. This scenario is relevant for line-of-sight multiple-antenna microwave backhaul links with sufficiently small antenna spacing at the transceivers. For the 2 by 2 multiple-antenna case, for a Wiener phase-noise process with standard deviation equal to 6 degrees, and at the medium/high SNR values at which microwave backhaul links operate, the upper bound reported in the paper exhibits a 3 dB gap from a lower bound obtained using 64-QAM. Furthermore, in this SNR regime the closed-form high-SNR expression is shown to be accurate.Comment: 10 pages, 2 figures, to appear in IEEE Transactions on Communication

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

Unified Capacity Limit of Non-coherent Wideband Fading Channels

In non-coherent wideband fading channels where energy rather than spectrum is the limiting resource, peaky and non-peaky signaling schemes have long been considered species apart, as the first approaches asymptotically the capacity of a wideband AWGN channel with the same average SNR, whereas the second reaches a peak rate at some finite critical bandwidth and then falls to zero as bandwidth grows to infinity. In this paper it is shown that this distinction is in fact an artifact of the limited attention paid in the past to the product between the bandwidth and the fraction of time it is in use. This fundamental quantity, called bandwidth occupancy, measures average bandwidth usage over time. For all signaling schemes with the same bandwidth occupancy, achievable rates approach to the wideband AWGN capacity within the same gap as the bandwidth occupancy approaches its critical value, and decrease to zero as the occupancy goes to infinity. This unified analysis produces quantitative closed-form expressions for the ideal bandwidth occupancy, recovers the existing capacity results for (non-)peaky signaling schemes, and unveils a trade-off between the accuracy of approximating capacity with a generalized Taylor polynomial and the accuracy with which the optimal bandwidth occupancy can be bounded.Comment: Accepted for publication in IEEE Transactions on Wireless Communications. Copyright may be transferred without notic

Capacity Results on Multiple-Input Single-Output Wireless Optical Channels

This paper derives upper and lower bounds on the capacity of the multiple-input single-output free-space optical intensity channel with signal-independent additive Gaussian noise subject to both an average-intensity and a peak-intensity constraint. In the limit where the signal-to-noise ratio (SNR) tends to infinity, the asymptotic capacity is specified, while in the limit where the SNR tends to zero, the exact slope of the capacity is also given.Comment: Submitted to IEEE Transactions on Information Theor

Multi-User Visible Light Communication Broadcast Channels With Zero-Forcing Precoding

This paper studies zero-forcing (ZF) precoding designs for multi-user multiple-input single-output visible light communication (VLC) broadcast channels. In such broadcast systems, the main challenging issue arises from the presence of multi-user interference (MUI) among non-coordinated users. In order to completely suppress the MUI, ZF precoding, which is originally designed for radio frequency (RF) communications, is adopted. Different from RF counterpart, VLC signal is inherently non-negative and has a limited linear range, which leads to an amplitude constraint on the input data signal. Unlike the average power constraint, obtaining the exact capacity for an amplitude-constrained channel is more cumbersome. In this paper, we first investigate lower and upper bounds on the capacity of an amplitude-constrained Gaussian channel, which are especially tight in the high signal-to-noise regime. Based on the derived bounds, optimal beamformer designs for the max-min fairness sum-rate and the maximum sum-rate problems are formulated as convex optimization problems, which then can be efficiently solved by using standard optimization packages