From Multi-Keyholes to Measure of Correlation and Power Imbalance in MIMO Channels: Outage Capacity Analysis

An information-theoretic analysis of a multi-keyhole channel, which includes a number of statistically independent keyholes with possibly different correlation matrices, is given. When the number of keyholes or/and the number of Tx/Rx antennas is large, there is an equivalent Rayleigh-fading channel such that the outage capacities of both channels are asymptotically equal. In the case of a large number of antennas and for a broad class of fading distributions, the instantaneous capacity is shown to be asymptotically Gaussian in distribution, and compact, closed-form expressions for the mean and variance are given. Motivated by the asymptotic analysis, a simple, full-ordering scalar measure of spatial correlation and power imbalance in MIMO channels is introduced, which quantifies the negative impact of these two factors on the outage capacity in a simple and well-tractable way. It does not require the eigenvalue decomposition, and has the full-ordering property. The size-asymptotic results are used to prove Telatar's conjecture for semi-correlated multi-keyhole and Rayleigh channels. Since the keyhole channel model approximates well the relay channel in the amplify-and-forward mode in certain scenarios, these results also apply to the latterComment: accepted by IEEE IT Trans., 201

On Outage Probability and Diversity-Multiplexing Tradeoff in MIMO Relay Channels

Fading MIMO relay channels are studied analytically, when the source and destination are equipped with multiple antennas and the relays have a single one. Compact closed-form expressions are obtained for the outage probability under i.i.d. and correlated Rayleigh-fading links. Low-outage approximations are derived, which reveal a number of insights, including the impact of correlation, of the number of antennas, of relay noise and of relaying protocol. The effect of correlation is shown to be negligible, unless the channel becomes almost fully correlated. The SNR loss of relay fading channels compared to the AWGN channel is quantified. The SNR-asymptotic diversity-multiplexing tradeoff (DMT) is obtained for a broad class of fading distributions, including, as special cases, Rayleigh, Rice, Nakagami, Weibull, which may be non-identical, spatially correlated and/or non-zero mean. The DMT is shown to depend not on a particular fading distribution, but rather on its polynomial behavior near zero, and is the same for the simple "amplify-and-forward" protocol and more complicated "decode-and-forward" one with capacity achieving codes, i.e. the full processing capability at the relay does not help to improve the DMT. There is however a significant difference between the SNR-asymptotic DMT and the finite-SNR outage performance: while the former is not improved by using an extra antenna on either side, the latter can be significantly improved and, in particular, an extra antenna can be traded-off for a full processing capability at the relay. The results are extended to the multi-relay channels with selection relaying and typical outage events are identified.Comment: accepted by IEEE Trans. on Comm., 201

The Capacity Region of Restricted Multi-Way Relay Channels with Deterministic Uplinks

This paper considers the multi-way relay channel (MWRC) where multiple users exchange messages via a single relay. The capacity region is derived for a special class of MWRCs where (i) the uplink and the downlink are separated in the sense that there is no direct user-to-user links, (ii) the channel is restricted in the sense that each user's transmitted channel symbols can depend on only its own message, but not on its received channel symbols, and (iii) the uplink is any deterministic function.Comment: Author's final version (to be presented at ISIT 2012

The Three-User Finite-Field Multi-Way Relay Channel with Correlated Sources

This paper studies the three-user finite-field multi-way relay channel, where the users exchange messages via a relay. The messages are arbitrarily correlated, and the finite-field channel is linear and is subject to additive noise of arbitrary distribution. The problem is to determine the minimum achievable source-channel rate, defined as channel uses per source symbol needed for reliable communication. We combine Slepian-Wolf source coding and functional-decode-forward channel coding to obtain the solution for two classes of source and channel combinations. Furthermore, for correlated sources that have their common information equal their mutual information, we propose a new coding scheme to achieve the minimum source-channel rate.Comment: Author's final version (accepted and to appear in IEEE Transactions on Communications

Deterministic Capacity of MIMO Relay Networks

The deterministic capacity of a relay network is the capacity of a network when relays are restricted to transmitting \emph{reliable} information, that is, (asymptotically) deterministic function of the source message. In this paper it is shown that the deterministic capacity of a number of MIMO relay networks can be found in the low power regime where \SNR\to0. This is accomplished through deriving single letter upper bounds and finding the limit of these as \SNR\to0. The advantage of this technique is that it overcomes the difficulty of finding optimum distributions for mutual information.Comment: Submitted to IEEE Transactions on Information Theor