On Stochastic Orders and Fading Gaussian Multi-User Channels with Statistical CSIT

Abstract

In this paper, fading Gaussian multiuser channels are considered. If the channel is perfectly known to the transmitter, capacity has been established for many cases in which the channels may satisfy certain information theoretic orders such as degradedness or strong/very strong interference. Here, we study the case when only the statistics of the channels are known at the transmitter which is an open problem in general. The main contribution of this paper is the following: First, we introduce a framework to classify random fading channels based on their joint distributions by leveraging three schemes: maximal coupling, coupling, and copulas. The underlying spirit of all scheme is, we obtain an equivalent channel by changing the joint distribution in such a way that it now satisfies a certain information theoretic order while ensuring that the marginal distributions of the channels to the different users are not changed. The construction of this equivalent multi-user channel allows us to directly make use of existing capacity results, which includes Gaussian interference channels, Gaussian broadcast channels, and Gaussian wiretap channels. We also extend the framework to channels with a specific memory structure, namely, channels with finite-state, wherein the Markov fading broadcast channel is discussed as a special case. Several practical examples such as Rayleigh fading and Nakagami-m fading illustrate the applicability of the derived results.

Reliability Bounds for Dependent Fading Wireless Channels

“…The problem of optimizing the joint distribution given marginal distributions can be formulated by the copula approach [16]. Recently, [17] exploits copulas and coupling to derive stochastic orders for multiuser fading channels to characterize ergodic capacity regions of multi-user channels [18]. However, most of the previous work on performance of diversity systems in fading wireless channels only considers the case of independent or positively correlated fading processes [19].…”

The Broadcast Approach in Communication Networks

“…Representative studies in the high SNR regime include characterizing the DoF region for the two-user multi-antenna interference channel in [ 139 , 140 , 141 , 142 , 143 , 144 , 145 ]; blind interference alignment in [ 146 , 147 , 148 , 149 , 150 , 151 , 152 , 153 , 154 , 155 ]; interference management via leveraging network topologies in [ 156 , 157 ]; and ergodic interference channels in [ 158 , 159 , 160 ]. In the non-asymptotic SNR regime, the studies are more limited, and they include analysis on the capacity region of the erasure interference channel in [ 161 , 162 ]; the compound interference channel in [ 163 ]; ergodic capacity for the Z-interference channel in [ 164 ]; ergodic capacity of the strong and very strong interference channels in [ 165 , 166 ]; and approximate capacity region for the fast-fading channels [ 167 , 168 ].…”

On Fading Channel Dependency Structures with a Positive Zero-Outage Capacity

“…The first upper bound R 0 n , based on the Fréchet-Hoeffding lower bound W , is evaluated according to (21). The second upper bound from Corollary 9 is calculated to…”