In this paper, fast fading Gaussian multiuser channels are considered. If the channel state information (CSI) is perfectly known to the transmitter, capacities have been derived for many cases in which the channels satisfy certain information-theoretic orders such as degradedness, or strong/very strong interference. We study the case when only the statistics of the CSI are known at the transmitter, which is an open problem in general. The main contributions of this paper are the following: First, we derive a sufficient condition to construct equivalent (having the same capacity region as the original channel) degraded Gaussian broadcast channels, which is based on the marginal distributions of the channel gains. To achieve this goal, we leverage three schemes: coupling, maximal coupling, and copulas, in addition to the same marginal property. The underlying idea of all schemes is to obtain an equivalent channel by changing the joint distribution in such a way that it satisfies a certain information-theoretic order while ensuring that the marginal distributions of the channels to different users are not changed. The construction of this equivalent multiuser channel allows us to directly apply existing capacity results. We then further derive the capacity regions of Gaussian interference channels with strong and very strong interferences, and also the secrecy capacity of Gaussian wiretap channels, while in all cases, the transmitters know only the statistics of the channels. Several practical examples such as Rayleigh fading and Nakagami-m fading illustrate the applicability of the derived results.

We investigate the application of copulas for characterizing channel orders, e.g., degradedness or strong/very strong interference, of Gaussian multiuser channels with statistical channel state information at the transmitter (CSIT). When there is solely statistical CSIT, identifying such channel orders is much more involved and, thus, the capacity remains unknown in general. We use the maximum copula to construct equivalent channels by modifying the joint distributions such that these newly constructed channels possess certain channel orders. We also derive sufficient conditions to attain these equivalent channels. We further discuss the meaning of achieving the maximum copula with respect to the concordance between the fading channels. We illustrate the theoretical results by numerical simulations, which visualize the joint probability distributions.

In this paper, ergodic capacities of fading Gaussian multi-user channels with only statistical channel state information at the transmitter are considered. The main contributions are twofold: First, we introduce a framework to classify random fading channels solely based on their joint distributions, such that we can construct equivalent channels in order to directly make use of existing capacity results. To attain this goal, we leverage three schemes: maximal coupling, coupling, and copulas in addition to the usual stochastic order with the same marginal property. Second, we apply the developed framework to Gaussian broadcast channels, Gaussian interference channels, and Gaussian wiretap channels to obtain novel capacity (region) results.

A coding theorem and converse are proved for a large-class of abstract stationary channels with time structure including the result by Kadota and Wyner (1972) on continuoustime real-valued channels as special cases. As main contribution, the coding theorem is proved for a significantly weaker condition on the channel output memory - called total ergodicity with respect to finite alphabet block-memoryless input sources - and under a crucial relaxation of the measurability requirement for the channel. These improvements are achieved by introducing a suitable characterization of information rate capacity. It is shown that the ψ-mixing output memory condition used by Kadota and Wyner is quite restrictive and excludes important channel models, in particular for the class of Gaussian channels. In fact, it is proved that for Gaussian (e.g., fading or additive noise) channels, the ψ-mixing condition is equivalent to finite output memory. Furthermore, it is demonstrated that the measurability requirement of Kadota and Wyner is not satisfied for relevant continuous-time channel models such as linear filters, whereas the condition used in this paper is satisfied for these models. Moreover, a weak converse is derived for all stationary channels with time structure. Intersymbol interference as well as input constraints are taken into account in a general and flexible way, including amplitude and average power constraints as special case. Formulated in rigorous mathematical terms complete, explicit, and transparent proofs are presented. As a side product a gap in the proof of Kadota and Wyner - illustrated by a counterexample - is closed by providing a corrected proof of a lemma on the monotonicity of some sequence of normalized mutual information quantities. An operational perspective is taken, and an abstract framework is established, which allows to treat discrete- and continuous-time channels with (possibly infinite input and output) memory and arbitrary alphabets simultaneously in a unified way.

The capacity regions of Gaussian broadcast channels depends on the knowledge of channel state information (CSI). When there is only statistical CSI at the transmitter and full CSI at the receiver, the ergodic capacity region is unknown in general. In this paper we investigate the relation between the degradedness and stochastic orders among channels from the transmitter to different receivers. We derive criteria to identify the degradedness for single and multiple-antenna cases when the channels belong to the usual stochastic order or the increasing convex order. Examples illustrate the usage of the derived criteria. We also show a case in which the channel enhancement technique can be applied even when there is only statistical CSIT.

Two theorems are proved for a cascade channel with two components, one theorem regarding input memory and the other regarding output memory. First, we show that if both components are asymptotically input-memoryless, then the cascade channel is asymptotically input-memoryless as well. Further, we prove that if both components are α-mixing and additionally the second component is causal and asymptotically input-memoryless, then the cascade channel is α-mixing. The results allow to study memory properties of complex models by analyzing basic building blocks. Further, they can be applied to analyze memory properties of information sources at the output of a channel. The results are relevant, e. g., in connection with coding theorems, concentration inequalities, or central limit theorems. The considered model includes discrete- as well as continuous-time channels and sources with completely arbitrary alphabets.

For channels with time structure we introduce a condition that characterizes infinite, asymptotically decreasing output memory called information regularity. We show that this condition is strictly weaker than asymptotic output-memorylessness, a property that was used to prove a coding theorem for continuous-time channels in case of infinite information capacity. We further show that the coding theorem still holds for information regular channels. We prove that Gaussian asymptotic output-memoryless channels have in fact finite output memory. This demonstrates that asymptotic output-memorylessness is quite restrictive. We consider discrete- and continuous-time channels with completely abstract alphabets in a unified framework and discuss practically relevant examples.

The tradeoff between average transmission rate and average delay is important for the system design of future wireless communication systems. In double-correlated multiple antenna channels, the spatial degrees of freedom allow to optimize the transmit strategy under throughput/delay priority. In this work, we maximize the effective capacity of a MIMO system with covariance feedback. Interestingly, the larger the delay requirement is, the more spatial degrees of freedom are used to avoid low instantaneous transmission rates. This fact is shown analytically by deriving a closed-form expression for the beamforming optimality range as a function of the spatial correlation, the SNR, and the QoS exponent. Numerical simulations illustrate the average effective capacity optimization and confirm the theoretical results.

The optimal transmit strategies of single-user multi-antenna systems with respect to average capacity maximization are well understood. However, the performance measure does neglect delay aspects which are important for higher layer design. Therefore, we consider the maximization of the effective capacity in a single-user multi-antenna system with covariance knowledge. The optimal transmit strategy is derived and the properties as a function of the decay-rate requirement of the buffer occupancy are analyzed. In particular, we show that the larger the decay-rate requirement, the smaller the beamforming optimality range, i.e., the more spatial eigenmodes are activated. This behavior is illustrated by numerical simulations and explained by the channel hardening effect.

Correlated scattering occurs naturally in frequency-selective fading channels and its impact on the performance needs to be understood. In particular, we answer the question whether the uncorrelated scattering model leads to an optimistic or pessimistic estimation of the actual average capacity. In the paper, we use majorization for functions to show that the average rate with perfectly informed receiver is largest for uncorrelated scattering if the transmitter is uninformed. If the transmitter knows the channel statistics, it can exploit this knowledge. We show that for small SNR, the behavior is opposite, uncorrelated scattering leads to a lower bound on the average capacity. Finally, we provide an example of the theoretical results for an attenuated Ornstein-Uhlenbeck process including illustrations.

We consider a discrete-time frequency- selective block-fading channel with Rayleigh fading and correlated scattering. This is relevant in the area of UWB and if transceiver filters are included in the capacity analysis. Under an average power constraint, we assume a single-user, single-antenna transmission with full CSI at the receiver and no CSI at the transmitter. For the employed model, we analyze the variance of the random capacity and the outage capacity. The variance together with the ergodic capacity are adequate means to estimate and basically characterize the behavior of the outage capacity via Chebyshev's inequality. Furthermore, expressions for high SNR are derived and the impact of correlated scattering compared to uncorrelated scattering is systematically studied on both, the ergodic and the outage capacity.

We study the ergodic capacity of a frequency-selective Rayleigh fading channel with correlated scattering, which finds application in the area of UWB. Under an average power constraint, we consider a single-user, single-antenna transmission. Coherent reception is assumed with full CSI at the receiver and no CSI at the transmitter. We distinguish between a continuous- and a discrete-time channel, modeled either as random process or random vector with generic covariance. As a practically relevant example, we examine an exponentially attenuated Ornstein-Uhlenbeck process in detail. Finally, we give numerical results, discuss the relation between the continuous- and the discrete-time channel model and show the significant impact of correlated scattering.