So-called improper complex signals have been shown to be beneficial in the single-antenna two-user Gaussian interference channel under the assumptions that all input signals are Gaussian and that we treat interference as noise (TIN). This result has been obtained under a restriction to pure strategies without time-sharing, and it was extended to the case where the rates, but not the transmit powers, may be averaged over several transmit strategies. In this paper, we drop such restrictions and discuss the most general case of coded time-sharing, where both the rates and the powers may be averaged. Since coded time-sharing can in general not be expressed by means of a convex hull of the rate region, we have to account for the possibility of time-sharing already during the optimization of the transmit strategy. By means of a novel channel enhancement argument, we prove a surprising result: proper signals are optimal if coded time-sharing is allowed. In addition to establishing this result, we present an algorithm to compute the corresponding achievable rate region.

We study the capabilities of a filter configuration where a linear filter is applied to an improper vector, and the output is processed by scalar widely linear filters afterwards. Assuming that this filter configuration is used to estimate a vector of interest from a noisy observation, we aim at finding the optimal filter coefficients in the sense of minimizing the mean square error. To this end, we propose a filter design algorithm based on alternating optimization. The resulting filter turns out to achieve an intermediate performance between the optimal widely linear filter and the optimal linear filter. As an application example, we discuss how the considered filter structure fits to the concept of linear transceivers in communication systems.

This paper considers the so-called partial decode-and-forward (DF) strategy for the Gaussian multiple-input multiple-output (MIMO) relay channel. Unlike for the DF strategy or point-to-point (P2P) transmission from source to destination, for which Gaussian channel inputs are known to maximize the achievable rates, the input distribution that attains the maximum achievable partial DF rate for the Gaussian MIMO relay channel has remained unknown so far. For some special cases, e.g., for relay channels where the partial DF strategy reduces to the DF or P2P transmission, it could be deduced that Gaussian inputs maximize the rate that can be achieved with the partial DF strategy. For the general case, however, the problem has remained open until now. In this paper, we solve this problem by proving that the maximum achievable partial DF rate for the Gaussian MIMO relay channel is always attained by Gaussian channel inputs. Our proof relies on the channel enhancement technique, which was originally introduced by Weingarten et al. to derive the (private message) capacity region of the Gaussian MIMO broadcast channel. By combining this technique with a primal decomposition approach, we first establish that jointly Gaussian source and relay inputs maximize the achievable partial DF rate for the aligned Gaussian MIMO relay channel. Subsequently, we use a limiting argument to extend this result from the aligned to the general Gaussian MIMO relay channel.

Proper (i.e., circularly symmetric) Gaussian signals are known to be capacity-achieving in Gaussian multiple-input multiple-output (MIMO) broadcast channels with proper noise in the sense that the sum rate capacity under a sum power constraint is achievable with proper Gaussian signaling. In this paper, we generalize this statement by proving that the optimality of proper Gaussian signals also holds under a shaping constraint, i.e., a sum covariance constraint instead of a power constraint. Moreover, we show that not only the sum rate optimal point, but the whole capacity region can be achieved with proper Gaussian signals. Finally, we prove that the worst-case noise in a MIMO broadcast channel with shaping constraints is proper.

We focus on a linear beamformer design in the downlink with statistical channel state information (CSI) at the transmitter, where the users' ergodic rates are balanced. Simplifying the fading channels to given vectors with random scalar factors, which is a good approximation for rural mobile or satellite communications (SatCom), the stochastic model mismatch is kept small albeit the ergodic rate structure now allows for adapting the perfect CSI balancing algorithms. Although there is no equivalent signal-to-interference-and-noise-ratio (SINR) reformulation for the ergodic constraints, tight inner approximations with SINR structure are found. Based on this observation, a locally optimal sequential approximation strategy is proposed and a fixed point based implementation is provided that requires only few iterations.

Proper Gaussian signals have been shown to be optimal in multiple-input multiple-output (MIMO) broadcast channels from an information theoretic point of view, i.e., capacity can be achieved with a strategy that transmits circularly symmetric complex Gaussian signals. In this work, we show that optimality of proper Gaussian signals does not necessarily hold if the transmit strategy is restricted to widely linear transceivers. The proof is performed by identifying a rate tuple that is achievable in a certain set of channels with widely linear transceivers and improper Gaussian signals, but lies outside the achievable rate region for widely linear transceivers and proper Gaussian signals.

Optimization of transmit strategies with linear transceivers in multiple-input multiple-output (MIMO) broadcast channels generally leads to nonconvex problems, which cannot be solved efficiently in a globally optimal manner. Instead, it is necessary to resort to suboptimal algorithms. In this paper, we evaluate the application of a gradient descent algorithm for the optimization of the energy efficiency in such a system. Since the quality of the obtained locally optimal solutions depends on the initialization, a successive stream allocation is introduced and combined with the gradient algorithm. Comparison with a globally optimal reference algorithm for the special case of single receive antennas shows that the obtained solutions are close to the global optimum. For the MIMO case, the energy per bit achievable with dirty paper coding, which is a lower bound for the case of linear transceivers, is used as benchmark, and good performance of the gradient-based methods is shown for MIMO systems as well.

The use of proper, i.e., circularly symmetric, complex Gaussian signals for all users is known to be optimal in broadcast channels with proper complex Gaussian noise from an information theoretic point of view, i.e., they are employed in the capacity-achieving strategy. However, such proper per-user transmit signals are not necessarily optimal for problems with quality-of-service (QoS) constraints if the transmit strategy is restricted to widely linear transceivers without time-sharing. This is shown by deriving the QoS feasibility region of the multiple-input multiple-output broadcast channel with improper Gaussian per-user transmit signals and widely linear transceivers.

We consider the problem of power minimization under per-user quality of service (QoS) constraints (expressed in terms of rates) in parallel multiple-input single-output (MISO) broadcast channels employing linear zero-forcing precoding. Solving the arising scheduling problem by an exhaustive search is prohibitively complex due to its combinatorial nature so that the use of successive user allocation schemes has been proposed. We show that existing schemes lead to strongly suboptimal solutions in systems with a low number of degrees of freedom and that better performance can be achieved with a new scheduling criterion. By introducing additional correction steps, we end up with an efficient close-to-optimum algorithm.