Abstract:
We study the conflict between two links in a multiple-input single-output interference channel. This setting is strictly competitive and can be related to perfectly competitive market models. In such models, general equilibrium theory is used to determine equilibrium measures that are Pareto optimal. First, we consider the links to be consumers that can trade goods within themselves. The goods in our setting correspond to beamforming vectors. We utilize the conflict representation of the consumers in the Edgeworth box, a graphical tool that depicts the allocation of the goods for the two consumers, to provide closed-form solution to all Pareto optimal outcomes. Afterwards, we model the situation between the links as a competitive market which additionally defines prices for the goods. The equilibrium in this economy is called Walrasian and corresponds to the prices that equate the demand to the supply of goods. We calculate the unique Walrasian equilibrium and propose a coordination process that is realized by an arbitrator which distributes the Walrasian prices to the consumers. The consumers then calculate in a decentralized manner their optimal demand corresponding to beamforming vectors that achieve the Walrasian equilibrium. This outcome is Pareto optimal and dominates the noncooperative outcome of the systems. Thus, based on the game theoretic model and solution concept, an algorithm for a distributed implementation of the beamforming problem in multiple-input single-output interference channels is provided.

Abstract:
We consider $K$ links operating concurrently in the same spectral band. Each transmitter has multiple antennas, while each receiver uses a single antenna. This setting corresponds to the multiple-input single-output interference channel. We assume perfect channel state information at the single-user decoding receivers whereas the transmitters only have estimates of the true channels. The channel estimation errors are assumed to be bounded in elliptical regions whose geometry is known at the transmitters. Robust beamforming optimizes worst-case received power gains, and a Pareto optimal point is a worst-case achievable rate tuple from which it is impossible to increase a link's performance without degrading the performance of another. We characterize the robust beamforming vectors necessary to operate at any Pareto optimal point. Moreover, these beamforming vectors are parameterized by $K(K-1)$ real-valued parameters. We analyze the system's spectral efficiency at high and low signal-to-noise ratio (SNR). Zero forcing transmission achieves full multiplexing gain at high SNR only if the estimation errors scale linearly with inverse SNR. If the errors are SNR independent, then single-user transmission is optimal at high SNR. At low SNR, robust maximum ratio transmission optimizes the minimum energy per bit for reliable communication. Numerical simulations illustrate the gained theoretical results.

Abstract:
A coding theorem and converse are proved for abstract channels with time structure that contain continuous-time continuous-valued channels and the result by Kadota and Wyner (1972) as special cases. As main contribution the coding theorem is proved for a significantly weaker condition on the channel output memory and without imposing extra measurability requirements to the channel. These improvements are achieved by introducing a suitable characterization of information rate capacity. It is shown that the previously used $\psi$-mixing condition is quite restrictive, in particular for the important class of Gaussian channels. In fact, it is proved that for Gaussian (e.g., fading or additive noise) channels the $\psi$-mixing condition is equivalent to finite output memory. 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 is closed in the proof of Kadota and Wyner regarding a lemma on the monotonicity of some sequence of normalized mutual informations. An operational perspective is taken and an abstract framework is established, which allows to treat discrete- and continuous-time channels with (possibly infinite) memory and arbitrary alphabets simultaneously in a unified way.

Abstract:
The 3-user discrete memoryless multi-way relay channel with circular message exchange and instantaneous relaying is investigated. We first show that this channel is effectively a 3-user interference channel with receiver message side information for every fixed (and instantaneous) relay mapping. Then, we extend the Han-Kobayashi coding scheme to this channel. Finally, we apply these results to Gaussian channels with amplify-and-forward relaying and present numerical results showing the gain of the proposed scheme compared to the state of the art.

Abstract:
Channel aware and opportunistic scheduling algorithms exploit the channel knowledge and fading to increase the average throughput. Alternatively, each user could be served equally in order to maximize fairness. Obviously, there is a tradeoff between average throughput and fairness in the system. In this paper, we study four representative schedulers, namely the maximum throughput scheduler (MTS), the proportional fair scheduler (PFS), the (relative) opportunistic round robin scheduler (ORS), and the round robin scheduler (RRS) for a space-time coded multiple antenna downlink system. The system applies TDMA based scheduling and exploits the multiple antennas in terms of spatial diversity. We show that the average sum rate performance and the average worst-case delay depend strongly on the user distribution within the cell. MTS gains from asymmetrical distributed users whereas the other three schedulers suffer. On the other hand, the average fairness of MTS and PFS decreases with asymmetrical user distribution. The key contribution of this paper is to put these tradeoffs and observations on a solid theoretical basis. Both the PFS and the ORS provide a reasonable performance in terms of throughput and fairness. However, PFS outperforms ORS for symmetrical user distributions, whereas ORS outperforms PFS for asymmetrical user distribution.

Abstract:
Spectral and energy efficiency in 3-way relay channels are studied in this paper. First, achievable sum rate expressions for 3-way relay channels are derived for different relaying protocols. Moreover, an outer bound for the capacity of the 3-way relay channel is presented. Next, leveraging the derived achievable sum rate expressions, two algorithms for joint power allocation at the users and at the relay are designed so as to maximize the system energy efficiency. Numerical results are provided to corroborate and provide insight on the theoretical findings.

Abstract:
This paper addresses the problem of resource allocation for systems in which a primary and a secondary link share the available spectrum by an underlay or overlay approach. After observing that such a scenario models both cognitive radio and D2D communications, we formulate the problem as the maximization of the secondary energy efficiency subject to a minimum rate requirement for the primary user. This leads to challenging non-convex, fractional problems. In the underlay scenario, we obtain the global solution by means of a suitable reformulation. In the overlay scenario, two algorithms are proposed. The first one yields a resource allocation fulfilling the first-order optimality conditions of the resource allocation problem, by solving a sequence of easier fractional problems. The second one enjoys a weaker optimality claim, but an even lower computational complexity. Numerical results demonstrate the merits of the proposed algorithms both in terms of energy-efficient performance and complexity, also showing that the two proposed algorithms for the overlay scenario perform very similarly, despite the different complexity.

Abstract:
Throughput and energy efficiency in 3-way relay channels are studied in this paper. Unlike previous contributions, we consider a circular message exchange. First, an outer bound and achievable sum rate expressions for different relaying protocols are derived for 3-way relay channels. The sum capacity is characterized for certain SNR regimes. Next, leveraging the derived achievable sum rate expressions, cooperative and competitive maximization of the energy efficiency are considered. For the cooperative case, both low-complexity and globally optimal algorithms for joint power allocation at the users and at the relay are designed so as to maximize the system global energy efficiency. For the competitive case, a game theoretic approach is taken, and it is shown that the best response dynamics is guaranteed to converge to a Nash equilibrium. A power consumption model for mmWave board-to-board communications is developed, and numerical results are provided to corroborate and provide insight on the theoretical findings.

Abstract:
Interference alignment (IA) is a promising technique to efficiently mitigate interference and to enhance the capacity of a wireless communication network. This paper proposes a grouping-based interference alignment (GIA) with optimized IA-Cell assignment for the multiple cells interfering multiple-input and multiple-output (MIMO) multiple access channel (MAC) network under limited feedback. This work consists of three main parts: 1) a complete study (including some new improvements) of the GIA with respect to the degrees of freedom (DoF) and optimal linear transceiver design is performed, which allows for low-complexity and distributed implementation; 2) based on the GIA, the concept of IA-Cell assignment is introduced. Three IA-Cell assignment algorithms are proposed for the setup with different backhaul overhead and their DoF and rate performance is investigated; 3) the performance of the proposed GIA algorithms is studied under limited feedback of IA precoders. To enable efficient feedback, a dynamic feedback bit allocation (DBA) problem is formulated and solved in closed-form. The practical implementation, the required backhaul overhead, and the complexity of the proposed algorithms are analyzed. Numerical results show that our proposed algorithms greatly outperform the traditional GIA under both unlimited and limited feedback.

Abstract:
We consider a multiple-input multiple-output (MIMO) interference channel (IC), where a single data stream per user is transmitted and each receiver treats interference as noise. The paper focuses on the open problem of computing the outermost boundary (so-called Pareto boundary-PB) of the achievable rate region under linear transceiver design. The Pareto boundary consists of the strict PB and non-strict PB. For the two user case, we compute the non-strict PB and the two ending points of the strict PB exactly. For the strict PB, we formulate the problem to maximize one rate while the other rate is fixed such that a strict PB point is reached. To solve this non-convex optimization problem which results from the hard-coupled two transmit beamformers, we propose an alternating optimization algorithm. Furthermore, we extend the algorithm to the multi-user scenario and show convergence. Numerical simulations illustrate that the proposed algorithm computes a sequence of well-distributed operating points that serve as a reasonable and complete inner bound of the strict PB compared with existing methods.