Signal Processing and Optimal Resource Allocation for the Interference Channel

In this article, we examine several design and complexity aspects of the optimal physical layer resource allocation problem for a generic interference channel (IC). The latter is a natural model for multi-user communication networks. In particular, we characterize the computational complexity, the convexity as well as the duality of the optimal resource allocation problem. Moreover, we summarize various existing algorithms for resource allocation and discuss their complexity and performance tradeoff. We also mention various open research problems throughout the article.Comment: To appear in E-Reference Signal Processing, R. Chellapa and S. Theodoridis, Eds., Elsevier, 201

Learning Equilibrium Play for Stochastic Parallel Gaussian Interference Channels

Distributed power control for parallel Gaussian interference channels recently draws great interests. However, all existing works only studied this problem under deterministic communication channels and required certain perfect information to carry out their proposed algorithms. In this paper, we study this problem for stochastic parallel Gaussian interference channels. In particular, we take into account the randomness of the communication environment and the estimation errors of the desired information, and thus formulate a stochastic noncooperative power control game. We then propose a stochastic distributed learning algorithm SDLA-I to help communication pairs learn the Nash equilibrium. A careful convergence analysis on SDLA-I is provided based on stochastic approximation theory and projected dynamic systems approach. We further propose another learning algorithm SDLA-II by including a simple iterate averaging idea into SDLA-I to improve algorithmic convergence performance. Numerical results are also presented to demonstrate the performance of our algorithms and theoretical results

On the Pareto-Optimal Beam Structure and Design for Multi-User MIMO Interference Channels

In this paper, the Pareto-optimal beam structure for multi-user multiple-input multiple-output (MIMO) interference channels is investigated and a necessary condition for any Pareto-optimal transmit signal covariance matrix is presented for the K-pair Gaussian (N,M_1,...,M_K) interference channel. It is shown that any Pareto-optimal transmit signal covariance matrix at a transmitter should have its column space contained in the union of the eigen-spaces of the channel matrices from the transmitter to all receivers. Based on this necessary condition, an efficient parameterization for the beam search space is proposed. The proposed parameterization is given by the product manifold of a Stiefel manifold and a subset of a hyperplane and enables us to construct a very efficient beam design algorithm by exploiting its rich geometrical structure and existing tools for optimization on Stiefel manifolds. Reduction in the beam search space dimension and computational complexity by the proposed parameterization and the proposed beam design approach is significant when the number of transmit antennas is larger than the sum of the numbers of receive antennas, as in upcoming cellular networks adopting massive MIMO technologies. Numerical results validate the proposed parameterization and the proposed cooperative beam design method based on the parameterization for MIMO interference channels.Comment: 27 pages, 4 figures, Submitted to IEEE Transactions on Signal Processin

Game theory and the frequency selective interference channel - A tutorial

This paper provides a tutorial overview of game theoretic techniques used for communication over frequency selective interference channels. We discuss both competitive and cooperative techniques. Keywords: Game theory, competitive games, cooperative games, Nash Equilibrium, Nash bargaining solution, Generalized Nash games, Spectrum optimization, distributed coordination, interference channel, multiple access channel, iterative water-filling

Game Theoretic Dynamic Channel Allocation for Frequency-Selective Interference Channels

We consider the problem of distributed channel allocation in large networks under the frequency-selective interference channel. Performance is measured by the weighted sum of achievable rates. Our proposed algorithm is a modified Fictitious Play algorithm that can be implemented distributedly and its stable points are the pure Nash equilibria of a given game. Our goal is to design a utility function for a non-cooperative game such that all of its pure Nash equilibria have close to optimal global performance. This will make the algorithm close to optimal while requiring no communication between users. We propose a novel technique to analyze the Nash equilibria of a random interference game, determined by the random channel gains. Our analysis is asymptotic in the number of users. First we present a natural non-cooperative game where the utility of each user is his achievable rate. It is shown that, asymptotically in the number of users and for strong enough interference, this game exhibits many bad equilibria. Then we propose a novel non-cooperative M Frequency-Selective Interference Channel Game (M-FSIG), as a slight modification of the former, where the utility of each user is artificially limited. We prove that even its worst equilibrium has asymptotically optimal weighted sum-rate for any interference regime and even for correlated channels. This is based on an order statistics analysis of the fading channels that is valid for a broad class of fading distributions (including Rayleigh, Rician, m-Nakagami and more). We carry out simulations that show fast convergence of our algorithm to the proven asymptotically optimal pure Nash equilibria.Comment: Accepted to IEEE Transactions on Information Theor

Hierarchic Power Allocation for Spectrum Sharing in OFDM-Based Cognitive Radio Networks

In this paper, a Stackelberg game is built to model the hierarchic power allocation of primary user (PU) network and secondary user (SU) network in OFDM-based cognitive radio (CR) networks. We formulate the PU and the SUs as the leader and the followers, respectively. We consider two constraints: the total power constraint and the interference-to-signal ratio (ISR) constraint, in which the ratio between the accumulated interference and the received signal power at each PU should not exceed certain threshold. Firstly, we focus on the single-PU and multi-SU scenario. Based on the analysis of the Stackelberg Equilibrium (SE) for the proposed Stackelberg game, an analytical hierarchic power allocation method is proposed when the PU can acquire the additional information to anticipate SUs' reaction. The analytical algorithm has two steps: 1) The PU optimizes its power allocation with considering the reaction of SUs to its action. In the power optimization of the PU, there is a sub-game for power allocation of SUs given fixed transmit power of the PU. The existence and uniqueness for the Nash Equilibrium (NE) of the sub-game are investigated. We also propose an iterative algorithm to obtain the NE, and derive the closed-form solutions of NE for the perfectly symmetric channel. 2) The SUs allocate the power according to the NE of the sub-game given PU's optimal power allocation. Furthermore, we design two distributed iterative algorithms for the general channel even when private information of the SUs is unavailable at the PU. The first iterative algorithm has a guaranteed convergence performance, and the second iterative algorithm employs asynchronous power update to improve time efficiency. Finally, we extend to the multi-PU and multi-SU scenario, and a distributed iterative algorithm is presented

Joint Transmit Precoding for the Relay Interference Broadcast Channel

Relays in cellular systems are interference limited. The highest end-to-end sum rates are achieved when the relays are jointly optimized with the transmit strategy. Unfortunately, interference couples the links together making joint optimization challenging. Further, the end-to-end multi-hop performance is sensitive to rate mismatch, when some links have a dominant first link while others have a dominant second link. This paper proposes an algorithm for designing the linear transmit precoders at the transmitters and relays of the relay interference broadcast channel, a generic model for relay-based cellular systems, to maximize the end-to-end sum-rates. First, the relays are designed to maximize the second-hop sum-rates. Next, approximate end-to-end rates that depend on the time-sharing fraction and the second-hop rates are used to formulate a sum-utility maximization problem for designing the transmitters. This problem is solved by iteratively minimizing the weighted sum of mean square errors. Finally, the norms of the transmit precoders at the transmitters are adjusted to eliminate rate mismatch. The proposed algorithm allows for distributed implementation and has fast convergence. Numerical results show that the proposed algorithm outperforms a reasonable application of single-hop interference management strategies separately on two hops

Cost-Efficient Throughput Maximization in Multi-Carrier Cognitive Radio Systems

Cognitive radio (CR) systems allow opportunistic, secondary users (SUs) to access portions of the spectrum that are unused by the network's licensed primary users (PUs), provided that the induced interference does not compromise the primary users' performance guarantees. To account for interference constraints of this type, we consider a flexible spectrum access pricing scheme that charges secondary users based on the interference that they cause to the system's primary users (individually, globally, or both), and we examine how secondary users can maximize their achievable transmission rate in this setting. We show that the resulting non-cooperative game admits a unique Nash equilibrium under very mild assumptions on the pricing mechanism employed by the network operator, and under both static and ergodic (fast-fading) channel conditions. In addition, we derive a dynamic power allocation policy that converges to equilibrium within a few iterations (even for large numbers of users), and which relies only on local signal-to-interference-and-noise measurements; importantly, the proposed algorithm retains its convergence properties even in the ergodic channel regime, despite the inherent stochasticity thereof. Our theoretical analysis is complemented by extensive numerical simulations which illustrate the performance and scalability properties of the proposed pricing scheme under realistic network conditions.Comment: 24 pages, 9 figure

Approximate Best-Response Dynamics in Random Interference Games

In this paper we develop a novel approach to the convergence of Best-Response Dynamics for the family of interference games. Interference games represent the fundamental resource allocation conflict between users of the radio spectrum. In contrast to congestion games, interference games are generally not potential games. Therefore, proving the convergence of the best-response dynamics to a Nash equilibrium in these games requires new techniques. We suggest a model for random interference games, based on the long term fading governed by the players' geometry. Our goal is to prove convergence of the approximate best-response dynamics with high probability with respect to the randomized game. We embrace the asynchronous model in which the acting player is chosen at each stage at random. In our approximate best-response dynamics, the action of a deviating player is chosen at random among all the approximately best ones. We show that with high probability, with respect to the players' geometry and asymptotically with the number of players, each action increases the expected social-welfare (sum of achievable rates). Hence, the induced sum-rate process is a submartingale. Based on the Martingale Convergence Theorem, we prove convergence of the strategy profile to an approximate Nash equilibrium with good performance for asymptotically almost all interference games. We use the Markovity of the induced sum-rate process to provide probabilistic bounds on the convergence time. Finally, we demonstrate our results in simulated examples

Joint User Scheduling and Beam Selection Optimization for Beam-Based Massive MIMO Downlinks

In beam-based massive multiple-input multiple-output systems, signals are processed spatially in the radio-frequency (RF) front-end and thereby the number of RF chains can be reduced to save hardware cost, power consumptions and pilot overhead. Most existing work focuses on how to select, or design analog beams to achieve performance close to full digital systems. However, since beams are strongly correlated (directed) to certain users, the selection of beams and scheduling of users should be jointly considered. In this paper, we formulate the joint user scheduling and beam selection problem based on the Lyapunov-drift optimization framework and obtain the optimal scheduling policy in a closed-form. For reduced overhead and computational cost, the proposed scheduling schemes are based only upon statistical channel state information. Towards this end, asymptotic expressions of the downlink broadcast channel capacity are derived. To address the weighted sum rate maximization problem in the Lyapunov optimization, an algorithm based on block coordinated update is proposed and proved to converge to the optimum of the relaxed problem. To further reduce the complexity, an incremental greedy scheduling algorithm is also proposed, whose performance is proved to be bounded within a constant multiplicative factor. Simulation results based on widely-used spatial channel models are given. It is shown that the proposed schemes are close to optimal, and outperform several state-of-the-art schemes.Comment: Submitted to Trans. Wireless Commu