Joint Spectrum and Power Allocation for D2D Communications Underlaying Cellular Networks

This paper addresses the joint spectrum sharing and power allocation problem for device-to-device (D2D) communications underlaying a cellular network (CN). In the context of orthogonal frequency-division multiple-access systems, with the uplink resources shared with D2D links, both centralized and decentralized methods are proposed. Assuming global channel state information (CSI), the resource allocation problem is first formulated as a nonconvex optimization problem, which is solved using convex approximation techniques. We prove that the approximation method converges to a suboptimal solution and is often very close to the global optimal solution. On the other hand, by exploiting the decentralized network structure with only local CSI at each node, the Stackelberg game model is then adopted to devise a distributed resource allocation scheme. In this game-theoretic model, the base station (BS), which is modeled as the leader, coordinates the interference from the D2D transmission to the cellular users (CUs) by pricing the interference. Subsequently, the D2D pairs, as followers, compete for the spectrum in a noncooperative fashion. Sufficient conditions for the existence of the Nash equilibrium (NE) and the uniqueness of the solution are presented, and an iterative algorithm is proposed to solve the problem. In addition, the signaling overhead is compared between the centralized and decentralized schemes. Finally, numerical results are presented to verify the proposed schemes. It is shown that the distributed scheme is effective for the resource allocation and could protect the CUs with limited signaling overhead

Normalized Nash Equilibrium for Power Allocation in Cognitive Radio Networks

International audience—We consider a cognitive radio system consisting of several secondary networks and primary user-terminals (primary-UTs). In a secondary network a secondary-base station (secondary-BS) transmits to a secondary-user terminal (secondary-UT) with certain power. Secondary-BSs are constrained to allocate transmitting powers such that the total interference at each primary-UT is below a given threshold. We formulate the power allocation problem as a concave non cooperative game with secondary-BSs as players and multiple primary-UTs enforcing coupled constraints. The equilibrium selection is based on the concept of normalized Nash equilibrium (NNE). When the interference at a secondary-UT from adjacent secondary-BSs is negligible, the NNE is shown to be unique for any strictly concave utility. The NNE is also shown to be the solution of a concave potential game. We propose a distributed algorithm which converges to the unique NNE. When the interference at a secondary-UT from adjacent secondary-BSs is not negligible, an NNE may not be unique and the computation of the NNE has exponential complexity. To avoid these drawbacks, we introduce the concept of weakly normalized Nash equilibrium (WNNE) which keeps the most of NNEs' interesting properties but, in contrast to the latter, the WNNE can be determined with low complexity. We show the usefulness of the WNNE when the utility function is the Shannon capacity. I. INTRODUCTION A traditional static spectrum access leads to spectrum under-utilization. Cognitive radio can enhance the spectrum utilization if primary network providers (license spectrum holders) allow secondary users (unlicensed users) to access the licensed spectrum provided that the primary users (subscribers of the primary network providers) are protected from the interference of secondary users [2]. Without proper policies for power and frequency band allocation, the transmission rates at primary-UTs' would degrade significantly and thus, a primary network provider would not allow secondary users to access the spectrum. Therefore, in a secondary network a secondary-BS must select its transmission power using cognitive radio technology such that the total interference from secondary-BSs at each primary-UT is below an acceptable threshold. In practice, each secondary-BS is an independent entity and selects its transmission power level in order to maximize onl

ECONOMIC APPROACHES AND MARKET STRUCTURES FOR TEMPORAL-SPATIAL SPECTRUM SHARING

In wireless communication systems, economic approaches can be applied to spectrum sharing and enhance spectrum utilization. In this research, we develop a model where geographic information, including licensed areas of primary users (PUs) and locations of secondary users (SUs), plays an important role in the spectrum sharing system. We consider a multi-price policy and the pricing power of noncooperative PUs in multiple geographic areas. Meanwhile, the value assessment of a channel is price-related and the demand from the SUs is price-elastic. By applying an evolutionary procedure, we prove the existence and uniqueness of the optimal payoff for each PU selling channels without reserve. In the scenario of selling channels with reserve, we predict the channel prices for the PUs leading to the optimal supplies of the PUs and hence the optimal payoffs. To increase spectrum utilization, the scenario of spatial spectrum reuse is considered. We consider maximizing social welfare via on-demand channel allocation, which describes the overall satisfaction of the SUs when we involve the supply and demand relationship. We design a receiver-centric spectrum reuse mechanism, in which the optimal channel allocation that maximizes social welfare can be achieved by the Vickrey-Clarke-Groves (VCG) auction for maximal independent groups (MIGs). We prove that truthful bidding is the optimal strategy for the SUs, even though the SUs do not participate in the VCG auction for MIGs directly. Therefore, the MIGs are bidding truthfully and the requirement for social welfare maximization is satisfied. To further improve user satisfaction, user characteristics that enable heterogeneous channel valuations need to be considered in spatial spectrum reuse. We design a channel transaction mechanism for non-symmetric networks and maximize user satisfaction in consideration of multi-level flexible channel valuations of the SUs. Specifically, we introduce a constrained VCG auction. To facilitate the bid formation, we transform the constrained VCG auction to a step-by-step decision process. Meanwhile, the SUs in a coalition play a coalitional game with transferable utilities. We use the Shapley value to realize fair payoff distribution among the SUs in a coalition

Mathematical optimization and game theoretic methods for radar networks

Radar systems are undoubtedly included in the hall of the most momentous discoveries of the previous century. Although radars were initially used for ship and aircraft detection, nowadays these systems are used in highly diverse fields, expanding from civil aviation, marine navigation and air-defence to ocean surveillance, meteorology and medicine. Recent advances in signal processing and the constant development of computational capabilities led to radar systems with impressive surveillance and tracking characteristics but on the other hand the continuous growth of distributed networks made them susceptible to multisource interference. This thesis aims at addressing vulnerabilities of modern radar networks and further improving their characteristics through the design of signal processing algorithms and by utilizing convex optimization and game theoretic methods. In particular, the problems of beamforming, power allocation, jammer avoidance and uncertainty within the context of multiple-input multiple-output (MIMO) radar networks are addressed. In order to improve the beamforming performance of phased-array and MIMO radars employing two-dimensional arrays of antennas, a hybrid two-dimensional Phased-MIMO radar with fully overlapped subarrays is proposed. The work considers both adaptive (convex optimization, CAPON beamformer) and non-adaptive (conventional) beamforming techniques. The transmit, receive and overall beampatterns of the Phased-MIMO model are compared with the respective beampatterns of the phased-array and the MIMO schemes, proving that the hybrid model provides superior capabilities in beamforming. By incorporating game theoretic techniques in the radar field, various vulnerabilities and problems can be investigated. Hence, a game theoretic power allocation scheme is proposed and a Nash equilibrium analysis for a multistatic MIMO network is performed. A network of radars is considered, organized into multiple clusters, whose primary objective is to minimize their transmission power, while satisfying a certain detection criterion. Since no communication between the clusters is assumed, non-cooperative game theoretic techniques and convex optimization methods are utilized to tackle the power adaptation problem. During the proof of the existence and the uniqueness of the solution, which is also presented, important contributions on the SINR performance and the transmission power of the radars have been derived. Game theory can also been applied to mitigate jammer interference in a radar network. Hence, a competitive power allocation problem for a MIMO radar system in the presence of multiple jammers is investigated. The main objective of the radar network is to minimize the total power emitted by the radars while achieving a specific detection criterion for each of the targets-jammers, while the intelligent jammers have the ability to observe the radar transmission power and consequently decide its jamming power to maximize the interference to the radar system. In this context, convex optimization methods, noncooperative game theoretic techniques and hypothesis testing are incorporated to identify the jammers and to determine the optimal power allocation. Furthermore, a proof of the existence and the uniqueness of the solution is presented. Apart from resource allocation applications, game theory can also address distributed beamforming problems. More specifically, a distributed beamforming and power allocation technique for a radar system in the presence of multiple targets is considered. The primary goal of each radar is to minimize its transmission power while attaining an optimal beamforming strategy and satisfying a certain detection criterion for each of the targets. Initially, a strategic noncooperative game (SNG) is used, where there is no communication between the various radars of the system. Subsequently, a more coordinated game theoretic approach incorporating a pricing mechanism is adopted. Furthermore, a Stackelberg game is formulated by adding a surveillance radar to the system model, which will play the role of the leader, and thus the remaining radars will be the followers. For each one of these games, a proof of the existence and uniqueness of the solution is presented. In the aforementioned game theoretic applications, the radars are considered to know the exact radar cross section (RCS) parameters of the targets and thus the exact channel gains of all players, which may not be feasible in a real system. Therefore, in the last part of this thesis, uncertainty regarding the channel gains among the radars and the targets is introduced, which originates from the RCS fluctuations of the targets. Bayesian game theory provides a framework to address such problems of incomplete information. Hence, a Bayesian game is proposed, where each radar egotistically maximizes its SINR, under a predefined power constraint