In this paper, we propose a novel class of Nash problems for Cognitive Radio (CR) networks, modeled as Gaussian frequency-selective interference channels, wherein each secondary user (SU) competes against the others to maximize his own opportunistic throughput by choosing jointly the sensing duration, the detection thresholds, and the vector power allocation. The proposed general formulation allows to accommodate several (transmit) power and (deterministic probabilistic) interference constraints, such as constraints on the maximum individual and or aggregate (probabilistic) interference tolerable at the primary receivers. To keep the optimization as decentralized as possible, global (coupling) interference constraints are imposed by penalizing each SU with a set of time-varying prices based upon his contribution to the total interference; the prices are thus additional variable to optimize. The resulting players' optimization problems are nonconvex; moreover, there are possibly price clearing conditions associated with the global constraints to be satisfied by the solution. All this makes the analysis of the proposed games a challenging task; none of classical results in the game theory literature can be successfully applied. The main contribution of this paper is to develop a novel optimization-based theory for studying the proposed nonconvex games; we provide a comprehensive analysis of the existence and uniqueness of a standard Nash equilibrium, devise alternative best-response based algorithms, and establish their convergence.
The joint optimization of the sensing and transmission strategies has been only partially addressed in the literature, even for simple CR scenarios composed of one PU and one SU. For example, in @cite_40 @cite_24 , the authors proposed alternative centralized schemes that optimize the detection thresholds for a bank of energy detectors, in order to maximize the . The optimization of the sensing time and the sensing time detection thresholds for a given missed detection probability and constant rate of one SU was addressed in @cite_26 @cite_44 and @cite_31 , respectively. A throughput-sensing trade-off for a fixed transmission rate was studied in @cite_48 . In @cite_9 (or @cite_47 ) the authors focused on the joint optimization of the power allocation and the equi-false alarm rate (or the sensing time) of a SU over multi-channel links, for a fixed sensing time (or detection probability). All the aforementioned schemes however are not applicable to scenarios composed of multiple SUs (and PUs). The case of multiple SUs and one PU was considered in @cite_33 (and more recently in @cite_23 ), under the same assumptions of @cite_9 ; however no formal analysis of the proposed formulation was provided.
@cite_47 @cite_26 @cite_33 @cite_48 @cite_9 @cite_24 @cite_44 @cite_40 @cite_23 @cite_31
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Collaborative spectrum sensing among secondary users (SUs) in cognitive networks is shown to yield a significant performance improvement. However, there exists an inherent trade off between the gains in terms of probability of detection of the primary user (PU) and the costs in terms of false alarm probability. In this paper, we study the impact of this trade off on the topology and the dynamics of a network of SUs seeking to reduce the interference on the PU through collaborative sensing. Moreover, while existing literature mainly focused on centralized solutions for collaborative sensing, we propose distributed collaboration strategies through game theory. We model the problem as a non-transferable coalitional game, and propose a distributed algorithm for coalition formation through simple merge and split rules. Through the proposed algorithm, SUs can autonomously collaborate and self-organize into disjoint independent coalitions, while maximizing their detection probability taking into account the cooperation costs (in terms of false alarm). We study the stability of the resulting network structure, and show that a maximum number of SUs per formed coalition exists for the proposed utility model. Simulation results show that the proposed algorithm allows a reduction of up to 86.6 of the average missing probability per SU (probability of missing the detection of the PU) relative to the non-cooperative case, while maintaining a certain false alarm level. In addition, through simulations, we compare the performance of the proposed distributed solution with respect to an optimal centralized solution that minimizes the average missing probability per SU. Finally, the results also show how In this paper, a cross-layer framework for joint distributed spectrum sensing, estimation and scheduling in agile wireless networks is presented. A network of secondary users (SUs) opportunistically accesses portions of the spectrum left unused by a network of licensed primary users (PUs). A central controller (CC) schedules the spectrum bands detected as idle for access by the SUs, based on compressed measurements acquired by the SUs and local feedback information from the PUs. The sparsity in the spectrum occupancy dynamics is exploited: leveraging the spectrum occupancy estimate in the previous slot, the CC needs to estimate only a residual uncertainty vector via sparse recovery techniques, thus few measurements suffice. The sensing probability of the SUs and the spectrum scheduling are adapted over time by the CC, based on the current spectrum occupancy estimate, and jointly optimized so as to maximize the SU throughput, under constraints on the PU throughput degradation and the sensing-transmission cost incurred by the SUs. The high dimensionality of the POMDP formulation is reduced by resorting to a compact state space representation via minimization of the Kullback-Leibler divergence. Simulation results demonstrate improvements up to 70 in the SU throughput over a scheme where sensing is done only locally at the CC, at a fraction of the sensing cost with respect to a scheme where sensing is done in each slot by the SUs. In this paper, we investigate the joint optimal sensing and distributed Medium Access Control (MAC) protocol design problem for cognitive radio (CR) networks. We consider both scenarios with single and multiple channels. For each scenario, we design a synchronized MAC protocol for dynamic spectrum sharing among multiple secondary users (SUs), which incorporates spectrum sensing for protecting active primary users (PUs). We perform saturation throughput analysis for the corresponding proposed MAC protocols that explicitly capture the spectrum-sensing performance. Then, we find their optimal configuration by formulating throughput maximization problems subject to detection probability constraints for PUs. In particular, the optimal solution of the optimization problem returns the required sensing time for PUs' protection and optimal contention window to maximize the total throughput of the secondary network. Finally, numerical results are presented to illustrate developed theoretical findings in this paper and significant performance gains of the optimal sensing and protocol configuration. In this paper, a new spectrum-sharing model called sensing-based spectrum sharing is proposed for cognitive radio networks. This model consists of two phases: In the first phase, the secondary user (SU) listens to the spectrum allocated to the primary user (PU) to detect the state of the PU; in the second phase, the SU adapts its transit power based on the sensing results. If the PU is inactive, the SU allocates the transmit power based on its own benefit. However, if the PU is active, the interference power constraint is imposed to protect the PU. Under this new model, the evaluation of the ergodic capacity of the SU is formulated as an optimization problem over the transmit power and the sensing time. Due to the complexity of this problem, two simplified versions, which are referred to as the perfect sensing case and the imperfect sensing case, are studied in this paper. For the perfect sensing case, the Lagrange dual decomposition is applied to derive the optimal power allocation policy to achieve the ergodic capacity. For the imperfect sensing case, an iterative algorithm is developed to obtain the optimal sensing time and the corresponding power allocation strategy. Finally, numerical results are presented to validate the proposed studies. It is shown that the SU can achieve a significant capacity gain under the proposed model, compared with that under the opportunistic spectrum access or the conventional spectrum sharing model. Because of the asynchronization between primary and secondary wireless networks, the synchronization between primary users (PUs) and secondary users (SUs) can be hardly guaranteed in nontime-slotted cognitive radio networks (CRNs). In this paper, we propose a novel framework for multichannel nontime-slotted CRNs, where the PUs randomly access and leave the licensed channels. Since the PUs cannot distinguish between primary and secondary signals, the PUs may sense a busy channel when the PUs start to reactivate during the SUs' transmission, thus generating a collision or entering the backoff stage. To guarantee the high-throughput transmission of the PUs and increase the channel utilization of the SUs, in this paper, we propose the wireless full-duplex spectrum sensing (FD-SS) scheme for SUs in multichannel nontime-slotted CRNs. Using our developed FD-SS scheme, the SUs can timely sense the PUs' reactivation during the same time when the SUs are transmitting their signals. Then, based on our proposed wireless FD-SS scheme, we further develop and analyze the wireless full-duplex cognitive medium access control (FDC-MAC) protocol for multichannel nontime-slotted CRNs. We conduct extensive numerical analyses, showing that our developed FD-SS scheme and FDC-MAC protocol can efficiently guarantee the high-throughput transmission of the PUs and increase the channel utilization of the SUs without requiring the synchronization between the PUs and the SUs over the multichannel nontime-slotted CRNs. In a cognitive radio scenario, we consider a single secondary user (SU) accessing a multichannel system. The SU senses the channels sequentially to detect if a primary user (PU) is occupying the channels and stops its search to access a channel if it offers a significantly high throughput. The optimal stopping rule and power control problem is considered. The problem is formulated as an SU's throughput-maximization problem under power, interference, and packet delay constraints. We first show the effect of the optimal stopping rule on packet delay and then solve this optimization problem for both the overlay system, where the SU transmits only at the spectrum holes, and the underlay system, where tolerable interference (or tolerable collision probability) is allowed. We provide closed-form expressions for the optimal stopping rule and show that the optimal power control strategy for this multichannel problem is a modified waterfilling approach. We extend the work to a multi-SU scenario and show that when the number of SUs is large, the complexity of the solution becomes smaller than that of the single-SU case. We discuss the application of this problem in typical networks where packets simultaneously arrive and have the same departure deadline. We further propose an online adaptation policy to the optimal stopping rule that meets the packets' hard-deadline constraint and, at the same time, gives higher throughput than the offline policy. Market-based mechanisms offer promising approaches for spectrum access in cognitive radio networks. In this paper, we focus on two market models, one with a monopoly primary user (PU) market and the other with a multiple PU market, where each PU sells its temporarily unused spectrum to secondary users (SUs). We propose a pricing-based spectrum trading mechanism that enables SUs to contend for channel usage by random access, in a distributed manner, which naturally mitigates the complexity and time overhead associated with centralized scheduling. For the monopoly PU market model, we first consider SUs contending via slotted Aloha. The revenue maximization problems here are nonconvex. We first characterize the Pareto optimal region, and then obtain a Pareto optimal solution that maximizes the SUs' throughput subject to the SUs' budget constraints. To mitigate the spectrum underutilization due to the price of contention, we revisit the problem where SUs contend via CSMA, and show that spectrum utilization is enhanced, resulting in higher revenue. When the PU's unused spectrum is a control parameter, we study further the tradeoff between the PU's utility and its revenue. For the multiple PU market model, we cast the competition among PUs as a three-stage Stackelberg game, where each SU selects a PU's channel to maximize its throughput. We characterize the Nash equilibria, in terms of access prices and the spectrum offered to SUs. Our findings reveal that the number of equilibria exhibits a phase transition phenomenon, in the sense that when the number of PUs is greater than a threshold, there exist infinitely many equilibria; otherwise, there exists a unique Nash equilibrium, where the a In this paper, we consider a cognitive radio system, consisting of a primary user (PU), a secondary user (SU) transmitter, and a SU receiver. The SUs are equipped with directional antennas. The SU transmitter first performs spectrum sensing (with errors) and then transmits data. We assume the SU and PU can coexist and the SU transmits at two power levels, according to the result of spectrum sensing (i.e., whether the spectrum is sensed idle or busy). We establish a lower bound on the ergodic capacity of the channel between SU transmitter and receiver, and study how spectrum sensing errors affect the bound. Furthermore, we explore the optimal SU transmit power levels and the optimal directions of SU transmit and receive antennas, such that the lower bound is maximized, subject to average transmit power and average interference power constraints. Through numerical simulations, we show that (compared with the case when the SUs use omni-directional antennas) directional antennas can significantly improve the lower bound in the presence of spectrum sensing errors, subject to the constraints. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. In this work we study joint pricing and power allocation for Dynamic Spectrum Access (DSA) networks with Stackelberg game. In our model, Primary User (PU) is the game leader and jointly determines its power allocation (to guarantee its QoS requirement) and the interference price charged to Secondary User (SU) (to reap revenue). Meanwhile, SU is the game follower and determines its power demand in response to PU's decisions. We quantify PU's and SU's benefit from the channel sharing model by deriving the Stackelberg equilibrium. Our results show that PU's equilibrium profit is asymptotically upper bounded with its marginal power cost and rate requirement. A distributed algorithm is proposed to find the equilibrium. We also propose an incentive-compatible mechanism for PU and SU to keep the social welfare optimum cooperatively. We extend our Stackelberg game to the multiple SUs scenario, where the interference among SUs results in a noncooperative power demand subgame. We propose a low-complexity heuristic algorithm for PU to maximize its profit. Our results show that PU can benefit by selecting multiple SUs to share its channel if SUs' mutual interference is limited.