In this paper, we propose a novel class of Nash problems for Cognitive Radio (CR) networks composed of multiple primary users (PUs) and secondary users (SUs) wherein each SU (player) competes against the others to maximize his own opportunistic throughput by choosing jointly the sensing duration, the detection thresholds, and the vector power allocation over a multichannel link. In addition to power budget constraints, several (deterministic or probabilistic) interference constraints can be accommodated in the proposed general formulation, such as constraints on the maximum individual aggregate (probabilistic) interference tolerable from the PUs. To keep the optimization as decentralized as possible, global interference constraints, when present, are imposed via pricing; the prices are thus additional variables to be optimized. The resulting players' optimization problems are nonconvex and there are price clearance conditions associated with the nonconvex global interference constraints to be satisfied by the equilibria of the game, which make the analysis of the proposed game a challenging task; none of classical results in the game theory literature can be successfully applied. To deal with the nonconvexity of the game, we introduce a relaxed equilibrium concept - the Quasi-Nash Equilibrium (QNE)- and study its main properties, performance, and connection with local Nash equilibria. Quite interestingly, the proposed game theoretical formulations yield a considerable performance improvement with respect to current centralized and decentralized designs of CR systems, which validates the concept of QNE.
@cite_32 @cite_37 @cite_33 @cite_9 @cite_25 @cite_17 In @cite_32 (or @cite_37 @cite_33 ), the sensing time and the transmit power (or the power allocation @cite_37 @cite_33 over multi-channel links) of one SU were jointly optimized while keeping the detection probability (and thus the decision threshold) fixed to a target value. In @cite_9 @cite_25 , the authors focused on the joint optimization of the power allocation and the equi-false alarm rate of one SU @cite_9 over multi-channel links, for a sensing time. The case of multiple SUs and one PU was considered in @cite_25 (and more recently in @cite_17 ), under the same assumptions of @cite_9 ; however no formal analysis of the proposed formulation was provided. Moreover, these papers @cite_9 @cite_25 @cite_17 did not consider the sensing overhead as part of the optimization, leaving unclear how to optimally choose the sensing time.
@cite_37 @cite_33 @cite_9 @cite_32 @cite_25 @cite_17
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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. 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. 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 a cognitive radio network, the secondary users are allowed to utilize the frequency bands of primary users when these bands are not currently being used. To support this spectrum reuse functionality, the secondary users are required to sense the radio frequency environment, and once the primary users are found to be active, the secondary users are required to vacate the channel within a certain amount of time. Therefore, spectrum sensing is of significant importance in cognitive radio networks. There are two parameters associated with spectrum sensing: probability of detection and probability of false alarm. The higher the probability of detection, the better the primary users are protected. However, from the secondary users' perspective, the lower the probability of false alarm, the more chances the channel can be reused when it is available, thus the higher the achievable throughput for the secondary network. In this paper, we study the problem of designing the sensing duration to maximize the achievable throughput for the secondary network under the constraint that the primary users are sufficiently protected. We formulate the sensing-throughput tradeoff problem mathematically, and use energy detection sensing scheme to prove that the formulated problem indeed has one optimal sensing time which yields the highest throughput for the secondary network. Cooperative sensing using multiple mini-slots or multiple secondary users are also studied using the methodology proposed in this paper. Computer simulations have shown that for a 6 MHz channel, when the frame duration is 100 ms, and the signal-to-noise ratio of primary user at the secondary receiver is -20 dB, the optimal sensing time achieving the highest throughput while maintaining 90 detection probability is 14.2 ms. This optimal sensing time decreases when distributed spectrum sensing is applied.