text: 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.
  @cite_47: In this paper, we consider a wideband cognitive radio network (CRN) which can simultaneously sense multiple narrowband channels and thus aggregate the perceived available channels for transmission. We study the problem of designing the optimal spectrum sensing time and power allocation schemes so as to maximize the average achievable throughput of the CRN subject to the constraints of probability of detection and the total transmit power. The optimal sensing time and power allocation strategies are developed under two different total power constraints, namely, instantaneous power constraint and average power constraint. Finally, numerical results show that, under both cases, for a CRN with three 6 MHz channels, if the frame duration is 100 ms and the target probability of detection is 90 for the worst case signal-to-noise ratio of primary users being -12 dB, -15 dB and -20 dB, respectively, the optimal sensing time is around 6 ms and it is almost insensitive to the total transmit power.
  @cite_26: 
  @cite_33: 
  @cite_48: Sequential sensing algorithms are developed for OFDM-based hierarchical cognitive radio (CR) systems. Secondary users sense multiple sub-bands simultaneously for possible spectrum availabilities under hard miss-detection constraints to prevent interference to the primary users. Accounting for the fact that the sensing time overhead can often be significant, a performance metric is developed based on the effective achievable data rate. An optimization problem is formulated in the framework of optimal stopping problems to maximize the average effective data rate by determining the best time to stop taking samples for sensing, as well as the best set of channels to use for data transmission. A basis expansion-based sub-optimal algorithm is derived to reduce the prohibitive complexity of the optimal solution.
  @cite_9: In cognitive radio (CR) networks, the radio access from opportunistic users depends on their capabilities to detect spectrum holes. Typically, the detection problem has been considered separately from the optimization of the transmission strategy. However, in a CR context, the detection phase has an impact on network efficiency as well as on the undesired interference generated towards licensed users. In this work, we consider the joint optimization of detection thresholds and power allocation across multichannel links, in order to maximize the aggregated opportunistic throughput, under a constraint on the interference generated towards the primary users.
  @cite_24: 
  @cite_44: An optimal wideband spectrum sensing framework which identifies secondary transmission opportunities over multiple nonoverlapping narrowband channels is presented. The framework, which is referred to as multiband sensing-time-adaptive joint detection, improves the overall secondary user performance while protecting the primary network and keeping the harmful interference below a desired low level. Considering a periodic sensing scheme, the detection problem is formulated as a joint optimization problem to maximize the aggregate achievable secondary throughput capacity given a bound on the aggregate interference imposed on the primary network. It is demonstrated that the problem can be solved by convex optimization if certain practical constraints are applied. Simulation results attest that the proposed wideband spectrum sensing framework achieves superior performance compared to contemporary frameworks. An efficient iterative algorithm which solves the optimization problem with much lower complexity compared to other numerical methods is presented. It is established that the iteration-complexity and the complexity-per-iteration of the proposed algorithm increases linearly as the number of optimization variables (i.e., the number of narrowband channels) increases. The algorithm is evaluated via simulation and is shown to obtain the optimal solution very quickly and efficiently.
  @cite_40: 
  @cite_23: In this paper, we consider a sensing-based spectrum sharing scenario and present an efficient decentralized algorithm to maximize the total throughput of the cognitive radio users by optimizing jointly both the detection operation and the power allocation, taking into account the influence of the sensing accuracy. This optimization problem can be formulated as a distributed non-cooperative power allocation game, which can be solved by using an alternating direction optimization method. The transmit power budget of the cognitive radio users and the constraint related to the rate-loss of the primary user due to the interference are considered in the scheme. Finally, we use variational inequality theory in order to find the existence and uniqueness of the Nash equilibrium for our proposed distributed non-cooperative game.
  @cite_31: In this paper, optimal multi-channel cooperative sensing strategies in cognitive radio networks are investigated. A cognitive radio network with multiple potential channels is considered. Secondary users cooperatively sense the channels and send the sensing results to a coordinator, in which energy detection with a soft decision rule is employed to estimate whether there are primary activities in the channels. An optimization problem is formulated, which maximizes the throughput of secondary users while keeping detection probability for each channel above a pre-defined threshold. In particular, two sensing modes are investigated: slotted-time sensing mode and continuous-time sensing mode. With a slotted-time sensing mode, the sensing time of each secondary user consists of a number of mini-slots, each of which can be used to sense one channel. The initial optimization problem is shown to be a nonconvex mixed-integer problem. A polynomial-complexity algorithm is proposed to solve the problem optimally. With a continuous-time sensing mode, the sensing time of each secondary user for a channel can be any arbitrary continuous value. The initial nonconvex problem is converted into a convex bilevel problem, which can be successfully solved by existing methods. Numerical results are presented to demonstrate the effectiveness of our proposed algorithms.
summary: 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.