We consider a Gaussian interference channel with independent direct and cross link channel gains, each of which is independent and identically distributed across time. Each transmitter-receiver user pair aims to maximize its long-term average transmission rate subject to an average power constraint. We formulate a stochastic game for this system in three different scenarios. First, we assume that each user knows all direct and cross link channel gains. Later, we assume that each user knows channel gains of only the links that are incident on its receiver. Lastly, we assume that each user knows only its own direct link channel gain. In all cases, we formulate the problem of finding a Nash equilibrium (NE) as a variational inequality (VI) problem. We present a novel heuristic for solving a VI. We use this heuristic to solve for a NE of power allocation games with partial information. We also present a lower bound on the utility for each user at any NE in the case of the games with partial information. We obtain this lower bound using a water-filling like power allocation that requires only knowledge of the distribution of a user's own channel gains and average power constraints of all the users. We also provide a distributed algorithm to compute Pareto optimal solutions for the proposed games. Finally, we use Bayesian learning to obtain an algorithm that converges to an $ε$-Nash equilibrium for the incomplete information game with direct link channel gain knowledge only without requiring the knowledge of the power policies of the other users.
This paper considers a distributed interference avoidance problem employing frequency assignment in the Gaussian interference channel (IC). We divide the common channel into several subchannels and each user chooses the subchannel with less amount of interference from other users as the transmit channel. This mechanism named interference avoidance in this paper can be modeled as a competitive game model. And a completely autonomous distributed iterative algorithm called Tdistributed interference avoidance algorithm (DIA) is adopted to achieve the Nash equilibriumT (NE) of the game. Due to the …
Determining how to approach the rate boundary of the Gaussian interference channel in practical system is a big concern. In this paper, a distributed rate-splitting (DRS) scheme is proposed to approach the rate region boundary of the Gaussian interference channel. It is shown that the DRS scheme can be formulated as a non-cooperative game. We introduce the Stackelberg equilibrium (SE) with multiple leaders as the equilibrium point of the non-cooperative game. Therefore, an iterative multiple waterlevels water-filling algorithm (IML-WFA) is developed to efficiently reach the SE of the non-coope…
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.
The multiple-input single-output interference channel is considered. Each transmitter is assumed to know the channels between itself and all receivers perfectly and the receivers are assumed to treat interference as additive noise. In this setting, noncooperative transmission does not take into account the interference generated at other receivers which generally leads to inefficient performance of the links. To improve this situation, we study cooperation between the links using coalitional games. The players (links) in a coalition either perform zero forcing transmission or Wiener filter pre…
This paper develops a new distributed power control scheme for a power splitting-based interference channel (IFC) with simultaneous wireless information and power transfer (SWIPT). The considered IFC consists of multiple source-destination pairs. Each destination splits its received signal into two parts for information decoding and energy harvesting (EH), respectively. Each pair adjusts its transmit power and power splitting ratio to meet both the signal-to-interference-plus-noise ratio (SINR) and EH constraints at its corresponding destination. To characterize rational behaviors of source-de…
In this paper, we consider simultaneous wireless information and power transfer (SWIPT) in relay interference channels, where multiple source-destination pairs communicate through their dedicated energy harvesting relays. Each relay needs to split its received signal from sources into two streams: one for information forwarding and the other for energy harvesting. We develop a distributed power splitting framework using game theory to derive a profile of power splitting ratios for all relays that can achieve a good network-wide performance. Specifically, non-cooperative games are respectively …
In this paper we analyze the interference channel as a conflict situation. This viewpoint implies that certain points in the rate region are unreasonable to one of the players. Therefore these points cannot be considered achievable based on game theoretic considerations. We then propose to use Nash bargaining solution as a tool that provides preferred points on the boundary of the game theoretic rate region. We provide analysis for the 2x2 intereference channel using the FDM achievable rate region. We also outline how to generalize our results to other achievable rate regions for the interfere…
In this paper, we consider a Gaussian multiple access channel with multiple independent additive white Gaussian interferences. Each interference is known to exactly one transmitter non-causally. The capacity region is characterized to within a constant gap regardless of channel parameters. These results are based on a layered modulo-lattice scheme which realizes distributed interference cancellation.
Based on closed-form interference alignment (IA) solutions, a low overhead distributed interference alignment (LOIA) scheme is proposed in this paper for the $K$-user SISO interference channel, and extension to multiple antenna scenario is also considered. Compared with the iterative interference alignment (IIA) algorithm proposed by Gomadam et al., the overhead is greatly reduced. Simulation results show that the IIA algorithm is strictly suboptimal compared with our LOIA algorithm in the overhead-limited scenario.
In this paper we discuss the use of cooperative game theory for analyzing interference channels. We extend our previous work, to games with N players as well as frequency selective channels and joint TDM/FDM strategies. We show that the Nash bargaining solution can be computed using convex optimization techniques. We also show that the same results are applicable to interference channels where only statistical knowledge of the channel is available. Moreover, for the special case of two players $2\times K$ frequency selective channel (with K frequency bins) we provide an $O(K \log_2 K)$ complex…
In the first part of this paper we have derived achievable transmission rates for the (single-band) interference relay channel (IRC) when the relay implements either the amplify-and-forward, decode-and-forward or estimate-and-forward protocol. Here, we consider wireless networks that can be modeled by a multi-band IRC. We tackle the existence issue of Nash equilibria (NE) in these networks where each information source is assumed to selfishly allocate its power between the available bands in order to maximize its individual transmission rate. Interestingly, it is possible to show that the thre…
We consider a wireless channel shared by multiple transmitter-receiver pairs. Their transmissions interfere with each other. Each transmitter-receiver pair aims to maximize its long-term average transmission rate subject to an average power constraint. This scenario is modeled as a stochastic game under different assumptions. We first assume that each transmitter and receiver has knowledge of all direct and cross link channel gains. We later relax the assumption to the knowledge of incident channel gains and then further relax to the knowledge of the direct link channel gains only. In all the …
We introduce conferencing-based distributed channel quantizers for two-user interference networks where interference signals are treated as noise. Compared with the conventional distributed quantizers where each receiver quantizes its own channel independently, the proposed quantizers allow multiple rounds of feedback communication in the form of conferencing between receivers. We take the network outage probabilities of sum rate and minimum rate as performance measures and consider quantizer design in the transmission strategies of time sharing and interference transmission. First, we propose…
We consider a wireless channel shared by multiple transmitter-receiver pairs. Their transmissions interfere with each other. Each transmitter-receiver pair aims to maximize its long-term average transmission rate subject to an average power constraint. This scenario is modeled as a stochastic game. We provide sufficient conditions for existence and uniqueness of a Nash equilibrium (NE). We then formulate the problem of finding NE as a variational inequality (VI) problem and present an algorithm to solve the VI using regularization. We also provide distributed algorithms to compute Pareto optim…
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…
This paper proposes an interference alignment method with distributed and delayed channel state information at the transmitter (CSIT) for a class of interference networks. The core idea of the proposed method is to align interference signals over time at the unintended receivers in a distributed manner. With the proposed method, achievable trade-offs between the sum of degrees of freedom (sum-DoF) and feedback delay of CSI are characterized in both the X-channel and three-user interference channel to reveal the impact on how the CSI feedback delay affects the sum-DoF of the interference networ…
We consider a network composed of two interfering point-to-point links where the two transmitters can exploit one common relay node to improve their individual transmission rate. Communications are assumed to be multi-band and transmitters are assumed to selfishly allocate their resources to optimize their individual transmission rate. The main objective of this paper is to show that this conflicting situation (modeled by a non-cooperative game) has some stable outcomes, namely Nash equilibria. This result is proved for three different types of relaying protocols: decode-and-forward, estimate-…
Recent results establish the optimality of interference alignment to approach the Shannon capacity of interference networks at high SNR. However, the extent to which interference can be aligned over a finite number of signalling dimensions remains unknown. Another important concern for interference alignment schemes is the requirement of global channel knowledge. In this work we provide examples of iterative algorithms that utilize the reciprocity of wireless networks to achieve interference alignment with only local channel knowledge at each node. These algorithms also provide numerical insig…
We consider a two-user Gaussian multiple access channel with two independent additive white Gaussian interferences. Each interference is known to exactly one transmitter non-causally. Transmitters are allowed to cooperate through finite-capacity links. The capacity region is characterized to within 3 and 1.5 bits for the stronger user and the weaker user respectively, regardless of channel parameters. As a by-product, we characterize the capacity region of the case without cooperation to within 1 and 0.5 bits for the stronger user and the weaker user respectively. These results are based on a …
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 tolera…
In this paper, we study the problem of cooperative interference management in an OFDMA two-tier small cell network. In particular, we propose a novel approach for allowing the small cells to cooperate, so as to optimize their sum-rate, while cooperatively satisfying their maximum transmit power constraints. Unlike existing work which assumes that only disjoint groups of cooperative small cells can emerge, we formulate the small cells' cooperation problem as a coalition formation game with overlapping coalitions. In this game, each small cell base station can choose to participate in one or mor…
Regenerating codes based on the approach of interference alignment for wireless interference channel achieve the cut-set bound for distributed storage systems. These codes provide data reliability, and perform efficient exact node repair when some node fails. Interference alignment as a concept is especially important to improve the repair efficiency of a failed node in a minimum storage regenerating (MSR) code. In addition it can improve the stored data security in presence of passive intruders. In this paper we construct a new code resilient against a threat model where a passive eavesdroppe…
The layered interference network is investigated with delayed channel state information (CSI) at all nodes. It is demonstrated how multi-hopping can be utilized to increase the achievable degrees of freedom (DoF). In particular, a multi-phase transmission scheme is proposed for the $K$-user $2K$-hop interference network in order to systematically exploit the layered structure of the network and delayed CSI to achieve DoF values that scale with $K$. This result provides the first example of a network with distributed transmitters and delayed CSI whose DoF scales with the number of users.
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/aggregat…
We consider a wireless communication system in which $N$ transmitter-receiver pairs want to communicate with each other. Each transmitter transmits data at a certain rate using a power that depends on the channel gain to its receiver. If a receiver can successfully receive the message, it sends an acknowledgment (ACK), else it sends a negative ACK (NACK). Each user aims to maximize its probability of successful transmission. We formulate this problem as a stochastic game and propose a fully distributed learning algorithm to find a correlated equilibrium (CE). In addition, we use a no regret al…
It is already well-known that interference alignment (IA) achieves the sum capacity of the K-user interference channel at the high interference regime. On the other hand, it is intuitively clear that when the interference levels are very low, a sum-rate scaling of K (as opposed to K/2 for IA) should be accessed at high signal-to-noise ratio values by simple ("myopic") single-link multiple-input multiple-output (MIMO) techniques such as waterfilling. Recent results have indicated that in certain low-to-moderate interference cases, treating interference as noise may in fact be preferable. In thi…
This paper studies the problem of distributed beam scheduling for 5G millimeter-Wave (mm-Wave) cellular networks where base stations (BSs) belonging to different operators share the same spectrum without centralized coordination among them. Our goal is to design efficient distributed scheduling algorithms to maximize the network utility, which is a function of the achieved throughput by the user equipment (UEs), subject to the average and instantaneous power consumption constraints of the BSs. We propose a Media Access Control (MAC) and a power allocation/adaptation mechanism utilizing the Lya…
We consider the problem of quantifying the Pareto optimal boundary in the achievable rate region over multiple-input single-output (MISO) interference channels, where the problem boils down to solving a sequence of convex feasibility problems after certain transformations. The feasibility problem is solved by two new distributed optimal beamforming algorithms, where the first one is to parallelize the computation based on the method of alternating projections, and the second one is to localize the computation based on the method of cyclic projections. Convergence proofs are established for bot…
Radio resource sharing mechanisms are key to ensuring good performance in wireless networks. In their seminal paper \cite{tassiulas1}, Tassiulas and Ephremides introduced the Maximum Weighted Scheduling algorithm, and proved its throughput-optimality. Since then, there have been extensive research efforts to devise distributed implementations of this algorithm. Recently, distributed adaptive CSMA scheduling schemes \cite{jiang08} have been proposed and shown to be optimal, without the need of message passing among transmitters. However their analysis relies on the assumption that interference …
This work considers coordination and bargaining between two selfish users over a Gaussian interference channel. The usual information theoretic approach assumes full cooperation among users for codebook and rate selection. In the scenario investigated here, each user is willing to coordinate its actions only when an incentive exists and benefits of cooperation are fairly allocated. The users are first allowed to negotiate for the use of a simple Han-Kobayashi type scheme with fixed power split. Conditions for which users have incentives to cooperate are identified. Then, two different approach…
This paper tackles the problem of how two selfish users jointly determine the operating point in the achievable rate region of a two-user Gaussian interference channel through bargaining. In previous work, incentive conditions for two users to cooperate using a simple version of Han-Kobayashi scheme was studied and the Nash bargaining solution (NBS) was used to obtain a fair operating point. Here a noncooperative bargaining game of alternating offers is adopted to model the bargaining process and rates resulting from the equilibrium outcome are analyzed. In particular, it is shown that the ope…
Three science and engineering problems of recent interests -index coding, locally recoverable distributed storage, and guessing games on graphs- are discussed and the connection between their optimal solutions is elucidated. By generalizing recent results by Shanmugam and Dimakis and by Mazumdar on the complementarity between the optimal broadcast rate of an index coding problem on a directed graph and the normalized rate of a locally recoverable distributed storage problem on the same graph, it is shown that the capacity region and the optimal rate region of these two problems are complementa…
Interference mitigation techniques are essential for improving the performance of interference limited wireless networks. In this paper, we introduce novel interference mitigation schemes for wireless cellular networks with space division multiple access (SDMA). The schemes are based on a virtual layer that captures and simplifies the complicated interference situation in the network and that is used for power control. We show how optimization in this virtual layer generates gradually adapting power control settings that lead to autonomous interference minimization. Thereby, the granularity of…
We consider a MIMO interference channel in which the transmitters and receivers operate in frequency-division duplex mode. In this setting, interference management through coordinated transceiver design necessitates channel state information at the transmitters (CSI-T). The acquisition of CSI-T is done through feedback from the receivers, which entitles a loss in degrees of freedom, due to training and feedback. This loss increases with the amount of CSI-T. In this work, after formulating an overhead model for CSI acquisition at the transmitters, we propose a distributed mechanism to find for …
In the past few years we have witnessed the paradigm shift from static spectrum allocation to dynamic spectrum access/sharing. Orthogonal Frequency-Division Multiple Access (OFDMA) is a promising mechanism to implement the agile spectrum access. However, in wireless distributed networks where tight synchronization is infeasible, OFDMA faces the problem of cross-band interference. Subcarriers used by different users are no longer orthogonal, and transmissions operating on non-overlapping subcarriers can interfere with each other. In this paper, we explore the cause of cross-band interference an…
This paper considers the problem of interference control through the use of second-order statistics in massive MIMO multi-cell networks. We consider both the cases of co-located massive arrays and large-scale distributed antenna settings. We are interested in characterizing the low-rankness of users' channel covariance matrices, as such a property can be exploited towards improved channel estimation (so-called pilot decontamination) as well as interference rejection via spatial filtering. In previous work, it was shown that massive MIMO channel covariance matrices exhibit a useful finite rank …
This letter studies the power allocation and scheduling problem in two-cell distributed interference subtraction system. Through the interference is cancelled at one receiver side and the analysis of objective function monotony, our key result is the decoupling of power allocation and scheduling without loss of optimality. Simulation exhibits the significant gains of our proposed algorithm over open-loop power allocation with non-cooperation proportional fair scheduling.
We study the problem of interference management in large-scale small cell networks, where each user equipment (UE) needs to determine in a distributed manner when and at what power level it should transmit to its serving small cell base station (SBS) such that a given network performance criterion is maximized subject to minimum quality of service (QoS) requirements by the UEs. We first propose a distributed algorithm for the UE-SBS pairs to find a subset of weakly interfering UE-SBS pairs, namely the maximal independent sets (MISs) of the interference graph in logarithmic time (with respect t…
In this paper, we consider the problem of maximizing the weighted sum energy efficiency (WS-EE) for multi-input single-output (MISO) interference channels (ICs) which is well acknowledged as general models of heterogeneous networks (HetNets), multicell networks, etc. To address this problem, we develop an efficient distributed beamforming algorithm based on a pricing mechanism. Specifically, we carefully introduce a price metric for distributed beamforming design which fortunately allows efficient closed-form solutions to the per-user beam-vector optimization problem. The convergence of the di…
We study the distributed optimization of transmit strategies in a multiple-input, single-output (MISO) interference channel (IFC). Existing distributed algorithms rely on stricly synchronized update steps by the individual users. They require a global synchronization mechanism and potentially suffer from the synchronization penalty caused by e.g., backhaul communication delays and fixed update sequences. We establish a general optimization framework that allows asynchronous update steps. The users perform their computations at arbitrary instants of time, and do not wait for information that ha…
It is shown that the performance of the maximal scheduling algorithm in wireless ad hoc networks under the hypergraph interference model can be further away from optimal than previously known. The exact worst-case performance of this distributed, greedy scheduling algorithm is analyzed.
In this letter, we investigate the problem of dynamic spectrum access for small cell networks, using a graphical game approach. Compared with existing studies, we take the features of different cell loads and local interference relationship into account. It is proved that the formulated spectrum access game is an exact potential game with the aggregate interference level as the potential function, and Nash equilibrium (NE) of the game corresponds to the global or local optima of the original optimization problem. A lower bound of the achievable aggregate interference level is rigorously derive…
Femtocell networks are promising for not only improving the coverage but also increasing the capacity of current cellular networks. The interference-limited reality in femtocell networks makes interference management (IM) the key to maintaining the quality of service and fairness in femtocell networks. Over-the-air signaling is one of the most effective means for fast distributed dynamic IM. However, the design of this type of signal is challenging. In this paper, we address the challenges and propose an effective solution, referred to as single-tone signaling (STS). The proposed STS scheme po…
In this paper 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. First we present a natural non-cooperative game theoretic formulation for this problem. It is shown that, when interference is sufficiently strong, this game has a pure price of anarchy approaching infinity with high probability, and there is an asymptotically increasing number of equilibria with the worst performance. Then we propose a novel non-cooperative M Frequency-Selective Interferen…
For multi-user transmissions over MIMO interference channels, each user designs the transmit covariance matrix to maximize its information rate. When passive radio-frequency (RF) energy harvesters are present in the network, the transmissions are constrained by both the transmit power limits and the energy harvesting requirements. A passive RF energy harvester collects the radiated energy from nearby wireless information transmitters instead of using a dedicated wireless power source. It needs multiple transmitters to concentrate their RF radiation on it because typical electric field strength…
In this paper, a game-theoretic model for studying power control for wireless data networks in frequency-selective multipath environments is analyzed. The uplink of an impulse-radio ultrawideband system is considered. The effects of self-interference and multiple-access interference on the performance of Rake receivers are investigated for synchronous systems. Focusing on energy efficiency, a noncooperative game is proposed in which users in the network are allowed to choose their transmit powers to maximize their own utilities, and the Nash equilibrium for the proposed game is derived. It is …
We consider joint optimization of artificial noise (AN) and information signals in a MIMO wiretap interference network, wherein the transmission of each link may be overheard by several MIMO-capable eavesdroppers. Each information signal is accompanied with AN, generated by the same user to confuse nearby eavesdroppers. Using a noncooperative game, a distributed optimization mechanism is proposed to maximize the secrecy rate of each link. The decision variables here are the covariance matrices for the information signals and ANs. However, the nonconvexity of each link's optimization problem (i…
Internet of Things (IoT) networks for smart sensor nodes in the next generation of smart wireless sensing systems require a distributed security scheme to prevent the passive (eavesdropping) or active (jamming and interference) attacks from untrusted sensor nodes. This paper concerns advancing the security of the IoT system to address their vulnerability to being attacked or compromised by the advancement of future supercomputers. In this work, a novel embedded architecture has been designed and implemented for a distributed IoT network that utilizes a master-slave full-duplex communication to…
This letter investigates the problem of distributed spectrum access for cognitive small cell networks. Compared with existing work, two inherent features are considered: i) the transmission of a cognitive small cell base station only interferes with its neighbors due to the low power, i.e., the interference is local, and ii) the channel state is time-varying due to fading. We formulate the problem as a robust graphical game, and prove that it is an ordinal potential game which has at least one pure strategy Nash equilibrium (NE). Also, the lower throughput bound of NE solutions is analytically…
This invited paper presents some novel ideas on how to enhance the performance of consensus algorithms in distributed wireless sensor networks, when communication costs are considered. Of particular interest are consensus algorithms that exploit the broadcast property of the wireless channel to boost the performance in terms of convergence speeds. To this end, we propose a novel clustering based consensus algorithm that exploits interference for computation, while reducing the energy consumption in the network. The resulting optimization problem is a semidefinite program, which can be solved o…
The interference channel is the simplest communication scenario where multiple autonomous users compete for shared resources. We combine game theory and information theory to define a notion of a Nash equilibrium region of the interference channel. The notion is game theoretic: it captures the selfish behavior of each user as they compete. The notion is also information theoretic: it allows each user to use arbitrary communication strategies as it optimizes its own performance. We give an exact characterization of the Nash equilibrium region of the two-user linear deterministic interference ch…
This paper investigates the problem of database-assisted spectrum access in dynamic TV white spectrum networks, in which the active user set is varying. Since there is no central controller and information exchange, it encounters dynamic and incomplete information constraints. To solve this challenge, we formulate a state-based spectrum access game and a robust spectrum access game. It is proved that the two games are ordinal potential games with the (expected) aggregate weighted interference serving as the potential functions. A distributed learning algorithm is proposed to achieve the pure s…
The introduction of device-to-device (D2D) into cellular networks poses many new challenges in the resource allocation design due to the co-channel interference caused by spectrum reuse and limited battery life of user equipments (UEs). In this paper, we propose a distributed interference-aware energy-efficient resource allocation algorithm to maximize each UE's energy efficiency (EE) subject to its specific quality of service (QoS) and maximum transmission power constraints. We model the resource allocation problem as a noncooperative game, in which each player is self-interested and wants to…
In this paper, multi-stream transmission in interference networks aided by multiple amplify-and-forward (AF) relays in the presence of direct links is considered. The objective is to minimize the sum power of transmitters and relays by beamforming optimization under the stream signal-to-interference-plus-noise-ratio (SINR) constraints. For transmit beamforming optimization, the problem is a well-known non-convex quadratically constrained quadratic program (QCQP) that is NP-hard to solve. After semi-definite relaxation (SDR), the problem can be optimally solved via alternating direction method …
This paper considers the minimization of transmit power in Gaussian parallel interference channels, subject to a rate constraint for each user. To derive decentralized solutions that do not require any cooperation among the users, we formulate this power control problem as a (generalized) Nash equilibrium game. We obtain sufficient conditions that guarantee the existence and nonemptiness of the solution set to our problem. Then, to compute the solutions of the game, we propose two distributed algorithms based on the single user waterfilling solution: The \emph{sequential} and the \emph{simulta…
In this paper, we study the transmission strategy adaptation problem in an RF-powered cognitive radio network, in which hybrid secondary users are able to switch between the harvest-then-transmit mode and the ambient backscatter mode for their communication with the secondary gateway. In the network, a monetary incentive is introduced for managing the interference caused by the secondary transmission with imperfect channel sensing. The sensing-pricing-transmitting process of the secondary gateway and the transmitters is modeled as a single-leader-multi-follower Stackelberg game. Furthermore, t…
