Two novel price-based algorithms for spectrum sharing in cognitive radio networks

According to the regulations of the Federal Communication Commission (FCC) [1], a large portion of the unutilized priced frequency spectrum and the scarcity in spectrum resource should be used by providing tools to utilize spectrum holes [2]. Recently, cognitive radio (CR) provides great flexibility by extending software radio to improve spectrum utilization [2‐6], which is now regarded as a hopeful wireless communication system. Primary users (licensed users) are willing to share frequency spectrum with secondary users (unlicensed users) which can adaptively adjust the transmission parameters to satisfy the requirements of quality of service (QoS) according to the environment information and opportunistically access those available frequency bands not occupied by primary users.

By this way, we can use the spectrum resource to enhance the system performance. We consider spectrum sharing as a spectrum trading process; therefore, price not only acts an important role in spectrum trading but also is an effective way to improve system utilization and performance to maximize the primary users' profits. The spectrum trading process indicates the values of both spectrum pricing and purchasing by allowing the spectrum trading between secondary users (SUs) and primary users (PUs). The price paid by SU to PU depends on the satisfaction to use that spectrum, while the price determines the PU's revenue.

In this article, we address the spectrum sharing problem in a cognitive radio environment, which consists of several SUs to compete with each other to demand opportunistic spectrum access to a single PU. We formulate this situation as an oligopoly market, where a few firms (i.e., SUs) compete with each other in terms of amount of commodity (i.e., the frequency spectrum) supplied to the market (i.e., PU) to gain the greatest profit.

A noncooperative game is used to analyze two situations, one case is that SUs receive the offered price by the PU and maximize their payoffs by the amount of their demand spectrum. Another case is that the main objection is to maximize the profit and revenue for all SUs and the PU, respectively. For these scenarios, we apply a dynamic game in which the selection of strategy by an SU is entirely determined by the pricing information obtained from the PU. Based on this information, each SU gradually adapts the size of its spectrum sharing which is controlled by the price function. To solve the corresponding optimization problem, we search the strategy space using swarm particle to identify the optimum behavior.

Compared with the current research on the spectrum sharing in a cognitive radio environment, the major contributions of this article are as follows. First, the idea is to bring together swarm particle algorithms and Nash strategy, and make the swarm particle algorithm to build the Nash equilibrium (NE). Nash-particle swarm optimization (PSO) is an alternative for multiple-objective optimizations as it is an optimization tool based on noncooperative game theory. Second, by applying bilevel techniques in the cognitive radio markets, we propose the concept and related definitions of nonlinear bilevel one-leader-multiple-follower (NBMF) decision problem and use swarm particle algorithm in designing the spectrum sharing scheme among PU and SUs for CR networks. We also build up a nonlinear NBMF decision model for strategic pricing problems, where the Stackelberg-Nash equilibrium is regarded as the solution.

The rest of this article is organized as follows. Section 2 addresses the related works on dynamic spectrum sharing in cognitive radio networks (CRN). Section 3 proposes the general NBMF decision model and introduces the Stackelberg-Nash equilibrium. We present the system model and describe the spectrum sharing and pricing strategy problem in Section 4. We develop Nash-PSO and NBMF-PSO algorithm as solutions to the NLMF, and the NBMF problems in Section 5. Then, we verify the effectiveness of the proposed algorithm to validate the NLMF and the NBMF decision model using simulation in Section 6, and finally we make conclusions in Section 7.

For the development of communication protocols, cognitive radio technology offers tremendous potential to improve the radio spectrum usage by allowing cognitive devices to opportunistically access vast portions of the spectrum. Dynamic spectrum access is a new paradigm, whereby a cognitive radio device opportunistically accesses the unutilized or underutilized spectrum bands. There are many important issues needed to be overcome to achieve the objective of dynamic spectrum access, including spectrum sensing, spectrum allocation, spectrum access/sharing, transmitter-receiver handshaking, and spectrum mobility [7]. In [8], the different spectrum sharing models are categorized as open sharing, hierarchical access, and dynamic exclusive usage models. Some of the spectrum sharing proposals can be identified as being hierarchical access methods, in that there is usually a primary system that owns the spectrum rights and a secondary system that wants to access this spectrum whenever possible. Dynamic spectrum sharing is a challenging in the design of CRNs due to the requirement of peaceful coexistence of both PUs and SUs, as well as the availability of wide range of radio spectrum.

Various techniques were used to model the spectrum sharing problems for CR networks. In [9], the conventional approach based on the centralized control is proposed. However, as the available spectrum holes in the CRN are rapidly changing, it is difficult to use centralized approach in the practical application. Other studies propose distributed approaches [10, 11]. The authors of [10] provide better adaptive capacity to cognitive radios, in dynamic communication environments. The efforts of [11] have been absorbed in applying the distributed ARQ in cognitive radio systems to make better the dependability of secondary links. Dynamic spectrum sharing through cognitive radios can significantly enhance the spectrum utilization in a wireless network. In spectrum sharing CR networks, the problem of fair resource allocation among secondary users was investigated in [12]. In [13], the fair, efficient, and power optimized (FEPO) spectrum sharing scheme is proposed to achieve efficient spectrum utilization. In [14], the biologically inspired spectrum sharing algorithm is introduced based on the adaptive task allocation model of an insect colony, which enables each cognitive radio in the same environment to fairly share the licensed or unlicensed spectrum bands.

Game theory [15] has been considered a feasible mathematical tool for solving the resource allocation problems in distributed CRNs. The fundamental concept of game theory is to resolve the competition and cooperation among multiple intelligent rational decision makers. The comparison between cooperative and noncooperative approaches has been presented in [16] through game theoretical analysis. The authors of [17] develop the optimal resource allocation strategies in secondary spectrum access problem using cooperative game theory. This work applies the concept of Nash bargaining solution to guarantee fairness and maximize the utility of the system optimality. In [18], the dynamic spectrum access problem is formulated as a noncooperative game, and the concepts of the correlated equilibrium and regret learning are used to solve the dynamic spectrum access problem. However, the abovementioned works do not consider the pricing issue in spectrum trading.

Pricing impacts the incentive of the PUs (or primary service providers) in selling the spectrum and the satisfaction of the SUs in buying the spectrum. A pricing process can maximize the utilities of both PUs and SUs according to the spectrum dynamics. Efficient pricing techniques not only increase the users' performance, but also improve network utilization in consideration of the rapid growth and variety of network demand. Researchers have already proposed and investigated to achieve dynamic spectrum sharing by various pricing and auction mechanisms [19‐21]. In [19], the problem of a CDMA operator participating in a dynamic spectrum allocation scheme is addressed in a cooperative framework based on multi-unit Vickrey auction. The operators maximize their revenue based on the users' willingness to pay. The authors of [20] use a power/channel allocation scheme that uses a distributed pricing strategy to improve the network's performance by a noncooperative model. An auction-based spectrum sharing approach is proposed [21], in which many SUs purchase channels from one PU or spectrum broker through an auction process to efficiently share spectrum among the users in interference-limited systems. The abovementioned methods do not include the interaction between PU and SUs.

Cognitive radios have been chosen as a pricing decision platform to realize the cognitive network operators who interact with a group of secondary users [22‐29]. In [22], a novel spectrum management policy based on Vickrey auction is proposed to construct the co-win situation that simultaneously satisfies four parties which are involved in CRN operations (i.e., PUs, CR users, operators, and regulators). In [23], a bandwidth auction game is proposed for dynamic spectrum sharing. A game theoretic Cournot model is presented in [24], which considers the problem of spectrum sharing among a PU and multiple SUs. However, it cannot further consider the profit of the primary user. In addition, a Bertrand model is presented in [25], where multiple service providers compete with each other to obtain the Nash equilibrium pricing. In [26], distributed algorithms were presented for three different pricing models (i.e., market equilibrium, competitive, and cooperative) via game theory among the primary users and secondary users. As such, the problem is treated from the point of view of the primary users. The authors of [27] and [28] analyze the PU and SU interactions exclusively without considering the hierarchical structure of the spectrum markets. In [29], the authors study a multiple-level spectrum sharing in cognitive radio among primary, secondary, and tertiary services. Therefore, a spectrum price model plays an important role in the interaction of PUs and SUs.

The bilevel programming problem (BLPP) has a wide variety of applications, and bilevel programming techniques have been applied with remarkable success in different domains such as decentralized resource planning [30], transport system planning [31], civil engineering [32], road network management [33], power market [34], economics, and management [35, 36]. The existing methods for solving BP can be categorized as traditional method and heuristic (stochastic) method. The traditional method includes K-best algorithm [37] and branch-and-bound algorithm [38], while the heuristic method includes genetic algorithm-based approach [39], adaptive search method related to the taboo search to solve such problems [40], and global optimization techniques based on convergence analysis [41].

The NLMF model considers the case, where the prices at the same time can be iteratively adapted for the strategies in terms of SUs' requested spectrum size, respectively. The NBMF decision model allows PU to choose its prices for spectrum sharing allocation such that its revenue can be maximized, and each SU competes noncooperatively and independently with each other to maximize its profit, which is determined by the demand spectrum of each SU. The hierarchical relation between them is considered by making the PU and the SUs decide sequentially. To the best of our knowledge, this article is the first to utilize swarm intelligence with game theory to the spectrum sharing scheme among PU and SUs for CR networks.

We consider the cognitive scenario of dynamic spectrum sharing consisting of only a PU and N SUs as shown in Figure 1. When a frequency spectrum is unoccupied by its corresponding PU, it can sell portions of the available spectrum b_i (e.g., time slots in a time division multiple access (TDMA)-based wireless access system) to the SU _i (i = 1, 2,…, N) at the offered price p. Both PU and SUs use adaptive modulation for wireless transmission. The spectrum demand of SUs depends on the transmission rate achieved due to the adaptive modulation in the allocated frequency spectrum and the price charged by PU. After obtaining the right to use the spectrum, SU uses an adaptive modulation to improve the performance.

We adopt a widely used transmission model by adaptive modulation, where PU and SUs dynamically adjust their transmission rate based on their corresponding channel qualities. Therefore, the spectral efficiency of the transmission for SU _i , k _i , can be obtained by (5) [46], where γ _i is the received signal-to-noise ratio (SNR) for SU _i ; and BE R i tar is the bit error rate (BER) at the target level, which is to guarantee the required quality of transmission.

As the owner of spectrum resources, PU has the right to determine the spectrum price. A PU adjusts the price of spectrum as the total requested spectrum changed, so the PU charges all of SUs at the same price. Let P(b) be the price function, which can be obtained as shown in (6) [24], where b_it is the size of spectrum demanded by SU _i at time t, and b = {b _i | i = 1, …, N} is the demand vector. Let us denote l and q as a fixed payment and the elasticity (i.e., slope) of the price function, respectively, while l _t and q _t are the values of l and q at time t, respectively. Therefore, the price function is convex if l _t , q _t , and α are assumed to be positive and greater than one; moreover, the price function is linear if α = 1. The item b it + ∑ j ≠ i b jt is the total sharing spectrum at time t. Consequently, the PU always determines the price function for the shared frequency spectrum in terms of the amount of spectrum demanded by SUs. The demand for the spectrum is larger, and the PU will charge a higher price in cognitive radio environment as α = 1. Let us denote w ₁ and w ₂ to be the worth values of the spectrum for the PU and SU, respectively; then, it is necessary for the condition w 1 × ∑ j ∈ b b j < P b < w 2 × ∑ j ∈ b b j to ensure that the PU is willing to share the spectrum with SUs, while N SUs are willing to buy the spectrum. In the NLMF mode, the price is determined by PU, and the values of w ₁ and w ₂ are set to 1 and 0, respectively. In the NBMF mode, the PU would never have predominated, and the part of its price will be transferred to the SUs. We get the values of w ₁ and w ₂ by estimating the values of l _t and q _t . Then, we can refer to this price and use the other spectrum directly by signing the contract without competition. A contract between PU and SUs ensures that PU will not deviate because of selfishness.

SUs define their spectrum demands by maximizing their payoff functions. Each SU's payoff function is defined as the subtraction between the earned revenue and the paid cost for sharing frequency spectrum with the PU. The revenue of SU _i can be obtained by R _i  × k _i  × b _i , while the cost of spectrum sharing is b _i P(b), where R _i is the user revenue of achievable per unit transmission rate. Let us define U _i (b) to be the profit function of each SU _i , which can be obtained by (7) [24].

To determine the optimal shared spectrum sizes for the SUs, their profit functions should be maximized with respect to the shared spectrum sizes b _i for i = 1, …, N. To obtain Nash equilibrium, we have to mathematically solve the marginal profit of SU _i . That is, we can derive the profit function with respect to the shared spectrum size and set it to zero as shown in (8). Each SU then solves its own equation to find the amount of its spectrum demand:

The Nash equilibrium is considered to be the solution of the game to ensure all SUs satisfied, where the Nash equilibrium is obtained using the best response (BR) function that is the best strategy of one player, given the others' strategies. Let us denote b _−i to be the set of strategies adopted by all SUs except SU _i , where b _−i  = {b _j | j = 1, 2, …, N for j ≠ i} and b = b _−i ∪ {b _i }. BR _i is denoted as the BR function of SU _i , given the size of the spectrum sharing by other SU's b _j , which is defined as (9). The set b * = b 1 * , … , b N * denotes the Nash equilibrium of any game if and only if (10) is satisfied, where b − i * denotes the set of BR _j for all SUs except SU _i :

A static game model is presented for the ideal case, where all SUs can entirely acquire the strategies and profit of the other SUs. Some numerical methods are required to solve Equation (8) to obtain Nash equilibrium. We formulate the following optimization problem with the objective, min ∑ i = 1 N b i − BR i b − i. The algorithm reaches the Nash equilibrium when the minimum value of the objective function is zero. Subsequently, to relax the supposition, a dynamic game model is presented for which the information of the other SUs is unknown to a specific SU. In this scenario, we regard nonlinear one-leader-multiple-follower (NLMF) model as a nonlinear multiple-objective optimization problem, so it can be modeled as a dynamic game by Nash-PSO algorithms to adjust the requested spectrum size. The objective of the NLMF model is to maximize the profit function of all respective SUs, which is defined as (11). When the channel quality is getting better, the transmission rate can be higher; accordingly, the demand and the offered price for channels will increase. The value of b_{t max} cannot make the supply short of demand, while the value of b_{t min} is zero as the channel quality is very bad, which implies that the SU has no demand for the channel.

A PU sells its spectrum resource at a fixed price per unit time; the revenue is the sold spectrum multiplied by the price. The PU sells a fraction of the spectrum to SUs according to the demand, where the revenue of the PU can be obtained by (12). In the game model, SUs purchase a fraction of the spectrum by the given price, and the PU decides the price to maximize its revenue; hence, it can be modeled to maximize its revenue as shown in (13). Under different channel qualities, SUs have a variety of demands. The parameters l _t and q _t are introduced to measure the negative impact from SUs to PU and find a feasible pricing region to guarantee the primary service and satisfactory for SUs. If l _t and q _t are given among a predefined range, a feasible pricing region can be found to guarantee that it may not produce the negative values from the payoffs of the SUs, respectively:

Because spectrum sharing and pricing strategy involve two hierarchical optimizations, there exists a game relationship among PU and SUs to compete selfishly in a noncooperative Nash game to maximize their individual utilities. A pricing mechanism is to guide every player toward rational behaviors, and any one's decision may affect the others', which is a typical bilevel decision problem with one PU and multiple SUs. By combining the NLMF model defined in (11) with the strategic pricing model defined in (13), we propose an NBMF decision model for a competitive strategic spectrum allocation in a pricing-based cognitive radio market as shown in (14):

For the spectrum trading, we consider two different pricing models, NLMF and NBMF, which are to hierarchically describe the strategic pricing problems in competitive cognitive radio markets. The NLMF model first considers the case that PU offers his price to SUs simultaneously. We use the Nash-PSO algorithm to build Nash equilibrium for multiple-objective optimization. In the NBMF model, SUs can observe the pricing strategy of PU and adapt their strategies accordingly from a bilevel angle. Therefore, we use an NBMF-PSO algorithm to estimate and adapt the strategies of SUs to achieve the best response and the strategy of PU to obtain the optimal solution. The Nash-PSO and NBMF-PSO algorithms will be discussed in the next section.

Kennedy and Eberhart first introduce the PSO in 1995 as a new heuristic method [47]. PSO works by flying a population of cooperating potential solutions called particles through a problem's solution space, accelerating particles toward better solutions [48, 49]. PSO has a good convergent performance and has been applied in many optimization problems including neural network training, multi-object optimization, and some project applications. In PSO, each particle is treated as a point in an n-dimensional space, where its m th particle can be represented by a vector X _m  = (x_{m 1}, x_{m 2},…, x _mn ), and it is treated as a potential solution that explores the search space by rate of position change called velocity, denoted by V _m  = (v_{m 1}, v_{m 2}, …, v _mn ). Let pb _m be represented as the personal best position of any particle, i.e., pb _m  = (pb_{m 1}, pb_{m 2}, …, pb _mn ), which is in accord with the position in search space where particle had the lowest (or highest) value as determined by the fitness function. In addition, gb is defined to be the global best position of particle in swarm, which yields the best position of all particles in its neighborhood. The particle update method lies in accelerating each particle towards the optimum value based on its present velocity, its previous experience, and the experience of its neighbors within a reasonable time limit. Let us denote M and w to be the size of the swarm and the inertia weight used to balance the global and local search abilities, respectively. The position and velocity of each particle can be updated according to (15) and (16) [41], where m (m = 1, 2,…, M) and d (d = 1, 2,…, n) are for the m th particle and the d-dimensional vector, respectively, while c₁ and c₂ are the positive constants; r₁ and r₂ are two uniformly distributed random numbers in the range [0,1]; and k denotes the iteration number. For simplicity and immunity to the global optimum, the PSO algorithm is employed in this article to develop a Nash-PSO algorithm and an NBMF-PSO algorithm to reach an optimal solution for the NLMF and NBMF strategic pricing problem in an oligopoly market:

In this section, we present two different spectrum sharing models. We employ a strategic pricing problem in a CR market to test the NLMF model with Nash-PSO algorithm and the NBMF decision model with NBMF-PSO algorithm developed in this article. We consider the cognitive radio environment with one PU and two SUs sharing a frequency spectrum of 15 MHz. We use the same parameters and the same method as [24] compared with the Nash-PSO algorithm. We obtain the same result with [24] dynamic game.

Numerical studies were carried out to evaluate the performances of the two different pricing models. In the proposed NBMF model, PU can share more spectrum sizes with higher price for unit of shared frequency spectrum to SUs, while PU achieves higher revenue and SU acquires more size of the sharing spectrum by the same price. The NBMF model is more satisfactory for both groups of PU and SUs than NLMF, and enlarges the PU's revenue and provides reasonable price to SUs.

This article applies a strategic pricing problem in a cognitive radio market to help for both PU and SUs to make the strategic decisions by the Nash-PSO and NBMF-PSO algorithms. We combine swarm particle algorithms with Nash strategy based on noncooperative game theory to obtain the Nash equilibrium in multiple-objective optimization problems. By thinking of the gaming and bilevel relationship between PU and SUs, the NBMF decision model can better reflect the features of the real-world strategic pricing problems in the cognitive radio markets and format these problems more practically. The proposed NBMF-PSO algorithm is quite effective for solving the strategic pricing problems defined by the NBMF decision model. In the literature, no other algorithm exists hierarchically for the strategic pricing problems when both the gaming and bilevel relationships are considered between PU and SUs. The NBMF-PSO algorithm makes SUs using Nash-PSO algorithm to gain their rational reactions and reach the Nash equilibrium, and PU obtains the optimal pricing and acquires the highest profit. Further research work will focus on building the optimal strategic pricing models for the multiple PUs and multiple SUs in cognitive radio network.