## 1. Introduction

With the development of Wireless Sensor Networks (WSNs), the radio spectrum resource, as one of the scarcest and expensive resources, gradually became a stumbling block. As wireless applications increase sharply, there are fewer and fewer unlicensed radio spectra, while licensed radio spectra are under-utilized. For unlicensed users lacking spectrum, solutions to the spectrum-sharing problem using dynamic spectrum borrowing and lending between unlicensed operators are inadequate [

1]. Cognitive Radio (CR), which is considered to be a prospective approach to realize dynamic spectrum access (DSA) [

2,

3], is widely used to improve spectrum utilization. It allows licensed users’ resources to be efficiently shared with unlicensed users, in exchange for potential profits.

Usually, there are many alternative licensed users for a WSN. In a CR-based WSN [

4,

5,

6], the spectrum demand for a licensed user directly depends on unit price and spectrum efficiency. To attract more buyers, licensed users need to compete with each other in the terms of spectrum price. In spectrum marketing, game theory provides a set of mathematical tools that can construct economic models to analyze the behaviors of self-interested users. Each type of game model, whether it is a cooperative or non-cooperative game, certainly has advantages and disadvantages [

7,

8,

9,

10]. Depending on different performances, their application environments are distinct.

On the basis of the Stackelberg game, the Distributed Optimization for Cognitive Radio (DOCR) scheme [

11] was designed as a hierarchical framework to optimize CR network performance. In this scheme, the spectrum of a licensed user is divided into sub-bands, each of which can only be accessed by one unlicensed user. Hence, there is no difference in that all licensed users are regarded as one. In the work presented in this paper, it is unnecessary for users to communicate with each other. Using a simple pricing function for licensed users, a distributed algorithm is introduced in the DOCR scheme to converge on Stackelberg equilibrium. The multi-leader multi-follower Stackelberg (MMS) scheme [

12] was proposed as an efficient spectrum sharing scheme. As leaders, multiple licensed users played a cooperative game and collaborated with each other to fairly distribute the outcome. As followers, multiple unlicensed users played a non-cooperative game using a self-interested strategy. During step-by-step iteration, a feedback learning process is repeated to find the best solution. Under widely-diverse network environments, the MMS scheme can find an effective solution to spectrum sharing, and offer an attractive performance balance. The two-stage resource allocation scheme, with combinatorial auction and Stackelberg game in spectrum sharing (TAGS) [

13] provided a feasible solution to the spectrum sharing problem, and ensured all individuals’ economic properties. A geographically-restricted combinatorial auction, without consideration of spectrum recall, decided the spectrum allocations, while a Stackelberg game was designed to determine all users’ strategies with respect to the potential spectrum recall. However, the existence of the broker, which collected all sealed-bid information, determined the optimal allocation, and calculated the payments and payoffs, limited the framework of the model.

Recently, another game model, which is often used to solve spectrum sharing problems, is auction [

14,

15,

16]. The Repeated Bayesian Auction (RBA) scheme [

17] could achieve an effective solution of spectrum sharing under widely-diverse system environments. Licensed users adaptively decided their prices using a Bayesian game, and shared bandwidth based on the double auction protocol. In each auction round, the auctioneer collected all the information about offers and bids, and determined the trade price. The dynamic auction would be repeated sequentially, every time period, until an efficient auction consensus was reached. The Repeated Auctions with Bayesian Learning (RABL) scheme [

18] investigated the problem of spectrum access in CR systems using monitoring and access costs. With incomplete information, a nonparametric belief update algorithm was proposed, based on the Dirichlet process. Although its convergence speed can be improved, it can achieve a good balance between efficiency and fairness. The Double Auction-based Spectrum Sharing (DASS) scheme [

19] allows free spectrum band trading between operators to improve the efficiency of the spectrum utilization. The DASS scheme investigated the practical wireless communication framework using adaptive adjustable bidding/asking strategies.

Although an auction is an effective way to find a solution for multi-leader multi-follower spectrum sharing, the auctioneer is a limitation of practicability. Some other game models, for example, the Bertrand Game [

20,

21] and the evolutionary game [

22], are presented to solve the multi-seller multi-buyer spectrum sharing problem. The Resource Pricing with Stackelberg Approach (RPSA) scheme [

20] used the Bertrand Game to solve the resource allocation problem in CR networks. In addition, it introduced a control parameter to quantify the negative impacts. With the control parameter, the services of licensed users can be guaranteed. From the viewpoint of meeting the demand of network communication, the Bertrand Game based Spectrum Sharing (BGSS) scheme [

21] was designed to solve the spectrum leasing and allocation problem. A flaw in the scheme is the principle that the spectrum requirements of unlicensed users must be satisfied. In the real world, an unlicensed user may choose not to trade if participating in the spectrum access game is deemed to be unfavorable.

To obtain the practicability and adaptability, the central controller (e.g., base station or auctioneer) cannot exist in the spectrum sharing model and there is no cooperation between licensed or unlicensed users. To deal with this matter, we designed a Strategic Bargaining based Spectrum Sharing (SBSS) scheme in heterogeneous WSNs (HWSNs). In HWSNs, unlicensed users have various signal-to-noise ratios (SNRs) for the same or different licensed users, which is more practical. Furthermore, to complete the spectrum trade between multiple licensed users and multiple unlicensed users, a non-cooperative strategic bargaining game was proposed to model the competition. It allows licensed and unlicensed users to adaptively decide their strategies. Without knowing other competitors’ information, each licensed and unlicensed user can carefully find the best strategy for themselves. Research regarding Nash bargaining [

23,

24] and HWSNs [

8] is lacking; nonetheless, this paper proposes a scheme that outperforms existing schemes, as follows:

In HWSN, not only are the differences (e.g., frequency band, bandwidth) between licensed users considered, but the discrepancies (e.g., hardware, space, and wireless environment) between unlicensed users are taken into account.

Since there is no need to know competitors’ information, the non-cooperative game model no longer needs a central controller (base station or auctioneer). The advantages are that users in our model are adaptive and networks are distributed, which cannot be achieved by most existing schemes.

The proposed scheme can be implemented in two scenarios according to the supply-and-demand relationship, i.e., less or more licensed radio spectrum supply than network demand.

In the rest of this paper, the system model, utility function, and strategic bargaining of the proposed scheme are described in

Section 2.

Section 3 presents a numerical performance analysis.

Section 4 summarizes the work and provides a discussion.

## 4. Discussion

In terms of simulation,

Figure 6 and

Figure 12 verify Proposition 3, that the proposed scheme can own at least one subgame-perfect equilibrium for SNRs with diversity. Except for the dishonesty degree (in

Figure 8) and the importance coefficient of unlicensed users’ data (in

Figure 10),

Figure 7 and

Figure 9 directly or indirectly prove that the supply-and-demand relationship is the determining factor for a subgame-perfect equilibrium (namely, NBS). However, there are two NBSs without any changing parameters. In fact, the different NBSs in

Figure 12 have different choices of unlicensed users, which have indirectly changed spectrum demand. In contrast,

Figure 8 and

Figure 9, not only prove the analyses in

Table 1, but also provide evidence that both sides of the game have no desire to be dishonest. In daily life, the “bargain” is a common phenomenon, while the “warn” is an extra requirement in this paper. For our bargaining model, the “warn” seems to be unreasonable; however, it is necessary in order to know all information at the discontinuous point in

Figure 11. With a discontinuous spectrum demand, a licensed user can no longer speculate the optimal strategy (not having the “bargain” and “warn”), which can be achieved by previous strategies if the spectrum demand is continuous.

All simulations prove that the proposed bargaining game can find a spectrum-sharing scheme, regardless of the HWSN. It can also be applied to various HWSNs with diverse spectra demands. If we take the fairness and trade success probabilities into consideration, a HWSN in which the offered load is less than 1.5 will be a good choice.