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Distributed Interference-Aware Cooperative MAC Based on Stackelberg Pricing Game Haixia Cui, Yide Wang, Member, IEEE, Quansheng Guan, Member, IEEE, and Han Zhang, Member, IEEE
Abstract—Cooperative communication can significantly enhance the efficient utilization of spectrum in wireless networks. The performance of wireless cooperative networks depends on careful medium access control (MAC) and resource allocation such as relay selection and cooperative link scheduling policy for interference management. Most of the previous centralized works rely on precise instantaneous channel state information (CSI). In this paper, considering the impact of multirelay link interference on relay selection and dynamic spectrum sharing, we propose a fully distributed relay MAC scheme for wireless cooperative networks based on a Stackelberg game framework with only one-hop local CSI, where source nodes that have their own information to send act as leader users and where the others act as follower users. In this scenario, each relay node prices its spectrum resource to the corresponding source node to maximize its revenue. In addition, the proposed scheme helps not only source nodes to find relay nodes by channel gains and obtain an optimal system performance but relay nodes to maximize their revenue by asking a suitable resource price as well. The interactions between the sources and relays iteratively lead to a Stackelberg equilibrium, in which the cooperation system achieves high throughput and low transmission delay. Simulation results are presented to show the effectiveness of the proposed approach. Index Terms—Cooperative communication, interference, medium access control (MAC), pricing, Stackelberg game theory.
I. I NTRODUCTION
T
HE COOPERATIVE communication technique creates an inherent spatial diversity and multiuser diversity that could be exploited to improve wireless spectral efficiency and Manuscript received April 24, 2014; revised July 31, 2014, September 4, 2014, and October 7, 2014; accepted October 18, 2014. Date of publication October 23, 2014; date of current version September 15, 2015. The work presented in this paper was supported in part by the National Natural Science Foundation of China under Grant 61201255, Grant 61471176, Grant 61002012, and Grant 61302058; by the Natural Science Foundation of Guangdong, China, under Grant S2012040007462, Grant S2013010016297, and Grant S2012040007588; and by Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing under Grant GXKL0614204. The review of this paper was coordinated by Dr. S. Zhong. H. Cui is with the School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510631, China, and also with Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada (e-mail: cuicuihang0715@ gmail.com). Y. Wang is with the Institute of Electronics and Telecommunications of Rennes, École Polytechnique de l’Université de Nantes, 44300 Nantes, France (e-mail:
[email protected]). Q. Guan is with the School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510006, China (e-mail:
[email protected]). H. Zhang is with the School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510631, China (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2014.2364734
reliability. By utilizing it suitably, most of the advantages of multiple-input–multiple-output techniques can be obtained with only one single-antenna equipment for the individual terminals. As a result, cooperative communication is now regarded as a promising approach to increase spectral efficiency, coverage scope, and network reliability and to reduce outage probability and symbol error rate for distributed wireless networks [1]. Furthermore, next-generation wireless communication networks are expected to support heterogeneous radio access, such as distributed ad hoc networks and centralized cellular networks, in which terminal users could randomly select to access. In contrast to centrally controlled networks, many challenges must be overcome to obtain the benefits of distributed wireless networks without knowledge of channel state information (CSI), such as medium access control (MAC) design, spectrum sharing and efficiency, interference avoidance, and transmission reliability [2], [3]. Therefore, how to use cooperative communication in distributed wireless networks for MAC design is important, and there is an urgent need to design a proper channel access/allocation algorithm for source/relay nodes that aims to increase the spectral efficiency and transmission reliability. In fact, the performance of cooperative communication in distributed wireless networks depends on careful resource allocations, signal constellation modulation, precoding, CSI error, medium access scheme, spectrum efficiency, relay selection, cooperation schedule policy, and so on [4]–[8]. For resource allocation, there are mainly two cooperative transmission strategies [4], namely, relay-based cooperative strategy and virtual antenna (VA) array-based cooperative strategy. For fully distributed purpose, VA-based cooperative strategy is not suitable and is not considered in this paper. Up to now, the existing literature has considered a variety of theoretical aspects for relaying protocols and power allocations to satisfy some performance criteria in physical layer [1], [9]–[12]. Most of the works focus on a centralized network framework, although, in [4] and [5], the distributed contentionbased MAC protocols requiring multiple access points are considered. Such approaches require complete and precise CSI to allocate resource, which is impossible in fully distributed networks, such as the ad hoc networks with channel estimation errors. Therefore, fully distributed upper layer aspects of cooperation communications merit further research. In general, within cooperative communication systems, why is the selfish relay node willing to supply cooperation under the situation in which each node has equal position in wireless distributed networks? Game theory is a natural and flexible tool that gives some new insights to the interaction
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CUI et al.: DISTRIBUTED INTERFERENCE-AWARE COOPERATIVE MAC BASED ON STACKELBERG PRICING GAME
and cooperation between autonomous nodes is illustrated in [13] and [14]. It could provide better fairness and service differentiation. In [6], [15], and [16], pricing of relay power resources is introduced to improve social welfare and reflect the quality of service of networks received by a wireless terminal receiver. In the distributed scenario, Wang et al. [6] and Zhang et al. [7] studied the problem of how relay should allocate its power and bandwidth among multiple equal competing terminal nodes using game theory. In addition, the proposed schemes can achieve comparable performance as that of centralized schemes. Although game theory could motivate selfish equal nodes to use system resource more efficiently, the multiple access interference (MAI) [17] is ignored in [6] and [7]. It is known that the distributed terminal nodes have the same chance to access the channel. Thus, the interference and collision between neighbor relay nodes, which access the channel simultaneously, may be important. Consequently, increasing the number of cooperative partners in repetition diversity networks would increase the collision probability, decrease the transmit power available for each node, and reduce the spectral/energy efficiency of the overall system [18]. Therefore, it is necessary to make an appropriate tradeoff between diversity and capacity. To solve this problem, Liu and Chen [19] proposed distributed threshold relaying (DTR) for cooperative wireless ad hoc networks. Each relay measures the signalto-noise ratios (SNRs) of source–relay and relay–destination channels using broadcast messages sent from the source to the destination. Then, it decides whether to perform or not the cooperation by two threshold tests. The most important is that the cooperation among multiple relays is coordinated via a distributed MAC scheme based on random backoff algorithm. Unfortunately, there was too much backoff delay and collision chance, although it can be easily implemented in distributed wireless networks. Motivated by these observations, this paper focuses on layer-2 MAC in distributed wireless cooperative networks and provides a novel cooperative MAC approach with equilibrium insights based on Stackelberg (leader–follower) game theory. The Stackelberg model is a strategic game in economics in which the leader takes action first and then the followers take action sequentially. The players of this game are a leader and followers, and they compete on resources. The Stackelberg leader is sometimes referred to as the market leader [20]–[25]. In our previous work, a power pricing scheme is proposed by the energy utilization efficiency [15], and an optimal crosslayer resource allocation is resolved by MAC layer and physical layer [16]. However, this paper emphasizes cooperative link scheduling policy with relay pricing for interference management based on the Stackelberg game. We take own cooperation resources as wares, benefits for relaying nodes as incentives, and price the cooperative relay nodes according to their channel condition. On the other hand, source nodes, as game leaders, select available relays based on both pricing and obtained profits. Relay nodes, as game followers, supply service for the relevant source nodes. Furthermore, the key point in this cooperative relay access control scheme is the contention resolution to mitigate MAI. Considering the current cooperative modes, the unselected relay nodes
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Fig. 1. System model. (a) Arbitrarily distributed nodes with multiple communication link access scenario. (b) Without MAC. (c) With MAC.
and source nodes would keep silent when the selected relays are transmitting to their destinations [26], [27], and all the frequency bands are exclusively allocated to these transmission logical pairs. In this paper, the free relay/source nodes continuously sense the spectrum without causing harmful interference to the transmitting logical links and then access the channel when it is possible. As far as we are aware, multirelay access spectrum utilization considering MAI has not been explicitly investigated in distributed wireless cooperative networks. In addition, we theoretically analyze the proposed algorithm, and simulation results show that it significantly increases the total system throughput than the existing algorithms. There are three major contributions of this paper: 1) An interferenceaware cooperative link model is derived for distributed MAC scheme in wireless ad hoc networks or sensor networks. 2) With consideration of various competition and fairness, Stackelberg game theory is used to solve the collision, resource sharing, and allocation problem. 3) A distributed interference-aware relay scheduling scheme is designed without total CSI. The remainder of this paper is organized as follows. Section II presents the system model and formulation of cooperative MAC problem. The proposed interference-aware multiple relay access scheme based on Stackelberg game will be detailed in Section III, followed by its performance analysis in terms of average duration and system throughput for virtual transmission cycle (VTC) in Section IV. Simulation results are presented and discussed in Section V. Finally, Section VI concludes this paper. II. S YSTEM M ODEL AND P ROBLEM F ORMULATION A. Cooperative Relaying Model Consider an ad hoc network scenario represented by a graph G (V , E), as shown in Fig. 1(a), where V is the set of fully distributed nodes, and E is the set of logical links operating on a shared wireless channel. The definition of logical links
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is referring to the actual communication pairs. Each node is equipped with a single antenna and works with a half-duplex mode such that the transmission and reception occur in different time slots. Furthermore, links formed by different transceivers compete with each other if they have a common source or destination node. In this paper, we employ amplify-and-forward relaying protocol. The relaying selection is based on signalto-interference-and-noise ratio (SINR) threshold, which is described as follows. We refer to the nodes having their own information to send as sources [see S1 and S2 in Fig. 1(a)] and others (except for the corresponding destinations of sources) as voluntary relays. Without loss of generality, once a source node accesses the wireless medium channel, it will occupy T duration to fulfill transmission frame communication, in which source and relay can adjust spectrum/time allocation by some access control algorithms to obtain the optimal system performance. Let W be the channel bandwidth of the system and N be the number of symbols that can be transmitted within T . If we assume that a well-defined multilevel quadrature amplitude modulation (QAM) is used, then [7] N = T /T0 ≈ T W
(1)
where T0 is the symbol period. After broadcast (phase 1) of Si , the SINR obtained at destination Di and that at relay rj are given, respectively, by ΓSi ,Di =
PSi GSi ,Di
k∈V,k=Si ,Di
ΓSi ,rj =
(2)
(1)
Pk Gk,Di + σ 2
PSi GSi ,rj
(3)
(1)
k∈V,k=Si ,rj
Pk Gk,rj + σ 2
(1)
where PSi and Pk denote the transmission power of Si and interference user k in phase 1, respectively; GSi ,Di , Gk,Di , GSi ,rj , and Gk,rj represent the channel gains from Si and interference user k to Di and rj , respectively; and σ 2 is the additive white noise power at the receiver. Without loss of generality, we assume that the white noise levels have the same
Prj Grj ,Di
k∈V,k=Si ,k=rj
yrj ,Di =
PSi GSi ,rj +
k∈V,k=Si ,k=rj
2 Gik = d−ε i,k |hi,k |
Θi = rj ∈ V | ΓSi ,rj ≥ α ∩ Γrj ,Di ≥ β × (Si , rj ) ∈ E, (rj , Di ) ∈ E
k∈V,k=rj
(5)
where α provides a measure of reliability of source–relay channel, and its value depends on the network environment and physical layer configurations; Γrj ,Di is the received SINR from relay rj to destination Di when there is a cooperative process; and β is used to assure the cooperative forwarding quality from the relay rj to destination Di . Furthermore, adjusting α and β can control the number of candidate relays, which not only mitigates excessive multiple access contentions but guarantees enough relays to participate in the cooperation as well. Note that the candidate relays selection is only based on one-hop-range CSI, which can be performed by distributed nodes easily, and only the selected candidate relays have the chance to be active relay transmitters. With rj ’s help and based on [6, eq. (7)], we can easily get the received signal at destination Di in the relaying process (phase 2) as (6), shown at the bottom of the page. xi is the transmitted information symbol with unit energy at source (1) node Si ; PSi GSi ,rj xi + k∈V,k=Si ,k=rj Pk Gk,rj xk is from all the transmitting nodes the received signal at node rj (2) in the first phase; k∈V,k=rj Pk Gk,Di xk is the received signal from other interfering nodes to the destination node in (2) phase 2; Pk denotes the transmission power of interference user k in phase 2; and η1 and η2 represent the additive white Gaussian noises in phases 1 and 2, respectively.
(1) Pk Gk,rj xk
(1) Pk Gk,rj
Prj Grj ,Di PSi GSi ,rj = xi + (1) PSi GSi ,rj + Pk Gk,rj + σ 2 k∈V,k=Si ,k=rj (2) + Pk Gk,Di xk + η2
(4)
where di,k denotes the distance from node i to k; ε denotes the path propagation loss exponent; and |hi,k | is assumed to be a Rayleigh distributed variable with the mathematic expectation being one. In case of failure of the direct transmission, each relay node needs to decide whether it should participate in cooperative transmission. According to Fig. 1(a), we define the candidate relays for Si as follows:
PSi GSi ,rj xi +
variance at different receivers. For any node pair i and k, the channel gain between them is calculated by [14]
+ η1
+
σ2
(2)
Pk Gk,Di xk + η2
k∈V,k=rj
Prj Grj ,Di
+
k∈V,k=Si ,k=rj
PSi GSi ,rj +
(1) Pk Gk,rj xk
k∈V,k=Si ,k=rj
+ η1
(1)
Pk Gk,rj + σ 2 (6)
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Using (6), the relayed SINR at destination Di in cooperative phase is expressed in (7), shown at the bottom of the page. B. Medium Access Model As shown in Fig. 1(a), it is assumed that S1 and S2 are out of each other’s transmission range and broadcast simultaneously. Then there would be a collision at node r2 since it is in the candidate relays set for both source nodes. As a result, node r2 would give up its cooperation chance for S1 and S2 at that time. On the other hand, to exploit cooperative diversity for multiuser systems, the more relay nodes are used, the better is diversity performance. However, multiple relay logical links for one source interfere with each other because they have common destination at the same time. Therefore, in this paper, we set the constraint that several cooperative logical links cannot serve for a source simultaneously. This is to say that, once one relay is admitted to access medium to help one source, this relay will be the only selected relay for this source. If it fails, another relay will be selected. For example, in Fig. 1(b) and (c), if r3 D2 and r1 D1 are interfering links, then if S2 uses r3 D2 , the system can only allow one transmission pair to take place in a given time slot. In contrast, through our MAC, two logical links r1 D1 and r4 D2 can take place in the same time slot, which can result in higher overall throughput. It is clear that relay access control scheme is a key point for system performance in distributed wireless cooperative networks. By definition, source node has its own information to send, i.e., its data arrival rate λ = 0, and relay node keeps idle and waits for cooperation, i.e., its data arrival rate λ = 0, as shown in Fig. 2(a). Note that, although r7 belongs to a source node and λr7 = 0, it cannot transmit information because it can hear S2 . Hence, r7 may serve as relay to compete for cooperation at this moment for S2 . From S2 ’s perspective, both r3 and r7 are in Θ2 (Θi , i = 2). Each relay compares two predefined thresholds (i.e., α and β) and takes some measures to contend channel access. This will become clearer when we elaborate upon the MAC protocol. We assume that all logical links are bidirectional and that the feedback channels are ideal. At a given transmission instant, the
Fig. 2. MAC layer in wireless cooperative networks. (a) S2 ’s perspective. (b) One VTC structure.
source node tries its best to follow direct transmission with no cooperation. If it is a successful transmission, an acknowledgement (Ack) signal is received as feedback. Otherwise, neighbor relay nodes might hear a negative-Ack (Nack) signal from source’s destination or due timeout. If relay node also fails, it will send an automatic repeat request until receiving Ack or reaching maximal repeat times. We can assume its procedure as a VTC, which starts at the beginning of a source node transmission and terminates in either receiving Ack or timeout, as shown in Fig. 2(b). Each VTC may be different, and it depends on the network environment. At the VTC process, the idle neighbor relay nodes always keep sensing Ack or Nack signals and calculate channel situation to prepare for cooperation. If they find that (5) is satisfied and that there are cooperation chances, they will broadcast their price to the corresponding sources for relay selection. Meanwhile, any node that is backlogged with packets to send or currently receiving will pause to its backoff procedure when the total carrier-sensing interference power exceeds a threshold.
PSi GSi ,rj Prj Grj ,Di
PSi GSi ,rj +
ΓSi ,rj ,Di = ⎛
k∈V,k=Si ,k=rj
⎜ Prj Grj ,Di ⎜ k∈V,k=Si ,k=rj ⎜ ⎜ PSi GSi ,rj + ⎝ k∈V,k=S ,k=r i
= Prj Grj ,Di
(1)
Pk Gk,rj +σ 2
k∈V,k=Si ,k=rj
⎞
(1) Pk Gk,rj +σ 2
+
(1)
Pk Gk,rj +σ 2
j
(1) Pk Gk,rj +σ 2
⎟ ⎟ (2) Pk Gk,Di + σ 2 ⎟ ⎟ k∈V,k=rj ⎠
PSi GSi ,rj Prj Grj ,Di +(PSi GSi ,rj +
k∈V,k=Si ,k=rj
(1) Pk Gk,rj +σ 2 )
k∈V,k=rj
(2) Pk Gk,Di +σ 2
(7)
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C. Problem Description Considering that MAC design is to determine the access channel opportunity for wireless terminal user subject to network reliability in this paper, the cooperative MAC problem in fully distributed wireless networks is to decide when and how source/relay nodes access the wireless medium channel. It is clear that a selfish distributed terminal user is willing to seek cooperative transmission and supply spectrum resource only if its profit is not lower than its cost. Therefore, relay pricing is needed to measure the obtained benefits. Moreover, to exploit the cooperative diversity, three fundamental questions should be considered. 1) Which node in candidate relays will be selected to forward information? 2) How much spectrum/time resources would be supplied by the relay? 3) How much should the source node pay for this help? However, for fully distributed wireless networks, it is difficult to collect the entire network information that can be obtained relatively easily in a centralized manner. More relays in the system will result in more local maximums, and searching the global optimal resource allocation would be a daunting task. Even if the global optimal solution can be found, it is still impractical since the central controller requires complete network knowledge, including interference channel gains. Inspired by [6], we address the access behaviors of source and relay using Stackelberg-game-based scheme. Incentives need to be provided by source to relay for relaying information with its spectrum/time resource. Consequently, pricing is employed by different candidate relays. There are two main factors that impact relay pricing in such networks, namely, source demand and relay competition. When source demand is high, relay can increase its price to achieve higher revenue. If there is competition among candidate relays, relay may decrease the price to attract more chances to gain more revenue. Each node takes its own information as premium and relaying information as best effort connection, which means that, if the situation admits, any node fulfills its own task first and takes cooperation communication as best effort benefits. This can be formulated as a cooperative game with leader and followers as players, and the Stackelberg game equilibrium can be obtained as the solution of the game. Definition 1 (Stackelberg equilibrium) [14], [22]: A Stackelberg game theoretic equilibrium in which one player acts as the leader and the others as followers is that the leader sets strategy taking account of the followers’ optimal response. Stackelberg equilibrium, which maximizes the revenue of the leader, is considered as a solution for the leader–follower game. Note that, if the source uses direct transmission, the achieved noncooperative data rate/payoff is RSi ,Di
N log2 (1 + ΓSi ,Di ). (8) = W log2 (1 + ΓSi ,Di ) = T
If the source works with relay cooperatively, the achieved cooperative date rate/payoff (at the output of maximal ratio
combining) is (i)
RSi ,rj ,Di =
N δ rj log2 (1 + ΓSi ,Di + ΓSi ,rj ,Di ) T
(9)
(i)
where δrj ∈ [0, 0.5] denotes cooperation bandwidth factor. A selfish node is willing to provide cooperation transmission only if the achieved cooperative gain is higher than the noncooperative payoff by consuming the same amount of energy resource. We consider in this paper the channel access problem without power control, which means that only the cooperation period is relevant. Compared with direct transmission, the rate increase that Si can obtain with the help of rj is ΔRi = max RSi ,rj ,Di − RSi ,Di , 0 . (10) This value is nonnegative since the source would not choose relay that cannot provide rate increase. In addition, the relay consuming more spectrum/time than source itself is impossible select as a candidate relay. III. C OOPERATIVE ACCESS A MONG D ISTRIBUTED N ODES W ITH M ULTIPLE ACCESS I NTEREFERENCE Here, we first formulate the optimization problem for cooperative MAC and relay selection as a Stackelberg game. Then, we derive the closed-form solution to the outcome of the presented game. Finally, we describe the proposed cooperative MAC protocol with pricing. A. Cooperation in the Leader–Follower Game In a distributed wireless access environment, it is possible that the source node proceeds to offer its needs by a Nack signal before relay’s response. This can be formulated as a cooperative Stackelberg game with the leader and followers as players, and the Stackelberg equilibrium can be considered as the solution of this game. The followers can observe the strategy of the leader and adapt their strategies accordingly to maximize the total revenue based on their price. We assume that the source/relay transmission power values are constant in this paper, and power control is out of our scope. Therefore, in this leader–followers cooperation, the source as leader is first randomly accessed into the wireless shared medium and offers its demand to followers. Then, the neighbor idle relays as followers hear the channel and calculate their channel gains when Nack signals are received. If they are in candidate relays set by (5), the relays will broadcast their price to the corresponding source to compete to help. Equation (10) shows that, for given CSI, the feasible payoffs for source nodes are only function of SINR. As a result, there exists a unique demand/supply-based profile for source game, given by solving the following optimization problem: δr(i) max Ui = ai f (ΔRi ) − qr(i) j j (i)
(11)
where qrj denotes the cooperation price; Ui denotes the instantaneous revenue of Si ; f (ΔRi ) represents a positive utility function of a data rate increase for Si ; and ai denotes the revenue gain per unit of function f (ΔRi ). The leader source
CUI et al.: DISTRIBUTED INTERFERENCE-AWARE COOPERATIVE MAC BASED ON STACKELBERG PRICING GAME
node can be modeled as a resource buyer, which aims to obtain the maximum rate benefits with minimum payment. The relay nodes as followers would sense the strategy of the source and adapt their approaches consequently. In particular, a follower having information about the leader’s broadcasting strategy would choose its best response accordingly. Subsequently, the leader realizes the fact that the follower would change strategy. Consequently, the leader can maximize its payoff based on the response of the follower. It is logical that each relay rj can be seen as a seller and aims to not only earn payment that covers its forwarding cost but obtain as many extra profits as possible as well. We introduce a parameter crj as the cost of relaying, and then the optimization problem for rj (i.e., seller-level game) is δr(i) − crj δr(i) max Urj = qr(i) j j j
(12)
where Urj denotes utility function for rj . We need to determine the cooperation access scheme for all source/relay nodes to optimize the overall network throughput subject to interference scenario. The objective functions (11) and (12) extend the logical link behavior into a network perspective by taking into account the interference. Based on the previous discussion, the interference set of logical links in distributed cooperative networks is mainly determined by relay selection. Link data rate and interference are the primary factors (i) that determine network performance. Let rj ∈ Θi denote the selected winning relay for source node Si , given by (i)
rj = arg max Ui
(13)
rj
which means that the relay providing the highest revenue would be selected as the winning relay. B. Follower’s Game The best response of relay as a follower can be found by taking the derivative of the instantaneous revenue from source ∂Urj (i)
∂qrj
∂δ (i) rj (i) = δr(i) + q − c =0 r r j j j (i) ∂qrj
which has a unique solution = c rj − qr(i) j (i)
(i) δ rj . (i) (i) ∂δrj /∂qrj
C. Leader’s Game The source node as a leader is aware of the fact that the followers will choose their best response to its strategy. The source tries to maximize its utility function based on the best responses of followers ∂Ui (i) ∂δrj
N log2 (1 + ΓSi ,Di + ΓSi ,rj ,Di ) T N (i) δ log2 (1 + ΓSi ,Di + ΓSi ,rj ,Di ) ·f T rj N log2 (1 + ΓSi ,Di ) − qr(i) − = 0. (16) j T
= ai
Therefore, taking f (x) = x as an example, in this case Ui = ai f (ΔRi ) − qr(i) δr(i) = ai ΔRi − qr(i) δr(i) j j j j (i) (i) = ai RSi ,rj ,Di − RSi ,Di − qrj δrj (i) N δ rj log2 (1 + ΓSi ,Di + ΓSi ,rj ,Di ) = ai T N log2 (1 + ΓSi ,Di ) − qr(i) δr(i) − j j T therefore qr(i) = ai j
N log2 (1 + ΓSi ,Di + ΓSi ,rj ,Di ). T
(15)
In particular, δrj is a function of channel gains of the source–destination, source–relay, and relay–destination links. If the source node has a lower transmit rate, it is willing to buy more resource from relays to obtain high system throughput, then the relay can ask higher price to the source when it has a better relay–destination link gain. Furthermore, the price is also affected by competition between candidate relays. If the relay with better relay–destination channel gain brings lots of interference, it will not be allowed to access the shared wireless channels, which is reflected by (2) and (7).
(17)
It is shown that the relay node will have a larger cooperative price by a better SINR at destination node in cooperative phase. However, if it asks a high price over its cooperative ability or bringing much interference, the source node maybe discarded it, which is determined by the follower’s game calculation. (i) Furthermore, from (15), if ΓSi ,Di = ΓSi ,rj ,Di , we have δrj = (i) 0.5 and qrj = ai (N/T ) log2 (1 + 2ΓSi ,Di ). Then, taking it into (15), we can get (i)
δ rj
(i) (i) ∂δrj /∂qrj
(14)
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= crj − qr(i) j
δr(i) = j
ai N + 2ΓSi ,Di ) − crj T log2 (1 . (i) 2 qrj − c rj
(18)
The revenue function of sources is defined with the prices offered by all candidate relays. Given these prices, a cooperative game between players could be solved by obtaining Stackelberg equilibrium. We technically define the cooperation quantity of relay nodes in function of the spectrum or period that they are willing to contribute for the relaying purpose. A selfish node is willing to offer cooperative transmission only if the achieved cooperative profit will not be lower than the cost. We note that the rational decision made by one source will definitely affect its relay’s choice. D. Cooperative MAC Protocol With Pricing The interference of logical cooperative links in a distributed manner is a bit complicated to be analyzed. We present a
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cooperative MAC based on pricing to approach the optimal scheduling in a distributed wireless network. In phase 1, source node can access the shared channel randomly with IEEE 802.11 distributed coordination function [2]. The covered neighbors of this source and its corresponding destination, which hear the transmitted information, have to be silent and pause to their backoff state. Collision avoidance and information exchange are based on request-to-send (RTS)/clear-to-send (CTS) shaking hands. Furthermore, with our proposed cooperative relay model, in phase 2, the covered neighbors of the selected relay have to be silent to ensure successful reception at destination. The multiple access channels also consist of two point-to-point logical links, namely, source–destination and relay–destination, which are active in separate time slots. Now, we can derive the interference-aware cooperative access control as follows. If the source transmission succeeds, the next data packet will go on, and it still sends information on this flow. Otherwise, candidate relays would prepare Stackelberg game with the source for cooperative relaying. Since each relay Θi in set is not aware of the status of others, collisions and interference might happen if more than one relay forward at the same time instant. To solve this problem, the candidate relays take part in leader–followers game with their corresponding source to obtain optimal relay accessing chance, which is neglected in DTR algorithm [14]. In DTR, the active relay generates a random backoff timer and the waiting time may be too long. Although it reduces the collision probability, it increases the delay penalty. In this procedure, RTS/CTSs contain potential destination/ source address list. Upon receiving RTS, the destination sends CTSs containing channel gain information to its source. Upon receiving all expected CTSs or timeout, i.e., the maximum feedback latency, the source determines the particular logical cooperative link on which the source information is relayed by (13), (14), (17), and (18). Other neighbor nodes will overhear the exchanges of RTS/CTS and update their sensing parameters. After backoff procedure, the optimal winning relay seizes the channel and forwards the received information. The destination combines signals received from the source and forwarded by the selected relay. If the destination decodes successfully, it feeds back an Ack to the source immediately. The current cooperative transmission cycle is finished. Otherwise, it sends a Nack to continue relay forwarding phase. It remains possible that relay–destination streams in two logical source links might interfere with each other or has a collision, resulting in low system performance, such as r1 − D1 and r3 − D2 . In this case, the Stackelberg game process could consider this problem and calculate the best relay to cooperative transmission that has high system performance. Therefore, at last, the interference links would not transmit in the same time slot with the proposed multiple access control. Generally, the relay forwarding phase continues until one of the following four events occurs [14]: a successful decoding at destination, reaching maximal retry limit, no candidate relay helping, and timeout. Here, “no candidate relay helping” means that there are no relays satisfying (5), and “timeout” presents that the waiting time exceeds the maximal value and the next transmission could begin. Note that the wireless channel would
be persistently idle if no relay exists or if the destination cannot decode. Once the maximum feedback latency timeout, the transmission also is terminated. When the current transmission cycle ends, the relay will clean out the local buffer. IV. P ERFORMANCE A NALYSIS A. Existence and Convergence of Cooperation Stackelberg Equilibrium Generally, a system is considered as feasible if the relay and price assignment vectors exist where the obtained revenues are no less than zero for all terminal nodes. Such vectors are regarded as feasible solution [3]. In a feasible system, the Stackelberg equilibrium is said to be standard if for all suitable relay selection and price parameters that take part in the game calculation, the following revenue properties (i.e., Ui and Urj ) are satisfied: positivity, monotonicity, and scalability [3]. Lemma 1: Equations (14) and (16) are referred to as Stackelberg equilibrium functions. The proposed cooperative MAC scheme is standard on (15) and (18) for all sources and relays. Proof: We first show that the revenue function Ui of (i) (i) source Si is jointly standard in δrj given that the relay price qrj is fixed. From (11), the revenue function is the gain of Si , then Ui > 0. (i) (i) (i) Suppose any two values of δrj , δrj (1) < δrj (2), we need to (i) (i) calculate the relationship of Ui {δrj (1)} and Ui {δrj (2)} for a (i) given a constant qrj . Recall that N (i) δ log2 1 + ΓSi ,Di + ΓSi ,rj ,Di U i = ai f T rj N log2 (1 + ΓSi ,Di ) − qr(i) − δr(i) . (19) j j T Since f (ΔRi ) is a positive utility function of increased data rate for Si , we have N log2 (1 + ΓSi ,Di + ΓSi ,rj ,Di ) T N (i) δ log2 (1 + ΓSi ,Di + ΓSi ,rj ,Di ) ·f T rj N log2 (1 + ΓSi ,Di ) − qr(i) − j T 2 N ∂ 2 Ui log2 (1 + ΓSi ,Di + ΓSi ,rj ,Di ) 2 = a i T (i) ∂ δ rj N (i) δ log2 (1 + ΓSi ,Di + ΓSi ,rj ,Di ) ·f T rj N log2 (1 + ΓSi ,Di ) ≤ 0. (20) − T ∂Ui
(i) ∂δrj
= ai
(i)
(i)
Thus, we can get Ui {δrj (1)} ≤ Ui {δrj (2)}, and Ui is in(i) (i) (i) creasing with δrj in δrj ∈ [0, 0.5] given a constant qrj .
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(i)
(i)
(i)
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For all δrj and υ > 1, comparing Ui (υδrj ) and υUi (δrj ) in an elementwise manner, we have = υUi δr(i) − Ui υδr(i) g δr(i) j j j N (i) δ log2 (1 + ΓSi ,Di + ΓSi ,rj ,Di ) = ai υf T rj N − log2 (1 + ΓSi ,Di ) T N − ai f υ δr(i) log2 (1 + ΓSi ,Di + ΓSi ,rj ,Di ) T j N − log2 (1 + ΓSi ,Di ) (21) T
price and revenue rather than the highest ones. Most important is that there is no price information exchange between the relay nodes. Therefore, the game equilibrium achieves in a fully distributed manner with one-hop local CSI.
and furthermore, since f (·) represents a positive increasing (i) function in δrj ∈ [0, 0.5] and it also has a maximum value in the whole range, then we can get 2 /∂ δr(i) f (·) ≤ 0, ∂ 2 Ui δr(i) ≤ 0. (22) j j
where γ denotes the SINR decoding threshold. 2) If the direct transmission fails with probability
Thus
(i) ∂g δrj (i)
∂δrj
(i) − U υδ = υ U δr(i) rj j
=−υ
τdir = T · Pr {ΓSi ,Di ≥γ }
Pr{relay} = 1 − Pr {ΓSi ,Di ≥γ }
(24)
(25)
without considering retransmission time, the conditional successful transmission probability by the winning opportunistic relay is Pr{success|Θi } = 1 − Pr max ΓSi ,rj ,Di < γ . (26) After phase 2, the cooperative duration part of transmission cycle is equal to
dδr(i) U δr(i) ≥0 j j
The transmission cycle can be calculated by taking into account the following cases. 1) The direct transmission is successful; thus, the transmission cycle is equal to
rj ∈Θi
(i)
υδrj
B. Analysis of System Throughput
(23)
· T · Pr {success|Θi } . τrelay = δr(i) j
(i)
δrj
(27)
The average duration of a VTC is
(i)
and g(δrj ) is an increasing function. (i) Furthermore, considering g(0) = 0, we can get that g(δrj ) is (i) not less than zero in the range of δrj ∈ [0, 0.5]. Therefore, we (i) can get g(δrj ) > 0 and claim the scalability of Ui . In a similar way, we can prove that the revenue function (i) Urj of each relay rj is standard in its own price qrj when its contribution is optimized and fixed. According to these results, we get the following properties of the proposed game algorithm when it is applied to a feasible system. 1) The proposed game scheme solution is unique if it has a fixed point. 2) Starting from any feasible initial price, the relay selection and resource cooperation after sufficient iterations between the leader and the followers gradually converge to a unique fixed point. Furthermore, as previously discussed, it is natural for relay to initialize its price as its cost price. Lowering the price than the cost would result in negative revenue, and setting the price above the cost would increase the risk of being discarded by the source. Therefore, we can conclude that starting from a feasible initial price vector, iteration updating process of the standard relay pricing converges to a unique fixed point. Note that the relays would opt out when the system is infeasible, such as the source node’s revenue becoming negative. By the proposed game-based access scheme, relays that have exceeded the interference threshold will give up transmission as described, which means that these relay nodes quit from the game. Some other candidate relays might propose a suitable
τtc = T + τrelay .
(28)
3) When no relay is willing to supply cooperation communication, i.e., the candidate relay set is empty with probability Pr{Θi = ∅}, the wireless channel is idle for the maximal timeout τ . Otherwise, the winning relay in candidate relays fails; the duration of VTC will undergo more τ . Combining these results, the average system throughput is given by Φ=
log2 (1+ΓSi ,Di ) . τdir +Pr{Θi = ∅}τ +τtc +Pr maxrj ∈Θi ΓSi ,rj ,Di < γ τ (29) V. N UMERICAL R ESULTS
A. Scenario Settings Here, we present the performance evaluation of the proposed scheme through simulations on the network with the combined topology shown in Figs. 1 and 2, where the channel gains are functions of the transmission distance d−ε , and ε = 2. S1 and S2 are out of each other’s transmission range and broadcast simultaneously. They would carry out random backoff algorithm based on IEEE 802.11. According to the definition, although r7 has its own information to send and belongs to source nodes, it cannot transmit information because it can hear S2 before its transmission. Hence, r7 may serve as relay to compete for cooperation at this moment for S2 . The transmission mode QAM is available at the physical layer, and the noise level is set to σ 2 = 10−8 W. We set the reception thresholds for data packet to be α = 3 dB, β = 5 dB, and γ = 6 dB. Moreover, the frame
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period T , bandwidth size W , and symbol length are set to be 5 ms, 10 kHz, and 100 bits, respectively. According to the channel model previously described, we vary SNR P/σ 2 to characterize the system performance, including the average transmission cycle delay and the system throughput. To compare with DTR in [14], the backoff window is set to 16, a time slot is 320 μs, and timeout is 5 ms. B. Numerical Results We present extensive simulation results of the proposed game MAC protocol against DTR [19] and centralized optimal control in [8]. In the simulations, the source nodes S1 and S2 have data packets to send and the following performance metrics are evaluated: 1) average delay: the transmission cycle for a logical links; and 2) system throughput: number of data bits successfully received by the destination D1 and D2 in unit time. First, we evaluate the average delay performance of the proposed game in Fig. 3. It is shown in Fig. 3(a) that the three streams that use different relays’ help have different access rates under independent channel situation, where the interference with each other is not considered. We also show that the average delay for our game-based access scheme increases with transmit power because higher power increases the direct transmission success probability, resulting in less of a chance for relay cooperation. As we know, the average transmission cycle would undergo multiple rounds of failed retransmit times. Therefore, the cooperative period increases with lower relay price. We can also see, as shown in Fig. 3(b), that with the improved SNR, the transmission from active relays is more likely to success and thus reduces the transmission cycle length. Compared with these two schemes in Fig. 3(c), although our game-based access scheme increases delay with increasing SNR at first, we can still conclude that the game-based access scheme results in less transmit delay than DTR. Fig. 4 plots the independent throughputs in separate multiple access channels without considering the interference and collision with each other. The figure shows that the DTR has higher throughput in a high-SNR region. There is one point that needs to be specified. The simulation scenario in Fig. 4 ignores the interference. Therefore, with the increasing SNR, most of the logical links could achieve direct transmission without needing cooperation. This is to say that, with improved SNR, the transmission from the source itself is more likely to success, reducing then the transmission cycle length and increasing the link throughput consequently. The proposed game-based scheme has longer cooperation period, resulting in lower throughput. However, in practice, this interference should not be ignored, which is the main contribution of this paper. Compared with the link throughput performance of DTR shown in Fig. 4, our game-based access scheme is advantageous at low–medium SNR in sparse networks. However, it has more preponderance with mutual interference and collision in dense networks, which is shown in Fig. 5. In the following simulation, we use a topology scenario referring to interference to study the entire system throughput performance. In links r1 − D1 , r3 − D2 , and r4 − D2 , there exist power fading interference, and sometimes, they could
Fig. 3. Average delay comparison. (a) Proposed game-based access scheme. (b) DTR scheme. (c) Comparison results.
not transmit data information simultaneously. It is observed in Fig. 5 that system throughput could obtain higher value by the proposed game-based access control scheme than that by the DTR. To compare the throughput performance with the centralized scheme, we set up a link-utility-based optimal
CUI et al.: DISTRIBUTED INTERFERENCE-AWARE COOPERATIVE MAC BASED ON STACKELBERG PRICING GAME
Fig. 4.
Throughput comparison (DTR without considering interference).
Fig. 5.
System throughput comparison.
cooperative MAC protocol in the same topology scenario [5]. Then, we can obtain a curve of the maximal throughput versus different SNRs. As shown in Fig. 5, the proposed game-based cooperative medium access scheme achieves almost the same maximal throughput as the centralized scheme. It is more obvious in the dense network scenario because there is more of a probability for collision and interference. The effect of decoding threshold γ is discussed by considering the same network environment as before in Fig. 6(a) and (b), which show the average delay and system throughput performance versus γ for the proposed scheme. It shows the functionality of decoding threshold: A large γ increases the average delay and reduces the system throughput. By adjusting γ, we can restrict the number of candidate relays to reduce the contention, particularly in the dense channels. Overall, the choice of γ depends on the quality-of-service requirements in terms of reliability or symbol error rate.
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Fig. 6. Average delay comparison.
VI. C ONCLUSION To improve the spectral efficiency of wireless distributed cooperative networks, we have proposed an interference-aware cooperative relay access control scheme based on Stackelberg game theory framework. Only one-hop local CSI is required; the proposed scheme is performed in a fully distributed manner based on the relay pricing game. Simulation results have shown that the cooperative communication technique has a significant impact on network performance, and our game-based relay access scheme is efficient and performs well in distributed wireless networks. ACKNOWLEDGMENT The authors would like to thank the editor and reviewers for their useful comments that helped improve the quality and presentation of this paper.
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Haixia Cui received the M.S. and Ph.D. degrees in communication engineering from South China University of Technology, Guangzhou, China, in 2005 and 2011, respectively. She was a Visiting Associate Professor with The University of British Columbia, Vancouver, BC, Canada, from July 2014 to July 2015. She is also an Associate Professor with the School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou. Her research interests are in the areas of cooperative communication, access control protocol, quality of service, and power control in wireless sensor/ad hoc networks.
Yide Wang (M’07) received the B.S. degree in electrical engineering from Beijing University of Posts and Telecommunications, Beijing, China, in 1984 and the M.S. and Ph.D. degrees in signal processing and telecommunications from the University of Rennes 1, Rennes, France, in 1986 and 1989, respectively. He is currently a Full-Time Professor with the École Polytechnique de l’Université de Nantes (Polytech Nantes), Nantes, France, where he is also the Director of Research. In 2008–2011, he was the Director of the Regional Doctorate School of Information Science, Electronic Engineering, and Mathematics. He is the author or coauthor of seven book chapters in four scientific books, 50 journal papers, and more than 100 national or international conferences. His research interests include array signal processing, spectral analysis, and mobile wireless communication systems.
Quansheng Guan (S’09–M’11) received the B.Eng. degree in electronic engineering from Nanjing University of Posts and Telecommunications, Nanjing, China, in 2006 and the Ph.D. degree from South China University of Technology (SCUT), Guangzhou, China, in 2011. From 2009 to 2010, he was a Visiting Ph.D. Student with The University of British Columbia, Vancouver, BC, Canada. From 2012 to 2013, he was a Postdoctoral Researcher with The Chinese University of Hong Kong, Shatin, Hong Kong. In 2013, he was a Visiting Scholar with Singapore University of Technology and Design, Singapore. He is currently an Associate Professor with the School of Electronic and Information Engineering, SCUT. His research interests include wireless communications and networking and networked interactions and economics. Dr. Guan received the Best Paper Award at the IEEE International Conference on Communications in China 2014.
Han Zhang (M’14) received the M.Sc. degree from the University of Liverpool, Liverpool, U.K., in 2005 and the Ph.D. degree from Sun Yat-Sen University, Guangzhou, China, in 2009. He is currently an Associate Professor with the School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou. His research interests include cooperative communications, multiple-input–multiple-output/orthogonal frequency-division multiplexing technology, and cognitive radio.
