Distributed Inter-Network Interference ... - Semantic Scholar

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Distributed Inter-Network Interference Coordination for Wireless Body Area Networks Gengfa Fang, Eryk Dutkiewicz, Kegen Yu, Rein Vesilo and Yiwei Yu Department of Electronic Engineering Macquarie University, Sydney, NSW, Australia Tel: +61-2-9850-9124, Fax: +61-2-9850-9128 E-mail: {gfang, eryk, kegen, rein, yiwei}@science.mq.edu.au Abstract—In this paper we consider the inter-network interference problem in Wireless Body Area Networks (WBANs). We propose a distributed inter-network interference aware power control algorithm motivated by game theory. A power control game is formulated considering both interference between nearby networks and energy efficiency of WBANs. We derive a distributed power control algorithm called ProActive Power Update (PAPU), which can efficiently find the Nash Equilibrium representing the best tradeoff between energy and network utility. A realistic power control procedure is proposed assuming limited cooperation between WBANs. We compare our algorithm with the ADP algorithm where users are punished for interfering with others and we show that our solution can utilize energy much more efficiently by only sacrificing a small amount of network utility. In addition, we show that by adjusting the energy price, PAPU provides a methodology for application scenarios where WBANs have different energy constraints and quality of service requirements.

I. I NTRODUCTION Whilst wireless technology continues to evolve for a broad range of new applications, wireless networks for medical applications such as patient monitoring, disability assistance and remote control of medical devices have led to the development of Wireless Body Area Networks. WBANs can monitor vital body signs such as heart-rate, temperature, blood pressure, ECG, EEG and pH level of patients. By replacing cables with wireless links, WBANs can provide less invasive and more comfortable and efficient systems both in hospital and outside the hospital. WBANs are of particular interest to the healthcare sector to provide efficient healthcare services and ongoing clinical management. According to the Population Division of United Nations, the world average ratio of total population aged 60 years or older in 2050 will reach 21%. Because of its greater user-friendliness and more efficient services, WBAN can greatly reduce the cost of healthcare in countries where there is a great shortage of healthcare resources like the number of doctors and nurses. To harmonize with the strong demands from both medical and healthcare societies, and information and communications technology (ICT) industries, IEEE 802.15.6 task group (TG6) was set up December 2007 to provide an international standard for a short range (i.e., human body range), low power and highly reliable wireless communication by defining new radio based physical (PHY) and media access control (MAC) layers for WBANs. So far hundreds of proposals on PHY, MAC and

system issues have been presented by Samsung, NICT, ETRI, GE, Zarlink, NICTA and others. Currently TG6 tries to merge related proposals into a baseline draft which is planned to be available in 2010. Unlike cellular networks, WBANs are randomly distributed networks where two or more WBANs may overlap with each other and interfere with each other due to the limited available frequency bands. For example in a crowded bus more than 10 people may sit close to each other, so that each person’s WBAN will interfere with the others. This inter-network interference may cause severe problems in WBANs. It will raise the SINR and as a result cause throughput degradation and packet loss. Packet loss also leads to energy waste and decrease in energy efficiency of WBAN nodes. Since stability is a critical issue in WBANs, interference may cause life critical packets loss and hence is a threat to patients’ lives when WBANs are used in the healthcare sector. To mitigate the inter-network interference, several centralized and decentralized algorithms have been developed for wireless networks. In centralized approaches [1][2], there is always a central coordinator like a Base Station in cellular telecommunication systems, which controls the medium access and transmission power so as to coordinate inter cell interference. This is not applicable in WBANs where each WBAN works independently in a distributed manner. On the other hand, some recent works [3],[4] and [5] consider inter-network interference cancelation for WLANs and sensor networks where CSMA based transmit/backoff media access protocols are used and assume fixed transmission power. Game theory has been applied to network resource allocation problem both in telecommunication networks and sensor networks. In [12], game theory is used to solve the flow control problem for variable rate traffic at a bottleneck node. In [11], game theory based distributed power control algorithms are proposed for both single channel and multiple channel wireless networks where the goal is to maximize the overall utility. Other related work on both channel allocations and power control for interference mitigation in wireless OFDMA systems are [8],[9]. Unlike the work above, we apply game theory to analyze power control for both inter-network interference coordination and efficient energy use in WBANs where power consumption is an important factor deciding the performance of WBANs.

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In this paper, we solve the power control problem under inter-network interference from nearby WBANs. Our objective is to find a power control strategy for WBANs to determine when to transmit and how much power to use for each transmission depending on the wireless channel state, interference level from nearby WBANs and energy constraint, so that WBANs can coordinate with each other to use less transmission power while maintaining high overall throughput. A game theoretic approach is applied to analyze the problem which turns each WBAN into a selfish player so as to require less communication overhead between players. To the best of our knowledge, this paper is the first to handle the internetwork interference problem in WBANs based on game theory and provide a realistic distributed inter-network interference aware power control algorithm. Our main contributions can be summarized as follows: • We formulate a power control game for WBANs, which considers inter-network interference between nearby WBANs, wireless fading channel and energy constraints of WBANs • The existence of a unique Nash Equilibrium is proved and a distributed convergence algorithm is presented to efficiently find the unique Nash Equilibrium requiring only very limited information exchange between WBANs. The convergence of the algorithm is proved as well. • We compare our distributed power control algorithm with a pricing based power control algorithm designed for interference compensation in sensor networks in terms of utility, power consumption and convergence speed. The rest of this paper is organized as follows: In Section II, we define the problem of power control for inter-network interference coordination and then formulate it as a power control game. In Section III, a game approach based solution is proposed to find a Nash Equilibrium and its convergence is analyzed and proved. Section IV includes performance simulations and it is followed by our conclusions in Section V. II. I NTERFERENCE AWARE P OWER C ONTROL G AME In this paper, we consider the power control problem in WBANs under interference from nearby networks which are transmitting concurrently. The goal of power control is to maximize the network utility by using as little energy for transmissions as possible. The network utility is measured according to Shannon’s capacity. Based on game theory, we express our objective function as a combination of utility gain and energy cost. The best effort based distributed power control algorithm is developed to make sure each player maximizes the objective function and all players converge efficiently to a Nash Equilibrium. Next we formulate the power control game. We consider a scenario of a set S = {1, ..., M } of WBANs where some WBANs’ transmission ranges may overlap with each other causing interference to other WBANs. As an example, Fig. 1 shows two WBANs interfering with each other. We assume a TDMA based media access control scheme

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K

K K

K

1RGH

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Fig. 1: Inter-network interference model in WBANs where hij is the channel gain between transmitter i and receiverj , and hij is the intra-network gain if i = j and inter-network interference gain for i = j.

is applied within each WBAN to avoid intra-network collision. We use term ’user’ to indicate the transmission link between a transmitter and a receiver at a certain time slot. The transmission can be either from a WBAN node to its gateway or vice versa. For example, in Fig. 1 user 1 is the communication link between GW1 and Node1, while user 2 is the link between GW2 and Node 2. Over the time-period of interest, we assume the channel gain of each user and interference gains are fixed. This is reasonable for block fading based wireless channels where the channel gain is constant within each block. We use hij to denote the channel gain between user i’s transmitter and user j’s receiver. User i’s received SIN R at the receiver side can be written as ri =

1 B



hii pi . j=i hji pj + n0

(1)

where pi and pj is the transmission power of user i and j; n0 is the background white noise power and B is the total channel bandwidth. The corresponding transmission rate of user i is a strictly concave function of the received SIN R and can be expressed as log(1 + ri ). In this paper, we also call the transmission rate the utility. Based on the definitions above, the problem we consider → here is to decide users’ transmission power − p = (pi , ..., pM ) to maximize the overall transmission rate and to minimize the transmission power of all users, where the transmission power of each user i must also satisfy the power constraint, i.e., pi ∈ [0, Pimax ]. This problem can be written as  max log(1 + ri ) i

min



pi

(2)

i

s.t. pi ∈ [0, Pimax ]. In practice, WBANs will not cooperate for power decision making purposes in (2), which means that each WBAN will decide its transmission power independently based on its belief of others’ choices. The problem definition in (2) indicates that each user is rational and self-interested. Bearing these considerations in mind, we model the power control problem in (2) as a Power Control Game and apply game methodology to study the non-cooperative power control game. Definition 1 (Power Control Game) We define an interference aware power control game among WBANs as follows:

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• • •

Players: there are M players with each player i ∈ {1, 2, ..., M } Actions: pi ∈ [0, Pmax ] for player i representing its transmission power Payoff function: πi (pi , p−i ) = log(1 +

1 B

 j=i

hii pi ) − ci pi hji pj + n0

where the payoff function for each player is defined as the difference between the utility function and cost function consisting of power price ci and power pi . For simplicity, we let B = 1 in the rest of the paper. As we show next, power price ci decides the trade-off between network utility and power efficiency. This is of great importance for WBANs where different WBANs have different utility and power efficiency requirements because of the dynamics of wireless channel states and different constraints on power and Quality of Service requirements. The price item can be dynamically set by the WBAN gateway according to the power state, QoS parameters of applications and interference to and from nearby WBANs. In this paper WBANs can either exchange information such as current transmission power, channel gain and interference to facilitate the decision making or WBANs can gather this information through their own measurements. The objective of the game is to coordinate the users’ transmission powers, i.e., when to transmit and at what power level to transmit to optimize overall performance in terms of total network utility and power efficiency. III. G AME T HEORY BASED S OLUTION In this section, we apply game theory to analyze the interference aware power control game in (2). According to game theory, players in the game are selfish and always try to maximize their own payoff, which compromises both gain (i.e., network utility) and cost (i.e., energy consumption). We firstly prove the existence of a unique Nash Equilibrium in the power control game and then provide a best effort based distributed algorithm for users to calculate their transmission power. The convergence of the power control algorithm is analyzed as well. A. Nash Equilibrium Definition 2 p∗i is a Nash Equilibrium in the Power Control Game defined above if and only if: p∗i = arg max πi (pi , p−i ) pi

for all user i and for all hi . Theorem 1 There exists a unique Nash Equilibrium in the Power Control Game in definition 1. Proof: According to Theorem 1.2 in [10], if Power Control Game has nonempty compact convex subsets of an Euclidean space for pi and the payoff functions πi are continuous in p and quasi-concave in pi , there exists a pure strategy Nash equilibrium. It is defined such that transmission power of each user pi has continuous values between zero and Pmax , so it

is clear that pi is a nonempty, convex and compact subset of an Euclidean space. The payoff function πi is obviously a continuous function of P according to its definition. For user i we have hii ∂πi (pi , p−i ) =  − ci = 0 ∂pi hji pj + n0 + hii pi j=i

which can be solved for pi , to lead to:  hji pj + n0 1 1 j=i − = − qi pi = ci hii ci where  hji pj + n0 j=i

(3) hii It is easy to prove that for pi ∈ [0, c1i − qi ], πi is strictly nondecreasing and then strictly nonincreasing for pi ∈ [ c1i − qi , Pmax ], so πi is a strictly concave function. According to Theorem 3 of [10], πi is strictly quasi concave. Therefore we can prove that there exists a unique Nash Equilibrium in the Power Control Game. qi =

B. Distributed Convergence Algorithm So far we have studied the Nash Equilibrium of the Power Control Game which is a static solution concept, in that it defines a state where all the players are playing best response simultaneously to other players’ choices, channel gains and interference. The question now is how to guarantee players can work together to reach this state in the continuous game where the inputs, such as channel gain and power state, of the game keep changing as time elapses. The challenges of this are: firstly players have to work in a distributed way, which means each player has to make decisions based on limited information about other players and the network; secondly the algorithm can quickly adapt to the fast network dynamics including the number of players, channel gain and level of interference so as to quickly converge to the Nash Equilibrium within a limited number of iterations and so that players’ payoff functions are maximized. Keeping these in mind we propose a simple distributed convergence algorithm for the nodes to quickly and easily find the Nash Equilibrium of the Power Control Game defined in Definition 1 above. We use the best response concept to calculate the Nash Equilibrium. In the Power Control Game, the transmission power of a player that maximizes its own payoff function is called best response to transmission powers chosen by other players and current channel gains. Let bi (p−i ) denote the best response of player i to a given interference power vector of other players. As described above, πi is a concave function over [0, Pmax ], and arg max πi (pi , p−i ) = c1i − qi , so we pi

have the following proposition: Proposition 1 The best response of user i in Power Control Game is given by  hji pj + n0 1 j=i (4) − bi (p−i ) = ci hii

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Based on Definition 1 and Proposition 1 above, the Nash Equilibrium can be reached if each user’s power is the best response given all the other users choices. In the distributed environment, however, each player makes the decision on the transmission power independently and asynchronously. In addition, wireless channel gains are also quite dynamic. So each player cannot make sure it calculates the best response based on the other users’ best responses and channel gains. The whole system has to take a number of iterations before it eventually converges to the unique Nash Equilibrium. In a static strategy game, players make decisions synchronously. However, it’s hard and expensive for all the WBANs in the Power Control Game to coordinate synchronously, therefore we design an otherwise simple and distributed event-driven Proactive Power Update algorithm (PAPU). We also discuss the stability and convergence of the PAPU algorithm. In the PAPU algorithm, user i’s transmission power is updated every time a predefined event happens, i.e., PAPU is event driven. There are two types of events which can drive the PAPU algorithm: other users’ power updating, i.e., −t t ptj = p−t j , ∀j = i or |SIN Ri − SIN Ri | ≥ SIN Rth . Each time an event happens, user i updates its transmission power according to (4). One important feature of PAPU is that users are myopic, which means they update their transmission powers according to an instant understanding of the parameters such as interference from the other users and channel gains, ignoring future impact on the system performance from their actions. Based on the above description of the PAPU algorithm, we now describe the Power Control protocol which includes the PAPU algorithm and the procedures in each WBAN as follows: Step 1: Each user i initializes its power p0i , p0−i and SIN Ri0 ; Step 2: At time t if user i updates its power, user i broadcasts its power pti to its neighbors through its Gateway; Step 3: If user i detects that its neighbor j’s power p−t j or its own measured SIN Rit is updated, user i updates power pti according to (4), and if pti = p−t i , gateway broadcasts this update to neighbors. If the PAPU algorithm is not converging during the power updating procedure, the whole system will not be stable, which means players’ transmission powers may oscillate indefinitely deviating from the Nash Equilibrium no matter how many iterations are taken. Since the convergence of PAPU decides whether the unique Nash Equilibrium can be reached, we now study the convergence issue. Since the interference channel gains from nearby WBANs are much smaller than the channel gains within WBANs, we assume that interference channel gains are symmetric and we use the average interference channel gain hji ≈ E[hji ] = hcross for analysis. According to the best response function given by (4), the power updating function can be written as pti =

1 hcross −t − n0 − P , ∀i, t ci hii −i

(5)

Let

Δpi = pi − p∗i ,

where p∗i is the transmission power of the ith player at the Nash Equilibrium. Then we have Δpti = −

hcross Δp−t −i , ∀i hii

Let  Δp = maxi | Δpi | and from (5) we have ||Δpt || ≤ (M − 1)max| i

hcross | || Δp−t || hii

It’s clear that we have a contraction mapping in (5) if (M − 1)max| i

hcross | < 1, hii

so that we now have the following sufficient condition for the convergence and stability of PAPU: |

1 hcross , i = 1, ..., M | < hii M

Thus, the system is stable and convergent under the PAPU algorithm if the above condition is satisfied. IV. P ERFORMANCE E VALUATION In this section, we evaluate the performance of the PAPU algorithm through simulation. We setup a network in a 10m x 10m square area where transmitters are placed randomly according to a uniform distribution. Receivers are randomly placed within a 6m x 6m square centered around the corresponding receivers. We compared the PAPU algorithm with the ADP algorithm in [11]. ADP is a game theory based power allocation algorithm designed for sensor networks. The ADP algorithm applies a pricing mechanism to coordinate interference among nearby nodes so as to improve the overall utility such as bandwidth. Our simulation is setup based on [11], for max /n0 = 40dB , and example, channel gains hij = d−4 ij , Pi B = 128. We first examine users’ total utility and average power consumption of the PAPU algorithm in a network with the number of users increasing from 2 to 38. Fig. 2 shows the users’ total utility as a function of the number of users in the network and Fig. 3 shows the average power consumption. Both the ADP and PAPU algorithms can increase the overall utility when the number of users increases, but PAPU outperforms ADP in that it can vastly save users’ power by 50% ˜ 80% by sacrificing only 10% ˜ 30% utility as shown by Fig. 2 and Fig. 3. This is a great advantage for energy constrained WBAN where long lifetime is the first priority. In addition, PAPU provides a mechanism to adjust the tradeoff between utility and power consumption through changing the power price. As shown in Fig. 2 and 3, increasing the power price leads to lower overall utility and average power consumption of each user. In practice, the power price can be decided by considering users’ QoS requirements and energy constraints.

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140

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ADP PAPU−10 PAPU−2

ADP

60

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PAPU−10

PAPU−1 PAPU−0.6

PAPU−2 PAPU−1

Users’Total Utility

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Users’Everage Iterations

PAPU−0.6

40

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10 0

0

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15 20 25 Number of Users: M

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Fig. 2: Users’ total utility as function of number of users in the network. Power price controls the tradeoff between utility and power consumption. 1 0.9

ADP PAPU−10

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PAPU−2 PAPU−1 PAPU−0.6

Users’Everage Power

0

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0.7 0.6 0.5 0.4 0.3 0.2

15 20 25 Number of Users: M

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Fig. 4: Users’ average number of iterations for reaching Nash Equilibrium.

has lower power consumption by sacrificing little utility. The effect of power pricing on utility, power consumption and convergence was also studied through simulations. Our future work will focus on the design of the MAC control to facilitate this power control algorithm and analyze the overall performance. What’s more, we will implement this algorithm on a WBAN hardware testbed by defining related MAC protocols to support the control procedures. Performance of the algorithm will be tested and verified on our WBAN hardware platform. R EFERENCES

0.1 0

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Fig. 3: Users’ average power consumption as a function of number of user. Power price controls the tradeoff between utility and power consumption.

The PAPU algorithm then provides the interface to explore the highest utility under the constraints on users’ energy. In practice, network environments change dynamically although we assume the channel gains are fixed in a short block of time. This requires that PAPU should converge as fast as it can so as to improve performance in terms of utility and power consumption. We examine the convergence of PAPU through simulations where all the parameters are the same as above. All users synchronously update their powers during each iteration and broadcast their updates to the other users. As shown in Fig 4, the average iteration number increases as a function of the number of users for both PAPU and ADP. PAPU can reach the Nash Equilibrium faster than ADP especially when users increase users power prices.. In general, PAPU has better performance from the points of power consumption and complexity especially for applications where energy efficiency is a big concern as it is in WBANs. V. C ONCLUSION We have presented a game theory based power control algorithm for inter-network interference coordination. We applied game theory to represent it as a power control game where payoff function reflects both utility and power consumption. We proved that there is only one Nash Equilibrium in the game. We proposed a best response based distributed power updating algorithm called PAPU and analyzed its convergence. Our numerical results show that PAPU converges quickly and

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