Access Strategy in Super WiFi Network Powered by Solar Energy Harvesting: A POMDP Method
Tingwu Wang, Jian Wang, Chunxiao Jiang, Jingjing Wang, Yong Ren
aa r X i v : . [ c s . I T ] J a n Access Strategy in Super WiFi NetworkPowered by Solar Energy Harvesting: APOMDP Method
Tingwu Wang, Jian Wang, Chunxiao Jiang, Jingjing Wang and Yong Ren
Department of Electronic Engineering, Tsinghua University, Beijing, 100084, P. R. ChinaE-mail: [email protected], [email protected], { jian-wang, jchx, reny } @tsinghua.edu.cn Abstract
The recently announced Super Wi-Fi Network proposal in United States is aiming to enable Internetaccess in a nation-wide area. As traditional cable-connected power supply system becomes impractical orcostly for a wide range wireless network, new infrastructure deployment for Super Wi-Fi is required. Thefast developing Energy Harvesting (EH) techniques receive global attentions for their potential of solvingthe above power supply problem. It is a critical issue, from the user’s perspective, how to make efficientnetwork selection and access strategies. Unlike traditional wireless networks, the battery charge state andtendency in EH based networks have to be taken into account when making network selection and access,which has not been well investigated. In this paper, we propose a practical and efficient frameworkfor multiple base stations access strategy in an EH powered Super Wi-Fi network. We consider theaccess strategy from the user’s perspective, who exploits downlink transmission opportunities fromone base station. To formulate the problem, we used Partially Observable Markov Decision Process(POMDP) to model users’ observations on the base stations’ battery situation and decisions on the basestation selection and access. Simulation results show that our methods are efficacious and significantlyoutperform the traditional widely used CSMA method.
I. I
NTRODUCTION
In order to expand the coverage area of wireless network, many algorithms and implemen-tations have been proposed. Recently, the Federal Communications Commission published theSuper Wi-Fi proposal, aiming to make use of lower-frequency white spaces between televisionchannel frequencies and create a nationwide wireless network. However, the ambitious task of building a countrywide network is confronted with many obstacles. An inevitable problem ishow to deploy practical backhaul and power supply system. Specifically, traditional cable-basedsystems may be not appropriate, considering the cost of deploying and maintaining the network.Despite all the above difficulties, many successful experimental deployments of Super Wi-Fisystem are accomplished accordingly. Wireless backhual has been proven to be effective asa replacement of cable backhaul [1]. Meanwhile, the fast developing energy harvesting (EH)technology provides an ideal power supply mode, which could make use of a wide range ofambient energy including piezoelectric, thermal, solar energy, etc.Given that the deployment of EH network is just emerging, new wireless protocols andmodification are required, as some preliminary studies pointed out in [2]. Specifically, fromusers’ perspective, when confronted with EH powered network, how to make efficient networkselection and access strategies is a practical and important problem. Different from traditionalnetworks, a prominent issue in EH powered networks is that the energy state and tendencyof one base station (BS) has to be taken into account when making BS selection and accessstrategies. In the literature, the access strategy problem in traditional wireless networks has beenstudied extensively, among which Markov Decision Process was used, with some challengesand solutions summarized in [3]. Access process among different users was deemed as a typicalgame process, and thus game theory, summarized in [4] as well as pricing theory investigated in[5], can be applied, respectively. In [6], the access strategy towards multiple base stations withnegative externality was considered. Recently, a POMDP MAC layer opportunistic access wasproposed by Dr. Zhao in [7], and a learning based approach to access between packet burstswas studied in [8].However, all the aforementioned studies on users’ access strategy did not consider the energyharvesting situation. In this paper, we propose a user access strategy for the fast booming SuperWi-Fi network, focusing on the influence of BS’s battery states. As long time transmission isnot guaranteed in EH network, the leaving and arriving of users are more frequent. Insteadof using a static system model, we consider a model where both the number of accessingusers and the charge of the BS’s battery are dynamic. Moreover, a new stochastic process forformulating users’ arrival and departure processes, as well as a battery state transition basedon a quasi-static formulation are combined to describe the system state transition. Consideringthat in EH powered wireless network, where the full knowledge of the system is unrealistic, we build a Partially Observable Markov Decision Process (POMDP) model to formulate the accessstrategy problem, i.e., users make the network access strategy by using the partially observedBSs’ battery states’ information. It is worth to mention that although our work focuses on solarenergy harvesting, the conclusion and the algorithm could be generalized to any access problemsin EH powered network.The rest of this paper is organized as follows. We describe the system model in Section II. InSection III, the POMDP access strategy is presented. Furthermore, we explain how to formulatethe POMDP states model in order to obtain the optimal access strategy. Also a suboptimalstrategy is proposed for simplifying the calculation. In Section IV, we evaluate the performanceof our proposed approach in contrast to several famous traditional algorithms, followed by ourconclusion in Section V. II. S
YSTEM M ODEL
As shown in Fig. 1, in an EH network with multiple BSs, where each BS is supplied by EHdevices and connected to the server by wireless backhaul. In each time slot, the BS harvests acertain quantity of solar energy, denoted as E H , and stores it into its battery. At the same time,to serve the users connected to the BS, energy E T is consumed for transmission. We denotethe battery quantity of the BS as Q B , which can be any value from to the battery volume B M . In every times slot, the BSs could serve multiple users, the number of which is denotedas S U = i, i = 0 , , . . . , N U − , where N U is the maximum number of users the BS couldserve simultaneously due to limited spectrum and coding ability. Note that different BSs in thenetwork could have different battery volume B M and maximum serving users N U .At the start of each time slot, users with new service demand could decide either to access orsense one of the BSs within its range. We denote the action as Φ = Φ ia for accessing the i th BS,and
Φ = Φ is for sensing. In the case of sensing, the BS will respond to the user by sending its next-time-slot system state in a short message which requires negligible energy consumption. In thecase of accessing, the user sends a request to the chosen BS. When the request is achievable, theBS activates user’s transmission immediately. Otherwise, the BS declines the request and informsthe user its next-time-slot system state, again with a low energy consuming short message. In theabove process, the short message could be used as observation by a user to update his/her beliefof the BS state (e.g., battery state, number of users in the system). Therefore, the user’s action Fig. 1. A schematic map of Super Wi-Fi system. has to be carefully chosen. On one hand, the users are intent to maximize their utility by makingenough access attempts. On the other hand, sensing is necessary, as the lack of information willresult in useless attempts, causing energy waste and access failures.From the BSs’ perspective, certain protections are needed, as malicious users could keepaccessing one BS and use up all the energy. To focus our work on formulation from the users’perspective and not to be distracted by protection details, a simple protection is used in ourwork. If a BS is currently not serving any users and the battery is low, the BS would reserve thelast quantity of energy that could serve a user for one time slot and forbid new users from usingit. Meanwhile, in our work, we consider rational users who could observe multiple BSs andchooses an action in every time slot to maximize the number of successful access. The numberof the observed BSs by the user is denoted as N A .III. POMDP BS A CCESS S TRATEGY
As POMDP could solve decision making problems of different decision horizon lengths underuncertainty, it perfectly depicts the above EH Super Wi-Fi model. In order to formulate theproblem, two key components in the system model, user number and battery, are carefullyconsidered.
A. User Model
As in traditional wireless network, the users arrive and leave the BS with certain probability[6]. Between adjacent time slots, new users may arrive and old users may leave or be forcedto leave when battery is insufficient. A revised birth and death process that considers forcedleaving are proposed as follow, ζ ( S ′ U | S U , Q B , Φ) = λ, if Q B is enough and S ′ U = S U + 1 , µS U , if Q B is enough and S ′ U = S U − , I ( S ′ U ) , if Q B is insufficient, , otherwise. (1)In the above equation, λ is the arriving rate and the µ ′ = µS U is the leaving rate of users. Theforced leaving is formulated by the indicator function I ( S ′ U ) , which indicates that S ′ U next timeslot is sure to be . Energy depletion happens when Q B − E T ≤ . B. Battery Formulation
The harvested energy E T is determined by the environmental parameters. Gaussian modelshave been proven effective in predicting solar intensity [9], [10]. The harvest model assumes thatthe solar intensity in a long time period are Gaussian distributed, and the solar intensity duringone single time slot, the length of which denoted as T L , remains unchanged. Thus, the solarintensity W e could be formulated as Gaussian distributed N ( x ; µ S , σ S ) with average intensity µ S and variance σ S . In current devices, the harvesting power per reference solar intensity is E H = W e J op V op Ω S T L η , where the J op and V op is the optimal operating point, the Ω S is thenumber of solar cells and the η is the efficiency [11].The transmitting power is set by BSs to provide enough SINR for the receiving users.Current power adjustment algorithms that use feedback are not valid, as the system state arefast changing between time slots. Therefore here a static power management is implemented,where the BS sacrifices some energy to insure a successful transmission every time slot. Thepower consumption in a BS is determined by the number of accessing users, which is de-noted as E T = Υ T ( S U , Q B , Φ) . As wide range telecommunication has negligible between-user interference, we assume the transmission power is proportional to the number of serving users, i.e., Υ T ( S U , Q B , Φ) = P T ( S U + Θ( S U , Q B , Φ a )) , where P T is the transmission power forsingle user. Θ( S U , Q B , Φ a ) is if the rational user could successfully access, otherwise it is .Correspondingly, we assume the battery volume B M = ρP T T L , where ρ is an integer. Note thatfor the nonlinear transmission power function, our method could still work by setting differentbattery levels in the below sections. When the required battery is more than the BS’s remainingbattery, the BS will provide a best effort service. Users with the higher priority are served. Inour case, the rational user has the lowest priority. Given the E H , E T , the battery in the nexttime slot could be calculated as, Q ′ B = min { Q B + E H − E T , B M } . (2)In EH powered BSs, the battery is a continuous value. But in a POMDP, the states have to bediscrete. Intuitively, we could use more battery states to approximate continuous value, but thisbrings much increase in the complexity of the algorithm. Luckily, a certain number of discretelevels could provide enough information during the decision making. We could set battery levelsaccording to the possible energy consumption in each time slot T L Υ T ( S U , Q B , Φ) . In the caseof linear power function, the levels are set as S B = ⌊ Q B / ( P T T L ) ⌋ . And the number of batterystates is N B = B M / ( P T T L ) + 1 = ρ + 1 . Thus, by knowing the battery states, the user wouldknow whether the battery is sufficient for transmission.The prediction of future battery states are based on transition probability between battery states.In order to calculate the transition probability, we assume the fluctuate of discrete battery state isquasi-static. i.e., the residue energy Q B − S B P T T L is uniformly distributed between [0 , P T T L ) .Although errors are brought by this assumption, the quasi-static assumption is proven to beeffective after a large number of time slots [10]. We denote the change of battery state betweentime slot as ∆ B = S ′ B − S B . Event ξ j represents that the real battery quantity change E H − E T isequivalent to more than j but less than j + 1 battery state change, namely ξ j := { j ≤ E H − E T P T T L ≤ j + 1 } . Then the probability that the battery state will change by ∆ B given E H and user actioncan be computed as follows Pr (∆ B = i | Φ , E H , ξ j ) = ( E H − E T ) P T T L − j, i = j + 1 , ( j + 1) − ( E H − E T ) P T T L , i = j, , otherwise. (3)In the equation, as mentioned in previous section, E T = Υ T ( S U , Q B , Φ) . When E H − E T ≤ ,the probability could be calculated the same way. The battery transition can be written asPr (∆ B = i | Φ) = Z ( i +1) ǫ T + E T iǫ T + E T Pr (∆ B = i | Φ , E H , ξ i ) N ( E H ; ¯ µ S , ¯ σ S ) dE H + Z iǫ T + E T ( i − ǫ T + E T Pr (∆ B = i | Φ , E H , ξ i − ) N ( E H ; ¯ µ S , ¯ σ S ) dE H . (4)In the equation, ǫ T = P T T L and ¯ µ S , ¯ σ S are scaled from µ S , σ S after the multiplication withharvesting device coefficients. C. System Transition Probability
The POMDP state is the overall system state, which combines all the BSs’ system state. Tomake the following math more readable and flexible, the system state S and S D = { S B , S U , . . . , S N A B , S N A U } are equivalent and used simultaneously. We have S = 1 , , . . . N S , where N S = ( N B N U ) N A .We first calculate the transition probability for a single BS. From conditionally independencewe have P ( S ′ U , S ′ B | S U , S B , Φ) = ζ ( S ′ U | S U , S B , Φ) δ ( S ′ B | S U , S B , Φ) . (5)The ζ ( S ′ U | S U , S B , Φ) is given in equation (1). And the battery transition is calculated based onthe equation (4) as follows δ ( S ′ B | S U , S B , Φ)= Pr (∆ B = S ′ B − S B | Φ) , if S ′ B ≤ N B − , P ∆ B =∆ MaxB ∆ B = S ′ B − S B Pr (∆ B | Φ) , if S ′ B = N B − . (6)When the battery is fully charged, S ′ B = N B − , all the extra harvested battery is abandoned.Note that we truncate the probability for ∆ B > ∆ MaxB as they are as small as zero by decimals.Thus the POMDP state transition is computed as T ( S ′ | S, Φ) = i = N A Y i =1 P (cid:16) S i, ′ B , S i, ′ U | S iU , S iB , Φ (cid:17) . (7) D. Observation Function and POMDP Iteration Algorithm
In POMDP formulation, the user only has the partial knowledge of the system. As mentionedabove, the user could get the target BS’s next-time-slot system state S OB and S OU at the end ofeach time slot. We use observation O to represent S OB , S OU . The observation probability functiongiven the system state in the next time slot is Z ( O | S ′ , Φ) = Pr (cid:18) O (cid:12)(cid:12)(cid:12)(cid:12) S t, ′ U , S t, ′ B (cid:19) = I S t, ′ U ,S t, ′ B (cid:16) S OU , S OB (cid:17) . (8) S t, ′ B and S t, ′ U are the system state of the target BS next time slot. The indicator function is when S t, ′ U = S OU , S t, ′ B = S OB or otherwise.The reward is define as R = 1 if the access succeeds, else R = 0 . Then the value function ofa single state is V Φ t ( S ) = R ( S, Φ) + γ X S ′ T ( S ′ | S, Φ) V πt − ( S ′ ) , (9)where π denotes the optimal action in that state. As no full knowledge is held for the user, we usea belief vector to denote the user’s system state belief β = [ β ( S = 1) , β ( S = 2) , . . . , β ( S = N S )] .Then the particular value function with a certain belief β is given by V Φ t ( β ) = X S R ( S, Φ) β ( S ) + γ X S X S ′ β ( S ) T ( S ′ | S, Φ) V πt − ( S ′ ) . (10)For simplicity, if we already know all the value function of at the time t − during iterations, analpha value vector α Φ t = [ α Φ t ( S = 1) , α Φ t ( S = 2) , . . . , α Φ t ( S = N S )] could be used to simplifythe value function as V Φ t ( β ) = P β ( S ) α Φ t ( S ) . Thus, the optimal action can be given by π ( β ) = arg max α Φ t X S β ( S ) α Φ t . (11)The corresponding value function V Φ t ( β ) could be calculated using action π ( β ) . However, thecorresponding optimal policy is not as easy as it seems to be, as the β has a continuous value,and even for the same Φ and t , there are still multiple possible α vectors during iterations. Butfortunately, the V t could be regarded as the function value of β in a hyper coordinate system,the axes of which are the components of β . As each set of α t vector could be regarded as a setof parameters of a hyper linear function, there is a dominated hyperplane structure in the model.The continuous belief space is divided by several α -vector-dominated hyperplanes into severalpartitions. The partitions of belief space in time t could be calculated given all the dominating α t − . The details of algorithm for solving the partitions could be find in a well written tutorial[12].After obtaining the optimal action, the user could act accordingly, and update its belief vectorafter receiving the observation by using the following formula. β ′ ( S ′ | Φ , O ) = P O Z ( O | S ′ , Φ) P S T ( S ′ | S, Φ) β ( S ) P S ′ P O Z ( O | S ′ , Φ) P S T ( S ′ | S, Φ) β ( S ) . (12) E. Suboptimal Access Policy
The optimal POMDP solution could be calculated off-line within seconds when the numberof states is small. However, the use of POMDP method is limited when N A is massive, andwhen the environment parameters, like solar coefficients µ S , σ , the birth rate λ and death rate µ of users, change quickly.The POMDP formulation will maximize success access ratio η A = N S /N T , where N S is numberof success access and N T is the number of the time slots. We propose a dual perspective ofsolving the problem by focusing on the harvested energy. We name it Energy Based (EB) Method.The problem is reformulated as, max Φ t ,t =0 , ..., N T − X N T t =1 E h H (cid:16) β t , Φ t (cid:17) i , (13)where the expectation function E[ · ] considers the probability of receiving different observationsand thus having different belief vector β t , and H ( β t , Φ t ) is the overall harvesting energy in allthe BSs as follows H (cid:16) β t , Φ T (cid:17) = X β t ( S ) N A X i =1 min (cid:16) E iH , E iT + B M − Q iB (cid:17) (14)In such a case, a suboptimal could be proposed by maximizing the system’s next-time-slotharvested energy, i.e., Φ (cid:16) β t (cid:17) = arg max E h H ( β t +1 , Φ t ) i , (15)When BS sensing is the optimal action, the user will choose to sense the BS that is not sensed forthe longest time. Due to the limited space, some key rationality of the EB method is summarized.First of all, when the solar intensity is strong, we could assume few users will be forced to leaveand thus the consumed energy by them are stable. As the transmission power is proportional tonumber of users, we could deduce that the more energy the system harvests, the more utility T he c on v e r gen c eo f be ll m an i t e r a t i on N A = 1,λ = 0.4,µ = 0.05,µ S = 1W e ,σ S = 0.5W e N A = 1,λ = 0.3,µ = 0.08,µ S = 1W e ,σ S = 0.5W e N A = 2,λ = 0.4,µ = 0.1,µ S = 1W e ,σ S = 0.5W e N A = 2,λ = 0.4,µ = 0.25,µ S = 1W e ,σ S = 0.5W e N A = 2,λ = 0.4,µ = 0.1,µ S = 0.2W e ,σ S = 0.1W e N A = 1,λ = 0.4,µ = 0.1,µ S = 0.2W e ,σ S = 0.1W e Fig. 2. Illustration of the convergence of the POMDP iteration algorithm the rational user could achieve. Besides, the EB method is an unselfish method, which wouldsacrifice some reward, but tends to protect overall utility. And EB method could use learningalgorithm to adjust to quick environmental changes.IV. S
IMULATION R ESULTS
In this section, the convergence and effectiveness of the algorithm are illustrated. Fig. 2shows the convergence of the POMDP iteration algorithm, where the y-axis means a user’svalue difference between two adjacent iterations and the discount factor is γ = 0 . . A Bellmanstopping criteria is used to determine the stop of iteration. In the figure, the α vector error showsthe convergence of the iteration algorithm. The POMDP simulation tool is provided by [12].As we can see from the results, our proposed POMDP algorithm converges exponentially undervarious parameter settings.The effectiveness of the algorithms is validated by comparing the η A under the overall timeslots N T = 10000 . In the simulation, parameters are used as follow. The reference benchmarksolar intensity is given as W e = 1 kW /m , which is the average intensity on the surface of Earth[13]. We use the data from work [14], where the optimal power per benchmark solar intensity W e is P H = J op V op = 1 . mW / W e , with a efficiency η = 75% . And there are Ω S = 40 cellsin one harvesting device. The time slot length is T L = 200 ms. Transmission power for servingone user is P T = 40 mW.In order to show the efficiency, several algorithms are implemented as comparisons. includ- A = 2 T heu t ili t y r a t i o POMD PEB MethodRandomCSMA /C DCSMA /C A (a) The utility ratio with arrival rate in single BS
The solar intensity normalized by reference intensity T heu t ili t y r a t i o POMD PEB MethodRandomCSMA /CDCSMA /CA (b) The utility ratio with solar intensity in single BSFig. 3. Single BS with S U = 0 , , , , N B = 8 ing Carrier Sensing Multiple Access/Collision Avoidance, Collision Detection (CSMA/CA andCSMA/CD). Note that here the “carrier sensing” means that one user senses the BSs, i.e., receivesthe short message from one BS, instead of the physical carrier. The CSMA/CD method stopsnew request when detecting a failure, and then an exponential back-off algorithm is used. After c failures, a random number of sleeping time slot between and c − is chosen. The CSMA/CDmethod would access the BS after the user senses the BS in the last time slot and knew that asuccessful service is available. In random access algorithm, the user simply chooses action with A = 2 T heu t ili t y r a t i o POMD PEB MethodRandomCSMA /C DCSMA /C A (a) The utility ratio with arrival rate in two BS
The solar intensity normalized by reference intensity T heu t ili t y r a t i o POMD PEB MethodRandomCSMA /CDCSMA /CA (b) The utility ratio with solar intensity in two BSFig. 4. Two BS with U N = 0 , , N B = 3 equal probability.In Fig. 3, we consider single BS with possible number of users from to , N B = 8 ,and the leaving rate µ = 0 . . In Fig. 3-(a), the µ S = 1 and σ S = 0 . , while in Fig. 3-(b),the arrival rate λ = 0 . . As shown in the figure, the performance of proposed POMDP issignificantly higher, with the EM method’s overall performance following at the second place,which validates the efficiency of our algorithms. From Fig. 3-(a), we can see that the CSMA/CDhas a good performance when the system is not busy, but the performance deteriorates quickly with the increasing arrival rate of users. In Fig. 3-(b), one prominent point is that even whenthe solar intensity is strong, the utilities of the traditional algorithms’ are saturated, failing tofurther enhance users’ utility, due to the reason that those algorithms are not able to make useof the EH information of the system. It is also worth mentioning that, as we predicted, whenthe solar intensity is strong, the suboptimal EB method will approach the proposed POMDPmethod, which can decrease the complexity to a large extent.In Fig. 4, multiple BSs are considered, with possible number of user from to , N B = 3 ,and the leaving rate µ = 0 . . In the figure, we find that when the possible serving positionsis limited, the crowded system makes the CSMA/CD method almost useless. In (b), a simpleanalysis of the CSMA/CD performance could be given. When the solar intensity is small, theutility of CSMA/CD increases with intensity due to more available sources. But when the solarintensity is strong, as the more users are staying in the BS, the user has less chances of beingserved, and the utility decreases. Also, in (b), the suboptimal EB method could outperformPOMDP method when the intensity is strong, which is mainly brought by the approximation inthe POMDP formulation, such as using the quasi-static approximation.V. C ONCLUSION
In this paper, we proposed a powerful POMDP algorithm to solve the access problem in EHpowered network, which is promising and instructive in building a national range Super Wi-Finetwork. The framework given in this paper is adjustable to EH problems other than the SolarEH one. To reduce complexity and adjust to environmental changes, a suboptimal EB methodis proposed as well. The effect of solar intensity, user arriving rate, leaving rate and many otherfeatures are considered, proving our work reliable and effective. Future work of this paper couldfocus on the prediction of system parameters and multiuser accessing scenario.R
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