论文研究EnergyEfficient Cooperative Communications with Shared Relay in Wireless Network.pdf

无线网络中基于共享节点高能效的协同通讯，邓厚， 黄刘生，随着移动设备数量的增加,无线网络中的能量高效性和服务质量越来越重要。最近几年,在不增加设备和天线的情况下,协同通讯被提出用来
国利技论文在线 http://www.paper.edu.cn le 1: Numerical Example of Transmission Power(w) DT CC Shared CC Trans. pair PsP 4 pair TI. Then, we can analyse the minimum total power consumption of three schemes from the table. Under the DT scheme, the total transmission power is 17w. When the CC scheme is used, the relay node is assigned to the transmission pair T2 by the jRPa algorithm, and the total transmission power is 14w. In the shared cc scheme, we consider the following scene, in which each source node uses the CC for t, 0<t< 1 units and dt for 1t units during one unit time. Thus, two transmission pairs are both assigned relay node for the dominant time, and the total transmission power is 12w, which is better than that of the CC scheme. Based on the description talked above, our contributions in this paper are listed OWS We define the problem of the Minimum Energy Consumption for capacity requirement (MEC)of CC with shared relay. It is proved that the MEC problem is NPhard As NPhardness, we propose the Shared Relay assignment for Energyefficient (SRAE) algorithm to solve this problem. We define two key terminologies of our proposed work including the profit ability and the power gain to easily introduce the srae algorithm We conduct abundant simulation experiments to evaluate the performance of our pro posed algorithIn. The siinulatioI results show that the srae algorithIn are efficient in decreasing the total energy consumption of the network The rest of the paper is organized as follows: Section 1 describes the system model and problem formulation. The detailed algorithm descriptions of srae are given in Section 2. The Simulation results are illustrated in Section 3. In Section 4, we discuss the related works. We conclude the paper in Section 5 1 Problem Description In this section, we first introduce the system model with some necessary Preliminaries of CC, based on which, the MEC problem will be formulated and its NPhardness will be proved 1.1 System Model The essence of cooperative communications is best explained by a wellknown threenode model (see Fig. 1). Transmission from s to d is done on a framebyframe basis. There are two time slots in each frame. In the first time slot. source node s make a transmission to 国利技论文在线 http://www.paper.edu.cn r K 1: A threenode schematic for cooperative communications destination node d with power Ps. Since the broadcast nature of the wireless communication this transmission is also overheard by relay node r. In the second time slot, node r forwards the data received in the first time slot to d with power P ii, where o is the variance of the received background noise at node i and hii represents the effect of pathloss, shadowing and fading between nodes i and j. We consider the amplifyandforwards(AF)and decodedandforward (DF)modes 9. Under the AF mode, it has been shown in 5 that the capacity froIn node s to lode d with the relay node T is CAF(s, r, d)=W. IAF(PS, P) re laF (Ps, P )1log2(1+asdS +pPsardPr)and w is the bandwidth. The capacity for the Df mode can be calculated by: CDP(s, r,d=W. IDr(Ps, P) where IDF(P, Pr)=, min log2(1+asr Ps), log2(1+aedEs ardPr) Under the direct transmission mode. source node s transmits data to destination node d in both time slots. The capacity from nodes to node d is given as follows d)=W·log2(1+aadP) There are three disjoint node sets in the wireless network including the source node set S=S1, S2,..., S(s1, the destination node set D=Id1, d2,..., dp, and the relay node set RI. Since each source node s; will communicate with an unique destination node di, we can obtain S=D. Let(Si, d; represents the transmission pair from node si to node di. Such a network configuration of CC has been widely adopted in the literatures 1,5 We assume that the relay node can be shared among multiple transmission pairs. Hence, in our system model, the transmission procedure of each sourcedestination pair can be divided into two parts. The first part is for communicating through onlly one relay node, the another is for direct transmission. For each transmission pair(S;, di), it will be assigned a cooperative transmission time ti,o< ti< 1, and time 1ti is for the direct transmission. In order to guarantee a certain level of QoS, each sourcedestination pair (si, d; ),I<i<n, must afford a specified capacity bi According to the above model, the problem of the Minimum Energy Consumption(MEC) for capacity requirement of CC with shared relay can be stated as follows: given a group of 国利技论文在线 http://www.paper.edu.cn communication sessions with the demand of capacity, and a set of shared relay node in the wire less network, find the optimal power control, relay assignment, and cooperative transmission time allocation such that the total energy consumption is minimized 1.2 Problem formulation In this part, we will formulate the MEC problem. Let lij be the binary variable, set to 1 if the relay node r; is assigned to Si. Since each sourcedestination pair will be assigned only one relay node at most. it obeys the following constraint ∑ <1,V r3 Moreover, we assume that each source node is assigned a cooperative transmission time ti. Then. we can obtain that each relay node is allocated not more than one unit by different source node which can be written as t;≤1,v;∈R. 5 2:s;∈S Next, In order to ensure that the capacity requirements of all source nodes are satisfied, it is necessary to formulate the capacity of each transmission pair. According to(1),(2), we can see that the capacity under AF and dF has the same form. So in our formulation, for both AF and DF, its capacity can be written as: Cii= CR(Si, ri, di)=w. IR(P3,, P,), where R is replaced by AF in the AF mode or DF in the DF mode. Thus, the capacity constraint can be formulated as ∑;Ct+CD(s,4)(1∑x;t) J:T∈B j:”∈R Finally, all of the parameters can be formally defined as ∈{0,1},P;,Pr∈[0,+∞),t∈[0,1,vs;∈S,vr∈B The mec problem of Cc with shared relay is presented as follows min ∑P1+∑P 2:S;∈S j:TER ,, subject to: (1)(7) As shown above, the nain factors that lead to the hardness of this problein including the lager number of constraints, t he multiplication of varia bles in constraint(6), and the binary nature of the decision variables. It is proved that the meC problem is NPhard in the following theorem Theorem 1. The MEC problem(defined above) is NPhard 国利技论文在线 http://www.paper.edu.cn Proof: In order to prove its NPhardness, we then show that MEC problem can be reduced to the 01 knapsack problem [11]. The 01 knapsack problem can be formulated as follows given n items, each with a weight wi and a value vi, where wi is an integer, determine the selection of each item to include in a collection so that the total weight is less than or equal to a given limit w and the total value is as large as possible, where w is an integer Then, given an input as listed above, we construct a meC problem as follows: in the constructed case, we have n, transmission pairs, each of which can be represented by (si, di) and one relay node r. Since there is only one relay node, the power of relay node can be ignored in the objective. We assume that source node si transmits data with a fixed cooperative com munication time ti, ti E0, 1. For each transmission pair(si, di), we can obtain the minimum power Pc of source node si such that the capacity constraint(6) is satisfied. Meanwhile, the minimum power pd of source node s, can be obtained such that the capacity of s; is more than or equal to bi whien source Iode si direct tranlsinits with destinatiOn node di. Let ti= Wi DDPC=vi, 1<isn and =W, where is an integer and large enough such that all the values of pt; are integer. Clearly, if there exists a collection A whose total weight is less than or equal to w and the total value is largest, we are able to find a shared relay assignment by assigning the relay node r to the transmission pair in A, and allocating cooperative commu nication time ti=W/W to the corresponding transmission pair in 4. This solution ensures that the energy consumption is minimum. On the other hand, if there exists a shared relay assignment whose energy consuption is niniinuIll, we can select the tranSInission pair thlat is assigned relay node, and the total value must, be largest 2 Algorithm Description Due to NPhardness, finding an optimal solution is infeasible. Instead, we prefer heuristics for the problein. The greedy strategy is oftel used to solve the optinization probleIn. We can iteratively select the appropriate shared relay assignment that minimizes the objective function. Based on this thought, in this section, we propose the shared relay assignment for energyefficiency(SRAE)algorithm to solve this problem. In order to easily introduce this Igorithm, we define some key terminologies of our proposed work Notice that the minimum power discussed in the following ensuring the demand talked in Section 3 on channel capacity Definition 1. Assume pl is the minimum total transmission power of (si, di) under dr'scheme pii is the minimun total transmis sion power if s: is assigned T, for one unit time. The profit ability of (si, di )and, is ai;=pdpi. We set ai;=0 when ai;<0 For example, in Table 1, P=9, pi=7, a1=2. Clearly, the higher the profit ability a is, the smaller the total power when si is assigned ri. Hence, the profit ability aij approximately represents the ability of ri to be assigned to s;. Then, we obtain the value of the matrix of the profit ability, which is determined by pd and pi. From(3). the minimum total transmission 国利技论文在线 http://www.paper.edu.cn Algorithm 1 Srae algorithm 1: Step 1: Initialization 2: Calculate the matrix of the profit ability through( 8)N(11) 3: Randomly initial the shared relay assignment 4: Obtain the TRT by(12), the TP by(13),(14), and the TPG by its definition 5: Step 2: Iterations 6: while true do gii is the maximum in TPG if gii >o then Si is reassigned ri 10: else break end if 13: Update the element of the TRT, TP and TPG corresponding to s; and T, through the ormula(12)~(14) 1: end while power of (si, di) under DT scheme is given as follows P sidi Under the AF mode, we can simplify the constraint CAF(Si,Ti,d >bi :d Ps, +12W)(asr Ps: +arad, P, +1)+as r, Ps, crd, P20 where Ps,, P20. Similarly, under the DF mode, the constraint CDr(si,r;,di)> i can be simplified as 1+anP127≥0, 1+asd p +ardp 11 where Ps, Pr,>0. There are Inally Inethods to obtain the Inlinimuln value of Ps: + Pr under two communication modes, such as the Lagrange Multiplier method, and we set pij=Ps, and pij=Pr, when the total power is minimum. Let Sr, be the set of source nodes that are assigned the relay node rj, and Rs, be the relay node that is assigned to the source node Si. In our algorithm, The time allocation and the power of relay nodes are based on the weight of th profit ability. That is t;=〈29,彐R,=Rs (12 国利技论文在线 http://www.paper.edu.cn 121“2,.s,≠ (13 Next, the minimum power of source node s, is obtained by binary search with the constraint t2+CD(s2,d2)(1t)=b2 (14 Definition 2. given a solution of the MeC problem, Assume Pmin is the total transmission power.Pmin is the total transmission power uhen(si, d; )is reassigned the relay node r;,where j=0 is represents(si, di) uses DT scherne. The power gain is i j=PminPiy o Clearly, if gii>0, the transmission pair(s,, di) can be reassigned the relay node r; so that the total transmission power will be decreased. There are three tables to maintain during the whole execution process of our algorithm. The first one is the table of relay assignment and time allocation(TRT), whose elements are represented as(Si,T;, t: ). The second one is the table of the power of the source nodes and the relay nodes(rP), whose elements are represented as P, or Pr The last one is the table of the power gain(TPG), whose elements are represents as gij. Before starting the iteration, we randomly give an initial relay assignment. The initial time allocation can be obtained by (12). The initial power of relay nodes and source nodes can be calculated by(13 )and (14). The matrix of the power gain can be obtained by its definition In each iteration, we search for the maximum gi; in the TPG. If gii >0, the reassignment can decrease the total transmission power by assigning ri to(si, di. After the reassignment the elements of the TRT, TP and TPG corresponding to si and ri should be updated. The iteration will be terminated if none of the power gain is more than 0. The detailed algorithm description is shown in Algorithm 1 3 Evaluation 3. 1 Simulation settings In the simulation, we consider a wireless network deployed in the area 500m x 500m randomly. The simulation use the same parameters as that in JRPA algorithm. We assume W22MHZ for each wireless channel. The variance of the background noise power is 10 ow at all nodes. For simplicity, we assume that hsd only includes the path loss component between nodes s and d is given by hxd =l sd 4, where sd is the distance between two nodes In our simulation we compare the result of the Srae algorithm with direct transmission (T) and the JRPA algorithM. We observe the impact of different paraIneters, such as the number of source nodes, the number of relay nodes, etc, on the performance of the minimum total transmission power in the network. We consider two kinds of required capacity. The first 国利技论文在线 http://www.paper.edu.cn 三 (a) Uniform capacity (b) Random capacity K 2: Total power vs. Number of relay nodes 乏 (a) Uniform capacity (b) random capacity 2 3: Total power vs. Number of transmission pairs one is that the required capacity is randomly selected from 1 to 10 Mbps. The other is that the required capacity is set to 8Mbps. All results are obtained by averaging over 20 random network lllstanlces 3.2 Simulation results We first observe the effect of the number of relay nodes on the total power consumption under 20 transmission pairs and two kinds of required capacity. As shown in Fig. 2, the relay node does not affect the performance in the DT scheme, the total power consumption of all nodes decreases along with the number of relay nodes under the JRPA algorithm and the Srae Igorithm. This is because as the number of available relay nodes increases, the transmission pairs can get more assistance from the relay nodes. Figure also shows that the srae algorithm can decrease much more total power consumption compared with the JRPa algorithm, due to the shared property of the relay node. When the number of relay node increase to 18, the Srae algorithIn call save about 48.5%c and 20.4% power consumption in Fig. 2(a)and about 54.8% and 21.6% power consumption in Fig. 2(b) compared with DT scheme and JRPA algorithm respectively 国利技论文在线 http://www.paper.edu.cn We then evaluate the total power consumption with the different number of transmission pairs. The number of relay nodes is set to 10. As shown in Fig 3, it is obvious that the total power consumption of the networks increases as the number of transmission pairs become larger Figure also shows that the Srae algorithm can decrease much more total power consumption compared with the JRPa algorithm, the reason of which is the same with the one mentioned in the previous experiment. From Fig3(a), the srae algorithm can save about 34. 1% and 14.4% power consumption on average compared with DT scheme and RPA aIgorithm respectively From Fig 3(b), the SraE algorithm can save about 38. 1% and 15. 1% power consumption on average compared with Dt scheme and JRPa algorithm respectively 4 Related work In this section, we briefly review the related works about energyefficiency cooperative communications and the technologies of relay assignment The literature[12 shows that the most energy hungry parts of a mobile phone are the wireless technologies and not the display or the CPu. Thus, as energy consumption increasing there are many research efforts focus on making the wireless communications more energy ef ficient in recently years. One of the technologies is cooperative communications. The energy efficiency of CC in wireless body area networks is investigated in [ 13. To minimize the en ergy consumption, the problem of optimal power allocation is studied with the constraint of targeted outage probability. In [14, the authors propose a novel energyefficient cooperative communication scheme to improve data transmission performance for wireless sensor networks y exploiting the wireless broadcast nature and the node overhearing capability. An oppor tunistic energyefficient cooperative communication method is studied in 15. Different from classical relaying selection schemes, which adopt either endtoend signaltonoise ratio or ca pacity as selection Metrics, the opportunistic relaying scheine uses all energy efficiency Metric for selecting the best relay or resorting to direct transmission The technologies of relay assignment is effective in improving performance of CC. There are also exists many studies. The relay node assignment problem is investigated in [10 in a network environment, where multiple sourcedestination pairs compete for the same pool of relay nodes in the network. A polynomial time algorithm is developed to solve this problem. In 16, the authors have designed an integrated optimal relay assignment scheme for cooperative networks, which considers both selfish and cheating behavior of network entities while guar anteeing socially optimal system performance. Wang et al. 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