ENERGY-CONSTRAINED networks, such as wireless

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1 366 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 8, AUGUST 8 Energy-Efficient Cooperative Communication Based on Power Control and Selective Single-Relay in Wireless Sensor Networks Zhong Zhou, Student Member, IEEE, Shengli Zhou, Member, IEEE, Jun-Hong Cui, Member, IEEE, and Shuguang Cui, Member, IEEE Abstract Cooperative communication with single relay selection is a simple but effective communication scheme for energyconstrained networks. In this paper, we propose a novel selective single-relay cooperative scheme, combining selective-relay cooperative communication with physical-layer power control. Based on the MAC-layer RTS-CTS signaling, a set of potential relays compute individually the required transmission power to participate in the cooperative communication, and compete within a window of fixed length. The best relay is selected in a distributed fashion with minimum signaling overhead. We derive power-control solutions corresponding to two policies on relay selection: One is to minimize the energy consumption per data packet, and the other is to maximize the network lifetime. Our numerical and simulation results confirm that the proposed scheme achieves significant energy savings and prolongs the network lifetime considerably. Index Terms Selective relay cooperation, energy efficiency, wireless sensor networks, power control. I. INTRODUCTION ENERGY-CONSTRAINED networks, such as wireless sensor networks, are composed of nodes typically powered by batteries, for which replacement or recharging is very difficult, if not impossible []. With finite energy, we can only transmit a finite amount of information. Therefore, minimizing the energy consumption for data transmission becomes one of the most important design considerations for such networks. (For example, in a sensor network used for ecological environment monitoring, low energy consumption and system lifetime are of paramount importance while the requirements on the throughput and delay are less critical.) Manuscript received December, 6; revised April 4, 7, August, 7, November 6, 7, and February 5, 8; accepted June, 8. The associated editor coordinating the review of this paper and approving it for publication is Dr. Yi-Bing Lin. The research of Z. Zhou and J.-H. Cui is supported by the National Science Foundation CAREER Grant No and the University of Connecticut Research Foundation. The research of S. Zhou is supported by the Office of Naval Research under grants N and N The research of S. Cui is supported in part by DoD under grant HDTRA-7--9 and NSF under grant CCF Part of this work was presented in MILCOM, Orlando, FL, Oct. 3-4, 7. Z. Zhou and J.-H. Cui are with the Computer Science and Engineering Department, University of Connecticut, Storrs, CT 669 ( zhz5@engr.uconn.edu, jcui@engr.uconn.edu). S. Zhou is with the Electrical and Computer Engineering Department, University of Connecticut, Storrs, CT 669 ( shengli@engr.uconn.edu). S. Cui is with the Electrical and Computer Engineering Department, Texas A&M University, College Station, TX, ( cui@ece.tamu.edu). Digital Object Identifier.9/TWC /8$5. c 8 IEEE Multi-input multi-output (MIMO) techniques based on antenna arrays can dramatically reduce the required transmission power under a certain throughput requirement due to spatial diversity. Even though each node could be limited in size to mount multiple antennas in wireless sensor networks, multiple nodes could collaborate on forming a virtual antenna array to achieve spatial diversity [], [3]. Such strategies are termed as cooperative communication schemes [], [3]. Various cooperative schemes have been developed so far. Distributed space-time coding for cooperative systems has been proposed in [4], [5], where a number of nodes transmit the different columns of a space time coding matrix simultaneously to the destination. Distributed beamforming schemes have been proposed in [6], [7], which require all cooperators to be synchronized and co-phased such that the signals from the cooperators can be combined constructively at the destination. Selective cooperation schemes have been investigated recently in [8] [], where a single relay or multiple relays are selected to collaborate on information transmission. In selective single relay cooperation, only one out of a set of potential candidates is chosen to aid the communication process, where the relay selection could be based on distance information [9] or instantaneous channel gains []. Energy efficiency of cooperative communication in a clustered sensor network has been investigated in [], []. In [], sensors collaborate on signal transmission and/or reception in a deterministic way. It is shown that if the long-haul transmission distance between clusters is large enough, cooperative transmissions can dramatically reduce the total energy consumption even when all the collaboration overhead is considered. In [], a random number of nodes cooperate with distributed space-time coding for inter-cluster transmissions. Because of the cooperation overhead, the energy efficiency of the cooperative communication may degrade with the increase of the number of cooperators, i.e., more cooperators may not be more energy-efficient []. Based on a simple relay selection strategy, the energy efficiency of selective-relay cooperation schemes is investigated in [8]. Energy allocation or power control can further improve the performance of cooperative communication. Optimal energy distribution among cooperative nodes is studied in [] to minimize the link outage probability. Based on the symbol error rate (SER) analysis, a power allocation scheme for a

2 ZHOU et al.: ENERGY-EFFICIENT COOPERATIVE COMMUNICATION BASED ON POWER CONTROL AND SELECTIVE SINGLE-RELAY 367 decode-and-forward cooperation protocol is presented in [3], where the source and the relays need to know the channel state information on all links. With such channel state information both at the source and the destination, the outage performance of different cooperative protocols has been analyzed in [4]. It is shown that power control could provide significant performance improvement. For two-node amplify-and-forward cooperation protocols, considerable energy savings can be obtained through power control even if only a few bits of quantized channel information are available at the source [5], [6]. The analysis in [4] [6] is based on the average power constraint where the average transmission power over all possible channel realizations is limited by a predefined value. In this paper, we consider the energy efficiency issue for selective single-relay cooperative schemes. Compared with multi-node cooperative schemes, single-relay cooperation requires neither cooperative beamforming nor distributed spacetime coding, where only the best relay out of a set of candidates participates in the data transmission. Selective single-relay cooperative schemes are easy to implement and incur less cooperation overhead, and can potentially achieve the same diversity-multiplexing tradeoff as that of multinode cooperative schemes []. Hence, single-relay-selection cooperative strategies are practically appealing and have also been discussed in [7] [9]. However, most existing results on selective cooperation schemes focus on the multiplexingdiversity tradeoff analysis, where a fixed power level is assumed at the source and relays []. Power control issues are investigated in [4] [6] from an information-theoretic point of view based on the outage probability analysis. Our focus here is on energy-efficient single-relay-selection cooperative solutions for wireless sensor networks. Our contributions are as follows. We propose a novel scheme jointly considering the MAC design and the physical layer power control. In this scheme, the power control and the node selection are unified into the MAC signaling procedure in a distributed fashion. We derive power-control solutions corresponding to two relay-selection policies: One is to minimize the overall energy consumption per packet, and the other is to maximize the network lifetime that is defined as the network operation time until the first node drains out its energy. Other policies could be similarly incorporated into the proposed scheme. Both numerical and simulation results demonstrate that the proposed scheme is highly energy-efficient. The rest of the paper is organized as follows. We describe the system setup in Section II. We present the cooperative solution to minimize the overall energy consumption per packet in Section III, and a counterpart to maximize the network lifetime in Section IV. Numerical and simulation results are given in Section V. We draw our conclusions in Section VI. There are many different definitions on network lifetime. We adopt this definition, which is one of the frequently used definitions, see e.g., [] [4]. This definition is particularly appropriate when a single node failure will be disastrous (for example, reducing network coverage or causing network partition). RTS CTS Relay Contention Relay selection phase (a) Source Transmitting (b) Relay Transmitting ACK Fig.. (a) The best node from all potential candidates (,,...,n) isse- lected to relay the message to the destination; (b) The overall communication process for one data burst. II. SYSTEM MODEL As shown in Fig. (a), the single-relay-selection cooperative communication scheme selects the best relay from a set of potential relay nodes, and then uses this best relay to aid the source-to-destination communication. Before describing the specific process, we make the following assumptions. A) The fading channels between nodes are flat in frequency, and remain constant during one burst data transmission (i.e., block-fading). A) The reciprocal channel from node B to node A is the same as the channel from node A to node B (this assumption has been used in e.g., [], [9]). A3) All nodes can adjust their instantaneous transmission power within the range of [,P max ], where P max is imposed by certain physical constraints (e.g., by the battery). For convenience, we fix the symbol duration T s, and use the transmission energy per symbol as the control parameter. The maximal transmission energy per symbol is then E max = P max T s. A4) One-hop transmission range is assumed, which means that the destination node is within the maximal transmission range of the source node. However, the source may still use a relay for -hop transmission if that is more energy efficient. As depicted in Fig. (b), the overall communication process for one data burst consists of three phases. Phase : Relay selection. When a source node has data to transmit, it first sends out a RTS (request-to-send) message with energy E max per symbol to contend for the shared wireless channel, as in the 8. protocol [5]. The destination node and the source s neighbor nodes (denoted as the set N s ) hear this message, based on which the channel gains between them and the source are estimated (denoted by h and h sk, k N s, respectively). After receiving the

3 368 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 8, AUGUST 8 RTS message, the destination node replies a CTS (clear-tosend) message with energy E max per symbol. Based on the information in CTS and the assumption A, the source node and the destination s neighbor nodes (denoted as the set N d ) estimate the channel gains from them to the destination, which are denoted as h and h jd, j N d, respectively. After a successful RTS/CTS exchange, all neighboring nodes of both the source and the destination become aware of this transmission event and refrain themselves from transmitting data to avoid collisions [5]. The relay candidate set N r is given as N r = N s Nd + {s}, where the extra s term means that we allow the source node itself to participate in the relay competition process and can act as its own relay if it is better than others, i.e., repetition coding may be used. After the RTS/CTS exchange, all overhearing nodes will calculate their priorities according to some predefined policies based on the information collected from RTS/CTS packets (two policies will be described in Section III and Section IV, respectively). Then they compete with each other within a time window, which is called the relay contention period. The competition process is executed as follows. Node i will listen to the channel in the relay contention period. If it has not heard any beacon message from other nodes for time t i (where the higher its priority is, the smaller t i is), it will broadcast one beacon message to grab the channel. In this way, the node with the highest priority will transmit first and win the competition to serve as the relay for cooperative data transmission. The competition is done within a fixed competition window of length T max. In some cases, it is possible that no relays can support the data transmission or multiple beacon messages collide. Under such circumstances, the source cannot decode beacon messages from others and no cooperative communication can be formed. If the source node cannot support the data transmission by itself, it will back off and wait for some random time before initiating another RTS. If the source node can support the data transmission by itself, it will transmit its packet directly to the destination. To assist the data transmission process with a predefined source-to-destination data rate R, each relay node determines the transmission energy per symbol E t for the source and the transmission energy per symbol E t for itself. Since the computation is done locally at the relay node, the relay node needs to inform the source node the calculated E t in its beacon message. The relationship among R, E t,ande t will be discussed in Section III and Section IV according to different design objectives. Phase : Source transmission. The source node sends out data with transmission energy E t per symbol. The selected best relay decodes the received data. The destination stores the received signal from the source and defers the decoding to the next phase. There will be some nodes who hear RTS but miss the subsequent CTS. A time-out mechanism is needed to reset those nodes to the initial state within a time window after receiving RTS. Similar to IEEE 8., network allocation vector (NAV) is also used in our protocol to solve the hidden terminal problem. NAV is a counter residing at each node that represents the amount of time that the transmission of previous packet takes. The NAV must be zero before a node attempts to initiate a packet transmission. The additional relay transmission phase in the cooperative protocol needs to be considered in the NAV calculation. Phase 3: Relay transmission. The best relay forwards the decoded data to the destination with transmission energy E t per symbol. The destination combines the received data and the stored signal (received in Phase ) for joint decoding. The transmitted signals in Phase and Phase 3 will have the same length and format, but with different power. If the destination can decode the message correctly, it will send back an ACK message with its maximal transmitting power to the source; note that relay nodes do not need to be acknowledged. The proposed protocol is fully distributed and easy to implement. Since the RTS/CTS exchange is implemented in the 8.-like MAC protocols anyway, the additional overhead is mainly due to the relay competition. Compared with data transmission, the relay competition period is short and may be negligible. In addition, since there is only one node selected to relay the transmission, it is much simpler than traditional distributed space-time coding or beamforming that requires multi-node cooperation. A similar scheme has been proposed in [], where potential relay nodes obtain the channel gains during the RTS/CTS exchange. Based on the channel pair (h si and h id for node i), the relays compete and only one is selected. Our differences from [] are: (i) we incorporate power control at the physical layer while [] does not; and (ii) our objective is to derive energy-efficient cooperative schemes, while [] studies the diversity-multiplexing tradeoff of single relay selection in the high power regime. Compared with direct transmission with power control at the source, our scheme can optimize the transmitting power distribution among the source and the relays. So when the channel condition from the source to the destination is not good, we can utilize the channels from the source to the relay and the relay to the destination, which will be more energy efficient than directly transmitting data from the source to the destination. While if the channel from the source to the destination is good enough, the source can transmit directly without the help of the relays. This will bring significant energy benefits to our scheme in fading environments. Another comparable alternative of our scheme is conventional twohop routing scheme with power control at both the source and the relay. In this scheme, the best relay is selected based on the available channel conditions. The transmission process is from the source to the best relay and then from this best relay to the destination. Compared with this twohop routing scheme, our cooperative scheme can take full advantages of the broadcasting nature of the wireless channel. Potentially, in our scheme, the destination can receive and combine signals from both the source and the relay, which makes it more energy efficient. While for the two-hop routing scheme, the destination can just receive signal from the relay and the signal combining is unavailable. Our simulation results in Section V-C also show that our scheme is more energy efficient than both direct transmission and the two-hop routing transmission with power control schemes. Further, in order to reduce energy consumption on radio listening, our scheme can also be combined with some node sleeping strategies, such as those proposed in [6], for sensor networks with low traffic density.

4 ZHOU et al.: ENERGY-EFFICIENT COOPERATIVE COMMUNICATION BASED ON POWER CONTROL AND SELECTIVE SINGLE-RELAY 369 We next present two power control solutions on E t and E t. The first solution is to minimize the overall energy consumption per packet transmission, while the second is to maximize the network lifetime. III. MINIMIZATION OF OVERALL TRANSMISSION ENERGY CONSUMPTION Minimizing the overall transmission energy consumption is one frequently used criterion in the protocol design for wireless sensor networks, e.g., for the design of routing protocols in [7], [8] and cross-layer strategies in [9] [3], where it has been proved [3] that minimizing the overall energy is equivalent to maximizing a lower bound of the average node lifetime. In this section, we specify how each relay node determines the power control strategy to minimize the overall energy consumption per packet, and how the priority parameter is defined for each relay candidate. A. Problem formulation For presentation brevity, we define = h, = h si, and G id = h id. Also, we normalize the noise variance to one and assume capacity-achieving codes over each link 3. The minimum required transmission energy to support a data rate R (bits per symbol) from the source to the destination shall satisfy: R log ( + E t + E t G id ), () when node i is used for relaying. The factor / in () is due to time sharing between the source and relay transmissions. From (), we obtain E t + E t G id. () On the other hand, node i has to decode the source signal successfully. Thus, the transmission energy must satisfy: log ( + E t ) R, (3) which translates to E t (R ). (4) Each node will independently carry out an optimization problem; for node i, thatis min E t,e t subject to f i (E t,e t )= N b R (E t + E t ) = N s (E t + E t ), E t E max, E t + E t G id, E t E max, (5) where N b is the length of the packet in bits and N s = N b /R is the length of packet in symbols. The objective function f i (E t,e t ) is proportional to the overall transmission energy 3 For practical codes, we could use the gap approximation of [3] such that the maximum supported rate is log ( + SNR/Γ) rather than the capacity of log ( + SNR), whereγ is the SNR gap [3]. consumed by one data packet if node i serves as the relay. The optimization problem is formed once for each data burst, where the length of the data burst will be upper bounded by the channel coherence time, since we assume that the channels remain invariant during the whole cooperative communication process as depicted in Fig. (b). Note that in the analysis herein, we neglect the energy consumption due to the RTS/CTS transmission and the relay competition. These energy consumption overheads are more or less fixed, regardless of which node is selected. We will present simulation results in Section V-C that account for these overheads. B. Power control solution In our protocol, we allow the source node to participate in the competition. We first present the power control solution computed at the source. For the source node, in (5) is replaced by G ss =, andg id in (5) is replaced by.the optimal power-control solution at the source node is then: (E t,e t )= (6) ( ) R,, R E max ( ) E max, R E max, E max < R E max (, ), > E max R If the source node wins the competition, it will transmit with energy E t per symbol at the first time slot, and with E t per symbol at the second time slot. Note that the bottom part of (6) means that the source cannot support the transmission and will not transmit. For convenience, we set E t = and E t = that lead to f i (E t,e t )= ; as such, the source will not contend during the relay competition window and keep silent. We now look at the power control solution at each relay node. The optimization problem in (5) can be easily solved by linear programming. The feasible solutions for (E t,e t ) form a polygon within the region [,E max ] [,E max ],where the optimal solution is one of the corner points of the polygon [33]. However, when, it is easier for the source to support the transmission to the destination solely, since there is no benefits of using the relay. When G id, if any valid solution (E t,e t ) can be reached by the relay, the source can have a better solution with the same E t whilealowere t. Hence, when either or G id, the relay node i will not participate in the relay competition and keep silent. In the following, we assume that the conditions < and < G id are satisfied. The feasible optimal power control solutions for node i, wherei N r {s}, arethe following: Case : Conditions: E max ( R ( ) G ) G id Solution: E t = (R ), E t = (R ) G id E max ( ). (7)

5 37 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 8, AUGUST 8 Case : Conditions: Solution: E max, ( R ( ) G ) >E max, G id G id E max E max, E t = (R ) G id E max, E t = E max. (8) In the second case, with the relay node reaching the maximum power, the source node also needs to contribute sufficient transmission power to support the data rate R. For other conditions, there are no feasible solutions, and node i will not participate in the relay competition. C. Signaling In order to find the optimal power control solution, node i needs to know parameters,,andg id.aswehave explained before, node i estimates based on the RTS message from the source and G id based on the CTS message from the destination. The concern is then how node i estimates. Since the destination already has after receiving RTS, we propose that the value of is included in the CTS message. After the RTS/CTS exchange, node i can then find its optimal solution on (E t,e t ) and the corresponding f i (E t,e t ). Each node in N r will participate in the competition process according to its priority, which is reflected 4 by a back-off time t i. Specifically, before sending out the beacon message, the ith relay candidate delays time t i as t i = f i(e t,e t ) f(e max,e max ) T max, (9) where T max is the pre-defined contention window length and f(e max,e max )=N s E max is independent of i. Hence, any node that has a f i (E t,e t ) lower than f(e max,e max ) gets a chance to be presented within the time window [,T max ]. Certainly, the node with the smallest f i (E t,e t ) will win. Collision among beacon messages might happen if the delay time of the best relay and those of other relays are too close. A detailed analysis on the collision probability is given in []; it was shown that this probability is small in the scenarios considered therein. Note that this collision probability is closely related to the length of the beacon message and how the delay time t i is defined. Here we choose (9) to compute the delay time t i for simplicity and we argue that the collision probability can be further reduced if a more delicate (possibly nonlinear or discrete) mapping between f i (E t,e t ) and t i is used. Analysis and algorithm development to reduce such collisions warrant further investigation. It should be noted that in some situations multiple nodes might believe that they have been selected as the best relay since some nodes could miss the beacons from other nodes due 4 The priority is inversely proportional to t i, i.e., the higher the priority for node i is, the smaller t i is. to channel fading. This could potentially lead to data collision at the destination in the relay transmission period. One way to overcome this problem is to let the relay node insert its unique ID into its beacon message. If the source node receives multiple beacon messages, it will select the best node and insert the ID of the selected relay into the data packet. A relay node who has sent out beacon messages will try to receive the data packets in the source transmission phase. If its ID is the same as the one specified in the data packet, it will relay the data transmission. Otherwise, it will not. This way, at most one relay node will actually assist in the data transmission. On the other hand, when the source node has not received any beacon messages from other nodes, and it cannot support this data transmission by itself, it will back off and initiate another RTS message later. IV. MAXIMIZATION OF NETWORK LIFETIME For wireless sensor networks, minimizing the energy consumption per packet may not directly translate to the maximization of network lifetime [] [4]. This is mainly due to the unevenly distributed traffic pattern and network topology. For many wireless sensor networks, prolonging the network lifetime may be more important than saving energy for individual nodes. However, network lifetime has different definitions in different application scenarios. In this paper, we define the network lifetime as the network operation time until the first node drains out its energy, as in [] [4]. Many routing and MAC protocols have been proposed to prolong the network lifetime [], [6], [34]. Cooperative communication, however, makes the situation more complicated. This is due to the fact that for cooperative communication schemes, cooperative nodes incur extra energy consumption locally in addition to that in the source and the destination nodes. We here incorporate a simple but effective approach proposed in [] into our selective relay scheme to maximize the network lifetime. Simply speaking, the strategy is to find an optimal power control solution that maximizes the minimum residual energy among all the nodes during each packet transmission [], which will be discussed as follows. A. Problem formulation and power control solution For the ith potential relay node, the power control optimization is formulated as follows: max g i (E t,e t ):=min(e src N s E t,e i N s E t ) E t,e t subject to E t E max, E t + E t G id, E t E max, () where E src is the current energy supply in the source node, E i is the current energy supply in the ith relay node, and N s = N b /R is the packet length in symbols as in (5). We propose that E src is included in the RTS message such that every relay candidate has this information, as will be further clarified in Section IV-B.

6 ZHOU et al.: ENERGY-EFFICIENT COOPERATIVE COMMUNICATION BASED ON POWER CONTROL AND SELECTIVE SINGLE-RELAY 37 (v) E max (E t ) R ( ) Gid E G t (E t ) R E max (v) E max (E t ) R ( ) EG t G id (E t ) E max ~ E t (v) R ( ) EG t Gid (E t ) E Emax max R (E t ) (a) Situation (b) Situation (c) Situation 3 Fig.. The feasible region corresponding to the power control solution in eq. (). To solve the problem in (), we replace the objective function with a new variable V, and reformulate () as: max V (a) E t,e t subject to E t E max, (b) E t + E t G id, (c) E t E max, (d) E src N s E t V, (e) E i N s E t V. (f) The objective function and all constraints in () are linear. Hence, the problem in () is a linear programming problem, which can be solved efficiently with standard procedures [35]. Note that when, there is no benefit ofusing relay i, asitismoredifficult for the source to communicate with the relay than with the destination, similar to the case discussed in the previous section. However, when G id (and < ), using the relay could still be beneficial if the energy level at the relay is high while the energy level at the source is low. This is different from the case discussed in the previous section. In the following, we assume that the condition < is always satisfied. We list all feasible solutions to () as follows. Case : Conditions: E max, ( R ( ) G ) E max, G id Solution: Ẽ t = G id(e src E i )+N s N s (G id + ) E t = Ẽ t, ( R ), Ẽ t < (R ) ( R ) Ẽt (R ) ( R ), Ẽ t > (R ) E t = (R ) E t. () G id The available solution space as well as the optimal solution for this case is shown in Fig.. Three situations of Fig. correspond to different values of Ẽ t as in (). Here, the intermediate result Ẽ t is the optimal solution of E t for the problem in () if we remove the constraint (b). When Ẽ t < (R ), one has to set E t = (R ) to satisfy the source to relay communication. When Ẽt > (R ),there is no energy benefit to use relay as the source to destination communication is already guaranteed with E t = (R ). Note that whether to use node i as a relay depends not only on the channel states (,,andg id ),butalsoonthe energy levels of the nodes. Compared with the solutions in Section III-B that only depend on channel state information, the solution structure herein are more complicated. Case : Conditions: >E max, ( R ( ) G ) G id E max Solution: Ẽ t = G id(e src E i )+N s N s (G id + ) ( R ), Ẽ t < (R ) E t = ( Ẽ t, R ) G si Ẽt E max E max, Ẽ t >E max E t = (R ) E t. (3) G id In this case, the optimal E t reaches the maximum energy constraint E max in certain situations. The same as Case, the intermediate result Ẽ t is the optimal solution of E t for problem () without the constraint (b). Case 3: Conditions: E max, ( R ( ) G ) >E max G id Solution: Ẽ t = (E i E src )+N s N s (G id + ), Ẽ t < E t = Ẽ t, Ẽt E max E max, Ẽ t >E max E t = (R ) E t G id (4) In this case, the optimal E t reaches the maximum energy constraint E max in certain situations. The intermediate result Ẽ t is the optimal solution of E t for problem () with the constraint (d) removed.

7 37 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 8, AUGUST 8 Case 4: Conditions: >E max, ( R ( ) G ) >E max G id Solution: Ẽ t = G id(e src E i )+N s N s (G id + ) Ẽ t = (R ) (E src E i ) G id + N s (G id + G id ) E t = Ẽ t, ( R ) E maxg id, E max, ( R ) < Ẽt E max and < Ẽt E max ( R ) < (R ) E maxg id and Ẽt >E max Ẽ t >E max and < (R ) E max G id E max E max E t = (R ) E t G id (5) In this case, both E t and E t could reach the maximal energy E max in certain situations. Here, the intermediate results Ẽt and Ẽt are the optimal solutions of E t and E t, respectively, for problem () with constraints (b) and (d) removed. As we have discussed before, the source node is allowed to participate in the competition. For the source node, in () is replaced by G ss = and G id in () is replaced by G id =. The optimal solution is the same as that for (6), except that the source needs to ensure a positive cost function g s (E t,e t )=E src N s (E t + E t ), which means that the source reaches a valid solution only if the whole packet can be supported by the current energy level E src. B. Signaling To find the power control solution that maximizes the network lifetime, node i needs to know parameters E src, E i,,,andg id. Again, we propose to use the RTS/CTS hand-shaking signals. In the RTS message, the source node includes its energy level E src as a parameter. After receiving the RTS message, node i retrieves E src and measures. The destination node estimates based on RTS, and then includes in its CTS message. When the relay node receives the CTS message from the destination, it can estimate G id and decode the contained. Each relay then calculates its g i (E t,e t ) according to (). If a valid solution is found, node i will participate in the competition process. It will attempt a beacon message if it does not receive any beacon message from others within a time delay t i = T max E src g i (E t,e t ) E src. (6) As such, the larger g i (E t,e t ) is, the less delay for node i and the more likely it will be selected as the best relay. V. PERFORMANCE EVALUATION In this section, we first present numerical results corresponding to the two policies discussed in Sections III and IV, respectively. We then present simulation results performed in ns-. For presentation brevity, Min Energy in the figures stands for the cooperative policy to minimize the overall energy consumption per packet, while Max Lifetime stands for the policy to maximize the network lifetime. Simulation results are averaged over network instances. A. Results for transmission energy minimization We assume a random network where cooperative nodes are distributed randomly in a circular area with a radius of meters. One data flow is initiated from one source to one destination which are separated a distance of m. We also assume that all nodes within the circular area can hear the RTS/CTS messages from the source and the destination nodes. The packet length is set to be bits. The symbol duration is T s = 4 s. The average signal strength is inversely proportional to the squared transmission distance. The channel gains are generated according to a Rayleigh fading channel model. The channel remains unchanged within one data burst, but changes independently from burst to burst (i.e., block fading). We compare the cooperative scheme with two direct communication schemes, which support the same data rate from the source to the destination with one-hop transmissions 5.For direct communication scheme, source node transmits at rate R = r all the time, while for direct communication scheme, source node transmits at rate r half of the time and then becomes idle for the other half. Both schemes achieve the same average data rate R = r as that of the cooperative case. Since is available, power control at the source node is used for both direct communication schemes. For the selective relay case, the overall energy consumption per packet is calculated as E overall =minf i (E t,e t ). (7) i N r Note that in our current energy consumption calculation, we have ignored the overhead due to the RTS/CTS exchange and the relay competition. These signaling periods are usually much less than the data transmission time, thus a small amount of energy is consumed. Nevertheless, such overheads will be considered later by simulations in Section V-C. Test Case : Overall energy consumption and outage properties with varying E max. We set data rate R =(bits per symbol). A total of n =relay nodes are randomly distributed in the whole network area. We change the maximum allowed energy consumption per symbol E max (same for all the nodes) 5 We consider a random network here, while both [] and [] deal with a clustered network where cooperative communication is used to facilitate intercluster communication. The networking scenarios are different. Furthermore, the main focus of this paper is a joint design between physical layer and MAC layer, while the schemes in [], [] are only at the physical layer. In this paper, MAC signalling provides channel state information to the physical layer for power control, while the instantaneous channel conditions are not known by the transmitters in [], []. As such, a direct comparison with [], [] is not conducted.

8 ZHOU et al.: ENERGY-EFFICIENT COOPERATIVE COMMUNICATION BASED ON POWER CONTROL AND SELECTIVE SINGLE-RELAY 373 Energy consumption per packet(j) Fig. 3. Outage probability Fig Min Energy Direct Scheme Direct Scheme Maximal transmitting energy per symbol (J) x 4 Energy consumption per packet as a function of E max. Min Energy Direct Scheme Direct Scheme Maximal transmitting energy per symbol(e max ) (J) x 4 Outage probability as a function of E max. from 5 J to J, and show the overall energy consumption in Fig. 3. We observe that compared with both direct communication schemes, cooperative communication achieves significant energy savings. For example, when E max =.5 4 J, the overall energy consumption per packet for the cooperative scheme is.54 J, while for the direct case, it is as high as.6 Jthatis about three times as that of the cooperative case. In terms of the outage probability that is defined as the probability that data rate R cannot be supported given the maximum power constraints, Fig. 4 shows that the proposed scheme achieves the smallest outage probability for moderate and large E max. Hence, unless the nodes are under extremely restrictive transmit-power constraints, the cooperative scheme outperforms direct communications in terms of both total energy consumption and outage probability. Test Case : Outage probability versus energy consumption with different numbers of relay nodes. Here, we set R = and change E max to obtain different outage probability and energy consumption pairs. This way, we obtain the relation- Outage probability 3 Min Energy: n= Min Energy: n=5 4 Min Energy: n= Direct Scheme Direct Scheme Energy consumption per packet (J) Fig. 5. Outage probability vs. energy consumption per packet. ship between the outage probability and the average energy consumption per packet. Fig. 5 shows that under the same outage probability, the cooperative scheme consumes much less energy than direct communication schemes in most scenarios. For example, if the required outage probability is,when n =, the energy consumption per packet is only.95 J; while for direct communication case, the consumed energy is about.3 J. Fig. 5 also shows that the energy benefit of our scheme increases with the number of nodes. This is reasonable since more cooperators can contribute more diversity gain that can be converted to energy efficiency. It should be noted that this observation is not in contradiction with the conclusion of [] that having more cooperators does not necessarily mean higher energy efficiency. This is because the circuit energy consumption overhead is considered in [] for cooperative nodes 6. Test Case 3: Outage probability versus energy consumption under different data rate R. Here, n = relay nodes are randomly distributed in the whole network area. We set R =, 3, 4 and compare the outage probability versus energy consumption with direct communication scheme (the better one of the two direct communication schemes). As shown in Fig. 6, the outage probability increases as the data rate R increases. Note that when R is large, e.g., R = 4,the advantage of the cooperative scheme only shows up at the lowoutage regime. This is reasonable since in order to achieve the same source to destination data rate, the cooperative scheme needs twice the rate as that of the direct scheme. For example, to achieve the end-to-end data rate of R = 4 bits/symbol, the cooperative scheme needs to transmit at 8 bits/symbol. When the outage probability is relatively high (e.g., in a low SNR scenario) the diversity benefits of the cooperative communication scheme will be offset by the 6 In our scheme, since only one relay node will be selected for data transmission, the overall circuit energy consumption of our scheme is much smaller than that of the scheme in []. We ignore the circuit energy consumption here for simplicity. We will take it into consideration in the simulation results in Section V-C.

9 374 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 8, AUGUST 8 Outage probability 3 R= relay case R= direct case R=3 relay case R=3 direct case R=4 relay case R=4 direct case Packets transmitted 4 x Max Lifetime Min Energy Direct Scheme Direct Scheme Energy consumption per packet (J) Fig. 6. of R. Network lifetime (s) Outage probability vs. energy consumption per packet as a function 3.5 x 4 Max Lifetime Min Energy Direct Scheme Direct Scheme Node number Fig. 7. The network lifetime with respect to the number of nodes in a uniform traffic scenario. doubled data rate. However, when the outage probability is low (e.g., in a high SNR scenario), the diversity benefits of the cooperative communication scheme will outweigh the cost of increasing the data rate, which renders the cooperative scheme more energy-efficient than the direct scheme. B. Results for network lifetime maximization We simulate a random network as follows. Multiple network nodes are uniformly distributed in a circular area with radius of meters. Every node randomly chooses a network node as its destination and generates its traffic according to a Poisson process. Average packet length is set to be bits and the symbol duration is T s = 4 s,. The initial energy of every node is set to be Joules. Test Case 4: Network lifetime with uniform traffic. Here, every node randomly chooses a network node as its destination and generates its traffic according to the same Poisson process with the average inter-packet arrival time set to be seconds Node number Fig. 8. The total number of packets transmitted with respect to the number of nodes in a uniform traffic scenario. In Figs. 7 and 8, we set R =and increase the number of the nodes in the network from 5 to 3. We see that with the increase of network size, network lifetime and the total number of transmitted packets of the cooperative scheme increase correspondingly 7. This is reasonable since more nodes means large cooperation diversity to explore. While for the direct communication schemes in our setting, the network lifetime will not change much with the increase of the network nodes 8. We can also see that the scheme designed with the lifetime criterion is more lifetime-efficient than all other schemes, with the knowledge of both the link state and the residual energy information on each node. In particular, its network lifetime is longer than that of the scheme minimizing directly the energy consumption despite the fact that its average energy for single packet transmission is larger, since it can balance the energy consumption across the whole network. However, if the energy levels of the nodes are not available, minimizing the energy consumption can indirectly prolong the network lifetime. In Fig. 9 we set the number of nodes to be and change R from to 4. We see that with the increase of data rate R the network lifetime decreases. This is because for a packet with the same number of bits, higher data rate will consume more energy than lower data rate. Correspondingly, the overall network lifetime will decrease. Nevertheless, under all situations, the scheme based on the lifetime criterion is better than the scheme based on the energy consumption criterion in terms of network lifetime. Compared with direct communication schemes, the advantage of cooperative communication decreases with the increase of data rate R. 7 Here, we ignore the effects of all potential collision events such as collisions among RTS/CTS messages. Since most sensor networks have low traffic density, these collision probabilities might be small and our results can provide good estimates. For networks with high traffic density, the number of successfully-transmitted packets may become much smaller due to collisions. Our results herein can serve as upper bounds. Nevertheless, collisions will be considered in the next section when we conduct simulations in ns-. 8 Reference [4] shows that for direct communication the network lifetime will increase with the number of nodes if spatial-temporal correlation in sensor data is exploited. We have not explored such spatial-temporal correlation in sensor data here.

10 ZHOU et al.: ENERGY-EFFICIENT COOPERATIVE COMMUNICATION BASED ON POWER CONTROL AND SELECTIVE SINGLE-RELAY 375 Network lifetime (s) 4.5 x Max Lifetime Min Energy Direct Scheme Direct Scheme Network lifetime (s) 5 x Max Lifetime Min Energy Direct Scheme Direct Scheme Data rate Fig. 9. The network lifetime with respect to the data rate R in a uniform traffic scenario Node number Fig.. The network lifetime with respect to the number of nodes in a nonuniform traffic scenario. This is because with the increase of the value of R = r, the difference between the energy to sustain rate r and that of rate r will increase, and hence will offset the benefit brought by cooperative communication. Test Case 5: Network lifetime with nonuniform traffic. Here, every node randomly chooses a network node as its destination and generates its traffic according to a Poisson process with the average inter-packet arrival time to be a random variable distributed uniformly within (, 6). In Fig. we set R =and increase the number of nodes from 5 to 3. Clearly, with nonuniform traffic, the scheme based on the network lifetime criterion achieves much longer lifetime than the scheme based on the energy consumption criterion and direct communications. This is reasonable since for other schemes, nonuniform traffic patterns will make the energy consumption unevenly distributed throughout the network and nodes with heavy traffic will drain out their energy quickly. The scheme based on the network lifetime criterion effectively balances the energy consumption within the network and thus prolongs its lifetime, which takes both the nodes energy status and the link states into consideration. C. Simulation results in ns- To test the impact of collisions and energy overheads, we simulate the proposed cooperative scheme using the network simulator ns- [36]. We modify its 8. MAC protocol implementation to incorporate the proposed scheme. We also make some modifications to its physical layer: if the received signal strength is higher than the signal sensing threshold, it will pass the received signal to the MAC layer. The modified MAC layer will store the received signal and do joint decoding after it has received the signals from both the source and the relay. The relay selection is also done at the modified MAC layer. In this set of simulations, we use the strategy of maximizing the network lifetime as in Section IV. For comparison, we have simulated the following three other schemes. Direct Scheme with power control at the source node. The selective relay scheme from []. Among its two policies, we choose policy, which selects the relay that maximizes the function h i,whereh i =min{,g id }. We term this scheme as MaxMin hereafter. Simulation results in [] show that policy has lower collision probability than policy in different network conditions. Power control was not considered in [], but we incorporate power control at both the source and the relay to reduce the transmission energy (for a fair comparison with our scheme). Two-hop routing scheme with power control at both the source and the relay. For the two-hop routing scheme, the best two-hop route (from the source to the relay and then from the relay to the destination) that minimizes the transmission energy is selected based on,,and G id. The transmission process is divided into two steps. In the first step, the source sends the packet to the best relay with power control, and the destination does not receive data in this step. In the second step, the best relay will relay the received data to the destination with power control. In order to avoid excessive traffic overheads for a centralized route selection process, the best relay is selected in a distributed fashion based on competitions similar to the mechanism of the proposed scheme. In this set of simulations, multiple network nodes are uniformly distributed in a circular area with radius meters. Every node randomly chooses a network node as its destination and generates the traffic with an average inter-packet arrival time randomly chosen within the interval (, 6). The symbol duration is T s = 4 s, and the packet length is bits. We set the overall rate as R =bits/symbol for both the direct and cooperative schemes. We change the format of the original RTS/CTS message (some fields are unnecessary in our situation) of 8. and set their lengths to be bytes (8 bits). The beacon message is set to be bytes (8 bits). The competition window of beacon message is set to be ms. The initial energy of every node is set to be

11 376 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 8, AUGUST 8.5 x 4 7 x 4 Network lifetime (s).5.5 Max Lifetime Direct scheme Two hop Routing MaxMin Packets Transmitted Max Lifetime Direct scheme Two hop Routing MaxMin Node number Fig.. The network lifetime versus the number of nodes via ns- simulation. Joules. All energy consumption including the energy spent on RTS/CTS are considered. In addition, we also consider the circuit energy consumption. We set the transmitting circuit power as 5 mw and the receiving circuit power as mw. For example, corresponding to a packet duration, the circuit energy consumption will be.5 3 J for the transmission and. 3 J for the reception, respectively. The underlying propagation model is the free space propagation model [37] with Rayleigh fading. The average signal strength degrades with square law over the transmission distance. We observe from Fig. that with the increase of the number of nodes, the network lifetime will increase correspondingly as we discussed before. When the number of nodes is relatively small, e.g., from 5 to, the network lifetime increases rapidly. But with further increase of the number of nodes, the network lifetime will not change much. This is mainly due to the collisions and the energy consumption of all control packets such as RTS/CTS. Fig. confirms that the proposed cooperative scheme still outperforms other schemes considerably, even when collisions and other sources of energy consumption are considered. By comparing Fig. with the numerical results in Fig., we observe that the network lifetime as well as the lifetime increase relative to the direct schemes become much smaller. For example, Fig. shows that when the number of nodes is and the data rate is R =, the theoretical lifetime is about s for the proposed policy of maximizing network lifetime, and is. 4 s for direct scheme. The cooperative protocol can increase network lifetime almost 4 times as that of the direct scheme in the ideal network condition. On the other hand, Fig. shows that the network lifetime is reduced to. 4 s for the proposed scheme and.5 4 s for the direct scheme in the practical network simulator, which takes into consideration other factors such as RTS/CTS, beacon collisions as well as the circuit energy consumption. The lifetime of the proposed scheme is now about twice of that of the direct scheme. This clearly shows that the extra energy consumption in practice such as RTS/CTS is non-negligible. One way to reap all the energy benefits of Node number Fig.. The total number of packets transmitted versus the number of nodes via ns- simulation. the proposed cooperative scheme is to considerably reduce the collision probability of RTS/CTS and beacon messages. For example, adaptive packet scheduling algorithms such as those in [38] can be combined with the proposed scheme to reduce the collision probability. Fig. depicts the total number of packets transmitted in the network versus the number of nodes. Compared with other schemes, the total number of packets transmitted in our scheme is much larger. For example, when the number of nodes equals, our scheme can transmit at least times more packets than the direct scheme before the first node dies. Compared with direct transmission, the proposed scheme explores the rich diversity provided by the relay channels, especially when the direct link are in deep fades but other links are in good conditions. Compared with the two-hop routing, the proposed scheme takes full advantage of the broadcasting nature of the wireless channel. VI. CONCLUSIONS AND FUTURE WORK In this paper we proposed an energy-efficient single-relayselection cooperative communication scheme for wireless sensor networks, where the MAC design and the physical-layer power control are incorporated into the node selection process in a distributed manner. Two policies, one is to minimize the overall energy consumption per packet and the other is to maximize the network lifetime, were proposed and analyzed. Numerical and simulation results confirmed that the energy efficiency of the proposed scheme is higher than those of direct communication and two-hop routing alternatives in the considered application scenarios. The proposed scheme can be viewed as one example of cross-layer (crossing MAC and physical layers) design for selective cooperative communication in energy-constrained wireless networks. Future Work: We plan to pursue our future work in the following directions. ) The collision probability of RTS/CTS and beacon message prevents to reap the full energy benefits of the proposed cooperative scheme. Reducing the collision probability via some adaptive scheduling strategies warrant

12 ZHOU et al.: ENERGY-EFFICIENT COOPERATIVE COMMUNICATION BASED ON POWER CONTROL AND SELECTIVE SINGLE-RELAY 377 further investigation. ) For asymmetric wireless channels, the channel measurements from the RTS and CTS may be different. The performance of the proposed scheme will degrade under this situation. We plan to extend our scheme to handle asymmetric channels. 3) Our scheme is for two-hop networking scenarios. When extended to multi-hop environments, with our current scheme the global optimality across the whole network can not be guaranteed. In order to achieve globally optimal solutions in multi-hop network scenarios, we believe that a joint design of our current scheme with the upper routing layer protocol is necessary. In fact, such cross-layer design problems are hot research topics nowadays [39], [4], and we would explore this direction in the future. REFERENCES [] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, A survey on sensor networks, IEEE Commun. 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13 378 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 8, AUGUST 8 Zhong Zhou (S 6) received B.Eng. in Telecommunication Engineering in and M.Eng. in Computer Science in 3, both from the Beijing University of Posts and Telecommunications, Beijing, China. He is currently working toward the Ph.D. degree in Computer Science and Engineering at the University of Connecticut (UConn), Storrs. Since January 6, he has been with the Underwater Sensor Network Lab and the Ubiquitous Networking Research Lab,UConn, as a graduate Research Assistant. His current research interests include underwater acoustic communication and networking, localization, and cross layer design for wireless networks. Shengli Zhou (M 3) received the B.S. degree in 995 and the M.Sc. degree in 998, from the University of Science and Technology of China (USTC), Hefei, both in electrical engineering and information science. He received his Ph.D. degree in electrical engineering from the University of Minnesota (UMN), Minneapolis, in. He has been an assistant professor with the Department of Electrical and Computer Engineering at the University of Connecticut (UConn), Storrs, since 3. His general research interests lie in the areas of wireless communications and signal processing. His recent focus is on underwater acoustic communications and networking. Dr. Zhou has served as an Associate Editor for IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS from February 5 to January 7. He received the ONR Young Investigator award in 7. Jun-Hong Cui (M 3) received her B.S. degree in Computer Science from Jilin University, China in 995, her M.S. degree in Computer Engineering from Chinese Academy of Sciences in 998, and her Ph.D. degree in Computer Science from UCLA in 3. Currently, she is on the faculty of the Computer Science and Engineering Department at University of Connecticut. Her research interests cover the design, modelling, and performance evaluation of networks and distributed systems. Recently, her research mainly focuses on exploiting the spatial properties in the modeling of network topology, network mobility, and group membership, scalable and efficient communication support in overlay and peer-to-peer networks, algorithm and protocol design in underwater sensor networks. She is actively involved in the community as an organizer, a TPC member, and a reviewer for many conferences and journals. She was a guest editor for ACM MCCR (MOBILE COMPUTING AND COMMUNICATIONS REVIEW) and Elsevier AD HOC NETWORKS. She now serves as an Associate Editor for Elsevier AD HOC NETWORKS. She co-founded the first ACM International Workshop on UnderWater Networks (WUWNet 6), and she is now serving as the WUWNet steering committee chair. Jun-Hong received US NSF CAREER Award in 7 and ONR YIP Award in 8. She is a member of ACM, ACM SIGCOMM, ACM SIGMOBILE, IEEE, IEEE Computer Society, and IEEE Communications Society. Shuguang Cui (S 99 M 5) received Ph.D. in Electrical Engineering from Stanford University, California, USA, in 5, M.Eng. in Electrical Engineering from McMaster University, Hamilton, Canada, in, and B.Eng. in Radio Engineering with the highest distinction from Beijing University of Posts and Telecommunications, Beijing, China, in 997. He is now working as an assistant professor in Electrical and Computer Engineering at the Texas A&M University, College Station, TX. From 997 to 998 he worked at Hewlett-Packard, Beijing, P. R. China, as a system engineer. In the summer of 3, he worked at National Semiconductor, Santa Clara, CA, on the ZigBee project. From 5 to 7, he worked as an assistant professor at the department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ. His current research interests include cross-layer optimization for resourceconstrained networks, hardware and system synergies for high-performance wireless radios, statistical signal processing, and general communication theories. He was a recipient of the NSERC graduate fellowship from the National Science and Engineering Research Council of Canada and the Canadian Wireless Telecommunications Association (CWTA) graduate scholarship. He has been serving as the TPC co-chairs for the 7 IEEE Communication Theory Workshop and the ICC 8 Communication Theory Symposium. He is currently serving as the associate editors for the IEEE COMMUNICATION LETTERS and IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY.