A Cross-Layer Strategy for Energy-Efficient Reliable ... - CiteSeerX

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 12, DECEMBER 2006

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A Cross-Layer Strategy for Energy-Efficient Reliable Delivery in Wireless Sensor Networks Hojoong Kwon, Student Member, IEEE, Tae Hyun Kim, Sunghyun Choi, Senior Member, IEEE, and Byeong Gi Lee, Fellow, IEEE

Abstract— In this paper, we investigate the problem of the lifetime maximization in wireless sensor networks under the constraint of end-to-end transmission success probability, by adopting a cross-layer strategy that considers physical layer (i.e., power control), MAC layer (i.e., retransmission control) and network layer (i.e., routing protocol) jointly. We decouple the problem into separate sub-problems of each layer and propose the optimal algorithm as well as an alternative heuristic algorithm with lower complexity for each sub-problem. We demonstrate through computer simulations that a trade-off relation exists between the network lifetime maximization and the reliability constraint, and the strategy that is designed by combining the proposed algorithm at each layer can significantly increase the network lifetime. We also investigate the effect of the retransmission control on the energy efficiency for different energy consumption models. Simulation results reveal that multiple retransmissions with low power yield little gain when the link distance is short and the power conversion efficiency of the amplifier increases with the transmission power. Index Terms— Wireless sensor networks, lifetime maximization, reliability, cross-layer strategy, power control, ARQ control, routing protocol.

I. I NTRODUCTION

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ECENTLY, wireless sensor networks have become an area of attractive research interest [1], [2]. Wireless sensor networks, in most applications, are required to be operating in the order of months to years but the constituent sensor nodes have limited battery power. Therefore it is one of the major challenges of sensor networks to maximize the network lifetime under power constraint. Most of the previous work have thus focused on network lifetime maximization, dealing mainly with the energy efficiency [1], [2]. In certain sensor networks, reliability becomes a critical factor when the information collected by the sensor nodes needs to be conveyed reliably to the sink node. There have been reported some research efforts on such reliability issues in wireless sensor networks [3]–[5]. In [3] and [4], the authors Manuscript received January 18, 2005; revised December 9, 2005; accepted February 12, 2006. The associate editor coordinating the review of this paper and approving it for publication was V. Leung. This work was in part supported by University IT Research Center Project. This work was presented in part at the IEEE Wireless Communications and Networking Conference, New Orleans, LA, 2005, and in part at the IEEE International Conference on Communications, Seoul, Korea, 2005. H. Kwon, S. Choi, and B.G. Lee are with the School of Electrical Engineering and INMC, Seoul National University, Seoul, 151-744, Korea (e-mail: [email protected]; [email protected]; [email protected]). T.H. Kim is with the Wireless Networking and Communications Group in the University of Texas, Austin, TX 78712 (e-mail: [email protected]). Digital Object Identifier 10.1109/TWC.2006.05038.

provided new MAC and transport layer protocols that can recover the delivery failure. On the other hand, in [5], the authors presented the link estimator, which can dynamically capture link connectivity, and the routing protocol, which can exploit such connectivity to achieve reliability. However, this work provides no measure to control the degree of reliability quantitatively. In this paper, we propose a cross-layer strategy that can maximize the network lifetime under the reliability constraint, which is given in terms of the average end-to-end success probability. We focus on a data gathering application, where a collection of sensor nodes report sampled data to a sink node periodically. In order to guarantee that the success probability of end-to-end (i.e., sensor-to-sink) transmission meets the requirement specified by the given application, the proposed strategy optimizes the physical layer (i.e., power control), the MAC layer (i.e., automatic retransmission request (ARQ) control), and the network layer (i.e., routing protocol) jointly as follows: First, at the network layer, we present a new routing algorithm that is different from conventional energy-efficient routing algorithms [6], [7]. The end-to-end success probability is the product of multiple per-hop success probabilities. Accordingly, the per-hop success probability required for the target end-to-end success probability increases as the number of hops increases. This requires a larger transmission power or more retransmissions at each link, thus leading to higher energy consumption. Therefore, choosing a path composed of a large number of short hops, which is preferred in conventional routing algorithms, is not always optimal for energy saving. We newly formulate a routing problem by additionally considering the energy required for reliable end-to-end transmission. It can be formulated into a linear optimization problem, similar to generic optimal routing problem [8]. We then propose an optimal algorithm as well as a heuristic costbased algorithm. Second, at the lower layers, we present power and retry limit allocation algorithms. The power and ARQ control determines the per-hop success probability of each link. For a multihop path, it is not necessarily optimal to make the perhop success probability equal for every link as each link has different time-varying link quality [9], [10]. Therefore, we formulate the problem of the average per-hop success probability optimization based on the channel statistics of each link, and then propose a near-optimal solution. We demonstrate by simulations that the strategy that is

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designed by combining the above algorithms at each layer increases the network lifetime significantly and that a tradeoff relation exists between the network lifetime maximization and the reliability constraint. Another contribution of this paper is in examining the use of retransmission in terms of energy efficiency. We consider the cases that the reliability is supported with and without retransmissions and study the effect of retransmissions on the performance for different energy consumption models. The rest of the paper is organized as follows: we first describe the system model in consideration in Section II. Then we present a joint optimizing strategy that considers power control and routing jointly in Section III, and present a strategy that additionally considers the ARQ control in Section IV. Finally, we compare the performances of the proposed two strategies through computer simulations in Section V, concluding the paper with Section VI. II. S YSTEM M ODEL We consider a sensor network composed of multiple sensor nodes and one sink node. Each sensor node periodically sends its acquired data to the sink node. We employ a time division multiple access (TDMA)-based medium access control (MAC) protocol, with the time divided into periodic MAC frames and with each MAC frame composed of multiple time slots. In each MAC frame, each sensor node generates one packet and is allocated with time slots to transmit the packet in such a way that no collision occurs.1 The duration of the time slot is made large enough to transmit a data packet and receive its acknowledgement (ACK) packet within a time slot. The sink node periodically broadcasts a control packet that contains the time slot allocation information. In order to minimize energy consumption, we arrange such that only the sending and receiving nodes are kept awake in each time slot while others stay in sleeping (or doze) state. Since there exists no interference from other nodes, transmission failure can be caused only by channel errors, which depend on the transmission power, channel gain, and noise power. The channel gain is given by the log-normal shadowing model [11], i.e., G(d) = G(d0 ) + 10n log10 (d0 /d) + Xσ ,

(1)

where d is the distance between the transmitter and receiver, d0 a reference distance, n the path loss exponent, and Xσ a zero-mean Gaussian random variable (in dB) with standard deviation σ, respectively. The probability of successful packet delivery (i.e., per-hop success probability) is a function of tx signal-to-noise-ratio (SNR), so it takes the form of f ( GP N ) for the transmission power P tx and the noise power N . We use the following function of per-hop success probability [11], which is based on the Mica2 mote [12] that is a widely-used sensor network platform [13], ¶ρ8F µ B 1 − γ2 RN f (γ) = 1 − exp , (2) 2 1 There have been lots of work on the TDMA scheduling for eliminating the collisions [19], [20]. We can use such algorithms, but the specific algorithm is out of scope of the paper.

where γ is the SNR, BN the noise bandwidth, R the data rate in bps, ρ the encoding rate, and F the frame length in bytes, respectively. Each sensor node can choose the transmission power from one of L values from [Pmin , Pmax ], where the gap between two consecutive levels, i.e., ∆P (dBm), is constant. We assume that the energy consumption for each packet transmission is modeled by the expression µ ¶ P tx 8F E tx (P tx ) = P cir + , (3) R η(P tx ) where P cir denotes the power consumption of the electronic circuitry and η the power conversion efficiency of the power amplifier, respectively. We assume that the energy consumprx tion for packet reception is fixed at E rx = 8F R P , where P rx denotes the power consumption in receive mode. We ignore the energy consumption in the sleeping mode, as it is known to be much smaller than that for packet transmission or reception [2]. ACK packets are transmitted with the maximum power, which is assumed to be high enough that no error occurs.2 We denote by E ack-tx and E ack-rx the energy consumptions for transmitting and receiving ACK packets, respectively. In the network environment where retransmission is allowed, we adopt a stop-and-wait ARQ scheme. For each failed transmission, we allow for retransmissions repeatedly until its retry limit is reached. In support of this, it is necessary to arrange such that the number of time slots allocated to each link is determined according to the corresponding retry limit. We take a centralized approach for controlling the overall network. Therefore, the sink node needs to have the knowledge of the channel information of each link. In order to minimize the signaling overhead, we arrange sensor nodes to report not the instantaneous channel condition at each time but the channel statistics (i.e., the mean determined by the distance and the variance of shadowing) which are measured during a predetermined period3 . Based on the channel information, the sink node determines (1) the transmission power, (2) the retry limit, and (3) the routing path for each sensor node such that the average success probability can be guaranteed, and then announces the resulting decision via control packets.4 III. J OINT O PTIMIZATION OF P OWER CONTROL AND ROUTING In this section, we consider the case that the reliability is supported only through the power control without retransmission. Each sensor node adapts its transmission power level according to the channel gain. We divide the problem into two constrained optimization sub-problems: The first sub-problem is to minimize the energy consumption while guaranteeing the reliability constraint by controlling the transmission power 2 In order to simplify the problem, we assume that ACK packet transmissions are error-free even if it can be easily relaxed. 3 The estimation of the channel statistics is beyond the scope of our paper. 4 Because of the centralized approach, there may be a limitation on applying the strategy in large-scale networks. However, large-scale networks usually consist of multiple clusters with all the sensor nodes in each cluster managed by a cluster-head. Then, it is possible to apply the proposed strategy to each cluster such that the cluster-head can play the role of a sort of the sink node in the proposed strategy.

KWON et al.: A CROSS-LAYER STRATEGY FOR ENERGY-EFFICIENT RELIABLE DELIVERY IN WIRELESS SENSOR NETWORKS

of each link along a given routing path. The second subproblem is to maximize the network lifetime by controlling the time fraction of using each routing path while considering the energy consumption determined by the above power allocation algorithm.

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In case the reliability constraint is too strict, there may exist no power allocation that meets all the constraints simultaneously. So it may happen that some paths do not attain the target end-to-end success probability threshold even if all the links are allocated with the maximum power level. In this case, we exclude such paths when considering the routing path selection in Section III.B. We can prove the optimality of the GPA algorithm under a certain condition.

A. Optimal Power Allocation Algorithm We develop the power control scheme that allocates the transmission power to each sensor over a given path as the solution of the first sub-problem. Let Gi and li denote a random variable corresponding to the channel gain normalized by the noise power and the power level at the i-th link, respectively. Then the average success probability at the i-th link is given by Z Ps (Gi , li ) = f (gPli )pGi (g)dg (4)

Proposition 1: When the power conversion efficiency η is a constant and the average per-hop success probability function is concave with respect to the SNR,5 the GPA algorithm is the optimal solution to the problem in (5).

where Pli ≡ 100.1∗{(li −1)∆P +Pmin } and pGi (g) is the probability density function of Gi . Assuming that the channel gains of different links are independent, QH the average end-toend success probability is given by i=1 Ps (Gi , li ), where H denotes the number of links over the path. Then the problem of minimizing the total energy consumption under the reliability constraint is formulated as follows: H X minimize {E tx (Pli ) + E ack-rx }

B. Routing Algorithms

i=1

subject to

+(H − 1) · (E rx + E ack-tx ) (5) H Y Ps (Gi , li ) ≥ Qs , li ∈ {1, 2, · · · , L}, i=1

where Qs denotes the target end-to-end success probability. Note that the energy consumed by the sink node for data reception and ACK transmission is excluded in Eq. (5), as the sink node is usually AC-powered, and hence its energy consumption is not of our concern. As li should be integer, the problem in (5) is a non-linear integer programming problem. Unfortunately, the integer programming problem is NP-complete [16]. So we develop a suboptimal algorithm using greedy approach. We first define an incremental gain that can be obtained by increasing power level, and devise a new algorithm based on it. Specifically, we introduce the incremental ratio ρi of the per-hop success probability contributed by the power level increment at the i-th hop to be ρi =

Ps (Gi , min(li + 1, L)) . Ps (Gi , li )

(6)

Then, we consider a greedy power allocation (GPA) algorithm that increases the power level of the link of which the increment is the highest as outlined below: 1) Allocate the lowest level to all links, i.e., li ← 1 for i = 1, 2, · · · , H. 2) Increase, by one, the power level of the link with the highest value of ρi , i = 1, 2, · · · , H, i.e., li∗ ← li∗ + 1 for i∗ = arg maxi ρi . 3) Repeat the above process until the end-to-end success probability becomes equal to or larger than the target value.

Proof: See the Appendix. The average per-hop success probability is a convex function in low SNR region where the greedy approach is not optimal. Therefore we can modify the GPA algorithm by increasing the initial power level to be close to an inflection point.

In general, there exist multiple routing paths between a particular sensor node and the sink node. For each path, it is possible to determine the energy consumption required to support the target reliability using the optimal power allocation algorithm presented in the previous subsection. If all the packets were routed through the path with the minimum energy consumption, the batteries of the sensor nodes along that path would be drained out quickly while the batteries of other sensor nodes would last longer. In order to maximize the network lifetime, it is necessary to route the packets such that the energy consumption is balanced among multiple paths, which we are going to formulate as the second subproblem. In support of this, we present two routing algorithms that determine how to distribute the traffic among multiple paths: One is the optimal routing algorithm based on a linear programming approach, and the other is a minimum-cost path routing algorithm having low implementation complexity. B1. Optimal Routing Algorithm We assume that there are S sensor nodes in the sensor network, each sensor node generates packets at the rate A, and a node s has Ds distinct paths to the sink. If a node r is on the path from node s to the sink, it can properly relay the packets originated from the source node only when they are successfully delivered through the intermediate links. Specifically, let hs,p,r denote the number of hops from node s to node r on the p-th path of node s, with the number set to infinity if the node r does not belong to the path. Then, the probability stx s,p,r that node r relays (or, transmits) a packet from node s is given by  Q  k∈Ks,p,r Ps (Gs,p,k , ls,p,k ), if 0 < hs,p,r < ∞, stx = 1, if hs,p,r = 0, s,p,r  0, if hs,p,r = ∞, (7) 5 The average per-hop success probability function is concave in the range of high success probability.

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where Ks,p,r ≡ {k | 0 ≤ hs,p,k < hs,p,r }, Gs,p,k is the channel gain of the corresponding intermediate link and ls,p,k is the power level of node k determined through the optimal power allocation algorithm. The probability srx s,p,r that node r receives a packet from node s is equal to the probability that the preceding node transmits the packet to tx node r, or srx s,p,r = ss,p,k , where k is the index of the preceding node (i.e., hs,p,k = hs,p,r − 1). So the rate of energy consumption by sensor node i for transmitting its own packets relaying the packets of other nodes is given by PS Pand Ds tx tx rx rx tx p=1 A(ss,p,i Es,p,i + ss,p,i Es,p,i )us,p , where Es,p,i = s=1 tx ack-rx rx rx ack-tx and us,p the time E (Pls,p,i ) + E , Es,p,i = E + E fraction that the p-th path of node s is used. Therefore, the time duration for the battery of node i to drain out is given by Ti = PS

Ei tx tx p=1 A(ss,p,i Es,p,i

PDs

s=1

rx + srx s,p,i Es,p,i )us,p

,

(8)

where Ei denotes the initial energy of node i. Now, we define the lifetime of the network to be the minimum of the lifetimes of all sensor nodes,6 i.e., T = min Ti . i

(9)

Then the problem of maximizing the network lifetime is formulated into a standard linear programming (LP) problem [15], as follows: minimize subject to

1 (10) T S Ds 1 A XX rx = (stx E tx + srx s,p,i Es,p,i )us,p T Ei s=1 p=1 s,p,i s,p,i + vi , for all i, Ds X

us,p = 1, for all s,

p=1

us,p ≥ 0, for all s, p, vi ≥ 0, for all i, where vi ’s are slack variables. Note that the second constraint indicates that each sensor node uses the available Ds paths in a mixed order and frequency during the network lifetime. We can determine the optimal value of us,p by solving the LP problem. Then sensor node s is supposed to use the p paths in proportion to the determined optimal values. B2. Cost-based Routing Algorithm The optimal routing algorithm derived above involves very high implemental complexity, thus making it impractical. So, we develop a suboptimal algorithm, called cost-based routing (CR) algorithm, that can possibly perform close to the optimal algorithm but has lower and tractable complexity. We first define the link cost function as the ratio of the required transmission energy for a packet transmission to the remaining energy, similar to the case in [6]. Specifically, we define the cost of the link originated from node i on the p-th 6 We use the min definition for the lifetime as it enables to formulate the problem into a linear programming problem.

path of node s as link Cs,p,i =

tx rx Es,p,i + Es,p,i , (E i /Ei )w

(11)

where E i denotes residual energy, and w a weighting exponent on the remaining energy. Note that the residual energy is normalized by the initial energy because sensor nodes might have different initial energy levels. The path cost is calculated as the sum of the costs of all the links along the path. Then, the CR algorithm selects the path with the least cost periodically.7 The path selection requires an additional knowledge on the residual energy of each sensor node. In order to support this, we may arrange all sensor nodes to report the residual energy periodically, but it results in a large transmission overhead. Instead, we take an alternative method that the sink node estimates the residual energy of all sensor nodes based on the energy consumption determined by the power allocation algorithm. IV. J OINT O PTIMIZATION OF P OWER , ARQ, AND ROUTING Now we consider the case where retransmission is allowed. It is difficult to control the transmission power and the retry limit of each link simultaneously. To simplify the problem, we assume that all sensor nodes use the same power level but different retry limit. Similar to Section III, we first minimize the energy consumption for guaranteeing the reliability constraint by controlling the retry limit allocated to each link for a given routing path and transmission power. Then we maximize the network lifetime by controlling the routing path selection and transmission power. When using the retransmission, as discussed in Section II, we should allocate multiple time slots to each link according to the corresponding retry limit, whereas one time slot was allocated to each link in the case without retransmission. Therefore, the time required for delivering a packet to the sink can become larger. However, packets are generated at each sensor node and routed to the sink node periodically. In order to make the network stable, the packet delivery latency should not be excessively long, so we consider an additional constraint on the network stability. A. Retry Limit Allocation Algorithm We denote by Mi the retry limit (including the first transmission and Mi − 1 retransmissions) at the i-th link. We assume that the transmission power is given by Pl . If we assume that the channel gain at each transmission is independent8 , the average probability of successful packet delivery is given by µ ¶Mi Z Psret (Gi , Mi ) = 1 − 1 − f (gPl )pGi (g)dg , (12) 7 While we used the min definition for the lifetime in Section III.B1, in the case of the cost-based algorithm, it may be easily extended to the median definition, by proceeding with the algorithm after simply excluding the sensor nodes that are drained of their energy. 8 The assumption is reasonable when the transmission time, which is a few tens to hundreds milliseconds in low-rate applications, is longer than the channel coherence time.

KWON et al.: A CROSS-LAYER STRATEGY FOR ENERGY-EFFICIENT RELIABLE DELIVERY IN WIRELESS SENSOR NETWORKS

and the average number of the total transmissions at the i-th link is given by ¡ ¢Mi R 1 − 1 − f (gPl )pGi (g)dg R N (Gi , Mi ) = . (13) f (gPl )pGi (g)dg Analogously to the problem in (5), the problem of minimizing the total energy consumption under the reliability constraint can be formulated as follows: H X

minimize

{E tx (Pl ) + E ack-rx

i=1

+(E rx + E ack-tx ) · 1(i < H)}N (Gi , Mi ) (14) H Y subject to Psret (Gi , Mi ) ≥ Qs , Mi ∈ {1, 2, · · · },

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node of node r (i.e., hs,p,k = hs,p,r − 1). Then the rate of energy consumption by sensor node i for transmitting its packets relaying the packets from other nodes is given by PS Pand Ds tx tx rx rx s=1 p=1 A(ss,p,i Es,p,i + ss,p,i Es,p,i )us,p . We consider how to put a stability constraint. We define by the path length of a routing path the sum of the retry limits of all the links along the path. Let Ls,p denote the path length of the p-th path of node s. Then, a MAC frame duration should be larger than the sum of the lengths of all the paths used in that frame. Therefore, we can put the stability constraint such that the average sum of the path lengths is bounded by the packet generation period, 1/A, that is, Ds S X X

us,p Ls,p ≤ 1/A.

(16)

s=1 p=1

i=1

where the function 1(C) is 1 when the condition C is met and is 0 otherwise. The problem in (14) is also a non-linear integer programming problem. So we design a greedy retry limit allocation (GRLA) algorithm, which is the same as the GPA algorithm except for the incremental ratio. We define an incremental ratio ρret i of the per-hop success probability contributed by the retry limit increment at the i-th hop to be ρret i =

Psret (Gi , Mi + 1) . Psret (Gi , Mi )

(15)

As will become clear through computer simulations later, the GRLA can possibly perform close to the optimal solution and has a lower complexity in computation. The computational complexity of the GRLA algorithm can be determined as follows: In each iteration, we need H comparisons to determine the link with the highest gain. The end-to-end success probability is multiplied at least by ∆min ≡ RPsret (Gi∗ , M i∗ )/Psret (Gi∗ , M i∗ − 1), where i∗ ≡ arg maxi gpGi (g)dg, and M i∗ is the smallest integer satQH isfying Psret (Gi∗ , Mi∗ ) k=1,k6=i∗ Psret (Gk , 1) ≥ Qs . Then the number of iterations is at most log∆min Qs and, therefore, the worst-case complexity of the GRLA algorithm is O(H log∆min Qs ). B. Routing and Power-Control Algorithms We now optimize the traffic distribution among the multiple paths. In addition, since the energy consumption of each path depends on the transmission power, we also need to optimize the transmission power. We present two algorithms that determine the routing path selection and the transmission power level: One is the optimal algorithm, and the other is a cost-based routing and power control algorithm. B1. Optimal Routing and Power-Control Algorithm We additionally define by Ns,p,r the average number of the transmissions by node r when the p-th path of node s is used, which is determined through retry limit allocation algorithm. As the energy consumption for the transmission tx rx and reception (i.e., Es,p,r and Es,p,r , respectively) should involve the energy consumption for the retransmissions, we tx rx get the relations Es,p,r = Ns,p,r (E tx + E ack-rx ) and Es,p,r = rx ack-tx Ns,p,k (E + E ), where k is the index of the preceding

Since the sink node can control the length of the MAC frame per frame basis, the stability of the network can be supported by mixing the frames with long and short durations appropriately. With the stability constraint set as above, we can formulate the problem of maximizing the network lifetime analogously to the problem of (10). The result is also a linear programming problem, so we can obtain the optimal routing algorithm. For each transmission power level, we can obtain the optimal network lifetime by applying the above routing algorithm in addition to the retry limit allocation algorithm. As the routing optimization problem may not yield any feasible solution if the stability constraint is too strict, we consider only the power levels for which the feasible solutions exist and then set the transmission power to the level that maximizes the network lifetime among the candidate power levels. B2. Cost-based Routing and Power-Control Algorithm We consider a low-complexity suboptimal algorithm, called cost-based routing and power-control (CRPC) algorithm. The CRPC algorithm first determines the transmission power as follows: For each transmission power level, we perform the retry limit allocation algorithm and calculate the energy consumption of the sensor nodes. The transmission power is set to the level that minimizes the average energy consumption. Then, the CRPC algorithm performs the cost-based routing algorithm as described below. The CRPC algorithm adopts the same link cost function as the CR algorithm in (11). Under the CRPC algorithm, it is not easy to adapt the frame duration per frame basis while meeting the stability constraint. Therefore, in order to simplify the problem, we support the stability constraint by keeping the duration of every frame smaller than the packet generation period. Specifically, if the sum of the path lengths is larger than 1/A, we perform the following reselection process: First, we determine the sensor node s∗ that gets the least cost increment when the minimum-cost path is replaced with another path as follows: ! Ã path path Cs,p − Cs,p ∗ ∗ s , (17) s = arg min min s p∈Ps Ls,p∗ − Ls,p s path where Cs,p is the cost of the p-th path of node s, p∗s the current path for node s, and Ps ≡ {p | Ls,p < Ls,p∗s }. Then,

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we set the routing path of node s∗ to the path that gets the least cost increment. This procedure is performed iteratively until the stability constraint is met. If a feasible solution does not exist, we increase the power level to the next level and then perform the retry limit allocation and the above routing algorithm again. V. N UMERICAL E VALUATION We conduct computer simulations in order to evaluate the performance of the proposed algorithms. We randomly place 80 sensor nodes in a 80 m x 80 m square sensor field and put the sink node at the center. For simulations, we take the parameter values based on the Mica2 mote as follows: R = 19.2 kbps, BN = 30 kHz, ρ = 2 (Manchester encoding), and F = 50 bytes. We also set d0 = 1 m, G(d0 ) = −55 dB, n = 4, σ = 4, and N = −105 dBm [11]. We use an energy model based on CC1000 [14] and determine the function of (3) by the curve fitting method. The resulting parameters are given by P cir = 15 mW, η(P tx ) = 0.06 exp(0.095P tx (dBm)), and P rx = 22.2 mW. We set the minimum and maximum transmission powers, Pmin and Pmax , to -20 and 15 dBm, respectively, and the number of power levels to 12. We set the size of ACK packets to 10 bytes. We supply each sensor node with an initial energy level of 250 J and set the target end-to-end success probability to 85%. We consider only the routing paths that have at most the length of 7 hops. For the control information delivery, in order to simplify the calculation of the signaling overhead, we assume a unicastbased scheme, which works as follows:9 The sink node transmits to each sensor node the control packet that contains the information on the link involving the corresponding node (i.e., the time slot to transmit or receive (10 bits), the destination node or the source node (7 bits), the transmission power (4 bits), and the retry limit (4 bits)). The size of the control packets depends on how many packets the corresponding sensor nodes should relay. We observe that 100 bytes are enough to convey all the relaying packets, so we set the control packet size to 100 bytes. The transmission of the control packets is conducted in reverse schedule to that the data packets are transmitted. Since the control packet is twice as large as the data packet, it takes two frames to deliver the control information. As will be shown below, for the costbased algorithm, we may transmit the control information periodically at a sufficiently large interval, thus incurring small signaling overhead. On the other hand, for the channel information report, we use the same period as for the route update. A. Joint Optimization of Power Control and Routing For performance comparisons, we consider four different schemes: 1) Non-optimal power allocation and CR (namely, NPA-CR), 2) GPA and CR (namely, GPA-CR), 3) GPA and optimal routing (namely, GPA-OR), and 4) non-optimal power allocation and random routing (namely, NPA-RR). In the case 9 There are other possible schemes. For example, we can adopt the reliable broadcast algorithms that were presented previously [21], [22]. In addition, when the sink node has a powerful transmitter, it can broadcast the control packet to all sensor nodes in a single hop.

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0

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150 Value of weight

200

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Fig. 1. Network lifetime of various schemes of algorithms with respect to weighting factor w.

of NPA algorithm, we take the following arrangement: The transmission power is allocated such that all links have the same per-hop success probability, which is set to the value that can guarantee the target end-to-end success probability for the path with the maximum number of hops. In the RR algorithm, we randomly choose a route for all sensor nodes. We first determine the value of the weighting factor w, which optimally makes balance between the energy consumption and the residual energy in the link cost for the CR algorithm. Fig. 1 shows the resulting performance of various different schemes with respect to the weighting factor w. We observe that the performance of the CR algorithm becomes close to that of the optimal routing algorithm when w lies between 20 and 100, regardless of the power allocation algorithms. Therefore, we set the value of w to 50 in the subsequent simulations. We examine the influence of the route update period of the CR algorithm to the network lifetime. Fig. 2 depicts the network lifetime of various different settings with (‘w/’) and without (‘w/o’) signaling overhead with respect to the route update period. The signaling overhead is not taken into consideration in the case of the OR algorithm as the frequency of the route update is usually hard to determine. Therefore, the OR algorithm serves as an upper bound to the actual performance. We observe from the figure that the network lifetime increases as the update period decreases, but this requires more signaling overhead, caused by frequent routing updates. Moreover, we observe that the performance loss from the signaling overhead is minimized to about 2.4% when the update period is 200 frames. This indicates that the signaling overhead is sufficiently low, so we set the update period to 200 frames in the subsequent simulations. We also examine how the network lifetime is affected by the number of power levels. Fig. 3 plots the network lifetime as the different number of power levels varies. We observe, as expected, that the performance improves as the number of power levels increases, but it requires higher implementation cost and signaling overhead for announcing the power information. Note that the network lifetime is saturated when the

KWON et al.: A CROSS-LAYER STRATEGY FOR ENERGY-EFFICIENT RELIABLE DELIVERY IN WIRELESS SENSOR NETWORKS 8000

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8000 GPA−OR GPA−CR NPA−CR NPA−RR

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Fig. 2. Network lifetime of various schemes with respect to route update period (w = 50).

0.855

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Fig. 4. Network lifetime of various schemes with respect to target end-to-end succuss probability (w = 50, update period = 200 frames).

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Fig. 3. Network lifetime of various schemes with respect to the number of power levels (w = 50, update period = 200 frames).

number of power levels is larger than 12. Fig. 4 shows the network lifetime with respect to the target end-to-end success probability. We observe that the network lifetime of each scheme decreases as the the target ene-to-end success probability increases. This implies that a trade-off relation exists between the network lifetime and the reliability constraint. We also observe that the GPA-CR scheme outperforms the NPA-CR and the NPA-RR schemes by about 17% and 75%, respectively. B. Joint Optimization of Power Control, ARQ Control, and Routing We consider four different schemes: 1) Non-optimal retry limit allocation and CRPC (namely, NRLA-CRPC), 2) GRLA and CRPC (namely, GRLA-CRPC), 3) GRLA and optimal routing and power control (namely, GRLA-ORPC), and 4) non-optimal retry limit allocation and shortest-path routing and power control (namely, NRLA-SRPC). In the case of NRLA algorithm, similarly to the NPA algorithm, the retry

5 −4

Fig. 5.

−2

0

2

4 6 Tx power (dBm)

8

10

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14

Energy consumption of greedy algorithm and the lower bound.

limit is allocated such that all the links have the same per-hop success probability. In the SRPC algorithm, the path cost is defined as the path length and all the other operations are the same as the CRPC algorithm. We set the weighting factor and the update period to 50 and 200 frames, respectively, which are the same values for the CR algorithm. We evaluate the performance of the GRLA algorithm. If we relax the integer constraint in the problem in (14), the problem can be transformed into the standard convex optimization problem [17]. Then we can solve the problem using the primaldual interior point method [18]. The optimal solution gives us the lower bound of the energy consumption. Fig. 5 shows the lower bound and the energy consumption for the GRLA algorithm averaged over all the paths with respect to the transmission power. We observe that the GRLA algorithm performs very close to the lower bound regardless of the transmission power, and the energy consumption depends on the transmission power. Fig. 6 shows the network lifetime with respect to the target end-to-end success probability, when the packet generation

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10 GRLA−ORPC GRLA−CRPC NRLA−CPRC NRLA−SRPC

7000

Ec E ret c (tx power = −8.75dBm) E ret c (tx power =−2.5dBm) ret E c (tx power = 2.5dBm) E ret c (tx power = 8.75dBm)

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0

Ecret

tx

tx

rx

ack-tx

ack-rx

= {E (P ) + E + E +E } R ∗ {1 − (1 − f (gP tx PG (g)dg))M } R · , (19) f (gP tx PG (g))dg R where M ∗ is the least integer in {m|1−(1− f (gP tx )PG (g) ∗ dg)M ≥ Ps }. Note that the energy consumption depends on the value of the fixed transmission power. Fig. 7 plots the energy consumption with respect to the link distance for the above two cases when the per-hop success probability Ps is set to 95%. We observe that only in the range of long distance, the retry limit control with the appropriate transmission power has better efficiency. This indicates that multiple transmissions with lower transmission power yield little energy gain. We may interpret the reason as follows: the Mica2 mote targets short range communications, so the energy consumption of the electronic circuitry, packet reception and ACK transmission, which is the cost incurred constantly at each transmission, is large compared with that of the power amplifier. Consequently, multiple transmissions are

8 Link distance (m)

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η : increasing function, w/ E cir, E rx & E ack η : increasing function, w/o E cir, E rx & E ack η : constant, w/o Ecir, E rx & E ack

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where P ∗ is the minimum transmission power required for supporting per-hop success probability Ps , which is given by R the minimum value in {P | f (gP )PG (g)gdg ≥ Ps }. However, when the retry limit control is used with the transmission power P tx , the energy consumption changes to

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1.1

Ratio of Eret c to Ec

Now we evaluate the use of retransmissions in terms of energy efficiency. We first consider the energy consumption for supporting per-hop success probability Ps at one link. The energy consumption, when the power control is used, is given by Ec = E tx (P ∗ ) + E rx + E ack-tx + E ack-rx , (18)

4

Fig. 7. Energy consumption of power control and retry limit control to support per-hop success probability of 95% with respect to link distance.

period is set to 400 slots. We observe that GRLA-CRPC outperforms NRLA-CRPC and NRLA-SRPC by about 20% and 65%, respectively. The CRPC algorithm performs poorer than the optimal algorithm because it bounds the absolute MAC frame duration. C. Comparison

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Fig. 8. The ration of Ecret to Ec with respect to link distance under various energy models.

not preferred. In addition, as the power conversion efficiency is an increasing function of the transmission power, it is not advantageous to use low transmission power. Fig. 8 supports this argument by showing the ratio of Ecret to Ec when the power conversion efficiency is constant and the energy consumption of the electronic circuitry, packet reception and ACK transmission is not considered. The figure demonstrates that in that case the energy efficiency can be improved by the additionally employed retry limit control. However, the retry limit control requires to consume more time resource due to the multiple transmission. Fig. 9 shows the network lifetime with respect to the target end-to-end success probability when the proposed strategies are applied without and with retry limit control. As expected, the first strategy (i.e., without retry limit control) yields a longer network lifetime than the second one does. Note that since the second strategy sets the same power level to all the links rather than optimizes the individual transmission power for each link, it incurs additional performance loss. We also observe that the network lifetime increases as the packet

KWON et al.: A CROSS-LAYER STRATEGY FOR ENERGY-EFFICIENT RELIABLE DELIVERY IN WIRELESS SENSOR NETWORKS 7400 GRLA−CRPC (1/A=600) GRLA−CRPC (1/A=400) GRLA−CRPC (1/A=375) GRLA−CRPC (1/A=350) GPA−CR

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Fig. 9. Network lifetime of various schemes with respect to target end-to-end succuss probability (w = 50, update period = 200 frames).

generation period increases. It happens because the number of the candidate paths increases as the stability constraint gets relaxed, thus resulting in more balanced energy consumption. However, the performance does not approach that of the first strategy only with power control even when the packet generation is very large, because all links are constrained to use the same transmission power. VI. C ONCLUDING R EMARKS In this paper, we have investigated how to maximize the network lifetime while guaranteeing the end-to-end success probability in wireless sensor networks. Noting that the energy efficiency and the reliability in wireless sensor networks depend on the features of each layer—the power control in the physical layer, the ARQ control in the MAC layer, the routing protocol in the network layer, we have designed crosslayer strategies by considering them jointly. The proposed strategies turned out to balance the trade-off between network lifetime and reliability constraint and provide a mean to control the reliability quantitatively while minimizing the energy consumption. The cross-layer strategies that we have proposed in this paper are two-fold—one consisting of the GPA and CR algorithms, and the other consisting of the GPLA and CRPC algorithms. The GPA and GPLA algorithms are designed to minimize the total energy consumption required to support the reliability constraint for each path by optimizing the power allocation and the retry limit allocation, respectively. On the other hand, the CR and CRPC algorithms are to maximize the network lifetime by taking balanced energy consumption among the constituent paths. In the case of CPRC algorithm, we additionally considered the stability constraint and optimized the transmission power of the sensor nodes. We have confirmed through simulations that the combination of power control, retry limit control, and routing optimization can increase the network lifetime remarkably over the non-optimal algorithms. We also evaluated the energy efficiency of using retransmissions for reliability support. We showed through numeri-

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cal results that the retransmission control is not helpful for energy efficiency when the link distance is short and the power conversion efficiency of the power amplifier is an increasing function of the transmission power. Noting that wireless sensor networks may be employed in various different environments, however, the retransmission control should be determined based on the target transmission range and the energy consumption characteristics of the given environment. The proposed strategy is based on a TDMA MAC protocol. While a TDMA protocol has the disadvantages of requiring overheads for signaling the scheduling information, it has a natural advantage over a CSMA protocol in terms of energy conservation since the duty cycle of the radio is small and no contention-introduced overhead is required. Furthermore, TDMA renders a easier means to control the reliability due to its contention-free transmission. On the other hand, in the CSMA-based networks, the per-hop success probability is affected by collision as well as by channel error. So, in order to support the reliability, it is necessary to control the back-off windows of sensor nodes. However, it is a challenging task as there exists dependency among different links. Future work is needed to extend the proposed algorithm to the CSMA-based networks. A PPENDIX P ROOF OF T HEOREM I Under the given condition, the problem in (5) is equivalent to minimizing the sum of the power levels of each link under the reliability constraint. For the proof, it suffices to show that the GPA algorithm is optimal to the problem of maximizing the end-to-end success probability under the constraint of limited total power level as follows: H X

maximize i=1 H X

subject to

hi (li )

(A1)

li ≤ N, li ∈ {1, · · · , L},

i=1

where hi (l) ≡ log Ps (Gi , l) and N is a positive integer. Let {li∗ (n)} and {li∗ (n + 1)} denote the optimal solution to the problem in (A1) for N = n and for N = n + 1, respectively. We first prove the following relation. For all i, li∗ (n + 1) ≥ li∗ (n),

(A2)

where li∗ (0) = 0. If there exist p and q such that lp∗ (n + 1) < lp∗ (n) and lq∗ (n + 1) > lq∗ (n), then the optimality of li∗ (n) yields the inequality H X i=1

hi (li∗ (n)) > hq (lq∗ (n + 1) − 1) +

H X

hi (li∗ (n + 1)).

i=1,i6=q

(A3) Since hi (x) is a concave function, we get the inequality hq (lq∗ (n + 1) − 1) − hq (lq∗ (n)) ≥ hq (lq∗ (n + 1)) − hq (lq∗ (n) + 1),

(A4)

where the equality holds when lq∗ (n + 1) − lq∗ (n) = 1. We combine the two inequalities (A3) and (A4) to obtain the

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inequality hq (lq∗ (n) + 1) +

H X

hi (li∗ (n)) >

H X

hi (li∗ (n + 1)),

i=1

i=1,i6=q

(A5) which contradicts the assumption that li∗ (n + 1) is the optimal solution for N = n + 1. This proves that the optimal solution satisfies the relation (A2). PH Since l∗ (n + 1) ≥ li∗ (n) for all i and i=1 li∗ (n + 1) − PH ∗ i ∗ i=1 li (n) = 1, there exists only one i such that li (n + 1) = ∗ li (n) + 1 while the others remain intact. Therefore, we get H X i=1

hi (li∗ (n + 1)) = max{hj (lj∗ (n) + 1) − hj (lj∗ (n))} j

+

H X

hi (li∗ (n)).

(A6)

i=1

Accordingly, it is optimal to allocate the additional unit power ∆P to the link that has the highest increment of hi (li ). R EFERENCES [1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “A survey on sensor networks,” IEEE Commun. Mag., vol. 40, pp. 102–114, Aug. 2002. [2] V. Raghunathan, C. Schurgers, S. Park, and M. B. Srivastava, “Energy aware wireless microsensor networks,” IEEE Signal Processing Mag., vol. 19, pp. 40–50, Mar. 2002. [3] C. Y. Wan, A. T. Campbell, and L. Krishnamurthy, “PSFQ: a reliable transport protocol for wireless sensor networks,” in Proc. WSNA’2002. [4] F. Stann and J. Heidemann, “RMST: reliable data transport in sensor setworks,” in Proc. SNPA’2003. [5] A. Woo, T. Tong, and D. Culler, “Taming the underlying challenges of reliable multihop routing in sensor networks,” in Proc. ACM SenSys’2003. [6] J.-H. Chang and L. Tassiulas, “Energy conserving routing in wireless ad-hoc networks,” in Proc. IEEE INFOCOM’2000, vol. 1, pp. 22–31. [7] S. Singh, M. Woo, and C. S. Raghavendra, “Power-aware routing in mobile ad-hoc networks,” in Proc. ACM MobiCom’1998. [8] D. Bertsekas and R. Gallager, Data Networks, Second Edition. Prentice Hall, 1991. [9] A. Savvides, C.-C. Han, and M. B. Strivastava, “Dynamic fine-grained localization in ad-hoc networks of sensors,” in Proc. ACM MobiCom’2001. [10] K. Whitehouse, A. Woo. F. Jiang, J. Polastre, and D. Culler, “Exploiting the capture effect for collision detection and recovery,” in Proc. Second IEEE Workshop on Embedded Networked Sensors (EmNetS-II), pp. 45– 52. [11] M. Zuniga and B. Krishnamachari, “Analyzing the transitional region in low power wireless links,” in Proc. IEEE SECON’2004, pp. 517–526 . [12] Crossbow, Mica2 Mote, http://www.xbow.com/Products/productsdetails. aspx?sid=62. [13] J. Zhao and R. Govindan, “Understanding packet delivery performance in dense wireless sensor networks,” in Proc. ACM SenSys’2003. [14] Chipcon, CC1000 Datasheet, http://www.chipcon.com/files/CC1000 Data Sheet 2 2.pdf. [15] S. G. Nash and A. Sofer, Linear and Nonliear Programming. McGrawHill, 1996. [16] C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, 1982. [17] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, 2003. [18] Y. Nesterov and A. Nemirovsky, Interior Point Polynomial Algorithms in Convex Programming. Philadelphia, PA: SIAM, 1994. [19] S. Gandham, M. Dawande, and R. Prakash, “Link scheduling in sensor networks: distributed edge coloring revisited,” in Proc. IEEE INFOCOM’2005, vol. 4, pp. 2492–2501. [20] S. Ramanathan, “A unified framework and algorithm for channel assignment in wireless networks,” ACM/Kluwer Wireless Networks, vol. 5, pp. 81-94, Mar. 1999. [21] W. Lou and J. Wu, “A reliable broadcast algorithm with selected acknowledgements in mobile ad-hoc networks,” in Proc. IEEE Globecom’2003, vol. 6, pp. 3536–3541.

[22] S.-J. Park, R. Vedantham, R. Sivakumar, and I. F. Akyildiz, “A scalable approach for reliable downstream data delivery in wireless sensor networks,” in Proc. ACM MobiHoc’2001. Hojoong Kwon (S’05) received the B.S. degree in electrical engineering and computer science from Seoul National University, Seoul, Korea, in 2002. He is currently working toward the Ph.D. degree in electrical engineering and computer science at Seoul National University. His current research interests include wireless communications and networking, with a current focus on cross-layer design for wireless networks, radio resource allocation, QoS provisioning, and energy-efficient communication protocols for wireless sensor networks. Tae Hyun Kim received the B.S. degree from Yonsei University in 2004, and the M.S. degree in electrical engineering and computer science from Seoul National University, Seoul, Korea in 2006, respectively. He is currently pursuing his Ph.D. at Wireless Networking and Communications Group in University of Texas at Austin, working in the area of MIMO-OFDM MAC protocol design focused on cross-layered benefits between MAC and physical layers for multi-hop networks. Also, his research interests include MAC layer design, routing techniques, network architecture, and high layer concerns for coexistence of ISM band wireless technologies. In Oct. 2005, he was awarded the Grand Prix of 1st RFID/USN Research Paper Contest by the Minister of Information and Communication, Korea. Sunghyun Choi (S’96-M’00-SM’05) is an assistant professor at the School of Electrical Engineering, Seoul National University (SNU), Seoul, Korea. Before joining SNU in September 2002, he was with Philips Research USA, Briarcliff Manor, New York, USA as a Senior Member Research Staff and a project leader for three years. He received his B.S. (summa cum laude) and M.S. degrees in electrical engineering from Korea Advanced Institute of Science and Technology (KAIST) in 1992 and 1994, respectively, and received Ph.D. at the Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor in September, 1999. His current research interests are in the area of wireless/mobile networks. He authored/coauthored over 80 technical papers and book chapters. He also holds four US patents and one Korea patent, and has several patents pending. He has served on the TPC of many conferences, and has been involved with many conference/workshop organizations. He is also an area editor of ACM SIGMOBILE Mobile Computing and Communications Review (MC2R) and an editor of KICS Journal of Communications and Networks (JCN). Since year 2000, he is an active participant and contributor of the IEEE 802.11 WLAN standardization committee. From 2004 to 2007, his research on IEEE 802.11(e) WLAN QoS is supported by Korea Ministry of Science and Technology (MOST) under Young Scientist Award program. Dr. Choi was a recipient of the Korea Foundation for Advanced Studies (KFAS) Scholarship and the Korean Government Overseas Scholarship during 1997-1999 and 1994-1997, respectively. He also received a Bronze award at Samsung Humantech Paper Contest in 1997. He is a senior member of IEEE, and a member of ACM, KICS, IEEK, and IEEK.

KWON et al.: A CROSS-LAYER STRATEGY FOR ENERGY-EFFICIENT RELIABLE DELIVERY IN WIRELESS SENSOR NETWORKS

Byeong Gi Lee (S’80-M’82-SM’89-F’97) received the B.S. and M.E. degrees from Seoul National University, Seoul, Korea, and Kyungpook National University, Daegu, Korea, both in electronics engineering, and the Ph.D. degree in electrical engineering from the University of California, Los Angeles. He was with Electronics Engineering Department of ROK Naval Academy as an Instructor and Naval Officer in active service from 1974 to 1979, and worked for Granger Associates, Santa Clara, CA, as a Senior Engineer responsible for applications of digital signal processing to digital transmission from 1982 to 1984, and for AT&T Bell Laboratories, North Andover, MA, as a Member of Technical Staff responsible for optical transmission system development along with related the standards works from 1984 to 1986. He joined the faculty of Seoul National University in 1986 and served as the Director of the Institute of New Media and Communications in 2000 and the Vice Chancellor for Research Affairs from 2000 to 2002. Dr. Lee was the founding chair of the Joint Conference of Communications and Information (JCCI), the chair of the Steering Committee of the Asia Pacific Conference on Communications (APCC), and the chair of the founding committee of the Accreditation Board for Engineering Education of Korea (ABEEK). He served as the TPC Chair of IEEE International Conference on Communications (ICC) 2005, as the President of Korea Society of Engineering Education (KSEE) and as a Vice President of Korea Institute of Communication Sciences (KICS). He was the editor of the IEEE Global Communications Newsletter, an associate editor of the IEEE Transactions

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on Circuits and Systems for Video Technology, and the founding Associate Editor-in-Chief and the Editor-in-Chief of the Journal of Communications and Networks (JCN). He served for the IEEE Communications Society (ComSoc) as the Director of Membership Programs Development, as the Director of Asia Pacific Region, as the Director of Magazines and as a Member-at-Large to the Board of Governors. He currently serves a Vice President of the ABEEK, as the Vice President for Membership Development of IEEE ComSoc and as the Executive Vice President of KICS. He is the founder and the first President of the Citizens’ Coalition for Scientific Society (CCSS), a non-government organization for the advancement of science and technology in Korea. Dr. Lee is a co-author of Broadband Telecommunication Technology, 1st & 2nd editions, (Artech House: Norwood, MA, 1993 & 1996), Scrambling Techniques for Digital Transmission (Springer Verlag: New York, 1994), Scrambling Techniques for CDMA Communications (Kluwer Publisher: Norwell, MA, 2001), and Integrated Broadband Networks (Artech House: Norwood, MA, April 2002). He holds seven U.S. patents with four more patents pending. His current fields of interest include broadband networks, wireless networks, communication systems, and signal processing. He received the 1984 Myril B. Reed Best Paper Award from the Midwest Symposium on Circuits and Systems, Exceptional Contribution Awards from AT&T Bell Laboratories, a Distinguished Achievement Award from Korea Institute of Communication Sciences (KICS), the 2001 National Academy of Science (of Korea) Award and the 2005 Kyung-am Academic Award. He is a Member of the National Academy of Engineering of Korea, a Member of Sigma Xi, and a Fellow of the IEEE.