Optimal Transmit Power and Packet Size in Wireless Sensor Networks in Shadowed Channel


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This paper investigates the effects of
shadowing on the optimal transmit power required to
sustain the network connectivity while maintaining a
predefined maximum tolerable Bit Error Rate (BER) in
a Wireless Sensor Networks (WSN). Optimization of
transmit power is of great importance in WSN since
sensor nodes are battery driven and optimization helps
to increase battery life by reducing inter node
interference significantly. An infinite Automatic Repeat
Request (ARQ) model has been considered to assess the
impact of shadowing and other network conditions on
energy requirement for successful packet transmission in
WSN. We also find the optimal packet length based on
energy efficiency. Effects of shadowing on optimal packet
size and energy efficiency in packetized data
transmission are also investigated. Further energy
consumption is minimized considering a variable packet
length based transmission. Use of optimal packet size
shows a significant reduction in energy spending.

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Optimal Transmit Power and Packet Size in Wireless Sensor Networks in Shadowed Channel

  1. 1. ACEEE International Journal on Communication, Vol 1, No. 2, July 2010 Optimal Transmit Power and Packet Size in Wireless Sensor Networks in Shadowed Channel Arnab Nandi, Dipen Bepari, Jibin Jose and Sumit Kundu, Member IEEE Department of Electronics and Communication Engineering National Institute of Technology, Durgapur Durgapur- 713209, India Emails: nandi_arnab@yahoo.co.in, dipen.jgec04@gmail.com, jibinjosepez@gmail.com, sumit.kundu@ece.nitdgp.ac.inAbstract - This paper investigates the effects of network connectivity in shadowed environment.shadowing on the optimal transmit power required to Several approaches have been proposed in literature tosustain the network connectivity while maintaining a prolong network lifetime. Sooksan et al. [1] evaluatedpredefined maximum tolerable Bit Error Rate (BER) in Bit Error Rate (BER) performance and optimal powera Wireless Sensor Networks (WSN). Optimization oftransmit power is of great importance in WSN since to preserve the network connectivity considering onlysensor nodes are battery driven and optimization helps path-loss and thermal noise. In [2] Bettstetter et al.to increase battery life by reducing inter node derived the transmission range for which network isinterference significantly. An infinite Automatic Repeat connected with high probability considering free-spaceRequest (ARQ) model has been considered to assess the radio link model. In [3] the relationships betweenimpact of shadowing and other network conditions on transmission range, service area and networkenergy requirement for successful packet transmission in connectedness is studied in a free space model.WSN. We also find the optimal packet length based on Narayanaswamy et al. [4] proposed a protocol thatenergy efficiency. Effects of shadowing on optimal packet extends battery life through providing low power routessize and energy efficiency in packetized datatransmission are also investigated. Further energy in a medium with path loss exponent greater than 2. Inconsumption is minimized considering a variable packet [5] a minimum uniform transmission power of an adlength based transmission. Use of optimal packet size hoc wireless network to maintain network connectivityshows a significant reduction in energy spending. is proposed considering path loss only. In this paper optimal transmit power is derived inKeywords -Wireless Sensor Networks, BER, Optimal shadowed channel while maintaining a certaintransmit power, Optimal packet size, ARQ, Shadowing. maximum tolerable BER. Since performance of WSN is likely to be affected by shadowing, it is important to 1. INTRODUCTION investigate the impact of shadowing on optimal power. The optimal power in presence of shadowing also Most of the research work on WSN assumes depends on routing and the Medium Access Controlidealized radio propagation models without (MAC) protocol used [1, 6-7]. In the present work weconsidering fading and shadowing effects. However carry out simulation studies to derive the optimalnetwork performance degrades due to shadowing and transmit power in presence of shadowing for a networkfading. Energy conservation is one of the most model employing square grid topology as in [1].important issues in WSN, where nodes are likely to Optimal transmit power is evaluated under severalrely on limited battery power. The connectivity of conditions of network such as node density, data rateWSN mostly depends on the transmission power of and different level of shadow fading.the source nodes. If the transmission power is not Here energy level performance of a square gridsufficiently high there may be single or multiple link sensor network is also studied in presence offailure. Again transmitting at high power reduces the shadowing [8-10]. We consider an infinite ARQ modelbattery life and introduces excessive inter node to successfully transmit a packetized data from oneinterference. So an optimal transmit power is required node to another node. A data packet is retransmittedfor each node to preserve the network connectivity infinitely till it is successfully received [8]. It isand prolong network lifetime. Different network assumed that the ACK / NAK from receiving node areconditions have significant impact on optimal transmit instantaneous and error free. We estimate energypower. Most of the previous research work in this efficiency of the network under different level offield assumes free-space radio link model and shadowing and node spatial density. A scheme basedAdditive White Gaussian Noise (AWGN) [1-3]. on variable packet size is also evaluated. In this schemeHowever shadow fading has significant impact on packet size corresponds to highest energy efficiency isnetwork performance. So, it is important to investigate used. This packet size, which contributes maximumoptimal transmit power required to maintain the efficiency, is called optimum packet length. Impact of 39© 2010 ACEEEDOI: 01.ijcom.01.02.08
  2. 2. ACEEE International Journal on Communication, Vol 1, No. 2, July 2010shadowing on optimal packet size is investigated. Use the random back-off time expires, node startsof optimal packet length based transmission shows transmitting a packet. The random back-off time helpssignificant reduction in energy spent compared to a to reduce interference among nodes in the same routefixed packet based transmission. Thus use of optimal and also among nodes in different routes. Throughoutpacket based transmission is seen to enhance network this paper, we assume that the random back-off time islifetime. exponential with mean 1 λt , where λt is the packet The rest of the following paper organized asfollows: In Section II, we describe the System Model transmission rate.and assumptions that are used in the derivation of The major perturbations in wireless transmission areoptimal transmit power and optimal packet size in the large scale fading and small scale fading [9-10]. Largepresence of shadowing. Section III shows simulation scale fading represents the average signal powerresults and discussions. Finally conclusions are drawn attenuation or path loss due to motion over large areas.in Section IV. This phenomenon is affected by prominent terrain contours (hills, forests, billboards, clumps of buildings, etc.) between the transmitter and receiver. The receiver II. SYSTEM MODEL is often represented as being “shadowed” by such We consider a topology of network as presented in prominences. The statistics of large-scale fading[1]. Figure 1 shows a two tier sensor network using provide a way of computing an estimate of path loss assquare grid topology [1, 8]. Distance between two a function of distance. This is described in terms of anearest neighbor is mean-path loss (nth-power law) and a log-normally distributed variation about the mean [10]. In the presence of shadowing, with a T-R separation of d, the path loss PL(d ) at a particular location is random and distributed log-normally about the mean distance dependent value of PL(d ) [9] PL(d ) dB = PL(d ) + Xσ (2) dB where Xσ denotes a zero mean, Gaussian random variable with standard deviation σ. Thus the received Fig. 1: Sensor nodes in square grid topology. signal power can be expressed asd link . It is assumed that N numbers of nodes aredistributed over a region of area A obeying square Psw (d ) dBm = Gt + Gr + PTx −  PL(d )  dB dB dBm  dBgrid topology. The node spatial density ρ sq is defined + Xσ ) (3)as number of nodes per unit area i.e., ρ sq = N A . Theminimum distance between two consecutive neighbors where Psw is the received signal power in shadowedis given by environment, PTx is the transmit power, Gt and G r N 1 are the transmitting and receiving antenna gain d link = × (1) respectively. Here we consider omni directional N −1 ρ sq ( Gt = Gr = 1) antennas at the transmitter and When the node density increases, minimum receiver. The carrier frequency is in the unlicensed 2.4distance between two nodes decreases following GHz band.equation (1). Here we assume a simple routing It can be assumed without loss of generality thatstrategy such that a packet is relayed hop-by-hop, source node is at the center of the network (see Fig. 1).through a sequence of nearest neighboring nodes, until If a destination node is selected at random, theit reaches the destination [6]. Therefore, we assume minimum number of hops to reach the destination canthat a route between source and destination exists. vary from 1 to 2i max , where i max is the maximum tierInfinite ARQ is considered between the pair. order. Counting the number of hops on a route from the Here we consider a simple reservation-based MAC source to each destination node and finding the averageprotocol, called reserve-and-go (RESGO) following value we determine the average number of hops. Using[1, 7]. In this protocol, a source node first reserves average number of hop we can evaluate the total energyintermediate nodes on a route for relaying its packets required to successfully deliver a packet from source toto the destination. A transmission can begin after a a final destination following equation (21). Assumingroute is discovered and reserved. If the destination that each destination is equally likely, the averagenode is busy, it waits for an exponential random back- number of hops on a route can be written as [1]off time before transmit or relay each packet. When 40© 2010 ACEEEDOI: 01.ijcom.01.02.08
  3. 3. ACEEE International Journal on Communication, Vol 1, No. 2, July 2010 n hop ≅ N 2 (4) Pint j =− for a − 1 transmission Rbit The received signal at the receiver is the sum ofthree components (i) the intended signal from a = 0 for no transmission of node j (8)transmitter, (ii) interfering signals from other activenodes, and (iii) thermal noise. Since the interfering The probability that an interfering node will transmitsignals come from other nodes, we assume that total and cause interference depends on the MAC protocolinterfering signal can be treated as an additive noise used. Considering the RESGO MAC protocol andprocess independent of thermal noise process. The assuming that each node transmits packets with lengthreceived signal S rcv during each bit period can be L packet , the interference probability is equal to theexpressed as [1] probability that an interfering node transmits during the N −2 vulnerable interval of duration L packet Rbit , where S rcv = S sw + ∑S j =1 j + nthermal (5) Rbit is the bit rate. This probability can be written as [7]where S sw is the desired signal in shadowed channel, λt L packet −S j is the interference from other nodes and n thermal is Rbit (9) p trans = 1 − ethermal noise signal. Assuming Binary Phase Shift Keying (BPSK) Thus S j appears with different probabilities ofmodulation, there can be two cases for the amplitude transmission as given belowof the S sw Pint j 1 Sj = with probability Ptrans Psw Rbit 2 S sw = = E bit for a + 1 transmission Rbit Pint j 1 =− with probability Ptrans Psw Rbit 2 =− = − Ebit for a − 1 transmission Rbit = 0 with probability (1 − Ptrans ) (10) (6) The thermal noise power can be written aswhere E bit is the bit energy of the received signal Pthermal = FkT0 B (11)in the presence of Rayleigh fading. The interference where F is the noise figure, k = 1.38 × 10 −23 J / K ispower received from node j can be written using the Boltzmann’s constant, T0 is the room temperatureFrii’s transmission equation [6,9-10] and B is the transmission bandwidth. The received PTx Gt Gr λ2 thermal noise signal is simply Pint j = (7) ( 4π ) 2 d linkν α α j nthermal = FkT0 B (12)  Size of the interference vector S j increases as the ν j is the multiplicative factor depends on the number of nodes increases in the network. Asposition of the interfering node. For example, the node interference from the first two tiers is significant, weat the corner of the second tier (Fig.1) is at a distance consider the interference from the first two tires only.2 2d link with respect to the center. So, in this case Next we derive the energy spent in successfully transmitting a data packet considering infinite ARQthe multiplicative factor isν j = 2 2 . It is observed between a pair of transmitting and receiving nodes. It is assumed that each packet consists of header, messagethat the significant part of the inter-node interference and trailer as shown in Fig. 2. So, transmitted packetcomes from the first two tires only. So we consider length can be expressed as [11],inter-node interference from first two tires only. For each interfering node j , the amplitude of the L packet = l h + l m + l t (13)interfering signal can be of three types [1]: Pint j Sj = for a + 1 transmission Rbit Fig. 2: Simple structure of a packet 41© 2010 ACEEEDOI: 01.ijcom.01.02.08
  4. 4. ACEEE International Journal on Communication, Vol 1, No. 2, July 2010 Now the energy efficiency (η ) is expressed as [12]:where l h , l m and l t are the header length, message E minlength and trailer length respectively. So, the energy η= ARQrequired to transmit a single packet is E packet PTx L packet lm = (21) ETx = (14) (l h + l m + l ack )(1 + nretrans ) Rbit Next we present our simulation results based on Here it is assumed that 75% of the transmit energy above system model.is required to receive a packet [12]. So, energyrequired to communicate, i.e. transmit and receive asingle packet is given by III. RESULTS AND DISCUSSION Table 1 shows the important network parameters PTx ( L packet + l ack ) E packet = × 1.75 + E d (15) used in the simulation study Rbit TABLE 1 Network Parameters used in the Simulationwhere E d is the decoding energy to decode a single Parameter Valuespacket and l ack is the acknowledge frame length. Path loss exponent (γ) 2 Number of nodes in the network (N) 289Since Forward Error Correction (FEC) technique is Node spatial Density (ρs) 10-7not used here, decoding energy and trailer length bothare assumed zero [11]. Thus the energy to Packet arrival rate at each node (λt) 0.5 pck/s Career frequency (fc) 2.4 GHzcommunicate a single packet is: Noise figure (F) 6dB Room Temperature (T0) 300k PTx (l h + l m + l ack ) E packet = × 1.75 (16) Transmission Power (PTx) 1mW, 100mW Rbit Fig. 3 shows route BER as a function of node spatial The minimum energy required to communicate a density. It is observed that BERroute performancepacket is the energy required to transmit and receive improves with the increase in node spatial density.the message bits ( lm ) only. This minimum energy can However it is seen that beyond a certain node densitybe derived by the following expression: the BERroute does not change with further increase in node spatial density and a floor in BER route, as denoted PTx l m by BERfloor appears. The desired signal power as well as E min = × 1.75 (17) Rbit the inter-node interference increases with increase in node density. As a result we obtain the BER floor. This is Now we consider an infinite ARQ scheme where a expected because, increasing node spatial densitydata packet is retransmitted infinitely until it is beyond a certain limit no longer improves the signal toreceived successfully. The average number of noise ratio (SNR), as the interfering nodes also becomeretransmission, n retrans can be expressed by the close enough to the receiver. It is seen that BER route performance degrades in shadowed channel. This isfollowing expression because in shadowed environment signal to interference ∝ noise ratio (SNIR) degrades. For a data rate of 5 Mbps n retrans = ∑ PER i =1 i link and node spatial density of 1.4 × 10−4 BERroute is 6.2 × 10 −4 without shadowing while it is 3.7 × 10−2 in shadowed 1 channel of standard deviation σ = 8 dB ≅ 1 (18) −1 PERlinkwhere PERlink is the packet error rate in a single hop.So, the energy spent to successfully deliver a packet isgiven by ARQ PTx (l h + l m + l ack ) E packet = × 1.75 × (1 + n retrans ) (19) Rbit Thus the total energy spent to successfully deliver apacket from source to destination is give by Fig 3: Route BER as a function of node spatial density with and ARQ without the presence of shadowing for two different level of E route = n hop × E packet (20) shadowing. 42© 2010 ACEEEDOI: 01.ijcom.01.02.08
  5. 5. ACEEE International Journal on Communication, Vol 1, No. 2, July 2010under same data rate and node spatial density. It is packet size from energy efficiency perspective [11-12].also observed that with increase in severity of Thus there exists an optimal packet size for a particularshadowing, i.e., as σ increases from 5 dB to 8 dB, network condition. It is seen that the energy efficiencyBERroute performance degrades. It is also seen that shows a steep drop for message lengths smaller than theBERroute degrades as bit rate decreases. This is due to optimal length. This behavior can be attributed to theincrease in vulnerable interval with decrease of bit rate higher overhead and start-up energy consumption of[7]. As a result, transmission probability of theinterfering nodes increases.In Fig. 4, we compare the smalleroptimal common transmit power as a function of bitrate in the presence of shadowing and withoutconsidering shadowing. Optimal common transmitpower is the minimum power sufficient to preservenetwork connectivity while satisfying a predefinedBER threshold (BERth) value at the end of a multihoproute. Here variation Fig. 5: Efficiency as a function of packet length for different node spatial density and shadowing environment. packets [11]. On the other hand, for message length larger than the optimal length, the drop in energy efficiency is much slower due to increase in average retransmission. With the increase in packet length the Fig 4: Optimal Power as a function of Bit Rate for different BER threshold at a node spatial density of 10-6. vulnerable interval increases and the probability of transmission of an interfering node becomes high. It isof optimal transmit power with bit rate is shown for observed that efficiency degrades with the increase invarious values of BERth. It is seen that optimal severity of shadowing. This is because with increase intransmit power increases as the data rate increases. It severity of shadowing the SNIR degrades. This resultsis mainly because of the high thermal noise introduced in more number of retransmissions for successfuldue to high bit rate. It is observed that optimal delivery of a packet. Thus the energy spent per packettransmit power required to transmit a data packet in increases, which reduces energy efficiency. Further thethe presence of shadowing is higher than the power optimum packet length decreases with the increase inrequired in absence of shadowing for same data rate. severity of shadowing. For example as shadow fadingFor example at a bit rate of 5 Mbps and BER th =10-2, increases from σ= 6dB to σ=8dB, size of optimalthe optimal transmit power is 5.3 mW without packet reduces from 240 bit to 150 bit for a node spatialshadowing. However for the same BER th and data rate density of 10-5. It is also seen that energy efficiencythe optimal transmit power is increased to 22.1 mW in improves with increase in node spatial density. Furtherpresence of shadowing with standard deviation 4 dB. the optimal packet length increases with increase inAs shadowing increases, in order to maintain node spatial density. Any packet size except optimalconnectivity with same level of BER th, transmit power size deteriorates the efficiency.also needs to be increased so as to compensate the Fig. 6 shows the comparison of energy requirementhigher level of shadowing. It is seen from Fig. 4 that for successfully transmission of a file of size 122 Kbytethere is a critical data rate, below which the desired in two cases – (i) a fixed packet length and (ii) anBERth cannot be satisfied for any level of transmit optimal packet size. In the first case we evaluate energypower. The critical bit rate occurs at the point where for two different typical fixed packet lengths i.e. 1000the BERfloor for that particular data rate becomes bit and 500 bit. In the second case we use optimalhigher than the desired BER th. Further it is seen that packet length corresponding to that particular nodecritical bit rate increases with the increase in severity spatial density as obtained from Fig. 5. It is observedof shadowing. that use of optimum packet size reduces the energy Fig. 5 shows the energy efficiency as a function of requirement significantly. In case of optimum packetpacket length for various level of shadowing and node size, less number of retransmissions is required asspatial density. It is seen that efficiency attains a peak compared to a fixed packet size case. For example, at avalue at a given packet size. The message length node spatial density of 4.3 × 10 −5 and bit rate of 5corresponding to maximum efficiency is optimal Mbps, the use of optimum packet size reduces energy 43© 2010 ACEEEDOI: 01.ijcom.01.02.08
  6. 6. ACEEE International Journal on Communication, Vol 1, No. 2, July 2010requirement by an amount of 13.5% as compared to a REFERENCEfixed packet size of 1000 bit. The optimal packet size [1] Sooksan Panichpapiboon, Gianluigi Ferrari,and Ozan K.shows excellent performance in the low node spatial Tonguz, “Optimal Transmit Power in Wireless Sensordensity region. For example, at node spatial density of Networks” IEEE Transaction on Mobile Computing, 4 × 10 −7 the required energy is 40 mJ for optimum Vol. 5, No. 10, October 2006, pp. 1432-1447. [2] C. Bettstetter and J. Zangl, “How to Achieve apacket length based transmission, while it is 90 mJ for Connected Ad Hoc Network with Homogeneous Rangea transmission based on a fixed packet length of 500 Assignment: An Analytical Study with Consideration ofbit. Border Effects,” Proc. IEEE Int’l Workshop Mobile and Wireless Comm. Network, pp. 125-129, Sept. 2002. [3] C.-C. Tseng and K.-C. Chen, “Power Efficient Topology Control in Wireless Ad Hoc Networks,” Proc. IEEE Wireless Comm. and Networking Conf. (WCNC), vol. 1, pp. 610-615, Mar. 2004. [4] S. Narayanaswamy, V. Kawadia, R.S. Sreenivas, and P.R. Kumar, “Power Control in Ad-Hoc Networks: Theory, Architecture, Algorithm and Implementation of the COMPOW Protocol,” Proc. European Wireless 2002 Next Generation Wireless Networks: Technologies, Protocols, Services, and Applications, pp. 156-162, Feb. 2002. [5] Q. Dai and J. Wu, “Computation of Minimal Uniform Transmission Power in Ad Hoc Wireless Networks,” Proc. IEEE Int’l Conf. Distributed Computing Systems Workshops (ICDCS), pp. 680-684, May 2003. [6] C.E. Perkins, Ad Hoc Networking, Addison-Wesley, Fig. 6: Energy consumption as a function of node spatial density 2001.using fixed and optimal packet size at a bit rate of 5 Mbps and σ = 4 dB. [7] G. Ferrari and O.K. Tonguz, “Performance of Ad Hoc Wireless Networks with Aloha and PR-CSMA MAC Protocols,” Proc. IEEE Global Telecomm. Conf. IV. CONCLUSION (GLOBECOM), pp. 2824-2829, Dec. 2003. In this paper we have investigated the optimal [8] Kezhu Hong and Yingbo Hua, "Throughput of Largetransmit power and optimal packet length for wireless Wireless Networks on Square, Hexagonal and Triangularsensor networks in lognormal shadowed channel. It is Grids", Fourth IEEE Workshop on Sensor Array andobserved that optimal transmit power required to Multichannel Processing 2006, pp 461-465, 12-14 July 2006.maintain network connectivity satisfying a given [9] Andrea Goldsmith, Wireless Communications, Cambridgemaximum acceptable BER threshold value in the University Press, 2005.presence of shadowing is more as compared to that in [10] B. Sklar, “Rayleigh Fading Channels in Mobile Digitalabsence of shadowing. It is also seen that optimal Communication Systems Part I: Characterization,” IEEEtransmit power increases with increase in severity of Communication Magazine, pp. 90-100, July 2003.shadowing. The BER performance degrades with [11] Sankarasubramaniam Y., Akyildiz I.F. and Mclaughlinincrease in severity of shadowing. An optimum packet S.W., "Energy efficiency based packet size optimizationlength, which maximizes energy efficiency, is also in wireless sensor networks", Proceedings of the Firstderived. The optimum packet size decreases with the IEEE International Workshop on Sensor Network Protocols and Applications 2003, pp 1-8, 2003.increase in severity of shadowing. Further it is seen [12] Kleinschmidt J.H., Borelli, W.C. and Pellenz, M.E, "Anthat optimal packet length increases with the increase Analytical Model for Energy Efficiency of Error Controlin node spatial density. It is also seen that transmission Schemes in Sensor Networks", ICC 07. IEEEbased on optimum packet saves energy significantly International Conference on Communications 2007, pp.and enhances network lifetime. Further energy 3895 - 3900, 24-28 June 2007.efficiency degrades with the increase in severity ofshadow fading and decrease of node spatial density.Thus shadowing has significant impact on choice ofoptimal power and optimal packet size whichenhances lifetime of network. 44© 2010 ACEEEDOI: 01.ijcom.01.02.08