Energy Efficient Virtual MIMO-based Cooperative Communications for Wireless Sensor Networks

Transcription

1 Energy Efficient Virtual MIMO-base Cooperative Communications for Wireless Sensor Networks Suharman K. Jayaweera Department of Electrical an Computer Engineering Wichita State University, Wichita, KS, 67226, USA. Abstract An energy-efficient virtual multiple-input multipleoutput MIMO)-base communications architecture is propose for energy-limite, istribute an cooperative wireless sensor networks. Assuming a space-time block coing SBC) base MIMO system, the energy an elay efficiencies of the propose MIMO-base communications scheme are erive using analytic techniques. he efficiency of the propose MIMO-base communication system is relate to the system an channel propagation parameters. hese investigations show that MIMO techniques can be mae to provie significant energy savings an elay efficiencies at the same time with juicious choice of system parameters at the esign level. Further, the epenence of energy efficiency of propose MIMO-base wireless sensor network on faing coherence time an the require amount of training is analyze. hese results justify the application of propose cooperative MIMO-base scheme in wireless sensor networks even after allowing for aitional training overheas. I. INRODUCION Although main power consumption term in a traitional wireless systems is ue to the energy require for actual transmissions, this may not be the case in an energy-limite wireless sensor network. In fact, in some cases it is the circuit energy neee for receiver an transmitter processing that is ominant. hus, in esigning energy efficient techniques for such sensor networks one shoul consier both circuit an transmission power consumption terms. Multiple-input-multiple-output MIMO), or multiple antenna, communication is one of the techniques that has gaine consierable importance in wireless systems uring recent years. However, a rawback of MIMO techniques is that they coul require complex transceiver circuitry an large amount of signal processing power that may lea to large power consumptions at the circuit level. hus, in evaluating the applicability of MIMO techniques to energy-limite wireless sensor networks, we nee to take into account the circuit power consumption as well as the transmit power consumption. Moreover, physically implementing multiple-transmit or receiver antennas on a small, energy-limite sensor might not be realistic. his makes irect application of ual antenna MIMO techniques in wireless sensor networks impractical. However, as reporte in [] it is possible to implement MIMO techniques in wireless sensor networks without physically having multiple antennas at the sensor noes via cooperative communications techniques. As reporte in [] an [2] such istribute MIMO techniques can offer consierable energy savings in cooperative wireless sensor networks even after allowing for aitional circuit power, communications an training overheas. In this paper we propose a new virtual MIMO-base cooperative communications architecture for energy-limite wireless sensor networks. In this istribute MIMO technique, virtual multiple transmit antenna arrays are create out of singleantenna sensor noes via local transmissions. We evelop techniques for evaluating the energy an elay efficiencies of the propose virtual MIMO-base sensor network. he epenance of these energy an elay efficiencies on system an propagation parameters such as transmission istance, constellation size transmission rate) an channel path loss parameter is investigate. Our numerical results suggest that with juicious system esign, propose virtual MIMO-base communications scheme can provie significant energy savings an elay efficiencies in wireless sensor networks. While our work extens the work in [], it has several novel concepts an refinements. First, we moify the basic virtual MIMO concept to suit to a specific sensor network architecture consisting of a set of ata collection noes an a ata gathering noe followe by analytical energy efficiency evaluation. Secon, we introuce several realistic moifications to the simplifie energy analysis technique evelope in [] by taking into account extra training overheas an the impact of the channel path loss parameter. his presentation is organize as follows: In Section II we present the propose virtual MIMO-base cooperative communications scheme for a wireless sensor network. Section III analyzes the energy an elay efficiencies of the propose virtual MIMO communications base wireless sensor networks compare to that of a traitional SISO communications base sensor network. Section III also etails the optimization

2 process neee in orer to achieve these energy efficiencies in a virtual MIMO-base system. In Section IV numerical examples are provie for comparing these energy an elay values with those of traitional wireless sensor networks employing SISO-base communications schemes. Finally, in Section V we give some concluing remarks. II. VIRUAL MIMO COMMUNICAIONS ARCHIECURE FOR COOPERAIVE WIRELESS SENSOR NEWORKS We consier a narrow-ban, flat faing, communication link connecting two wireless sensor noes. As in [], we will omit the energy consumption in baseban signal processing blocks an will assume uncoe communication. In all numerical results we assume a flat Rayleigh faing moel unless state otherwise. he MIMO technique that we consier in this paper is the Alamouti scheme or space-time block coes that provie its generalization to more than 2 transmit antennas [3]. A virtual V-BLAS base scheme for sensor networks was given in [4]. he sensor noes in a wireless sensor network can be of small imensions. hus, it may not be realistic for these sensor noes to have multiple antennas. However, it is possible to implement a virtual MIMO communication architecture in such energy-limite, istribute wireless sensor networks via sensor cooperation, as reporte in []. he energy efficiency analysis provie in [], base on a particular system moel showe clearly the possibility of applying MIMO techniques to istribute wireless sensor networks an the potential energy savings. Below we propose a new wireless sensor system moel that is relevant in a number of wireless sensor network applications with cooperative processing. Fig.. Noes N m m Noes N m Noes N m Noes N 2 N R 3 Data Gathering Noe A Virtual MIMO Communications Base Wireless Sensor Network. A common scenario in istribute wireless sensor networks is that of a lea-sensor an a set of ata collection noes see Fig. ). For example, in [5] such a system moel was employe for investigating the energy efficiency of istribute coing an signal processing. his moel consists of a large collection of low-en ata collection sensors that are connecte over a wireless link with a high-en ata gathering noe DGN) which may act as a lea-sensor or a fusion center. In this type of sensor networks, the ata collection sensors are typically subject to strict energy constraints while DGN is not. he ata collection noes collect ata on a physical phenomenon of interest. his physical ata is communicate to the DGN which performs require joint an cooperative processing over a wireless link. In such a wireless sensor network moel, the propose virtual MIMO-base communications can be achieve as follows: Suppose a set of ata collection noes have ata to be sent to the DGN. Each of these sensors which are assume to be close to each other broacasts their ata to the others in the set using a time-ivision multiple-access scheme. his step is known as the local communications at the transmitter sie. At the en of this step each of the ata collection noes have ata from all the sensor noes. his enables space-time block coing assuming each ata collection noe correspons to a istinct transmit antenna element in a centralize multiple transmit antenna system. Once the spacetime coing is performe each sensor noe transmits the space-time coe symbols corresponing to a specific transmit antenna element to the DGN. his step is known as the longhaul communications. he DGN is assume to be ifferent from the low-en ata collection noes. First, it oes not have any energy constraints attache to it or compare to the ata collection noes, the DGN has much longer battery life). Secon, this sensor can be of larger physical imensions thus enabling it to have multiple receiver antenna capability. his allows realization of true MIMO capability with only the transmitter sie local communications. his moel is one of the simplest of this type. here are several ways in which one can generalize this type of a cooperative MIMO-base wireless sensor network. For example, a network may consists of a number of ata gathering noes as oppose to a single ata gathering noe that is assume here. In such a system there are ifferent ways to realize MIMObase energy-efficient communications. Another possibility is that not all ata collection noes cooperate as one virtual transmit antenna system. In some istribute wireless sensor networks there might be a large number of ata collection sensors scattere over a large area. It may be more convenient an efficient) to esign the system so that the sensor noes that are close to each other will group together to create a virtual multiple-transmit antenna system. hus, in a given wireless sensor network we may have a collection of such

3 virtual multiple-transmit antenna systems as epicte in Fig.. All these groups will be communicating with either a single or multiple DGN s. In our energy efficiency analysis below, however, we focus on a simple moel where we have only one DGN an all ata-collection sensors form a single virtual transmit antenna array. Since wireless channels can be subject to faing it is realistic to assume that the long-haul communications in step two of our architecture is over a faing channel. However, if local communications at the ata collection noes are over a very short istance, then the channel in this situation may either be best moelle by an AWGN or a faing channel. We will consier both these possibilities for local communications among ata collection noes. III. ENERGY AND DELAY EFFICIENCY OF HE PROPOSED VIRUAL MIMO COMMUNICAIONS ARCHIECURE Energy consumption of the propose cooperative MIMObase scheme consist of two terms: the energy require for local communication among ata collection sensors an the energy require for the long-haul communications from ata collection noes to the DGN. We assume that there are N number of ata collection sensors an the DGN is equippe with N R number of receiver antenna elements N R can be unity). he average energy per bit per sensor noe for local communications is enote by Ē i, for i =,..., N. Let us enote by Ēl the average energy per bit for the long-haul communication. If we assume that each sensor noe has L i number of bits to transmit to the DGN then the total energy require in orer to communicate the ata from all noes to the DGN is given by E MIMO = N L i Ēi i= + Ēl N L i. ) We assume that the maximum separation between two ata collection sensors is m meters an that the constellation size for local communications is optimize for this worst-case istance []. he optimize constellation size use by the i- th sensor noe for local communications is enote by b i. Similarly, let us assume that the long-haul communications istance is meters note that m an thus we assume that this istance is the same for all ata collection noes) an the constellation size for long-haul communications b l is optimize for this transmission istance. As iscusse in [], [6], the total power consumption along the signal path can be ivie into two main components: the power consumption of all the power amplifiers P P A an the power consumption of all other circuit blocks P C. During the local communications of sensor i, for i =,..., N, other N sensor noes all act as receivers. hus, the i= circuit energy consumption in this case consists of that of one transmitter circuit an that of N receiver circuits: P i,c P DAC + P mix + P filt + P synth ) + N ) P LNA +P mix + P IF A + P filr + P ADC + P synth ).2) where P DAC, P mix, P filt, P synth, P LNA, P IF A, P filr an P ADC are the power consumption values for the D/A converter DAC), the mixer, the active filters at the transmitter sie, the frequency synthesizer, the low noise amplifier LNA), the intermeiate frequency amplifier IFA), the active filters at the receiver sie an the A/D converter ADC), respectively. he power consumption values P DAC, P ADC an P IF A are evaluate base on the moels evelope in [6]. Assuming that the power consume by the power amplifiers is linearly epenent on the transmit power, the power consumption of the power amplifiers uring local communications Pi,P A can be approximate as, Pi,P A = + αi ) P i,out for i =,..., N 3) where αi = ξi /η with η being the rain efficiency of the RF power amplifier an ξi being the peak-to-average ratio PAR) for local communications that epens on the moulation scheme an the constellation size. hroughout this paper we assume M-QAM systems, so that ξi = 3 M 2 i Mi + Mi [7] with Mi = 2 b i. he transmit power Pi,out in 3) can be calculate accoring to the link buget relationship P i,out = 4π)2 κ mm l N f G t G r λ 2 Ē i,br b 4) where m is the local transmission istance, κ is the path loss parameter, G t an G r are the transmitter an receiver antenna gains respectively, λ is the carrier wavelength, M l is the link margin compensating the harware process variations an other aitive backgroun noise or interference, N f is the receiver noise figure, Ēi,b is the average energy per bit require for a given bit-error-rate BER) specification an R b is the system bit rate. Note that the receiver noise figure N f is given by N f = Nr N o where N r is the power spectral ensity PSD) of the total effective noise at the receiver input an N o is the single-sie thermal noise PSD at the room temperature []. In case of an AWGN local channel we have, for i =,..., N, M i ) 2 N o Ē i,b = 3b i Q 4 P b b i 2 b i ),5)

4 where P b is the target average bit error rate. Note that 5) is vali an exact) when b i is even. When b i is o we may obtain an ) approximate Ē i,b value by ropping the term in the enominator of the argument of 2 b i inverse Q-function in 5). Similarly, when the local channel is Rayleigh, we have, for i =,..., N, Ē i,b = 2 M i ) N o 3b i 2 Pb b i 2 b i ) 2 he proper operation of the Alamouti scheme requires perfect channel state information CSI) at the receiver which results in the nee for training. he results in [8] suggest that in general we nee the number of training symbols greater than or equal to the number of transmit antennas if both training an ata symbols were to use the same transmit energy. In a practical system the require number of training bits can be a function of the operating SNR an thus coul be much higher than this minimum require value. In orer to incorporate this extra energy term, suppose that the block size is equal to F symbols an in each block we inclue pn training symbols where we assume that p symbols are use to train each transmitter an receiver antenna pair. he effective bit rate of the system is then given by R eff b = F pn R b. 7) F If the faing coherence time is c, then the maximum block size can be about c R s symbols where R s is the symbol rate. We may obtain a best case energy consumption value by setting F = c R s. he faing coherence time can be estimate via the relationship c = 3 4f m π where the maximum Doppler shift f m is given by f m = v λ with v being the velocity. Hence, the total energy per bit Ēi require for local communications is given by Ē i Ē i = 3 µ η where R eff, i,b 4π) 2 κ m M ln f G tg rλ 2 = P i,p A +P i,c R eff, i,b ) M i 2 Mi + M i for i =,..., N : Ē i,b + P i,c b i Rs. 8) is the effective bit rate for the local communications using M-ary QAM an we have efine µ = Reff, i,b F pn F R i,b =. Note that µ specifies the energy penalty incurre ue to extra symbols neee for channel estimation. In 8) αi epens on the constellation size Mi. Since R i,b = b i R s, for a given banwith B an a symbol rate R s = B, the bit rate R i,b also epens on the constellation size Mi, however, is inepenent of Mi ). R i,b R eff, i,b the ratio Results observe in [] suggest that the key to achieving energy savings with virtual MIMO techniques in a istribute wireless sensor networks is to optimize the rate constellation size) of the communications system over the transmissions istance. Assuming an M-QAM system, this optimization results in the etermination of the constellation size M for various values of. Such rate-optimize transmission is possible when each sensor a priori has knowlege on other sensor locations. hus, in a rate-optimize sensor network each noe. transmits 6) using a constellation size Mi that minimizes the total energy per bit Ēi in 8) for each transmission istance m. Similarly, the energy per bit Ē l require for long-haul communications can be compute via Ēl = P l P A +P l c R eff,l where P l P A, P l c an R eff,l are the energy consumption in power amplifiers, energy consumption in circuits an the effective bit-rate uring long-haul communications. Since, there are N R number of receiver antenna elements at the ata gathering noe are listening while the virtual multiple transmit antenna system create by the set of N ata collection sensors is transmitting P l c N P DAC + P mix + P filt + P synth ) + P synth + N R P LNA + P mix + P IF A + P filr + P ADC ). 9) Note that in 9) we have use the fact that N R receiver antennas are co-locate at the DGN thus allowing them to share the same frequency synthesizer. he power amplifier energy consumption PP l A is given by 3) with P i,out replace by Pout, l the require transmit power for the long-haul communication. he only ifference in computing Pout l using 4) is that epening on the values of N R an N we will have ifferent values for the average energy per bit require for a specifie bit-error-rate Ēl b. For example when N = 2, the bit error rate of an M-ary QAM, Alamouti scheme base MIMO system M = 2 b ) with a square constellation is given by, for b 2, N P b l = 4 ) N R b 2 b/2 2 N N R + Ēb l /2No N N R k=0 2 k ) N N R + k + k + Ēb l /2No k 0). When b 2 is o, we will use 0) after ropping the term 2 b/2 ) as an upper-boun for the BER for b =, the M-ary QAM reuces to a BPSK system). We may compute Ē l b by inverting 0). Again, the constellation size bl for the long-haul communications is optimize in orer to minimize the total energy consumption obtaine from 9) an 0). able-i shows the optimal constellation size b for each longhaul transmission istance for a SISO an a 2 2 MIMO

5 otal Energy Consumption per Bit in mj log scale) otal Energy Consumption of 2 by 2 Virtual SBC MIMO with Rate Optimize M QAM 0 0 SISO with kappa=2, p=0 MIMO with kappa=2, p=0 SISO with kappa=2, p=0 MIMO with kappa=2, p=0 SISO with kappa=3, p=0 MIMO with kappa=3, p=0 SISO with kappa=3, p=0 MIMO with kappa=3, p=0 SISO with kappa=3.5, p=0 0 MIMO with kappa=3.5, p=0 SISO with kappa=3.5, p=0 MIMO with kappa=3.5, p=0 0 2 Energy Efficiency %) Energy Efficiency of 2 by 2 Virtaul MIMO Compare to SISO) with Rate Optimize M QAM Local channel Rayleigh faing kappa = 2, p=0 kappa = 2, p=0 kappa = 3, p=0 kappa = 3, p=0 kappa = 3.5, p=0 kappa = 3.5, p=0 kappa = 4, p=0 kappa = 4, p=0 Local channel Rayleigh faing Long haul ransmission Distance in Meters ) a) Long haul ransmission Distance in Meters ) Fig. 2. Energy Comparison of 2 2 Virtual MIMO- an SISO-base Systems with Rate Optimize M-QAM as a function of a) otal Energy per Bit b) Energy Efficiency. b) system employing the Alamouti scheme, assuming p = 0 an κ = 3. ABLE I OPIMIZED M-QAM LONG-HAUL CONSELLAION SIZES. m) b SISO b In contrast to the virtual MIMO-base scheme, the total energy require in communicating the same amount of ata by a traitional wireless sensor network base on SISO techniques will be E SISO = N L i Ēi SISO, ) where the average energy per bit Ēi SISO for the transmission from sensor noe i to DGN can be obtaine as a special case of the above long-haul istance communications with N = N R =. Note that, to be fair in our comparisons we assume that the SISO-base system also employs an optimize constellation size b SISO i for the long-haul istance. he other parameter of interest in employing cooperative MIMO-base communications in an energy-constraine wireless sensor network is the total elay encountere. In the case of traitional approach the total time require for transferring all the ata is given simply by i= N SISO L i = s b SISO i i= 2) where s B is the symbol time. Similarly, the total time require in cooperative MIMO-base approach is given by N ) N MIMO L i i= = s + L i b l. 3) b i= i When the training overhea is also taken into account the total elay values can be obtaine from 2) an 2) by replacing s with an effective symbol time eff s. Delay Efficiency %) Delay Efficiency of 2 by 2) MIMO Vs. SISO with Rate Optimize M QAM L = 20kbits, Local channel Rayleigh faing with p = 0 with p = ransmission Distance in Meters ) Fig. 3. Delay Efficiencies of Virtual 2 2 MIMO an SISO with Rate Optimize M-QAM κ = 3 an Local Channel is Rayleigh). IV. NUMERICAL RESULS In Fig. 2 we have shown the energy comparison between a sensor network using propose virtual MIMO communications an the traitional SISO as a function of long-haul transmission istance. For simplicity, Fig. 2 assumes that there are only two ata collection noes in the network an that the ata

6 gathering noe has 2 receiver antennas i.e. a network with one cluster having a 2 2 virtual MIMO architecture). While Fig. 2a shows the actual total energy values Fig. 2b shows he corresponing energy savings efine as ESISO E MIMO ). E SISO Note that in all simulations we have assume B = 0 khz, f c = 2.5 GHz, P mix = 30.3 mw, P filt = 2.5 mw, P filr = 2.5 mw, P LNA = 20 mw, P synth = 50 mw, M l = 40 B, N f = 0 B, G t G r = 5 Bi an η = 0.35, as in []. Figure 2 shows the enormous energy savings a virtual MIMO-base system can offer in a well-esigne wireless sensor network as a function of the long-haul transmission istance. For example, as can be seen from Fig. 2b, when κ = 3 an p = 0, the 2 2 MIMO system offers 50% of energy savings compare to a SISO-base system for = 4 meters. Note that the performance of virtual MIMO is worse than that of SISO for very short istances in particular for < m ). his is to be expecte ue to the local communications penalty involve in virtual MIMO implementation. If we were to take into account the extra training overhea incurre in virtual MIMO system, the same 50% of energy saving is achieve at a slightly increase long-haul transmission of = 44 for a conservative value of p = 0 training symbols per each antenna pair). hus, even with training overheas, the propose virtual MIMO architecture can improve the energyefficiency of wireless sensor networks significantly. In [], the results were base on an ieal propagation channel in which κ = 2. However, for typical wireless channels we may have 2 < κ < 5. As we observe from Fig. 2b, for more realistic vales of κ the energy savings offere by virtual MIMO compare to SISO) become even more significant. For a typical value of κ = 3.5, for instance, more than 70% of energy can be save at a mere istance of 40 by using virtual MIMO communications architecture. Another important observation from Fig. 2b is that as κ increases the reuction in energy savings ue to the training overhea penalty in virtual MIMO system ecreases. Moreover, the maximum achievable energy savings also improves as κ increases. he elay efficiency efine as SISO MIMO ) of the SISO virtual MIMO-base communications architecture is shown in Fig. 3. he elay efficiency is an important measure in comparing the performance of propose virtual MIMO scheme with that of the traitional SISO-base communications ue to the extra local communication step neee in virtual MIMO communications architecture. However, as we see from Fig. 3 there is a winow of transmission istances in which the virtual MIMO scheme outperforms the SISO-base scheme in terms of the en-to-en elay roughly 20 < < 50 for the parameters in Fig. 3). hus, in situations where both elay an energy efficiency are important it is still possible to carefully esign a sensor network so that virtual-mimo base communications architecture can provie significant performance improvement. In less elay restrictive applications however, it is possible to operate outsie the elay-efficient istance winow an achieve even higher energy efficiencies. V. CONCLUSIONS We have propose a new virtual MIMO communications architecture for energy-limite wireless sensor networks. We have provie analytical methos to obtain the energy consumption values for such virtual MIMO communications architecture base sensor networks taking into account transmission, circuit an aitional training energy requirements. Our results show that even with extra energy overhea requirements, virtual MIMO-base techniques can offer substantial energy an elay efficiencies in wireless sensor networks provie the system is esigne juiciously. hese inclue careful consieration of transmission istance requirements an rate optimization. ACKNOWLEDGMEN his research was supporte in part by Kansas NASA EP- SCoR program uner grant KUCR # FED3344/KAN3345, an in part by a National Institute of Aviation Research NIAR) fellowship. REFERENCES [] S. Cui, A. J. Golsmith, an A. Bahai, Energy-efficiency of MIMO an cooperative MIMO techniques in sensor networks, IEEE Journ. Select. Areas. Commun., vol. 22, no. 6, pp , Aug [2] S. K. Jayaweera, Energy analysis of MIMO techniques in wireless sensor networks, in 38 th Annual Conf. on Inform. Sci. an Syst. CISS 04), Princeton, NJ, Mar. 2004, also available at [3] S. M. Alamouti, A simple transmit iversity technique for wireless communications, IEEE Journ. Select. Areas. Commun., vol. 6, no. 8, pp , October 998. [4] S. K. Jayaweera, An energy-efficient virtual MIMO communications architecture base on V-BLAS processing for istribute wireless sensor networks, in First IEEE Intl. Conf. on Sensor an A-hoc Commun. an Networks SECON 2004), Santa Clara, CA, Oct. 2004, also available at [5] J. Chou, D. Petrovic, an K. Ramachanran, A istribute an aaptive signal processing approach to reucing energy consumption in sensor networks, in Proc. 2 st Annual Joint Conf. IEEE Computer an Commun. Soc., IEEE INFOCOM 2003, vol., [6] S. Cui, A. J. Golsmith, an A. Bahai, Energy constraine moulation optimization for both uncoe an coe systems, IEEE rans. Commun., 2003, submitte. [7], Energy-constraine moulation optimization for coe systems, in Proc. IEEE Globecom Conf., San Francisco, CA, USA, December [8] B. Hassibi an B. M. Hochwal, How much training is neee in multiple-antenna wireless links? IEEE rans. Inform. heory, vol. 49, no. 4, pp , Apr