Distributed Beamforming with Uniform Circular Array Formation in Wireless Sensor Networks

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1 Distributed Beamforming with Uniform Circular Array Formation in Wireless Sensor Networks Chen How Wong, Zhan Wei Siew, Aroland Kiring, Hoe Tung Yew, Kenneth Tze Kin Teo Modelling, Simulation & Computing Laboratory, Material & Mineral Research Unit School of Engineering and Information Technology Universiti Malaysia Sabah Kota Kinabalu, Malaysia Abstract Collaborative beamforming (CB) has been introduced in the context of wireless sensor networks (WSNs) to enhance the communication range and energy efficiency of the networks. CB relies on a subset of nodes in the network which acts as a virtual antenna array to collectively transmit a common signal to an intended location. Due to random deployment of the sensor nodes in the networks, proper selection of participating nodes to perform distributed CB is vital to achieve better array pattern synthesis. Different topologies of the participating nodes will produce different impact on transmission gains. In this paper, a node selection method based on uniform circular array formation is presented. The analysis is carried out with the assumption that the sensor nodes are randomly distributed with uniform distribution. Statistical evaluation on the average beampattern is carried out to demonstrate the behavior and properties of the mainlobe, and sidelobe level (SLL) for the selected scheme. Keywords collaborative beamforming; circular array; wireless sensor networks I. INTRODUCTION Wireless sensor networks (WSNs) are networks of distributed sensor nodes that have sensing, processing and communication capabilities [], [2]. They are deployed for continuous data collecting in numerous applications such as habitat monitoring, volcanic monitoring, and natural disaster detection [3], [4]. However, in order to realize the typical applications of the WSNs, one major problem required to cope with is to establish communication link between batterypowered sensor nodes and the intended location or access point which might be located far outside the transmission range of a single node. To improve energy efficiency of the networks, network protocol such as low energy adaptive clustering hierarchy (LEACH) is proposed [5], [6]. Efforts to enhance LEACH using Fuzzy [7], [8] and Adaptive Particle Swarm Optimization algorithm [9] which has shown prominent results in prolonging the lifetime of the sensor nodes. However, those efforts only consider energy efficiency as primary constraints. Recently, collaborative beamforming (CB) has been proposed to tackle both energy efficiency and transmission range problem []. In CB, a subset of selected nodes transmit proper weighted common signal to an intended location. The transmitted signals are combined in the direction of the intended location for further processing. As a result, it does not only increase transmission range as compared with a single node but also improve energy efficiency by spreading the required transmission energy over other nodes []. Several efforts have been done to investigate the feasibility of CB in WSNs context [2]. In order to perform CB in WSNs, the prerequisite step is achieving phase synchronization among nodes. The main reason is because each node has independent local oscillator. Several synchronization techniques are proposed in [], [2] which have shown the practicability of CB. Investigation on the resultant beampattern is crucial to understand whether CB achieves reasonable beampattern with sharp beamwidth. Due to random deployment of the sensor nodes in the networks, selection of participating nodes that perform CB is the key factor that determines the characteristic of the beampattern. By using random array theory developed by [3], analysis is carried out by [4] which consider sensor nodes are uniformly distributed in the networks. The analysis is extended to Gaussian distribution by [5]. Node selection method based on uniform linear array (ULA) has been proposed by [6]. Solution based on ULA is optimized using genetic algorithm by [7] and showed reduction in sidelobe level (SLL). Motivated by [6], this paper investigates a node selection scheme based on uniform circular array (UCA). The optimal participating nodes are selected based on circular line least square fitting technique. This paper is organized as follow. In section II, the model of the WSNs and the geometric of UCA are presented. The node selection method based on UCA sensor nodes is provided in section III. In section IV, the beampattern evaluation metric is explained. The simulation results and discussions are presented in section V. Lastly, the paper is concluded in section VI. II. SYSTEM MODEL A. Sensor Networks Model The geometrical coordination for a cluster of randomly distributed nodes and the intended location is shown in Fig /2/$3. 22 IEEE 75

2 z Intended location z O θ o r (θ,φ ) r (θ 2,φ 2) r (θ3,φ 3) r θ y x Sensor node Cluster head φ y x r (θ i,φ i) φ φ o O Figure. Geometrical coordination for a cluster of sensor nodes and intended location. Without loss of generality, the sensor nodes are assumed to be deployed in the x-y plane of the networks. Few assumptions are made in the WSNs in order to simplify the analysis. The assumptions are following: The locations of nodes are randomly distributed in the networks following a uniform distribution. Each of the node location is known. Intended location and sensor nodes are stationary in the networks. The intended location point is located in far-field. All sensor nodes have equal capabilities and each sensor node has a single isotropic antenna. Data sharing is permitted among nodes in a cluster networks. Mutual coupling effects between sensor nodes are negligible as they are alienated enough. There is no reflection and scattering effect on the signal. In addition, the sensor nodes are assumed have been prefectly synchronized in phase by either technique in [2], [3]. This is to avoid any phase and frequency offset which will significantly affect the beampattern behavior. B. Geometric of Uniform Circular array UCA has been widely implemented in many applications such as wireless communication, radar system and sonar system. One of the advantages for UCA as compare to the ULA is it works well in all azimuthally directions and no major lobe on the opposite direction. In UCA, sensor nodes are placed on the x-y plane. The number of sensor nodes, N, located in a circular ring with radius of R and the spacing between nodes is d as illustrated in Fig. 2. The intended location is described in spherical coordinate (r o, θ o, φ o ). The elevation angle and azimuth angle correspond to θ [, ] and φ [-, ] respectively. The ith node locations is represented by polar coordinate (r i,φ i ) The array factor of the N sensor nodes is expressed in (). AF( N ( jkr(cos( θ φi ) + βi ) θ, = Iie () i= where Figure 2. Uniform circular array. kr = N d i i= (2) φ = 2 π ( i + ) N (3) i / βi kr cos( θo φi ) = (4) The amplitude excitation is represented by I i with ith node in the array. The internodes spacing is represented by d i from node ith to ith+. k=2 /,is the wave number, and is the wavelength of the transmission frequency. The normalized beampattern of UCA can be described by (5). AF( θ, G ( θ, = (5) 2 max AF( θ, III. UNIFORM CIRCULAR ARRAY BASED NODE SELECTION UCA based node selection scheme is intended to select sensor nodes following the geometric shape of UCA, thus, the beampattern approximately behaves as the UCA. In order to perform CB in WSNs, the selected participating sensor nodes must share the transmission data among each other within the active cluster. A node which acts as cluster node must be elected to communicate with the surrounding nodes before CB can be performed. The best cluster head is assumed to be found in the networks. To simplify the analysis, the location of the cluster head is assumed to be located in the center of the active cluster. The required total number of sensor nodes, N must first be decided before to construct the virtual UCA in the networks /2/$3. 22 IEEE 76

3 This number is usually decided based on the receive power requirement at the intended location []. The virtual UCA is then constructed based on the total number of sensor nodes. Each of the sensor nodes is located uniformly on the circle with radius of R. To avoid occurrence of grating lobe, the internodes spacing for the virtual UCA should equal or less than half of the transmission wavelength. This constrain is described in (6). 2 R ( i + ) / 2 π N λ (6) The nodes location V(r i,φ i ) of the virtual UCA act as the reference of the scheme to select the participating nodes. The closest node C(r i,φ i ) will be compared with the virtual UCA nodes to determine whether it is among the participating nodes to perform CB. In this case, condition in (7) must be fulfilled by the nodes in order to be selected. C r, φ ) = minv ( r, φ ) S( r, φ ) (7) ( i i i i i i where V(r i,φ i )-S(r i,φ i ) is the Euclidean distance between the virtual node and the neighbor node inside the active cluster. The flowchart of the UCA based node selection scheme is illustrated in Fig. 3. IV. BEAMPATTERN PROPERTIES EVALUATION METRIC The UCA based node selection method has to be evaluated in order to investigate the beampattern behavior. It is essential to compare the beampattern performance between both virtual UCA and the node selection method. A. Average beampattern A single realization of CB using UCA based node selection method does not provide insight into the effect due to randomly distribution of sensor nodes in the networks. To inspect this effect, averaging of the beampattern selection method over large samples of presumable realizations is required. The average beampattern is defined in (8). { G( θ, } P av = E (8) Where E{.} denotes the statistical expectation value of the large samples of presumable realizations. B. Standard Deviation of the Average Beampattern Standard deviation is required to investigate the variation of CB beampattern for all presumable realizations from the average. A low standard deviation means the beampattern tend to be close to average beampattern, on the other hand, high standard deviation represents a large spread of beampattern. The standard deviation of the average beampattern is defined in (9). Desired number of nodes in the UCA array s = n n k= 2 (( G( θ, ) ) (9) k P av Construct the virtual UCA array Comparing virtual nodes and neighbor nodes distance Where n denotes the sample size of the presumable realization and k is represent the sample number. C. Sidelobe Region Peak In practice, it is vital to reduce the beampattern levels in the sidelobe region while achieving certain mainlobe beamwidth. The statistical distribution of the maxima sidelobe peak of the CB presumable realization should be considered in the analysis. The definition of the sidelobe region is referred in (). Closest nodes? End yes no Γ = max G( θ, () ( θ, φ ) sidelobe region By taking out the sidelobe peak over a large number of beampattern samples based on the node selected method, the complementary cumulative distribution function (CCDF) can be computed. The CCFF of the maximum sidelobe peak can provide the probability of a particular realization which has sidelobe peak below a normalized threshold, P o as in (). Figure 3. Uniform circular array based node selection method. P out Pr( Γ > P) = () /2/$3. 22 IEEE 77

4 V. SIMULATION RESULTS AND DISCUSSION The statistical properties of the beampattern based on UCA node selection method can be investigated by simulation using different parameters on the WSNs model. Table I summarizes the simulation parameter of several cases. Morte Carlo simulations were conducted with trials for each of the cases. The evaluation metric in section IV is used to investigate the beampattern properties. To analyze the effect of the node selection method on the total CB nodes number, simulation result of case has been compared in term of average beampattern, standard deviation of the average beampattern and sidelobe region peak. The results are shown in Fig. 4, Fig. 5 and Fig. 6. The average beampattern in Fig. 4 shows that for both case (a) and (b) are closely follows the beampattern of their respective virtual UCA in the mainlobe region. For sidelobe region, the value oscillates similarly to their respective virtual UCA but with lower level. This indicates virtual UCA has high probability of obtaining high SLL at the angle corresponding to the local maxima of the average beampattern. In Fig. 5, standard deviation of the average beampattern for both case (a) and (b) is zero at angle φ=. Value of standard deviation increase and oscillate akin to their virtual UCA as the angle points away from the intended direction. This indicates each sample of beampattern is deterministic and approximated closely to the mainlobe of the average beampattern. This implies that the directivity and 3dB beamwidth of each sample does not spread away from the average beampattern. By looking at Fig. 4 and Fig. 5, the SLL of case (b) is much lower compare to case (a). This implies that increase number of CB nodes will reduce in SLL of the average beampattern. The CCDF of the sidelobe region peak is shown in Fig. 6. For case (a), the probability of highest SLL with - db is. and achieving similar sidelobe level as the virtual UCA is.28 at -3.5 db. For case (b), the probability of highest SLL with -4.3 db is. and achieving similar sidelobe level as the virtual UCA is.7 at -7.9 db. This shows a significant reduction in SLL by increasing the number of CB nodes. TABLE I. Sensor deploment area (m 2 ) Total CB nodes number Cluster radius, m Frequency (MHz) Virtual UCA radius, m Total node in the network SIMULATION PARAMETER FOR DIFFERENT WSNS CASES Case Case 2 (a) (b) (a) (b) Power Gain Power Gain CCDF Case (a) Ideal UCA (a) Case (b) Ideal UCA (b) Figure 4. Average beampattern for case. case (a) case (b) 3dB beamwidth Figure 5. Standard deviation of the average beampattern for case case (a) case (b) sidelobe peak (a) sidelobe peak (b) X: Y:.72 X: Y: Sidelobe Peak Level (db) Figure 6. CCDF of Sidelobe Peak Lvevl for case /2/$3. 22 IEEE 78

5 To analyze the effect of the node selection method on the virtual UCA radius, simulation result of case 2 has been compared in terms of average beampattern, standard deviation of the average beampattern and sidelobe region peak. In Fig. 7 and Fig. 8, both results have similar properties as presented in Fig. 4 and Fig. 5. Therefore, it again verifies the previous analysis that the directivity and 3dB beamwidth of each sample closely resemble the average beampattern. By observing Fig. 7 and Fig. 8, case 2(b) has narrow 3dB beamwidth compare to case 2(a). However, SLL of case 2(b) is much higher compared to case 2(a). This implies that an increase in virtual radius will produce narrow beamwidth with trade off in increase of SLL. The CCDF of the sidelobe region peak is shown in Fig. 9. For case 2(a), the probability of highest SLL with -2.6 db is. and achieving similar sidelobe level as the virtual UCA is.86 at -3.9 db. For case 2(b), the probability of highest SLL with -4.3 db is. and it achieves similar sidelobe level as the virtual UCA is.7 at db. This shows significant increase in SLL as the virtual radius of the UCA is increased. Power Gain (db), Power Gain case 2(a) Ideal UCA 2(a) case 2(b) Ideal UCA 2(b) Figure 7. Average beampattern for case 2. case 2(a) 3dB beamwidth 2(a) case 2(b) 3dB beamwidth 2(b) Figure 8. Standard deviation of the average beampattern for case 2. CCDF - -2 case 2(a) case 2(b) sidelobe 2(a) sidelobe 2(b) X: Y:.77 X: Y: Sidelobe Peak Level (db) Figure 9. CCDF of Sidelobe Peak Level for case 2. VI. CONCLUSION Statistic evaluations have been conducted on the UCA based node selection method. Based on the analysis, by increasing the radius of virtual UCA, the beamwidth of the beampattern can be significantly reduced with an increase in SLL. By simulating the CCDF of the sidelobe region peak, the virtual UCA formation in the distributed WSNs can be analyzed. Hence, it can serve as a tool to analyze the design of virtual UCA for the node selection method. For future work, using sensor array reference model of different topologies or formation might achieve better performance of CB. ACKNOWLEDGMENT The authors would like to acknowledge the financial assistance of the Universiti Malaysia Sabah Research Grant Scheme, grant no. SLB4-TK-/2, and Universiti Malaysia Sabah Postgraduate Scholarship Scheme. REFERENCES [] I.F. Akyildiz, S. Weilian, Y. Sankarasubramaniam, and E. Cayirci, A survey on sensor networks, IEEE, Communications Surveys & Tutorials,vol 4, no 4, pp. 2 4, 22, doi:.9/mcom [2] R.V. Kulkarni, A. Forster, and G.K. Venayagamoorthy, Computational intelligence in wireless sensor networks: A Survey, IEEE, Communications Surveys & Tutorials, vol 3, no., pp , 2, doi:.9/surv [3] A. Mainwaring, J. Polastre, R. Szewczyk, D. Culler, and J. Anderson, Wireless sensor networks for habitat monitoring, Proc. ACM International Workshop on Wireless Sensor Networks and Applications, pp , 22, doi:.45/ [4] G. Werner-Allen, J. Johnson, M. Ruiz, J. Lees, and M. Welsh, Monitoring volcanic eruptions with a wireless sensor network, Proc. 2nd European Workshop on Wireless Sensor Networks, pp. 8-2, 25, doi:.9/ewsn [5] W. Heinzelman, A. Chandrakasan, and H. Balakrishnan, Energyefficient communication protocol for wireless microsensor networks, Proc. 33rd Annual Hawaii International Conference on System Sciences, pp.35-34, 2, doi:.9/hicss /2/$3. 22 IEEE 79

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