ARTICLE
Year : 2010  |  Volume : 27  |  Issue : 2  |  Page : 124-137

Mobile Sensor Deployment Optimization for k-Coverage in Wireless Sensor Networks with a Limited Mobility Model

Xingzhen Bai¹, Shu Li², Juan Xu^2
1 Department of Computer Science and Technology, Tongji University, Shanghai 201804; College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, China
² Department of Computer Science and Technology, Tongji University, Shanghai 201804, China

Correspondence Address:
Xingzhen Bai
Department of Computer Science and Technology, Tongji University, Shanghai 201804; College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510
China

DOI: 10.4103/0256-4602.60166

Abstract

Sensor deployment is one of the key issues in wireless sensor networks (WSNs). An optimal placement of sensors is propitious to the maximum possible utilization of the available sensors, balancing node energy consumption, and prolonging the network lifetime. In this paper, we consider the mobile sensor deployment optimization for k-coverage of sensor networks with limited mobility. Since a mobile sensor's cost is higher than that of a static sensor, we want to allow partial sensors to move to fill the coverage holes and vacancies. Through the analysis of the node distribution of randomly deployed sensor networks, we present the density of the vacancy for k-coverage of sensor networks, and the number of mobile sensors required to move to fill the coverage holes and vacancies. Moreover, since sensor mobility consumes much more energy than sensing and communication, we restrict sensors to move in a limited mobility model, i.e., the disk-based mobility model, which can reduce the sensor moving distance greatly. In this paper, we attempt to improve k-coverage of the mobile sensor networks using the improved particle swarm optimization ­algorithm under limited mobility. Simulation results show that few mobile sensors in the disk-based mobility model can ­realize the k-coverage, which reduces the cost of the sensor networks and moving distance of mobile sensors.

Keywords: k-coverage, Limited mobility, Particle swarm optimization, Wireless sensor networks.

1.Introduction

• We analyze the node distribution in the randomly deployed sensor networks, which shows that there are coverage holes and vacancies in random WSNs. We present that the density of coverage vacancies in random sensor networks is and the number of mobile sensors required to move for coverage improvement is
• In order to save much more energy consumed during the sensor moving process, we restrict mobile sensors to move in a limited mobility model, i.e., the disk-based mobility model, which can reduce the sensor moving distance greatly.
• We realize the mobile sensor deployment optimization for k-coverage using the improved PSO algorithm. Different from paper ^[4] , particles move in a limited model, which guarantees that mobile sensors move in the disk-based mobility model. Simulation results show that few mobile sensors in the disk-based mobility model can also realize the k-coverage, which can reduce the cost of the sensor networks and moving distance of mobile sensors.

2.Coverage Analysis in Randomly Deployed Sensor Networks

Combining with equation (2), we can get

We assume that the sensing radius of the sensor is fixed. From equation (5), if the density is large enough, the percentage of the uncovered area, which is about , can be made arbitrarily small. However, the probability that there exists a connected coverage hole larger than πr ² approaches 1 for a network with a constant sensor density as the network size . Hence, a constant sensor density l of cannot guarantee that there are no big holes in the network as the network size grows, even though most areas of the field will be covered ^[10] .

Theorem 1 shows that the random deployment of sen sors in WSNs cannot provide a complete coverage, and there may be coverage holes especially as the network size grows. As shown in [Figure 1], 100 sensors with a radius of 10 are randomly deployed in a square region; the WSN cannot cover the region completely, and the total expected area covered by sensors is about 76.2%.

In order to reflect the degree of sensor uniform coverage, we will analyze the k-coverage (k > 1) of the sensors in randomly deployed sensor networks in theorem 2.

Lemma 1: If any disk with a radius of r, centered at one point in M, covers at least k sensors, region M is k-covered.

Proof: From the definition of the k-coverage, any point in the monitored region is covered by at least k sensors; apparently, the disk with a radius of r centered at any point in M covers at least k sensors.

Theorem 2: If sensors are distributed uniformly and ­independently with a density λ in the square region M with an area S, the expected density of the coverage vacancy λ_V for k-coverage is

Proof: Since the sensor density is λ, there are n = λS sensors uniformly and independently scattered in the network. The number of sensors in a region with area of A in M, is denoted as n _A. When n is large, it is Poisson's distribution with a mean of λA ^[10] :

From Lemma 1, if the square region M is k covered, any disk with a radius of r in M covers at least k sensors. However, some disks may cover fewer sensors than k due to the randomness in the sensor deployment. If a disk i covers n _i <k static sensors, we can say that disk i has vi = k - n _i vacancies.

As shown in [Figure 2], when k = 3, we can see that disks N1, N2, and N3 cover at least three sensors and have not any node vacancy. However, disk N4 covers only two sensors and has a node vacancy. According to the Poisson approximation, n _i will be asymptotically independently and identically distributed as

The random variable vi = max {ni ,k}-ni , will be distributed as

The expected number of vacancies in a disk will be

According to Stirling's approximation

The expected density of vacancies λ_v in M is about:

From equation (12), if sensors are scattered randomly in the monitored region according to (8), the density of the sensor vacancy will increase with the increase in k. Random deployment cannot provide the k-coverage of sensor networks, and the density of the node vacancy changes within randomly deployed networks.

From the coverage analysis above, we can see that the coverage of randomly deployed sensor networks is not optimal, the random deployment strategy has low efficiency for the k-coverage of large sensor networks, and many areas in the monitored region have more than k sensors, while some areas have less than k sensors. In order to improve the coverage rate, we may scatter randomly more static sensors to fill the coverage holes and vacancies, but the density of static sensors needs to grow with the network size as where which shows that the coverage efficiency for randomly deployed sensor networks becomes worse as the network size increases. Mobile sensors can relocate themselves to fill the vacancies so that the randomness in sensor deployment can be compensated. Hence, mobility can be used to improve network coverage efficiency.

The mobile sensor networks can almost surely achieve deterministic sensor deployment for the optimal coverage intuitively. However, mobile sensors are much more expensive than static sensors. In order to reduce the network cost, it is preferable to allow only small parts of sensors to move to improve the coverage. From the above sensor distribution analysis in randomly deployed WSNs, the expected vacancy density and the number of vacancies in region M is λ_vS as. Combining this with equation (8), we can get that is to say we can fill the coverage holes and vacancies by moving about sensors. This activates us to use small parts of sensors to move to improve the coverage, which can reduce the cost of sensor networks. In section 5, we will allow small fraction of sensors to move to realize the sensor deployment optimization for k-coverage on PSO in limited mobility.

3.The Sensor Detection and Limited Mobility Models

3.1 The Sensor Detection Model

There are mainly two types of sensor detection models at present, the binary detection model and the probability model. We assume that each sensor has a detection range r, and sensor si is deployed at a point (x _i, y _i)For any point P(x, y), the Euclidean distance between s _i and P(x, y) is denoted as d(s _i, P).

Equation (14) shows the binary detection model expressing the detection probability C _xy(S _i)of a point P(x,y) by sensors s _i.

In the binary sensor model, the detection probability of the event of interest is 1 within the sensing range r; oth erwise, the probability is 0. In reality, it has limitations due to the imprecise detection probability, which plays a significant role in sensor detection. Hence, a detection error range r _e(r _e < r)is introduced to measure the uncertainty of sensor detection ^[12] . A probabilistic detection model is expressed as

Where α₁ , α₂ , β₁ , β₂ are parameters measuring the ­detection probability; λ1 and λ2 are input parameters, and their definitions are as follows:

In the measurement process, several related sensors measure the point cooperatively, which can enhance the measurement probability, and the joint probability is given below:

Let C _th(k) be the desired threshold for k-coverage; we assume that the point is covered by at least k sensors

Moreover, we assume that all sensors know their ­locations with the use of GPS system or other ­localization algorithm.

3.2 The Sensor Limited Mobility Model

As we know, sensors have limited energy, and sensor mobility consumes much more energy than sensing and communication. If a mobile sensor moves over a long distance, its entire energy supply may be depleted in the moving process. In this paper, we consider that the sensor mobility is limited, i.e., each sensor moves only once over a short distance, which is realistic in practice. DARPA has already conducted research on a class of Intelligent Mobile Land Mine Unite ^[9] that is similar to our limited mobility model in this paper. In ^[9] , the authors introduce flip-based sensors for network coverage improvement, and the results show that the appropriate flip distance can achieve a better coverage, and reduce the number of flips. However, as shown in [Figure 3]a, the flip-based sensors in region 1 can only move to the left, right, top, and bottom regions, which limits sensors to move in four directions, and may lose the optimal moving opportunities in other regions, such as 2, 4, 6, and 8 regions.

Different from the above sensor mobility, we limit mobile sensors to move only once in the disk with a radius R, R = l. r(l = 1, 2, 3,.......), centered at their initial positions. For example, in [Figure 3]b node s1 is allowed to move only once in disk C1. In contrast to the flip-based sensor mobility model, the disk-based sensor mobility model can enhance the sensor mobility opportunity under the same limited moving distance, which can advance the search speed for mobile sensors' optimal positions. We apply the disk-based mobility model to the sensor deployment optimization process on PSO, which not only achieves a better coverage, but also reduces the movement distance greatly, compared with that in the unlimited mobility model.

4.Realization of The Sensor Deployment Optimization'

The sensor deployment optimization is the process to search the optimal position of the mobile sensors for k-coverage. In this paper, we apply the improved PSO, i.e., the PSO under limited mobility, to realize the sensor deployment optimization.

During the sensor deployment optimization process, sensors move to form an optimally distributed topology according to the execution of algorithm at the base station. We examine that only few of the sensors moving in the limited distance can also realize k-coverage optimization of sensor networks. The stimulation reflects that the result is satisfactory.

4.1 Particle Swarm Optimization Algorithm

PSO, inspired by social behavior of bird flocking, is an outstanding algorithm for solving multidimension function optimization in continuous space and has a series of advantages, such as, high-speed regional convergence and efficient global searching ability. PSO has come to be widely used as a problem-solving method in engineering and computer science ^[13] .

The particles fly through the multidimensional search space with each particle representing a possible solution to the problem. All of particles have fitness values, which are evaluated by the fitness function to be optimized, and have velocities, which direct the flying of the particles. PSO is initialized with a group of random solutions and then searches for the optimal solution by updating generations.

The PSO formulae define each particle in the ­D-dimen sional space as where i represents the particle number and d is the dimension. The memory of the previous best position of the ith particle is represented as and a velocity along each dimension as

The updating equation is as follows,

where, c1 and c2 , two positive constants, are acceleration coefficients. r1 and r2 are two random functions in the range ^[0,1] . ω(t) is the inertia weight, and considered to be crucial for the PSO's convergence. The inertia weight is employed to control the impact of the previous history of velocities on the current velocity of each particle. Thus, the parameter ω(t) regulates the trade-off between the global and local oration ability of the swarm. A large inertia weight facilitates global exploration, while a small one tends to facilitate local exploration. A suitable value for the inertia weight v(t) balances the global and local exploration ability and reduces the number of iterations required to locate the optimal solution. Generally, it is better to initially set the inertia to a large value, and gradually decrease it to get more refined solutions ^[14] :

where MaxLoops is the number of maximum generations.

Moreover, v _ij should be confined to a given range

the search space, the position of particles is updated as

4.2 Sensor Coverage Optimization Under Limited Mobility

Considering the characteristic of sensor deployment optimization of mobile sensor networks, we abstract the vectors consisting of mobile sensor locations as input parameters. Let the number of mobile sensors be nd and the search space of PSO algorithm be D = 2n _d ; then the particle location vector is . The elements denote the x-coordinates and y-coordinates of mobile sensors from 1 to n _d in turn. The fitness is the k-coverage value of the corresponding location vector of particles.

Since mobile sensors move in the disk-based mobility model, the particle location is limited correspondingly, i.e.,

where k = 1, 2, which can guarantee the disk-based mobility model.

The main procedure of the sensor deployment opti miza tion in the limited mobility model is described in [Figure 4] as follows.

5.Performance Evaluation

In this section, we mainly focus on the performance analysis of the sensor deployment optimization for k-coverage in the limited mobility model. In ^[4] , authors assumed that all sensors are mobile, and move in the unlimited mobility model. Differently, we consider few of sensors move in the disk-based mobility model in the process of sensor deployment optimization. In the following experiments, we use the probabilistic detection model in different scenarios.

For all these simulations, distances are measured in units of m. Each sensor has a sensing radius of 6 m (r = 6) and a detection error range of 3 m(r _e = 0.5r).The parameters of the probability model are set as Acceleration coefficients c1 and c2 are both set as 2. We have used 40 particles (m = 40), which are denoted by mobile sensors' coordinates. MAX_LOOPS is the maximum iteration of the improved PSO algorithm, and not less than the run time for the optimal coverage rate of sensor networks. MAX_LOOPS is set as 200 here. The coverage rate is calculated as a fitness value in each generation. Since the sensor deployment is random, 50 experiments have been made to achieve the average results. The simulations were run on a Pentium 2.0 GHz PC using Matlab 7.0.

5.1 Test 1

We first consider that deployed sensors are all mobile, and move in the disk-based mobility model. For k = 3, we assume that 80 mobile sensors are randomly distributed in the square region M with an area of 50 x 50 m. As shown in [Figure 5]a, the initial 3-coverage rate is about 62.13%. We assume that the limited region for sensors' mobility in the limited mobility model is the disk with a radius of 2r ( R = 12) centered at their initial positions.

[Figure 5]b and c show the sensor distribution after the ­execution of the PSO algorithm in the unlimited and the disk-based mobility models, respectively. In ­[Figure 5]b, the 3-coverage rate is about 96.12% in the unlimited mobility model, and in [Figure 5]c, the 3-coverage rate is about 93.71% in the disk-based mobility model, and the coverage rate in the disk-based mobility model is less than that in the unlimited mobility model. As shown in [Figure 6], if we increase the limited distance, the coverage rate also increases; the 3-coverage rate can almost reach the optimal coverage value in the disk-based mobility model, but it needs R = 24 in the flip-based mobility model.

In [Figure 7], with the change in the size of the extended network, the optimized 3-coverage rate in the disk-based mobility model can almost reach the optimal coverage value in the unlimited mobility model. If the number of sensors is 60 (80, 100), we can get the optimal coverage rate in the disk-based mobility model as R = 12 ( R = 18, R = 24). We can see that the moving distance of the sensor network with a large size is larger than that of a sensor network with a little size. That is to say, under the identical limited moving distance, the coverage rate of the network with a little size is higher than that of the network with a large size. In [Figure 7], if R = 18, the optimal 3-coverage rate of the network with 80 mobile sensors is higher than that of a network with 100 sensors.

With the increase in the number of mobile sensors, the coverage rate in the disk-based mobility model can reach the optimal value in the unlimited mobility model, even though the limited msoving distance increases ­correspondingly.

In [Figure 8], we consider k = 2, k = 1, with 60 and 30 mobile sensors randomly deployed in M, respectively. The 2-coverage rate in the disk-based ­mobility model can almost reach the optimal ­coverage rate in the ­unlimited mobility model as R = 12, and the ­1-coverage rate reach the optimal coverage rate as R = 6.

Moreover, due to the unbalanced energy consumption in the process of surveillance of sensor networks, some sensors may die due to battery loss, which also brings about coverage holes and vacancies. Mobile sensors can also be used to improve the coverage rate.

We also consider 80 mobile sensors deployed in region M with an area of 50 x 50 m. As shown in [Figure 5]b, the optimal 3-coverage rate is about 96.12% after sensor initial deployment optimization. We assume that there are 10% invalid sensors after a period of surveillance of the sensor network, and invalid sensors are distributed randomly. In [Figure 9], there are eight invalid sensors because of being out of work, and invalid sensors are labeled as black "*." The 3-coverage rate is dropped to about 74.72%.

We allow mobile sensors to move to the coverage holes and vacancies for 3-coverage improvement. In [Figure 10], the optimal 3-coverage rate in the unlimited mobility model can reach about 85.87%. In the disk-based mobility model, the optimized 3-coverage rate can also increase with the increase in the limited moving ­distance. The optimized 3-coverage rate in the disk-based mobility model can almost reach the optimal coverage value as R = 18.

5.2 Test 2

From the analysis in section 3, we know that number of few mobile sensors needed to fill the vacancies for k-coverage is about . The number of mobile sensors in M with 80 sensors for 3-coverage is about 16, and we first assume that there are 64 static sensors and 16 mobile sensors in the sensor network. Since sensors are deployed randomly, the initial distribution of sensors may be uneven, and the distribution of some sensors is excessively centralized. The selection of a mobile sensor can make an impact on the coverage improvement. If selected sensors to move are mostly deployed in the sparse regions, the optimized coverage rate in the limited mobility model is lower than that with most mobile sensors in dense regions. We select the mobile sensors randomly in this section. In our view, the selective probability of sensors in dense regions is greater than that in the sparse regions.

As shown in [Figure 11]a, static and mobile sensors are ­randomly distributed in the monitored region; static ­sensors are labeled as red "*" and mobile sensors are labeled as black "*." In [Figure 11]a, we can see that the randomly selected sensors mainly locate in dense regions. The mobile sensors can also move in the unlimited and disk-based mobility models as in test 1.

[Figure 11]b shows the sensor distribution after the execu tion of the PSO algorithm in the unlimited mobility model, and the 3-coverage rate is about 92.14%, which is less than the optimal 3-coverage rate of 96.12% when all sensors are mobile. This is because the initial distribution of static sensors is uneven, and the distribution of some static sensors is excessively centralized, as shown in ­[Figure 11]a. The mobility of few mobile sensors may bring new coverage holes and vacancies, and the coverage rate after the optimization algorithm is less than that obtained when all sensors are mobile. If we increase the number of mobile sensors, the optimized coverage rate also increases. As shown in [Figure 12], the 3-coverage rate can reach 95.83% when the number of mobile sensors is 22.

In order to save much energy during the mobile sensor movement, we also restrict the mobile sensors to move in the disk-based mobility model as in test 1. Assuming the number of mobile sensors n_d = 22 and the limited moving distance R = 18 m, as shown in [Figure 11]c, ­3-coverage rate is about 92.46% after the execution of the PSO ­algorithm in the limited mobility model. In ­[Figure 13], the ­3-coverage rate increases with the increase in the limited moving distance R, and the optimal coverage rate can be realized as .

For k = 2 and k = 1, the number of mobile sensors required to move for 2-coverage and 1-coverage optimization is about 13 and 9, respectively. As shown in [Figure 14], the 2-coverage rate can almost reach the optimal coverage value with 13 mobile sensors moving in the disk-based mobility model as R = 18, and the 1-coverage rate can reach the optimal coverage value with 9 mobile sensors as R = 12.

Similar to test 1, we also consider the sensor deployment optimization with the mobility of partial sensors when some sensors die due to battery loss. For simplicity, we also consider the sensor distribution described in [Figure 9]. Since eight sensors are out of work, it requires more than eight mobile sensors to move to the coverage holes and vacancies for the 3-coverage improvement. We assume that sensors selected to move are distributed randomly in M. As shown in [Figure 15], with the increase in the number of mobile sensors, the optimized 3-coverage rate increases correspondently. When the number of mobile sensors is at least 12, the 3-coverage rate can reach the optimal coverage value as all sensors are mobile.

In [Figure 16], we allow 12 mobile sensors to move in the disk-based mobility model for the 3-coverage ­improvement. The 3-coverage rate can almost reach the optimal coverage value as R = 24.

5.3 Test 3

The consumed energy of mobile sensors in the moving process is related to the sensor moving distance, so we compare the average moving distance in the disk-based mobility model with that in the unlimited mobility model to evaluate the energy efficiency of the sensor mobility in the disk-based mobility model. In [Figure 17], as the size of the extended network changes from 60 sensors to 100 sensors, the difference in the average moving distance of mobile sensors for the sensor deployment optimization for 3-coverage between two mobility models is obvious, especially when the number of sensors is great. When the number of mobile sensors is 80, the average moving distance in the disk-based model is about 12.1 m. In contrast, the average distance of mobile sensors in the unlimited model is about 23.5 m, which is bigger than that in the disk-based mobility model. It is clear that the sensor deployment optimization in the disk-based mobility model can reduce the sensor moving distance, which would reduce the energy consumption and enhance the energy efficiency greatly.

The method considered in this paper is a centralized manner, and there is much location information transmitted between sensors and the base station. The energy is mainly consumed by transmitting sensor location information. We use the energy dissipation model described in ^[15] , and assume that the sensor location information is 100 bit. In [Figure 18], as the size of the extended network changes from 60 sensors to 100 sensors, the energy consumption increases correspondently. As shown in [Figure 18], when the number of sensors in WSNs is 80, the consumed energy with all sensor mobility is about 8009.8µJ; however, the energy with 16-sensor mobility is about 4786.1µJ. Comparing with all sensors' mobility, there is less sensor location information transmitted from the base station to mobile sensors, so the energy consumption with partial sensors' mobility is lower than that with all sensors' mobility.

The run-time of the improved PSO algorithm will change with the number of mobile sensors. The run-time is the number of iterations of the improved PSO algorithm. We consider the run-time of the PSO algorithm for different network sizes. As shown in [Figure 19], as the number of mobile sensors increases from 70 to 100, the run-time of the coverage optimization algorithm increases correspondingly. In [Figure 19], for n = 1, 2, and 3, the run-time for k-coverage of mobile sensor networks with different sizes is different, e.g., as n = 70, 80, and 90, the corresponding run-time of the improved PSO algorithm for 3-coverage is about 121, 139, and 163 respectively.

6.Discussion

Since sensor deployment is random, the sensor deploy ment optimization efficiency is affected by the initial distribution of sensor networks. The limited ­moving distance is affected by the distribution of the sensor network. If the distribution of sensors is more uneven, the moving distance of mobile sensors is larger. A wrong selection of the moving distance will not get the optimal coverage rate as in the unlimited mobility model. There is the minimum moving distance for k-coverage optimization of a given mobile sensor network, under which we can get the optimal coverage rate as in the unlimited mobility model.

Moreover, our sensor deployment optimization algorithm is a centralized manner. There is much sensor location information transmitted to the base station for the optimization process as the size of sensor networks increases. In the larger sensor network with a large number of sensors, there is a large amount of computation for the improved PSO algorithm, which will increase the computing cost, and decrease the convergence speed. We can divide the whole detecting area into several groups containing smaller number of sensors. In each group, the parallel PSO algorithm can be used to realize the sensor deployment optimization easily. In addition, the distributed coverage improvement algorithm can also help to advance the convergence speed and enhance the scalability of sensor networks. The parallel PSO algorithm and distributed optimization algorithm on sensor deployment are our next research work.

7.Conclusion

In this paper, we mainly discuss the sensor deployment optimization for coverage in mobile sensor networks. Through the analysis of the node distribution in randomly deployed sensor networks, we know that there are coverage holes and vacancies in randomly deployed ­wireless networks; the density of a sensor vacancy is about and the density of vacancies increases evidently as k increases. We derive the number of mobile sensors used to fill the vacancies to be ­Considering that the nodes have very limited energy resources, we restrict the sensor move in the limited model, i.e., the disk-based mobility model, during the execution of PSO. The simulation results show that sensor node move in the limited region can almost realize the k-coverage of sensor networks, which reduces the move distance greatly than in the unlimited model. Considering the cost of mobile sensors to be more expensive than that of static sensors, we allow few of sensors to be mobile for k-coverage in the limited and unlimited mobility models; the hybrid sensor network can also achieve a satisfactory coverage rate in the limited model, which will provide guidelines for sensor deployment in large-scale sensor networks.

8.Acknowledgments

This work is partially supported by the International Science and Technology Cooperation Foundation of Shanghai Municipality under grant (no. 075107005), the National High-Tech Research and Development Plan of China under grant (no. 2007AA01Z136), and Research Project of "SUST Spring Bud" (no. 2008BWZ047).

Authors

Xingzhen Bai was born in Shandong, China, in 1977. He received his M.S. degree from Shandong University of Science and Technology at Qingdao, China, in 2006.Now he is a doctoral candidate in Tongji University at Shanghai, China. His research interests include wireless sensor networks, Ad hoc networks and cognitive networks.


Shu LI was born in Shandong, China, in 1980. She received her B.S. and M.S. degrees on Computer Science and Technology from Shandong University at Shandong, China, in 2002 and 2005 respectively. She is a doctoral candidate in Tongji University at Shanghai, China. Her research interests include wireless/mobile networks, ad hoc networks, wireless mesh networks and the application of wireless networks for vehicle transportation.


Juan Xu received her M.S. degree in Control Theory and Control Engineering from Guangxi University, China, in 1999. She is currently pursuing her Ph.D. degree in computer software and theory. Since 1999, she has been a teacher with the School of Electronics and Information Engineering, Tongji University, China. Her current research interests are primarily in ultra wide band wireless sensor network, mobile and ad hoc network, mesh network and pervasive computing.

 

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Figures

  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12], [Figure 13], [Figure 14], [Figure 15], [Figure 16], [Figure 17], [Figure 18], [Figure 19]

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