A Distributed and Collaborative Beamforming algorithm for a self-organizing Wireless Sensor Network

Physical Communication 4 (2011) 172–181

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A Distributed and Collaborative Beamforming algorithm for a self-organizing Wireless Sensor Network✩ M.F. Urso a,∗ , S. Arnon b , M. Mondin a , E. Falletti a , F. Sellone a a

Dipartimento di Elettronica, Politecnico di Torino, C.so Duca degli Abruzzi, 24, 10129 Torino, Italy

b

Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva IL-84105, Israel

article

info

Article history: Received 24 November 2010 Received in revised form 1 June 2011 Accepted 7 June 2011 Available online 15 June 2011 Keywords: Distributed and Collaborative BeaMForming (DC-BMF) Self-localization Phased Array Wireless Sensor Network (WSN)

abstract In this paper the scenario where sensors of a Wireless Sensor Network (WSN) are able to process and transmit monitored data to a far collector is considered. The far collector may be a Base Station (BS) that gathers data from a certain number of deployed WSNs, in applications such as earthquake, tsunami, or pollution monitoring. In this paper, the possible use of Distributed and Collaborative BeaMForming (DC-BMF) technique is analyzed, with the goal of enhancing the capability of a single sensor to communicate its data to the far collector. This technique considers nodes as elements of a phased array, where the phases of the signals at each antenna node are linearly combined in order to adjust the directional gain of the whole array. In particular, a novel self-localization technique for WSNs performing DC-BMF is studied, a closed form solution for beamforming gain degradation is derived and the evaluation of the power consumption of the proposed DC-BMF algorithm is provided. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The advent of sensor network technology [1] is allowing tackling new applications, which had been considered unapproachable in the past. One such application involves a WSN with a certain number of sensor nodes randomly placed in the space, deployed to collect information from the environment. The nodes process sensed data, if necessary, and then send them to a far away point, for example a BS that collects data from a certain number of deployed WSNs. This information needs to travel over a relatively long distance, which may set heavy transmission gain requirements over the WSN. Furthermore, computational costs must typically be kept as low as possible and uniformly distributed in time and among nodes, in order to

✩ The work was partially supported by the COST 297 (HAPCOS) project.

∗

Corresponding author. Tel.: +39 3478740607; fax: +39 0110904099. E-mail address: [email protected] (M.F. Urso).

1874-4907/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.phycom.2011.06.003

maximize the WSN lifetime [2], whose common definition is the shortest life among the nodes [3]. In this paper we examine the possibility of exploiting collaborative diversity [4] among the nodes to achieve a large transmission range, employing what we denote as Distributed and Collaborative BeaMForming (DC-BMF). This technique considers nodes as elements of a phased array, where the same data are synchronously transmitted by all the nodes, each employing a proper phase, tuned in order to shape the Array Factor (AF) and enhance the directional gain of the whole array [5]. We then discuss the practical details of its implementation and analyze its performance in the presence of non-idealities. Precise power consumption estimation and evaluation of the minimum number of nodes required to obtain a given beamforming gain are presented, proving the feasibility of the DC-BMF algorithm in a practical scenario. Furthermore, a novel solution for distance estimation is presented, based on the joint use of Carrier Phase Tracking (CPT) and range measurement techniques. Part of this paper was presented in our earlier conference paper [6], where the idea of

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Distributed Collaborative Beamforming was introduced within the framework of HAP applications. Some prior art considers the problem of beamforming in a narrowband environment, with precisely known elements location and response, is well documented in the literature [5] [7]. In [8] it has been shown that randomly generated arrays with a large number of elements can form a good beam pattern with high probability, and in [9] the performance of a blind centralized beamforming algorithm operating on a randomly distributed sensor array has been investigated. The coordination of collaborating sensors is considered in [10] and [11], while in [12], Ochiai et al. analyze the achievable performance of a collaborative beamforming technique for randomly and uniformly distributed sensors in a two dimensional disk of given radius. A study on practical collaborative beamforming implementation is proposed in [13], while the problems of sensor localization and synchronization are discussed in [12] and [14]. Authors in [15] provide strategies for selecting the participating nodes in a DC-BMF scheme, while [16] considers the application of DC-BMF to WSNs, modeling the localization error of the sensor nodes with a Gaussian probability density function. The rest of the paper is organized as follows. Section 2 provides a summary of the system model and some theoretical remarks on phased arrays. The two main sources of beamforming gain degradation, i.e. localization and time synchronization inaccuracies, are described in Sections 3 and 4. Furthermore, in Section 3 the novel self- localization technique based on the use of classic CPT and range measurement techniques is described. In Sections 5–9, the problems involved in the Distributed and Collaborative BeaMForming (DC-BMF) algorithm are described, such as the algorithm steps, the effects of the localization error and the consequent selection of the number and location of the collaborative nodes. Section 10 discusses the limitations on the maximum number of nodes and the relative achievable gain, Section 11 contains the power consumption evaluation, while the conclusions are drawn in Section 12. 2. System model and phased arrays theory In Fig. 1 the reference system scenario is depicted [12]. The WSN nodes are supposed to lie on the x–y plane and the far away target location is given in spherical coordinates (A0 , φ0 , θ0 ). Each sensor-node location is expressed in polar coordinates [17]: the kth node has coordinates (rk , ακ ). Furthermore, θ ∈ [0, π] represents the latitude of a point, while φ ∈ [−π , π] represents its longitude. The same assumptions as [12], are considered, i.e. the location of each node is chosen randomly, following a uniform distribution within a disk of radius Rmax , the channel is assumed quasi-stationary, with known attenuation during the localization and beamforming processes, each node is supposed equipped with a single ideal isotropic antenna, and mutual coupling effects among antennas belonging to different nodes are supposed negligible due to their distance. A transmitting phased array is a system able to coordinate a certain number of sensors to simultaneously

173

Fig. 1. System model.

transmit a signal (each sensor adding a specific phase offset) in order to obtain the effect of electronically steering the overall beam of the array toward an a priori known direction. The target, toward which the array shapes the beam, ideally receives a linear combination of all the signals transmitted by the array. The AF, previously cited, is defined in [12] as F (φ, θ|r , ψ) =

=

N 1 − jψk j 2π dk (φ,θ ) e e λ N k=1 N 1 −

N k=1

ej

2π

λ [dk (φ,θ )−dk (φ0 ,θ0 )]

(1)

where

ψk = −

2π

λ

dk (φ0 , θ0 )

(2)

is the initial phase of the kth node, r = [r1 , . . . , rN ], ψ = [ψ1 , . . . , ψN ], and dk (φ, θ ) =



A20 + rk2 − 2A0 rk sin(θ ) cos(φ − αk )

(3)

is the Euclidean distance between the kth node and the target location (A0 , φ0 , θ0 ), λ is the wavelength of the radiofrequency carrier and N is the number of nodes of the array. Another assumption is that the well known far field approximation A0 ≫ rk holds. Furthermore, we do not loose generality if we consider θ = π /2. Given these hypotheses, we can rewrite (3) and (1), as dk (φ, θ = π /2) ≈ A0 − rk cos(φ − αk )

(4)

F˜ (φ | r , ψ)

=

N 1 −

N k=1

 exp j

2π

λ



rk [cos(φ0 − αk ) − cos(φ − αk )] (5)

where F˜ (φ | r , ψ) is the approximated version of the AF that will be considered in the following. 3. Self-localization In a WSN, self-organization capabilities are important because they provide the network with the ability to collect, share and exploit all the external information to perform its task autonomously. In our framework the

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assumption is that there are at least three nodes, denoted as Anchor Nodes, with perfect knowledge of their correct position. The Anchor Nodesmay be equipped with GPS receivers, and should possibly be deployed with maximum angle separation, as better explained in Section 6. Another assumption is that localization knowledge in the network must be shared in the same inertial system position as the target (whose position is supposed known within the network). These are reasonable assumptions since the target position could be simply stored in memory, even if it changes continuously. Given a set of I reference points (the Anchor Nodes), where the generic anchor node i has polar coordinates (ri , αι ), Cartesian coordinates (Xi = ri cos(αι ), Yi = ri sin(αι ), Zi = 0) and where typically I = 3, in order to determine the unknown coordinates (Xk , Yk , Zk ) of the generic node k with triangulation techniques, it is necessary to determine the set of distances Dki between node k and node i by solving the set of I equations linking (Xi , Yi , Zi ), (Xk , Yk , Zk ) and Dki [18,19]. Assuming that: (a) all the involved nodes belong to the same cluster; (b) the local communication channel among the nodes has an high Signal-to-Noise Ratio (SNR); (c) the network does not change its topology during the localization algorithm evaluation; (d) the Anchor Nodes are deployed with the maximum angle separation and using the method for ML distance estimation described in this paper as Algorithm II, the self-localization algorithm can be stated as follows [20]:

the Received Signal Strength (RSS) methods, we derive a novel procedure that jointly exploits both of them through a Maximum Likelihood Estimator (MLE). If the CPT method is used, node i transmits a sinusoid sTX i (t ) with unitary strength and known initial phase ψi (which can be supposed to be zero without loss of generality). The RX ,l corresponding signal sk,i (t ) received at node k at the lth reception, in Line-Of-Sight (LOS) conditions, is attenuated, affected by noise and with a certain phase offset ϕk,i : sTX i (t ) = sin(2π fc t + ψi ) RX ,l

sk,i (t ) = Skl ,i sin(2π fc t + ψi − ϕk,i ) + ηk,i (t ).

⌢CPT

node k, and as D k,i the estimated distance obtained with CPT techniques in free space conditions (without phase ambiguity), is given by ⌢CPT

D k,i =

3.1. Maximum likelihood distance estimator We are interested now in a precise yet low consumption method to determine the distances Dk,i . At the best of our knowledge there is a lack of such a method. Beginning from the fact that the most common distance estimation techniques are based on Carrier Phase Tracking (CPT) and

λ λ (ϕ¯ k,i ) = (ϕk,i + δϕk,i ) 2π 2π

(7)

where we suppose that the measured phase is affected by a random error δϕk,i that follows a Tikhonov distribution, 2 with zero mean and variance σδϕ , which is the typical phase jitter model for Phase-Locked-Loop circuits [21]. The probability density function of the random variable ϕ¯ k,i , centered in the expected value ϕk,i is: fϕ k,i (x) =



1 2π I0



1

 exp

cos(x − ϕk,i )

2 = K (σδϕ ) exp



2 σδϕ

2 σδϕ



Algorithm I: self-localization 1. The I nodes with known positions start broadcasting a pilot tone and send information about their coordinates. The frequency of the pilot tone broadcasting is application dependent and is a parameter that, in mobile applications, must be also tuned to the known mobility of the nodes. 2. Under the assumption that all the nodes lie on the x–y plane, the kth node estimates its I distances Dk,i (see the novel Algorithm II). The operation is repeated by the whole nodes of the same collaborating network. 3. Using the estimated distances and the broadcasted position of each Anchor Node, each other node in the network solves the well known triangulation scheme and finds its coordinates (Xk , Yk , Zk ). 4. The localization error of this algorithm is dependent on the quality of the distance estimate, and given the statistical characteristics of the distance estimation error, the triangulation error can be calculated as shown in [18,19].

(6)

If we denote as ϕ¯ k,i = ϕk,i + δϕk,i the random variable representing the (noisy) phase measurement performed at

cos(x − ϕk,i ) 2 σδϕ

 ,

|x − ϕk,i | ≤ π

(8)

where

 2 K (σδϕ )=

2π I0

1

−1 .

2 σδϕ

If the RSS method is used, node k receives from node i a certain number r of symbols with known transmitted power PTX , which will be used to compute the average received signal strength R¯ SS k,i which, expressed in dB, usually differs from the average received power PRX through a constant offset POFF (a known parameter which depends on the front-end gain [22]), so that P RX = RSS k,i + POFF . Under the hypothesis of unitary isotropic antenna gain and constant known attenuation, the noisy ⌢RSS

estimate D k,i of the distance Dk,i can be evaluated from

the measured received power P¯ RX . For simplicity we will assume free loss propagation, obtaining the expression: 

¯





R¯

−P

−P



PRX −PTX SS k,i TX OFF λ λ 20 20 = 10 = 10 (9) 4π 4π where R¯ SS k,i is a random variable, typically obtained by

⌢RSS D k,i

averaging a certain number r of received power measurel

ments χ¯ kl ,i at node k, where S k,i is the received signal amplitude measured at the l-th reception, due to the ideal

M.F. Urso et al. / Physical Communication 4 (2011) 172–181

transmitted amplitude Skl ,i and the additive zero-mean Gaussian noise δ Skl ,i with variance σ 2 introduced by the channel and the measurement, so that R¯ SS k,i =

=

r 1−

r l=1

χ¯

r l=1

r l =1

(S¯kl ,i )2 =

the ML estimate D k,i of Dk,i using Eq. (13).

(Skl ,i + δ Skl ,i )2 .

(10) 4. Time synchronization

In particular, in the IEEE 802.15.4-2006 Standard, the average signal strength is evaluated over r = 8 symbols [23], whose amplitude is affected by additive white Gaussian noise. As a consequenceR¯ SS k,i , the average of the l

square of r independent random variables S k,i with mean value Skl ,i and identical variance σ 2 , is distributed according to the following noncentral chi-square distribution: 

fRSS k,i (x; r , ρ) =

r

 

2σ 2

ρ

x

r −2 4



  √  r xρ [r (x + ρ)] I r −2 2 2σ 2 σ2

(11)

with mean value µRSS = ρ + σ 2 and variance σR2SS = 2σ 2 r

(σ 2 + 2ρ), where ρ =

Skl ,i and Iν (z ) is the modified Bessel function of the first kind of order ν . From (7) and (10) node k computes two estimates of the same quantity. It can be proven that, in this case, the minimum variance estimator for Dk,i is the Maximum Likelihood (ML) one, which achieves the Cramer Rao 1 r

∑r

l =1

⌢CPT

2 rDk,i u22 K (σδϕ )

24σR2SS



 (ru2 + Dk,i ) cos(u1 − Dk,i ) × exp − + . 2 σR2SS σδϕ

(12)

Deriving and solving with respect to the expected value ⌢ML

Dk,i , the best estimate of D k,i can be expressed as

√ ⌢ML

D k,i =

−b +

When a Request for Collaboration Packet is broadcasted through the network, this must already be synchronized in time, i.e. the nodes must share a common time scale, because of the necessity of perform the same task (for example, sending the information to the target) at the same time. Many time synchronization algorithms can be exploited for this task [25,26], with different precisions and power consumptions needed to maintain the network synchronized. In fact, any residual time offset among the nodes would cause an added phase offset to each signal sent to the target, and, consequently a gain degradation of the beam pattern of the entire collaborating network. This degradation can be mitigated using a more precise time synchronization algorithm or using a larger number of nodes composing the collaborating network, in order to compensate the degradation and satisfy the Eb /N0 requirements for the desired Bit Error Rate (BER). 5. Distributed and Collaborative BeaMForming algorithm (DC-BMF)

⌢RSS

Bound [24]. Denoting as u1 = D k,i and u2 = D k,i the available measures, the ML function can be expressed as the joint probability density function, i.e. the product of the individual probability density functions of the two random variables: g (Dk,i |u1 u2 ) =

⌢RSS

⌢ML

r 1−

× exp −

2. Node k receives at least r symbols from node i (according to Algorithm I—step 2), which are part of the packet that contains the positions of Anchor Nodes. These symbols are used to compute the estimate D k,i according to Eq. (9). 3. Given the results of Eqs. (7) and (9), node k computes

l k,i

r 1−



175

b2 − 4ac

(13)

2a

2 2 where a = σR2SS b = σδϕ − σR2SS u1 c = −σδϕ σR2SS . ⌢ML

The evaluation of D k,i is not computationally intensive, since only u1 and u2 change from one measurement to the next, while all the other parameters can be precomputed and stored from previous estimations. The distance estimation algorithm can therefore be stated as follows: Algorithm II: A novel Distance Estimator 1. Node k receives a pilot tone from node i (according to ⌢CPT

Algorithm I—step 1) and computes a D k,i according to Eq. (7).

The DC-BMF implements the theory developed in the previous sections. In the implementation we assume two type of node the InfoNode, e.g the node possessing the information that must be transmitted, and the SlaveInfoNodes, e.g. the nodes that help the InfoNode to transmit the information message to the target, via collaborative beamforming. In order to implement the DC-BMF algorithm, the nodes must perform the steps that follow: Algorithm III: DC-BMF 1. InfoNode broadcasts a Request for Collaboration Packet (RCP). 2. The M surrounding nodes (which are all candidates to form the current random array) answer with their position and their power level, contending the medium with a CSMA/CA access protocol. 3. The InfoNode selects a subset of N candidate SlaveInfoNodes that will perform collaborative beamforming. 4. The InfoNode computes the beamforming phase offsets for each SlaveInfoNode. 5. The InfoNode transmits to each SlaveInfoNode in the subset: a. the information message to be sent to the target; b. the quantized beamforming phase; c. the Time-To-Send (TTS) information needed to achieve synchronous transmission. 6. The SlaveInfoNode simultaneously transmit the information message to the target, via collaborative beamforming.

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M.F. Urso et al. / Physical Communication 4 (2011) 172–181

6. Beamforming gain degradation due to inaccurate estimates In Sections 3 and 4 we have described two important processes used in DC-BMF algorithm, i.e. time synchronization and nodes localization. Since they are not ideal and precise, but they are the output of two different estimation processes, they inevitably add errors to the DC-BMF output, affecting the final beamforming gain degradation of a real deployment. Degradation due to time synchronization is not addressed in the present paper, since it depends on the selected protocol. We will only focus on the effect of localization errors, estimation that is introduced in this paper for the first time. It is worth mentioning that also the fact that the phase offset sent by the InfoNode to the SlaveInfoNodes is represented as a quantized number in order to save memory and energy can be considered as a further source of gain degradation. The loss is however negligible if the phase is quantized on four or more bits [21]: for this reason this effect will be disregarded in what follows, supposing that at least four bits are used. Finally, here we are going to relate the beamforming gain degradation only with the 2D localization error. In order to do that, given the described scenario, we have estimated the probability density function of the maximum gain of the AF of the whole network, according to the following hypothesis:

Fig. 2. Histogram of the beamforming implementation loss. Each bar represents the difference (in dB) between the AF maximum amplitude of an ideal beamformer, and that of a real one, for a number of nodes in the selected subset N = 2, 8, 64, 489.

(a) the localization error is a 2D uniformly distributed random variable over a given region; (b) the degradation is not the same for all the signal Directions Of Arrival (DOAs). Given the total number of nodes, the localization error can be measured as the distance between the estimated position and the real position of each node. If the pdf of the estimated position is known, it is possible to apply the error to the beam pattern expression and quantify the difference between the ideal and the real AF. The experimental distribution (obtained by Monte Carlo simulation) of the beamforming gain degradation for two nodes is shown in Fig. 2, and has an exponential shape with high Lambda parameter. As the number of considered nodes increases, due to the Central Limit Theorem, the distribution tends to become Gaussian. Furthermore, the mean value tends to increase with N, while the variance of the distribution tends to become stable. This novel knowledge about the statistics of the beamforming gain degradation allows us to calculate the worst-case loss in function of the number of nodes and the maximum localization error. This is of prominent importance in order to guarantee that the communication will respect the theoretic link budget. It is worth mentioning that 3D localization error is not considered here. It is well known [27] that in RSS-based methods for 3D positioning, the vertical error component (on the z-axis) is typically predominant over the horizontal one (on the x–y plane) due to the limited vertical offset that can be imposed to the various sensors in flat environments, with respect to the horizontal offsets. The best way to

Fig. 3. Uncertainty region that surrounds the kth node, observed from the central reference node (placed at the origin of the axis).

mitigate this effect is to place the Anchor Nodeswith maximum angle separation [27], as also stated in Section 3. For sake of simplicity, the estimation methods developed in this paper are investigated only considering a 2D setup and the aforementioned configuration. 7. Localization error In order to derive a closed form solution of the degradation due to localization error, we put the InfoNode in the origin of our reference system and we calculate the localization error of the generic kth node, with polar coordinates (rk , ακ ) respect to the reference node, e.g. the InfoNode. As shown in [12], both the polar coordinates can be affected by errors, denoted as δ rk for rk and δαk for αk . Furthermore, we suppose −δ rmax ≤ δ rk ≤ δ rmax and −δαmax ≤ δαk ≤ δαmax . For sake of simplicity, we define here a novel uncertainty region, which resembles a curved trapezoid, as depicted in Fig. 3. A region, that describe in a simpler way the curved trapezoid, is the circle with radius equal to the maximum amplitude uncertainty, denoted as ρk,max (Fig. 3).

M.F. Urso et al. / Physical Communication 4 (2011) 172–181

18

14

16

Degradation dB

12 10

R = 0.1 R = 0.03 R = 0.01 R = 0.005 R = 0.001 R = 0.0001

8 6 4 2 0

Variance of Degradation dB

16

R = 0.1 R = 0.03 R = 0.01 R = 0.005 R = 0.001 R = 0.0001

14 12 10 8 6 4 2 0

0

100

200

300

400

500

600

0

100

Number of Nodes Fig. 4. Comparison between the simulated beamforming gain degradation D(N , Rk ) (solid line) and the related curve obtained with the evaluation of the closed form expression of Table 1 (dashed line).

rk

≈



2 [1 − cos(δαmax )]

(14)

(15)

supposing δ rmax ≪ rk . Assuming the localization error known in function of Rk , the total gain loss is finally defined as:

¯ (N , Rk ) + V (N , Rk ) D(N , Rk ) = D

600

(16)

¯ (N , Rk ) of that is, the sum of the mean gain degradation D one of the pdf s of Fig. 2, and a further gain degradation margin V (N , Rk ), given by the 1 − σ standard deviation of the same pdf. Given the localization errors described here, we have related them with the beamforming gain degradation, resulting in the plots of Fig. 4. In Fig. 5 the value of V grows as Rk increases. For larger Rk , V has a short transient as the number of nodes increases, suddenly reaching a stable value on a specific horizontal asymptote. We have conservatively selected the degradation margin V = 9 dB for any number of nodes, when Rk ≥ 3% and we have selected V = 0 dB otherwise. Finally, beamforming gain degradation has been modeled with the closed form expressions shown in Table 1. These values may be easily memorized in the nodes using a look-up table, so when one node needs to act as InfoNode, it automatically knows how many SlaveInfoNodes it must ask for collaboration.

Rk

0.01 4 log10 (N /1.8)

0.0001

0.2 log10 (N /1.8)

0.001

0.45 log10 (N /1.8)

0.005

3 7 log10 (N /4)

0.01



From ρk,max we finally define a new quantity called Rk , that can be seen as the reference localization error. This error evolves in function of δ rk and δαk . This allows us to describe the degradation due to localization errors only in relationship with a single variable for each node k:

ρk,max

500

Fig. 5. Variance (in dB) of degradation D(N , Rk ) for several values of the maximum normalized localization error Rk .

D( N , R k )

2 ρk2,max = 2rk [1 − cos(δαmax )](rk + δ rmax ) + δ rmax

≈ 2rk [1 − cos(δαmax )](rk + δ rmax ).

200 300 400 Number of Nodes

Table 1 Closed forms expressions for beamforming gain degradation depicted in Fig. 5.

The quantity ρk,max can be expressed as:

Rk =

177

 4

 4



4.9 log10 (2N )

>0.03

8. Link budget and related number of collaborative nodes In order to select the number of collaborating nodes, InfoNode must solve the equation

¯ (N )|Rk + V (N )|Rk ) GWSN (N )|Rk = 10 log10 (N ) − (D ≥G

(17)

where G is the required gain in dB for a given scenario. Table 2 gives an example of this, where the link budget between a Base Station (BS) [28] and a WSN is developed. Then, GWSN (N ) is the gain of a N-nodes WSN and must be ¯ (N ) and V (N ) are the beamforming larger than G. Finally, D losses, previously described, and Rk is the maximum normalized localization error. The behavior of GWSN (N ) as a function of N and Rk is shown in Fig. 6 and is similar in shape to the behavior of D(N , Rk ). The considered WSN-to-BS represents a meaningful scenario, where the designer is allowed to spread many autonomous WSNs within the coverage area of a single BS, with radius of 2.5 km. Considering this as an upper limit, then the required total gain that the furthest WSN must be able to express to reach the BS depends on the desired BER, as shown in the last rows of Table 2. Considering BER = 10−2 , and the curves depicted in Fig. 5, at least 33 nodes must collaborate together if the localization error is under the 0.5%, while if it is around 1%, 422 nodes are needed. Considering BER = 10−3 , 55 nodes are needed with a localization error of ma 0.5% and 750

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M.F. Urso et al. / Physical Communication 4 (2011) 172–181

30 25

Gain dB

20 15 10 5 0 R = 0.03 R = 0.01 R = 0.005 R = 0.001 R = 0.0001

-5 -10

0

100

200

300

400 500 600 700 Number of nodes

800

900 1000

Fig. 6. Gain GWSN (N ) vs. number of nodes N for several values of the maximum normalized localization error Rk . Table 2 WSN-to-BS link budget. TX

Tx antenna gain of each sensor node (dBi) Transmitted power (maximum power in TX for a CC2430 [22]) (dBW) Total Tx power EIRP (dBW)

0

−29.44 −29.44

Propagation Loss in rural areas, according to for a WSN-to-BS link (dB) [28] height: 40 m, Max coverage: 2.5 km, path-loss coefficient: 2.5 Atmospheric attenuation (dB) Lognormal shadow/fade allowance (dB) Total propagation loss

136.00

RX

Rx implementation loss (dB) Rx antenna gain (dBi) Rx RF front-end noise figure (dB) Rx Ant. Op. Temp. (100 K + 910 K) (dBK) Rx G/T (dB)

1.7 22.09 4.2 29.99 −13.69

Boltzmann Constant (dBJ/K) Uncoded bit-rate given by the IEEE 802.15.4 standard [23] (bps) Info data rate (dB) Carrier frequency (GHz)

−228.6

Parameters

Results

BER O-QPSK Eb /N0 (dB) Required gain (G) (dBi)

CHANNEL

with 1% localization error. Finally, by considering BER = 10−4 , only localization error of 0.5% can be taken into account (leading to 90 collaborating nodes), while with 1% error the number of needed nodes is too large and no more meaningful. 9. Selection of the nodes subset As seen before, the InfoNode can ask for collaboration to the entire network or only to a subset of nodes, depending on the InfoNode estimates gain e to reach the target. This gain is the theoretical (link budget based) gain, added with losses due to imperfect localization and parameters uncertainty. The theoretical gain can be memorized a priori within a static network. Then, a small implementation loss can be accounted due to parameters uncertainty: we denote it as beamforming gain degradation. It is unknown at InfoNode, since it depends on the localization error, on the clock misalignment for each node in the network and, also, on the quantization of the phase. Indeed, if the network is static and the localization knowledge is periodically updated, then it can be proved that localization errors tend to decrease with

0 6.2 147.20

250 000 53.9 2.4 10−2 4.3 15.00

10−3 6.8 17.46

10−4 8.4 19.07

time. If the network is not static but each node is able to calculate its position periodically, InfoNode could use as localization error a statistically estimated upper bound (Section 7 provides some results about beamforming gain degradation). Once the number of collaborating nodes has been set, a fast procedure to select the correct subset could be applied. In particular, InfoNode needs to select a subset of N sensors within the WSN that will perform the beamforming task. The cardinality of this subset is smaller than the total number of sensors M belonging to the network. The specific nodes are chosen accordingly to the following two requirements: (a) nodes must be as sparse as possible, in order to statistically increase the AF value [8]; (b) candidate nodes with higher energy must be selected first, in order minimize the variance of the energy in the subset. Algorithm IV: A Novel Selector of the Nodes Subset 1. InfoNode sorts the candidate nodes giving each of them a value that takes into account their residual available

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energy and their distance from the surrounding ones (assuring that sparse nodes will be selected). 2. InfoNode sorts the candidates in descending order with respect to the selection metric. 3. InfoNode selects the first N nodes.

Rmax = 4 m could contain a maximum of M = 363 nodes, while with Rmax = 12 m we could have a maximum of M = 3265 nodes. In summary, in the examples that follow we will consider two reference values [29]:

This simple but effective algorithm avoid to pick nodes destined to run out for low residual energy, or to pick nodes too closer, that cannot statistically guarantee a good shape of the beam pattern.

• on grass covered ground, a single-hop network with radius Rmax = 4 m can have a maximum number of nodes M = 363, leading (ideally) to a maximum beamforming

10. Constraints on the number of nodes If the network must collectively deliver, at least, the required gain G, and if the number of collaborating nodes N must be smaller or equal to the total number of nodes M that belong to the WSN, then it is possible to relate the density of a deployed network to its ability to success in the WSN-to-BS communication. M is constrained by the WSN radius Rmax and by the maximum density Z of deployable nodes per surface unit, which is related with the far field condition (and also with the requirements of the considered application). The WSN radius Rmax can be considered equal to half the maximum distance reachable by a transmission broadcasted by a single node (due to its maximum transmission power, under the hypothesis that multi-hop is not considered). Given Z and Rmax , it is possible to evaluate the maximum number of reachable nodes and, consequently, the maximum gain GWSN (M ) they provide collectively. These constraints eventually bind the choice of the reachable targets. As seen before, a BS like the one addressed in the Link Budget of Table 2 is not reachable with BER 10−4 . The transmission range of a typical WSN node strongly depends on the ground conditions [29]; it can be considered equal to 13.1 ft (4 m) if the node lies on a grass covered ground and 40 ft (12 m) if it lies on short grass covered ground. In ideal free space conditions, the range of a WSN node could be up to 7 km. The far field condition states that two transceiver points must be positioned at a distance Ff which satisfies the inequality: Ff ≥

D2f

(18)

λ

where Df is the dimension of the transmitter and λ is the operating wavelength. In the hypothesis of having a transmitting node of dimension Df = 10 cm, transmitting at 2.4 GHz, so that λ@ 2.4 GHz = 12.5 cm, we would have Ff ≥ 8 cm. In order to be conservative, let us consider four times that quantity, setting the far field condition to Ff = 32 cm. At this point the near field region (the region in which the transmission can be considered as occurring in near field) is a circle with radius Rnf =

Ff + Df 2

gain of 25.5 dB;

• on short grass covered ground, a single-hop network with radius equal to Rmax = 12 m can have a maximum number of nodes M = 3265, leading (ideally) to a maximum beamforming gain of 35.1 dB. 11. Number of operations and energy consumption The type and number of operations required by DC-BMF are listed in Table 3, while Table 4 summarizes the corresponding energy consumption (considering the localization coordinates αk and rk quantized on 4 bits). As far as localization is concerned, while the Anchor Nodes are asked to broadcast their information, the other nodes consume energy to receive those data and elaborate their own position. Furthermore, it is worth mentioning that the non-compulsory tasks, e.g. localization and time synchronization, must be performed only when needed. Eventually, it can be stated that:

• the Localization task costs in average 0.9 mJ per node, all M nodes must perform this operation periodically, at least once (it clearly appears that energy consumed for computation is not relevant); • in order to send an entire packet of 54 bytes to the target using DC-BMF, the InfoNode consumes 0.35 mJ, while the N SlaveInfoNodes involved in the collaboration consume 0.3 mJ each and, finally, the (M–N ) nodes not involved in the collaboration consume 0.14 mJ each, staying idle. If a single node was in charge of sending alone the information to the target, then it would require a total power Ptx = 28 mW in order to assure a BER of 10−2 and Ptx = 49 mW for a BER of 10−3 . These values are excessively high for the radio of a traditional WSN node, and even if the transmission lasted only 1.72 ms (time necessary to send a 54 bytes packet at the considered bit-rate of 250 kbit/s), the node would not have the capability of generating such that power. So, the solution could be exploiting 422 collaborative nodes that uses simultaneously Ptx = 1 mW and consume in average 0.54 mJ, divided in 62.6 mJ for the single InfoNode and in 0.4 mJ for the other 421 SlaveInfoNodes. In average the WSN consume 5 times the energy of single transmission, but with this method it is confident to success in the communication. 12. Conclusions

(19)

leading, in the considered scenario, to Rnf = 21 cm. This leads to a maximum density Z of 7.2 nodes per squared meter. In this case, a circular region with radius

In this paper, the signal processing algorithm needed by a Wireless Sensors Network in order to perform Distributed Collaborative Beamforming has been proposed and analyzed in a practical scenario. The novelty in this

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M.F. Urso et al. / Physical Communication 4 (2011) 172–181 Table 3 Number of operations (steps denoted with ∗ are not mandatory for each cycle). Anchor nodes for localization or InfoNode Elementary tasks

Specific steps

Consumed energy

∗

6 tx

tx 6 Pmax · Tn

∗

Synchronization

Depends on selected algorithm

Request for collaboration (RCP)

1 tx M rx

Self-localization

tx Emax · Tn M E rx · Tn comp

1000 operations

Nodes subset selection Information tx

E10 000 · # oper 10 000

(N − 1) tx

tx Emax · (N − 1 ) · T n

1 tx

tx Emax · Tn

Specific steps

Consumed energy

6(M − 3) rx

6(M − 3)P rx · Tn

SlaveInfoNodes Elementary tasks ∗

Self-localization

1000 · M operations

comp

E10 000 · M ·# oper 10 000

Synchronization∗

Depends on selected algorithm

Request for collaboration (RCP)

M rx M tx

ME rx · Tn tx M Emax · Tn

Nodes subset selection

(N − 1) rx

(N − 1)E rx · Tn

Information tx

1 tx

tx Emax · Tn

Table 4 Energy consumption for WSN-to-BS communication. Comparison between DC-BMF and a single node transmission. DC-BMF Pe = 10

−2

Single TX node

(Rk = 1%, phase quantized on 4 bits), N = 422

E = 0.54 mJ Var[E ] = 3.9 (mJ)2

Ptx = 1.1 mW EInfoNode = 62.6 mJ ESlaveInfoNode = 0.4 mJ

G = 14.2 dB → (Aeq = 3.2 m2 ) or Ptx = 28 mW, or Etx = 0.1 mJ

Pe = 10−3 (Rk = 1%, phase quantized on 4 bits), N = 750 E = 0.51 mJ Var[E ] = 4.2 (mJ)2

Ptxt = 1.1 mW EInfoNode = 108.75 mJ ESlaveInfoNode = 0.4 mJ

paper is given by the development of: (a) an ML distance estimator for the WSN scenario based on the joint exploitation of CPT and RSS measurements; (b) the definition of a beamforming algorithm denoted DC-BMF; (c) a complete treatment of the beamforming gain degradation in function of the localization error; (d) a comparison of the power consumption between DC-BMF and a single node transmission. The recent emergency events in many areas of the world indicate the possible developing interest for the WSN technology for environmental monitoring applications. References [1] I.F. Akyildiz, W. Su, Y. Sankarasubramaniam, E. Caryirci, A survey on sensor networks, IEEE Commun. Mag. 40 (8) (2002) 102–114. [2] S. Arnon, Deriving an upper bound on the average operation lifetime of a wireless sensor network, IEEE Commun. Lett. 9 (2) (2005) 154–156.

G = 16.7 dB → (Aeq = 5.8 m2 ) or Ptx = 49 mW, or Etx = 0.2 mJ

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M.F. Urso et al. / Physical Communication 4 (2011) 172–181 [12] H. Ochiai, P. Mitran, H.V. Poor, V. Tarokh, Collaborative beamforming for distributed wireless ad hoc sensor networks, IEEE Trans. Signal Process. 53 (11) (2005) 4110–4124. [13] S. Luskey, C. Jin, A. Van Schaik, Energy savings from implementation collaborative beamforming for a remote low power wireless sensor network, in: Proc. of 1st International conference on Wireless Broadband and Ultra Wideband Communication AusWireless, 2006, March 2006. [14] R. Mudumbai, G. Barriac, U. Madhow, On the feasibility of distributed beamforming in wireless networks, IEEE Trans. Wireless Commun. 6 (5) (2007) 1754–1763. [15] K. Zarifi, A. Ghrayeb, S. Affes, Distributed beamforming for wireless sensor networks with improved graph connectivity and energy efficiency, IEEE Trans. Signal Process. 58 (3) (2010) 1904–1921. [16] M.F.A. Ahmed, S.A. Vorobyov, Collaborative beamforming for wireless sensor networks with Gaussian distributed sensor nodes, IEEE Trans. Wireless commun. 8 (2) (2009) 638–643. [17] C.A. Balanis, Antenna Theory: Analysis and Design, Wiley, New York, 1997. [18] J.B.Y. Tsui, Fundamentals of Global Positioning System Receivers: A Software Approach, John Wiley & Sons, Inc., 2000. [19] P. Misra, P. Enge, Global Positioning System, 2nd ed., in: Signal, Measurements and Performance, Ganga-Jamuna Press, ISBN: 09709544-1-7, 2006. [20] C. Savarese, J.M. Rabaey, J. Beutel, Locationing in distributed ad-hoc wireless sensor networks, in: Proc. of IEEE Int. Conf. on Acoustics, Speech, and Signal. Proc. ICASSP, May 2001, pp. 2037–2040. [21] A.J. Viterbi, Principles of Coherent Communication, McGraw-Hill, New York, 1966. [22] CC2430 Data Sheet (rev. 2.1), Texas Instrument, 2007. [23] IEEE, IEEE Std. 802.15.4-2006, Wireless Medium Access Control, MAC and Physical Layer, PHY, Specifications for Low-Rate Wireless Personal Area Networks, LR-WPANs, IEEE, 2006. [24] H. Cramer, M.R. Leadbetter, Stationary and Related Stochastic Processes, Wiley, New York, 1967. [25] F. Sellone, H. Khaleel, M.F. Urso, M. Franceschinis, M. Mondin, Accuracy-Driven Synchronization Protocol, in: Proc. of 2nd Int. Conf. on Sensor Tech. and Applications, SENSORCOMM 2008, August 2008. [26] S. Ganeriwal, R. Kumar, M.B. Srivastava, Timing synch protocol for sensor networks, in: Proc. of 1 st International Conference on Embedded Network Sensor Systems, 2003, pp. 138–149. [27] A. Coluccia, F. Ricciato, On ML estimation for automatic RSS-based indoor localization, in: 5th International Symposium on Wireless Pervasive Computing, ISWPC’10, 2010, pp. 495–502. [28] S. Saunders, Antennas and Propagation for Wireless Communication Systems, Wiley, 2000, 409 pp. [29] R.A. Abd-Alhameed, K.V. Horoshenkov, Y.F. Hu, C.H. See, D. Zhou, Measure the range of sensor networks, October 2008. http://www.mwrf.com/Article/ArticleID/19915/19915.html.

M.F. Urso, Ph.D., was born in Torino, Italy. He received both his Bachelor and Master Degrees in Communications Engineering from Politecnico di Torino, Italy, respectively in 2003 and 2005. He received his Ph.D. in Electronics and Communications Engineering in 2008 from Politecnico di Torino as well. In 2008 he was a visiting Ph.D. student at WSN Berkeley Lab, University of California at Berkeley (CA). Since 2009 he has been with the Dipartimento di Elettronica of Politecnico di Torino, as a postdoc researcher, focusing his activity on distributed and collaborative signal processing algorithms applied to sensor networks. In particular his expertise spans the following fields: time synchronization algorithms, distributed and collaborative beamforming, classification and segmentation algorithms for pattern recognition, self localization for WSN, TinyOS programming, WSN applied to health care scenarios. From 2009 to mid-2011 he collaborated with the Pervasive Radio Technology (PeRT) research Lab of Istituto Superiore Mario Boella (ISMB) on the field of hybrid localization and networks of people. Dr. Urso is also co-founder and CEO of moltosenso s.r.l. (www.moltosenso.com), an R&D company headquartered in Turin and active on Wireless Sensor Network (WSN) System design.

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S. Arnon is presently a faculty member in the Electrical and Computer Engineering Department at Ben-Gurion University (BGU) Israel, and the founder and director of the Satellite and Wireless Communication Laboratory, which works in the areas of laser satellite communication and terrestrial optical wireless communication systems. After receiving his Ph.D. from BGU, Prof. Arnon was a postdoctoral associate (Fulbright Fellow) at LIDS, Massachusetts Institute of Technology (MIT). His research has produced more than fifty journal papers in the areas of satellite, optical and wireless communication. During part of the summer of 2007, he worked at TU/e and PHILIPS LAB, Eindhoven, Nederland on a novel concept of a dual communication and illumination system. He was a visiting professor during the summer of 2008 at TU Delft, Nederland. Prof. Arnon has been continuously taking part in many national and international projects in the areas of satellite communication, remote sensing, wireless networks, cellular and mobile communication. He consults regularly with start-up and well-established companies in the areas of optical, wireless and satellite communication.

M. Mondin is Associate Professor at Dipartimento di Elettronica, Politecnico di Torino. Her current interests are in the areas of signal processing for communications, modulation and coding, simulation of communication systems, and quantum communication. She holds two patents. She is Associate Editor for IEEE Transactions on Circuits and Systems-I. She has been acting as a reviewer for several international scientific IEEE and IEE journals; she has been Guest Editor for the EURASIP Journal on Wireless Communications and Networking (2009) and the International Journal of Digital Multimedia Broadcasting (2009 and 2010), and she has been the member of the technical-scientific committees of various international conferences. She has organized an invited session on QKD at the conference ISABEL 2010. She has been principal investigator for Politecnico di Torino in several national PRIN projects concerning the integration of satellites and high altitude platforms for broadband data transmission, Co-PI for the NATO Collaborative Linkage Grant and National Coordinator of the PRIN 2007 project ‘‘Feasibility study of a Earth-satellite quantum optical communication channel’’. She authored and co-authored more than 50 articles on international journals and more than 100 contributions to international conferences, and two books in Italian.

E. Falletti obtained her M.Sc. and Ph.D. degrees in Electronics and Communications Engineering from Politecnico di Torino, Italy. Currently she is with the Istituto Superiore Mario Boella, in Torino, where she is responsible of projects on the analysis and design of signal processing algorithms for GNSS digital receivers. Her research interests have been focused on array signal processing, wireless channel modeling, communications from High Altitude Platforms and signal processing for digital receivers.

F. Sellone, Ph.D., received the Degree in Electronic Engineering in 1998, and the Ph.D. in Electronic Engineering in 2002, both from Politecnico di Torino, Italy. He has more than ten years of experience in the field of applied research. He was an Assistant Professor at Politecnico di Torino, founding the SmartAnt research Group, with more than 30 master thesis in the field of Smart Antennas and Wireless Sensor Networks, publishing more than forty papers in international journals and conferences. He has gained experience in hardware design of smart sensors and firmware development.