Distributed Transmit Beamforming: Data Funnelingin Wireless Sensor Networks

Wayes Tushar∗†, David Smith†∗ and Tharaka Lamahewa∗ The Australian National University, †National ICT Australia (NICTA)

wayes.tushar@anu.edu.au, david.smith@nicta.com.au and lamahewa@gmail.com

Abstract—In this paper, utilizing data funneling and dis-tributed beamforming, we propose a novel cooperative cross-layertransmission scheme to reduce the transmit energy of sensornodes while communicating over long distances in a wirelesssensor network. We show that the proposed transmission schemerequires less transmit energy, compared to direct beamformingand direct single link transmission, to achieve the same symbolerror probability (SEP) at the receiver. Considering batteryenergy consumption, we show that our proposed transmissionscheme is capable of increasing the life time of sensor nodes thatneed to communicate over long distances. We also show improvedperformance in terms of a routing metric.

I. INTRODUCTION

It is often important to conserve energy while transmitting

data in ad hoc networks since the individual nodes are typically

powered by batteries that may be difficult to replace or

recharge [1]. Given the application area and network resource

constraints, local computations often consume significantly

less energy than the communications [2]. Communication

via the on-board radio is the most expensive operation of

sensors [3]. In radio communications in free-space, the sig-

nal strength decreases proportionally to the square of the

propagation distance [4]. Therefore protocol design for sensor

networks, which will allow energy consumption reduction of

the sensors for communications and an increase in network

lifetime has been widely researched recently [2].

Two popular methods of energy savings in a wireless sensor

network are (i) distributed transmit beamforming (DTB) and

(ii) data aggregation (or data funneling) [5]. DTB is a trans-

mission technique where two or more radios cooperatively

form a virtual antenna array, and obtain diversity gains against

channel fading and array gains from increased directivity.

DTB increases M -fold energy efficiency of wireless sensor

networks for M transmitters [6]. Data funneling/aggregation

is another method to save the sensor energy by routing

data packets through low cost communication paths while

communicating over long distances. Numerous data aggrega-

tion [5], [7]–[10] and DTB [6], [11]–[15] techniques have been

proposed in the literature which are directly or partially related

to the increase in lifetime of wireless sensor networks. While

either of the two methods can be used separately, in this paper

we incorporate DTB with data funneling and propose a novel

transmission technique for transmission of data over long

distances. The scheme essentially uses cooperative layered col-

laborative beamforming. We show that layered collaborative

beamforming gives more impressive performance in terms of

energy savings to achieve a SEP at the receiver with respect

to direct beamforming and direct single link transmission for

the same source-receiver pair. To adapt DTB to our system

we consider a clustered network where each cluster consists

of multiple cooperative sensors (CS). In this work we consider

that the signal is funneled through clusters from source to the

receiver, one or more clusters are assigned to a given layer for

DTB collaboration. DTB is used for transmission of signal

from one layer to another. Thus our main contributions in this

work are:

• Combining DTB and data funneling for long-range com-

munications in sensor network to save total system en-

ergy.

• We show that significant energy savings are possible for

the sensors in the distant cluster while considering the

energy spent by each sensor for transmission from it’s

cluster over long distance compared to direct beamform-

ing and direct single link transmission.

• We show that for the proposed scheme, to achieve a

SEP of 10−3 at the receiver, the battery energy of the

sensor can be saved by up to 36% compared to direct

beamforming and thus, it increases the network life time.

• We show improved performance in terms of routing by

adopting this cross-layer scheme.

The rest of the paper is organized as follows. We describe

the system model in Section II. The funneling of data and the

performance measure are explained in Section III. Simulations

results and performance comparison with other transmission

techniques are given in Section IV, both at the physical OSI

layer1 and routing (or network) OSI layer, and concluding

remarks are given in Section V.

II. SYSTEM MODEL

The architecture of the sensor network is shown in Fig. 1.

The whole network area is divided into different layers and

all the sensors in each layer are organized into different

clusters. Each cluster consists of M number of cooperative

sensors (CSs) with a single cluster head (CH), and (M − 1)cluster members (CM). The CH in each cluster is assumed to

1Here we use the term ‘layer’ interchangeably to mean layers of sensorclusters for DTB with data funeling and Open Systems Interconnection (OSI)layers (e.g., PHY, MAC, routing, application), hence for the latter we alwaysuse the term OSI layer.

2012 Australian Communications Theory Workshop (AusCTW)

978-1-4577-1962-2/12/$26.00 ©2012 IEEE 49

Fig. 1. System model for data funneling using distributed transmit beam-forming

have more computational ability and responsible for reception

and detection of the beamformed signal. All the M CSs in

a cluster follow an uniform distribution and can hear each

other. The clusters can be formed using any general cluster

formation scheme that ends up with a single CH with multiple

cooperative CMs in each cluster [16], [17]. The layers can

be defined as the regions the receiver (R0 in Fig. 1) wishes

to monitor. We consider the location of R0 as the origin and

each layer is numbered from the origin as z1, z2, ..., zl. Similar

to [5], we assume that CHs will be informed by a directional

flood (DF) initiating from R0 about the layers they belong to.

CH will share this information with the fellow CMs.

Here we consider a time-slotted uni-directional transmission

scheme which is appropriate for wireless sensor networks. At

time slot n a sensor node i of cluster j in layer zl wishes to

transmit a message sm(n) to the receiver, where sm(n) is a

m-ary phase shift keying (PSK) signal which consists of Lsymbols. All the sensors access sm(n) and collaborate with

each other to beamform the signal towards the CH of cluster

k in layer zl−1 (towards R0 if l = 1). For beamforming the

signal, each CS independently synchronizes itself and adjusts

its initial phase to a beacon sent from the CH in zl−1 (from R0

if l = 1) as in a closed loop case [18]. The channel between

the CS i in cluster j of zl and the receiving CH in cluster kof zl−1 is considered as

gk,zl−1

j,zl(i, n) =

√bmh

k,zl−1

j,zl(i, n), (1)

where bm is the large scale effect (i.e., bm ≈ G/(dkj )α/2 [18],

where α is the path loss exponent and G is a constant and dkjis the distance from the center of cluster j to CH in k of

zl−1 (R0 if l = 1) and is independent of i) and hk,zl−1

j,zl(i, n)

is independently and identically distributed (i.i.d.) complex

Gaussian random variable with mean zero and variance σ2.

The CH of cluster k in zl−1 receives the signal, detects it and

shares with the CMs in its own cluster. Then in the next time

slot, upon receiving the beacon, the CSs of cluster k beamform

their own information along with the information received in

the previous time slot from cluster j towards the closest CH

in the next layer zl−2. Eventually the message from the source

reaches R0.

A. Transmit beamforming

For transmit beamforming we assume that perfect channel

state information (CSI) is available at the transmitting sensors

and we also consider an interference free system. Now at time

slot n, the transmitted signal from each CS i in cluster j of

zl towards the CH of cluster k in zl−1 is

xk,zl−1

j,zl(i, n) = sm(i, n)

√Esμia

k,zl−1

j,zl(i, n), (2)

where Es is the transmit energy, μi is a scalar of the order

of 1/√M used to adjust the transmit energy [18] and is same

for all CSs, ak,zl−1

j,zl(i, n) is the beamforming weight which is

the conjugate of the channel gain from CS i of cluster j to

the CH in cluster k, i.e., ak,zl−1

j,zl(i, n) = (g

k,zl−1

j,zl(i, n))∗.

The received signal at the CH of cluster k in layer zl−1 is,

ykj,zl−1(CH,n) =

M∑i=1

xk,zl−1

j,zl(i, n)g

k,zl−1

j,zl(i, n) + w(n), (3)

where w(n) is the zero mean additive white Gaussian noise

with variance σ2n. The noise variance is considered the same

for all communication links.

From (1), (2) and (3),

ykj,zl−1(CH,n) =

M∑i=1

√Esμism(i, n)bm|hk,zl−1

j,zl(i, n)|2 + w(n).

(4)

Therefore the received signal will be the sum of the scaled

version of the signal of node i. It is assumed that the signal is

demodulated and decoded at the CH of zl−1 (at R0 for l = 1)

using the maximum likelihood (ML) method [19].

III. DATA FUNNELING AND PERFORMANCE MEASURES

The proposed data funneling with DTB protocol consists of

two phases: (1) Setup phase and (2) communication phase. The

setup phase starts with the initiation of DF from R0 towards

the network area. The packet of DF consists of the location

of the receiver and the specific time period for the sensors

in each layer to beamform their signal towards the next CH.

Upon receiving the DF, each CH records the distance of the

closest CH, update the packet with its location and sends it

towards the next layer. The setup phase ends as soon as the

DF reaches the last layer in the sensor network.

Communication phase initiates when a sensor in a cluster

has information to send to the receiver R0. The message

is funnel through the clusters using DTB as described in

Section II. The communication phase ends as soon as the

message reaches R0. The proposed protocol for the two phases

of the data funneling using DTB is summarized as a flow chart

in Fig. 2 and Fig. 3 respectively.

A. Performance measures

From (4) the instantaneous signal to noise ration (SNR) at

the receiving point (RP) (which is a CH in zl−1 or R0 if l = 1)

50

is,

γ =

μ2i b

2mEs

(M∑i=1

∣∣∣hk,zl−1

j,zl

∣∣∣2)2

σ2n

=b2mμ2

iEsξ2

σ2n

, (5)

where, ξ �M∑i=1

∣∣∣hk,zl−1

j,zl

∣∣∣2. Since |hk,zl−1

j,zl| is Rayleigh dis-

tributed, ξ follows an Erlang distribution with shape parameter

M and rate parameter σ2 [18].

Now following [18], an upper bound for the average SEP

for m-PSK can be derived for the proposed scheme as,

Ps ≤ m− 1

m

⎛⎝1 +

sin2(πm

)σ2 μ2

i b2mEs

σ2n/ξ0

sin2(

(m−1)πm

)⎞⎠

−M

, (6)

where, ξ0 > 0 andμ2i b

2mEs

σ2n/ξ0

can be expressed asμ2iG

2Es

dασ2n/ξ0

.

From (6), it can be seen that SEP is a function of bm and

the number of collaborating nodes M in the cluster. Since bmis distant dependent path loss, average SEP Ps is a function

of the distance between the source cluster and RP, and M ,

i.e., Ps ≤ f(drs,M), where with drs we indicate the distance

between the source cluster center and RP. Note that for fixed

drs, the SEP decreases as the number of cooperative sensors Mat the transmitting cluster increases. As a result direct beam-

forming from a cluster with multiple sensors (M > 1) always

lower the SEP at R0 compared to single link transmission.

But, as we proposed, the incorporation of data funneling

with distributed transmit beamforming provides even better

results in terms of SEP at R0 than direct beamforming alone.

Start

Divide thenetwork

into layers(z1, z2, · · · , z�)

Initiatedirectionalflood (DF)

CH inlayer z�

1. Receive DF2. Estimate

distance3. Update

the location

End setup phase

Is z�thelast

layer(z� =z1)?

Send theupdated

flood to thenext layer

No

� = � − 1

Yes

Fig. 2. Setup phase of the data funneling using distributed transmitbeamforming protocol.

Start

Receiving CH1. Detect

the receivedsignal

2. Sharethe detected

signalwith CM

IsRe-

ceiv-ing

CH=R0?

End of phase

Beamformtowards the

next CH

1. Receivebeacon fromadjacent CH2. Calculate

beamformingweights

Aggregateown data

with detectedsignal

yes

no

Fig. 3. Communication phase of the data funneling using distributed transmitbeamforming protocol.

In the data funneling algorithm, the distance from the source

cluster to R0 is divided into multiple small distances by plac-

ing intermediate clusters between them. The distance between

the intermediate clusters are smaller than the source to receiver

distance dR0s . Assuming all the clusters have identical number

of CSs, from (6) SEP at RP is dominated by the distance

between the clusters. Therefore, beamforming and detection

along these small distances lead to performance improvement,

which is explained as follows.

Equation (6) can be expressed as,

Ps ≤ m− 1

m

(1 +

G′

(drs)α

)−M

, (7)

where G′ = Es

(sin( π

m )

sin((m−1)π

m )

)2σ2

σ2nG2μ2

i ξ0. From (7), for a

particular m-ary modulation scheme and constant number of

sensors M in each cluster, SEP at a RP depends on the distance

drs between the source and the RP and the SEP increases

with the distance drs. Therefore, transmission over multiple

small distances performs better than beamforming over a long

distance.

IV. RESULTS AND PERFORMANCE ANALYSIS

A. Performance at the Physical OSI Layer

We run a Monte Carlo simulation for the proposed scheme

to transmit 104 bits (Nb = 104) in each transmission, and

compare the results with direct beamforming and single link

transmission for the same source-destination pair. The variance

of channel between the clusters are scaled by the square of

distance (i.e., α = 2) between them to incorporate the path loss

effect. The variance of noise of the smallest link is considered

and assumed same in all transmission links.

We divide the network area into three different layers z1, z2and z3. As in Fig. 1, z1 contains cluster 1, z2 contains cluster

2 and 3 and finally z3 contains cluster 4 and 5. We assume

51

5 10 15 20

10−4

10−3

10−2

10−1

100

System SNR (dB)

SE

P

Direct single link BPSKDirect Beamforming BPSKData funneling BPSKDirect single link QPSKDirect Beamforming QPSKData funneling QPSK

Fig. 4. Comparison of SEP at the receiver for different type of transmissionschemes with BPSK and QPSK modulation respect to system SNR (dB).

each cluster contains 5 sensors including the CH. The distance

from clusters 1, 2, 3, 4 and 5 to the receiver R0 are dR01 =

400λ, dR02 = 700λ, dR0

3 = 1000λ, dR04 = 1400λ and dR0

5 =1300λ, respectively, where λ is the wave length of the signal.

We consider the transmission from cluster 4 to the receiver R0.

The distance between the clusters along the funneling path

of cluster 4 are d34 = 487.2λ, d13 = 613.24λ, dR01 = 400λ,

respectively, where the distances are calculated from the polar

coordinates of the clusters with respect to the receiver R0.

We consider two examples. In the first example, we run

the simulation for direct single link transmission, direct

beamforming from cluster to the receiver and proposed data

funneling scheme for the same noise and fading environ-

ment and show that the proposed scheme provides noticeable

improvements over the other two transmission schemes in

terms of overall system’s transmit energy savings to achieve

a same SEP at the receiver. In the second example we run

the simulation considering the energy spent by the sensors at

the furthest distant cluster to send a signal to the receiver R0

over a long distance and show that significant improvement

in transmit energy savings is possible with the proposed data

funneling scheme.

Fig. 4 shows the SEP at the receiver with respect to system

SNR for binary phase shift keying (BPSK) and quadrature

phase shift keying (QPSK) modulation schemes. The system

SNR is defined as the ratio of system’s total transmit power

to the noise power. To make the system SNR same for all

transmission schemes, the transmit energy of each sensor is

scaled as follows for the three different type of transmissions:

Single link energy: Esingle = M√

EsμmLpath

Direct Beamforming: EBF =√

EsμmLpath (8)

Data funneling: EDfun =√

Esμm,

where Lpath is the number of funneling hops from cluster 4to the receiver for the proposed scheme.

−5 0 5 10 15 20 25 30

10−4

10−3

10−2

10−1

100

Transmit SNR (dB)

SE

P

Direct single link BPSKDirect Beamforming BPSKData funneling BPSKDirect single link QPSKDirect Beamforming QPSKData funneling QPSK

Fig. 5. Comparison of SEP at the receiver for different type of transmissionschemes with BPSK and QPSK modulation respect to the transmit SNR incluster 4 transmitters.

It can be observed that for both type of modulation schemes,

data funneling provides transmit energy savings of 1 dB and

10dB (for the same noise variance in all links SNR can

be translated to transmit energy) for the whole system to

achieve a SEP of around 10−3 with respect to direct distributed

beamforming and direct single link transmission, respectively.

We now consider the energy spent by the sensors in a distant

cluster (cluster 4) for transmitting signals to the receiver R0.

We observed that significant energy savings are possible using

the proposed scheme compared to direct beamforming and

single link transmission. The observed output for both BPSK

and QPSK modulation schemes are plotted in Fig. 5.

From Fig. 5, the transmit energy savings for data funnel-

ing over direct beamforming scheme is around 11.5 dB for

BPSK to achieve a SEP of 10−3 at the receiver. For QPSK

modulation scheme it is of the order of 10 dB to achieve

the same SEP at the receiver. The reason for this significant

improvement is that for direct beamforming the transmitters

in cluster 4 have to overcome a distance of dR04 while for data

funneling the transmitters only need to transmit over a distance

of d34 where dR04 >> d34. This saving is particularly useful for

the application scenarios where the location of distant cluster

4 is not easily accessible for battery replacement but has easy

access to the other clusters. This improvement of SEP can be

explained from (7). From (7), for direct beamforming from

cluster 4 to R0, the upper bound for SEP is,

PR0,dirs,4 ≤ m− 1

m

⎛⎝ 1

1 + G′

(dR04 )2

⎞⎠

M

. (9)

Now if we assume the SEP is very small in the intermediate

paths between the cluster, then for data funneling, the upper

bound of SEP from cluster 4 to the receiver R0 can be

52

0 5 10 15 20 25 30

10−4

10−3

10−2

10−1

100

Transmit SNR (dB)

SE

P

SEP for funneling

Upper bound of SEP for funneling

SEP for directbeamforming

Upper bound of SEP for directbeamforming

SEP for single link transmissionUpper bound of SEP forsingle link transmission

Fig. 6. Upper bounds of SEP at the receiver for BPSK modulation scheme forsingle link transmission, distributed transmit beamforming and data funnelingwith beamforming from the distant cluster 4.

expressed as,

PR0,dfs,4 ≤ P 3

s,4 + P 1s,3 + PR0

s,1

≤(m− 1

m

)[(1 +

G′

(d34)2

)−M

+

(1 +

G′

(d13)2

)−M

+

(1 +

G′

(dR01 )2

)−M]. (10)

Considering all other parameters unchanged (i.e., Es, σ2,M

and m), from (10), PR0,dfs,4 < PR0,dir

s,4 for d34, d13, dR01 <<

dR04 . Therefore, data funneling using transmit beamforming

performs better than direct beamforming for large distance

communication in terms of SEP at the receiver.

In Fig. 6 we plot the upper bound of SEP based on (9)

and (10) (considering G′ = 7 × 105) as well as the SEP at

the receiver for BPSK for all three transmission schemes with

respect to the transmit SNR of the sensors in cluster 4. We can

observe that the upper bounds are consistent with our analysis

in (9) and (10). The received SEP at the receiver for all the

transmission schemes are also well below the upper bound of

SEP.

We now compare the battery energy consumption of the

sensors in the distant cluster. For example, we consider the

power consumption characteristics of Rockwell’s WINS node

which represents a high-end sensor node and is equipped

with a powerful StrongARM SA-1100 Intel processor [20].

Though relation of the transmit SNR to the battery power

is application specific, we assume that the noise power is

such that the 0 dB transmit SNR in the proposed system

is equivalent to a transmit power of 0 dBm (1 mW) [20].

With this assumption, in order to achieve a SEP of 10−3

at the receiver the battery energy savings for data funneling

with distributed transmit beamforming with BPSK modulation

scheme is 36% over direct beamforming which indicates a

significant energy savings of the sensor’s battery. Therefore

the improvement of transmit energy as well as the battery

power savings when compared to single link transmission

and direct beamforming to achieve the same SEP at the

receiver with typical modulation schemes, clearly emphasizes

the effectiveness of the proposed scheme for low energy data

transmission over large distances.

B. Routing OSI Layer Performance

We also compare the performance of the proposed scheme

with direct beamforming (from Fig. 5, the improved perfor-

mance over direct beamforming is also an indication of the

improvement over direct transmission as well) based on a

routing metric given in [17]. An energy efficient and power

aware routing protocol should have a lower cost value for the

link cost function [17]:

Di = wiEi, (11)

where Di is the cost for the transmitting sensor node i, Ei

is the transmit energy of node i and wi is a dimensionless

coefficient defined by,

wi =B0i

B0i −Btx. (12)

In (12), B0i is the new battery power of sensor i and Btx is

the required battery power for a transmission of signal. It is

easily observed from (12) that, less remaining battery energy

(i.e., more energy consumption for transmission) results in a

much bigger value for the coefficient wi.

In Table I we list the values of the coefficient wi for

both direct beamforming and the proposed scheme for a list

of particular value of SEP at the receiver. We consider that

each sensor is using a 4W-E27 motion sensor battery and

the consumption characteristics of the sensors are equivalent

to Rockwell’s WINS node [20]. From Table I, the value of

the coefficient of the proposed scheme is always lower than

the value of the direct beamforming case, which refers to the

energy saving of the battery of the proposed scheme.

In Fig. 7, we show the cost of achieving the same SEP

at the receiver for both the proposed scheme and the direct

beamforming scheme. It shows that the cost of transmission

for a sensor node can be significantly reduced for long distance

transmission using our proposed scheme. For example, to

achieve a SEP of 10−3, the proposed scheme requires 0.076times the cost compared to direct beamforming scheme, which

is a significant cost reduction in terms of energy savings.

TABLE ICOMPARISON OF THE COEFFICIENT wi , FROM (12), TO ACHIEVE THE

SAME SEP AT THE RECEIVER

SEP wi,DF wi,DB

0.13 0.2245 0.30290.08 0.25 0.32890.043 0.2579 0.35590.0180 0.2658 0.40630.0063 0.2739 0.6273.0014 0.2903 0.6273

53

0 0.02 0.04 0.06 0.08 0.1 0.120

10

20

30

40

50

60

70

80

SEP

Cos

t to

achi

eve

a pa

rtic

ular

SEP Data funneling

Direct beamforming

Fig. 7. Comparison of the cost to achieve the same SEP at the receiver.

Hence collaborative beamforming across multiple clusters, and

data funeling through clusters, gives significant improvement

in terms of routing performance.

V. CONCLUSION

Combining data funneling and distributed beamforming

we proposed a cross-layer transmission scheme to transmit

signals from a cluster of sensors to a distant receiver. The

proposed scheme shows significant energy savings for an

acceptable SEP at the receiver for communication from sensors

in the distant cluster. The proposed scheme also shows overall

system energy savings. The transmit energy savings should

significantly increase the battery life time of sensor networks

when our proposed scheme is adapted, as well as improve the

efficiency of routing.

ACKNOWLEDGMENT

NICTA is funded by the Australian Government as rep-

resented by the Department of Broadband, Communications

and the Digital Economy and the Australian Research Council

through the ICT Centre of Excellence program. This work was

performed while the co-author Tharaka Lamahewa was at the

Australian National University.

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