Acta Polytechnica Vol. 52 No. 5/2012

Energy Estimation of Distributed Phase-shift Beamforming

Viktor Černý

Dept. of Computer Science and Engineering, Faculty of Electrical Engineering, Czech Technical University, Technická 2,
166 27 Praha, Czech Republic

Corresponding author: cernyvi2@fel.cvut.cz

Abstract
Ad-hoc and sensor networks are composed of small, low-power devices, which can connect between themselves without the
help of an infrastructure. Research in this area has been both extensive and intensive and is still very far from exhaustion.

Our work in this area is aimed at developing a new type of communication between groups of modules capable of
connecting clusters (groups) of devices which are separated by distances greater than the maximum transmission range of
the devices themselves, without the help of relays or signal repeaters. In this paper we study the energy requirements
for bidirectional communication between two clusters separated by a distance greater than the maximum transmission
range of the modules, in the classic way (with the use of repeaters or relays) and by applying distributed phase-shift
beamforming.

Keywords: ad-hoc networks, beamforming, phase-shift, distributed.

1 Introduction
Phase-shift beamforming is a method extensively used
in radio networks, in which devices are equipped with
multiple antennas. By injecting in each antenna el-
ement a signal slightly shifted in phase (delayed),
because the signals travel slightly different distances
towards the receiver, for a favourable phase combina-
tion, the two signals will meet at the receiver in phase
and thus, will have energy higher than each of the
signals taken separately. Such antenna systems (or
antenna arrays) have been named “smart antennas”
because, based on this method, the radiation pattern
of the transmitter antenna array can be modified —
making its signal stronger or weaker in desired direc-
tions — without physically orienting the device, just
by modifying the phase of the signals coming to each
antenna element.
The case studied in this paper is of modules that

are not equipped with antenna arrays — each device
has only one single antenna. In order to be able to
use the method of phase-shift beamforming, multi-
ple devices have to share the same information to
be sent and be able to synchronise the transmitted
signals precisely. Such a mechanism has already been
proposed in [6], [7], [8] and [1], however these papers
ignore the fact that crystals are not perfect and phase
synchronisation between the modules is lost due to
the clock being slightly faster at one module than the
other.
Our aim is briefly to present a method for syn-

chronizing the transmitted signals, simpler than the
method in [3], and to evaluate the energy requirements
for bidirectional communication between two clusters
of modules (separated by a distance greater than their

(a) (b)

(c) (d)

Figure 1: Different radiation patterns corresponding
to different phase combinations of the signals injected
into the elements of an antenna array.

maximal transmission range) in the method proposed
here and in the classic way of installing repeaters
(relays) between two clusters.

This paper is structured as follows: the second sec-
tion presents the distributed phase-shift beamforming
mechanism and the proposed device, the third section
is a theoretical approach towards the required energy
estimations, the fourth section contains the experi-

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Acta Polytechnica Vol. 52 No. 5/2012

(a)

(b)

(c)

Figure 2: (a) A network divided into two clusters.
(b) The two clusters can be connected by installing
repeaters. (c) The two clusters can be connected by
distributed phase-shift beamforming.

ments and the results and the paper is concluded in
the fifth section, where future work is also proposed.

2 Distributed Phase-Shift
Beamforming

There are four types of radio communications from
the channel perspective: SISO, SIMO / MOSI, MISO
/ SOMI and MIMO. SISO (Single Input — Single
Output) is the classic type — one antenna at the
transmitter, one at the receiver. SIMO / MOSI (Sin-
gle Input — Multiple Output) works at the basis
of signal processing at the receiver; the transmitter
is equipped with only one antenna and the receiver
with multiple antennas. Noise affects the antennas
at the receiver slightly differently and, with the use
of signal processing, the useful signal can be sepa-

rated from the noise. MISO (Multiple Input — Single
Output) describes communications where the trans-
mitter has multiple antennas, regulated by different
initial phases, such that the signals coming from these
antennas superimpose at the receiver antenna, thus
creating a stronger signal. MIMO (Multiple Input —
Multiple Output) combines the properties of SIMO
and MISO to present this technique here would be
both space-consuming and beyond the scope of the
paper.
To exemplify the properties of beamforming, let

us consider four antennas A1, A2, A3 and A4 sym-
metrically placed at coordinates (x,y): A1(−λ/2, 0),
A2(λ/2, 0), A3(0,−λ/2) and A4(0,λ/2) and acting as
an antenna array. Each antenna is assumed to have a
perfectly circular radiation pattern in the horizontal
plane, as in Fig. 1a (λ is the wavelength of the signal).
If all the antennas are fed identical and in-phase sig-
nals, the radiation pattern of the whole array becomes
as in Fig. 1b. If the signal injected in antenna A4
is dephased at −90° and at +180° respectively tak-
ing as a reference the other three identical remaining
signals, the radiation pattern of the array becomes
as depicted in Fig. 1c and Fig. 1d respectively. In
conclusion, we can manipulate the radiation pattern
of a transmitter equipped with an antenna array by
altering the initial phases of the signals injected into
the element antennas composing the array.

Let us now consider an ad-hoc network where all the
modules are randomly placed over a 2D surface and
each module is equipped with only one single antenna.
Let us also assume that, due to the random placement
of the modules, two clusters are formed, without the
possibility of direct communication between them, as
in Fig. 2a. There are three ways to interconnect the
devices by increasing the transmission power (this
will drain the batteries faster and can be limited by
the hardware of the transceiver), by using higher gain
antennas (sometimes unsuitable because it will lead
to physically bigger antennas) or by placing repeaters
between the two clusters, as in Fig. 2b.
We are currently developing a fourth way for the

clusters to interconnect: the modules of one cluster
will beamform their signal thus creating a virtual
transmitter whose power will be sufficient to transmit
directly to the other cluster — as in Fig. 2c.
If we assume the network presented in Fig. 2b,

where the network is formed by two disjoint clusters
K1 and K2, connected by a relay set R, the conditions
for a connected network are: R 6= ∅, R∩K1 6= ∅ and
R ∩ K2 6= ∅. Assuming a source module s ∈ K1
and a destination module d ∈ K2, connected by a
“best route” discovered by a routing algorithm of
some sort, as in Fig. 2b, then for each bidirectional
communication between s and d, in order to have
reliable communication, any repeater r ∈ R has to
perform four steps:

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Acta Polytechnica Vol. 52 No. 5/2012

1. receive the data packet from the previous module;

2. transmit the data packet to the next module;

3. receive acknowledgement from the next module;

4. transmit the acknowledgement to the previous
module.

In the same time, the end devices performed only two
operations: s transmitted a data packet and received
an ACK, while d received a data packet and sent an
ACK.

In conclusion, because the number of operations
performed by each relay is greater than the number
of operations performed by each end device, we can
expect that the batteries will exhaust at the relays
sooner than at the end devices. In order to prevent
this situation, we can install batteries with higher
capacities at the relays, or we can increase the num-
ber of relay modules. There are however scenarios in
which this improvement is impossible: for example,
when there is a river in the area when the relay mod-
ules should be installed. In this case, the clusters are
permanently disconnected.

By applying distributed phase-shift beamforming, s
will broadcast the data packet to its neighbours, and
then the whole group of modules will transmit the
data packet directly to d in a synchronized manner.
In order to reply, d will broadcast its ACK locally
to its own neighbours and then the whole group of
modules will transmit in the ACK a synchronized
manner directly to s — as in Fig. 2c.

It is beyond the scope of this paper to present how
the different modules will know how much to delay
(dephase) the signals in order to superimpose correctly
at the receiver — the cluster discovery mechanism
has been studied, and the results were published in
[5]. We can assume that in order to send a message
from s to d, each module m ∈ K1 has a precise phase
delay ∆φm which must be used so that cluster K1
can transmit to d properly; similarly for the cluster
K2 in order to have communication from d back to s.

The difficulty with this mechanism consists in main-
taining the constant phase delay between different
modules: the oscillator crystals are not identical, and
even minute imperfections, over long periods of time,
will lead to the loss of precise phase delays. One
solution might be to repeat the phase discovery al-
gorithm presented in [5], however this is not feasible
due to its exponential complexity. Another solution
that we have employed is if module s is capable of
transmitting simultaneously on two frequencies: fd
— on which data is sent, and fs — which is a plain
sine wave used for synchronization. Synchronization
frequency fs was chosen t times higher than data
frequency fd, where t is a constant.
Thus, module s is responsible for broadcasting in-

formation to its neighbours and for maintaining the

synchronization of its neighbours during beamformed
transmission to d. Each neighbour of m of s receives
the synchronization signal fs. Through a phase-locked
loop it locks its own data signal fd and then adds to it
the corresponding phase delay ∆φm. In this manner,
the signals coming to d from all the modules in K1
will meet in phase and thus their power will increase,
assuring transmission beyond the maximum range of
any individual module separately.

The internal architecture of the module is presented
in Fig. 3 and it is currently patent pending, under
Patent Application, Reg. No. 2011-25254 / 2011-785,
2011. The components are the following:

1. Power supply — provides electric power to the
active components.

2. Internal logic unit — performs the main tasks
of the module (initiate phase search, dictates
the regime based on channel access methods,
computes the phase increment, etc.).

3. Carrier generator — generates two in-phase syn-
chronised sine waves: one wave has frequency fd
and is the data carrier, the other has frequency
fs = tůfd and is the synchronisation signal. This
can be achieved for example by involving a crys-
tal capable of generating fs and then a frequency
divider which generates fd from fs, by dividing
it to t > 1.

4. Transceiver — using a modulation technique, this
is responsible for sending and receiving informa-
tion on the data wave.

5. Phase synchroniser — this is in essence a phase-
locked loop (PLL) capable of synchronising two
waves.

6. Phase delayer — delays the phase of a signal by
a given amount.

7. Mode switch — commutes the module from one
regime (or mode of operation) to another.

8. Antenna — the antenna used for transmitting
and receiving; it must allow frequencies fd and
fs to pass through.

3 Energy Estimation
Case A. Let us start with classic bidirectional store-
and-forward communication between two radio mod-
ules M1 and M2, separated by distance D, in free
space, as in Fig. 4a. For a classic bidirectional commu-
nication, the minimal number of packets is 4: DATA
(M1 → M2), ACK (M2 → M1), DATA (M2 → M1)
and ACK (M1 → M2). We can assume that the size
of the ACK packet is k times larger than the size of
the DATA packet, where 0 < k < 1 and we note that

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Acta Polytechnica Vol. 52 No. 5/2012

Figure 3: Device capable of distributed phase-shift beamforming. The full functioning of the device is described
in the Patent Application Form [4].

sizeof(ACK) = k sizeof(DATA). From the laws of
electromagnetic propagation in free space (FSPL) it
can be seen that the received power decreases with the
distance squared. For energy estimation, because the
methods are compared with each other, it is safe to
assume (in order to simplify the calculus) that the an-
tennas have no gain. In the same manner, we consider
the receiving operation as being totally passive (no
energy required). In this case, in milliwatts, according
to FSPL we can write that PR ∼ PTD2 . The received
power is proportional to the transmitted power and
is inreversely proportional to the squared distance.
Thus, the energy E required to transmit a data packet
over distance D can be written as:

E ∼ D2 sizeof(DATA) (1)

and we can choose the constant to balance this inequal-
ity as C (dependent on the antenna gains, apertures,
minimal required power at the receiver, the environ-
ment of propagation and sizeof(DATA)), thus:

E(DATA) = CD2. (2)

In this case, E(DATA) = CD2 = ED and
E(ACK) = kCD2 = EA = kED. The total energy
required for the minimal bidirectional communication
becomes:

Etot = 2(ED + EA) = 2CD2(1 + k). (3)

The energy need per single module is:

Emod = (ED + EA) = CD2(1 + k). (4)

Case B. Let us now consider the same case, though
now between M1 and M2 there is a repeater R, placed
at distances D1 and D2 from M1 and M2 respectively,
as in Fig. 4b. For duplex store-and-forward commu-
nication, the minimal number of data packets is 8:
DATA(M1 → R), DATA(R → M2), ACK(M2 → R),
ACK(R → M1), DATA(M2 → R), DATA(R → M1),
ACK(M1 → R) and ACK(R → M2).

In order to send one data packet from M1 to M2
through R, the total energy required will be, according
to (2):

E = E1+E2 = CD21 +CD
2
2 = C

(
D21 +(1−D1)

2) (5)
It can be seen that E has its minimal value when

D1 = D2 = D, thus the most efficient way (from the
energy point of view) to place a repeater is to place it
in the middle of the distance between the modules. In
this case, we obtain: E(DATA) = C

(
D
2

)2
= CD

2

4 =

ED
4 and in the same manner: E(ACK) = kC

(
D
2

)2
=

EA
4 =

kED
4 . The total energy need is:

Etot = 4
(
E(DATA) + E(ACK)

)
= 4
(
ED
4

+
kED

4

)
= CD2(1 + k). (6)

The energy drain per end-module is given by:

Emod = E(DATA) + E(ACK) =
1
4
CD2(1 + k) (7)

and for the relay:

ER = 2
(
E(DATA) +E(ACK)

)
=

1
2
CD2(1 +k). (8)

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Acta Polytechnica Vol. 52 No. 5/2012

M1 M2D1 D2

D

(a) Two modules. (b) Two modules and one repeater.

(c) Two modules and N relays. M modules per cluster.

(e) M modules per cluster and one relay. (f) M modules per cluster and N relays.

(g) M modules per cluster, phase-shift beamforming.

Figure 4: Different module placements.

It can be seen that even in this most effective case,
the need on the router is twice the need on any end-
device, thus the router will exhaust its battery twice
as fast as any of the modules. However, if the router
can allow for a battery twice the capacity of any
end-module, this will compensate the higher power
need.

Case C. If between the devices there are N relays,
as in Fig. 3.27c, then the average power consumption
becomes per end device (the same as in (7)):

Emod = E(DATA) + E(ACK) =
1
4
CD2(1 + k), (9)

and per repeater:

ER = 2
(
E(DATA) + E(ACK)

)
=

1
2N

CD2(1 + k).
(10)

The total energy need remains the same as in (6).
Thus, installing more repeaters can compensate the
rapid exhaustion of the battery seen in Case B.

Case D. Assuming the same topology as in Case A
(Fig. 4a), though with n data packets per end-device,
then:

Etot = 2nCD2(1 + k),

and the energy drain per end-module:

Emod = nCD2(1 + k).

Case E. Supposing the same topology as in Case B
(Fig. 4b), though with n data packets per end-device,
we obtain:

Etot = nCD2(1 + k), (11)

Emod =
n

4
CD2(1 + k), (12)

ER =
n

2
CD2(1 + k). (13)

Case F. Assuming the same topology as in Case C
(Fig. 4c), though with n data packets per end-device,
we obtain:

Etot = nCD2(1 + k), (14)

Emod =
n

4
CD2(1 + k), (15)

ER =
n

2N
CD2(1 + k). (16)

Case G. Considering now M modules per cluster,
each generating n data packets, as in Fig. 4d, then:

Etot = 2MnCD2(1 + k), (17)
Emod = nCD2(1 + k), (18)

Case H. Considering now M modules per cluster,
each generating n data packets and one repeater in

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Acta Polytechnica Vol. 52 No. 5/2012

the middle, as in Fig. 4e, then:

Etot = MnCD2(1 + k), (19)

Emod =
n

4
CD2(1 + k), (20)

ER =
Mn

2
CD2(1 + k). (21)

We assumed for this case that distance D is much
greater than the distances between the modules of a
cluster.

Case I. Considering now M modules per cluster,
each generating n data packets and N repeaters in
the middle, as in Fig. 4f, then:

Etot = MnCD2(1 + k), (22)

Emod =
n

4
CD2(1 + k), (23)

ER =
Mn

2N
CD2(1 + k). (24)

Case J: Let us consider two clusters, separated by
a distance D that is much greater than the cluster
size (a squared area d×d meters — Fig. 4g). Each
cluster contains M modules. Let us note the energy
that a module of a cluster needs to broadcast a data
packet to the other members of the same cluster as
EBD and the energy that a module of a cluster needs
to broadcast an acknowledgement packet to the other
members of the same cluster as EBA. Let us also
assume that each module has equal participation in
the cluster in spreading the load, in beamforming and
generating data traffic. We can then write that:

• the energy to broadcast data in the cluster is
EBD = sED and

• the energy to broadcast acknowledgement in the
cluster is EBA = sEA = ksED.

The steps required for 1-packet two-way communi-
cation between modules A1 and B1 are:

1. module A1 broadcasts data in cluster A on fre-
quency fd, Fig. 5a;

2. cluster A is synchronised by A1 on frequency fs
and in one step transmits data to module B1,
Fig. 5b;

3. module B1 broadcasts an acknowledgement in
cluster B on frequency fd, Fig. 5c;

4. cluster B is synchronised by B1 on frequency fs
and in one step transmits the acknowledgement
to module A1, Fig. 5d;

5. module B1 broadcasts data in cluster B on fre-
quency fd, Fig. 5e;

6. cluster B is synchronised by B1 on frequency fs
and in one step transmits data to module A1,
Fig. 5f;

7. module A1 broadcasts the acknowledgement in
cluster A on frequency fd, Fig. 5g;

8. cluster A is synchronised by A1 on frequency fs
and in one step transmits the acknowledgement
to module B1, Fig. 5h.

The energy requirements for each step are:

Step 1 — module A1 broadcasts data in cluster A
on frequency fd, Fig. 5a:

• at A1: E1 = EBD = sED;
• at other modules: 0.

Step 2 — cluster A is synchronised by A1 on fre-
quency fs and in one step transmits data to
module B1, Fig. 5b:

• at each Ai: E2 = E(DATA)M =
CD2

M
;

• A1 has also to synchronise the cluster: E3 =
ESD = tEBD, where t is a constant;

• at modules belonging to cluster B: 0.

Step 3 — module B1 broadcasts the acknowledge-
ment in cluster B on frequency fd, Fig. 5c:

• at B1: E4 = EBA = sEA;
• at other modules: 0.

Step 4 — cluster B is synchronised by B1 on the
frequency fs and in one step transmits the ac-
knowledgement to module A1, Fig. 5d:

• at each Bi: E5 = E(ACK)M =
kCD2

M
;

• B1 has also to synchronise the cluster: E6 =
ESA = tEBA, where t is a constant;

• at modules belonging to cluster A: 0.

Step 5 — module B1 broadcasts data in cluster B
on frequency fd, Fig. 5e:

• at B1: E7 = EBD = sED;
• at other modules: 0.

Step 6 — cluster B is synchronised by B1 on fre-
quency fs and in one step transmits data to
module A1, Fig. 5f:

• at each Bi: E8 = E(DATA)M =
CD2

M
;

• B1 also has to synchronise the cluster: E9 =
ESD = tEBD, where t is a constant;

• at modules belonging to cluster A: 0.

Step 7 — module A1 broadcasts the acknowledge-
ment in cluster A on frequency fd, Fig. 5g:

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Acta Polytechnica Vol. 52 No. 5/2012

A1 local DATA bcast. Beamformed DATA transmission A → B1.

B1 local ACK bcast. Beamformed ACK transmission B → A1.

B1 local DATA bcast. Beamformed DATA transmission B → A1.

A1 local ACK bcast. Beamformed ACK transmission A → B1.

Figure 5: Steps of a beamformed bidirectional communication.

• at A1: E10 = EBA = sEA;
• at other modules: 0.

Step 8 — cluster A is synchronised by A1 on fre-
quency fs and in one step transmits the acknowl-
edgement to module B1, Fig. 5h:

• at each Ai: E11 = E(ACK)M =
kCD2

M
;

• A1 also has to synchronise the cluster:
E12 = ESA = tEBA, where t is a constant;

• at modules belonging to cluster B: 0.

The total energy required by the whole network
becomes the sum of E1 to E12, where some of the
terms have to be multiplied by M (the number of
nodes):

Etot = 2
(
EBD + M

CD2

M
+ tEBD

+ EBA + Mk
CD2

M
+ tEBA

)
. (25)

We have previously seen that ED ∼ D2 and we noted
ED = CD2. In the same manner, because the dis-
tances between modules belonging to the same cluster

have the same order with cluster size d, we can write
that EBD ∼ d2 and EBD = Cd2. Thus, by replacing
these values into (25) we obtain:

Etot = 2
(
Cd2+CD2+tCd2+kCd2+kCD2+tkCd2

)
= 2C(1 + k)

(
(1 + t)d2 + D2

)
. (26)

Energy need per device: for module A1: EA1 = E1 +
E2 + E3 + E10 + E11 + E12:

EA1 = Cd
2 + tCd2 + kCd2 + tkCd2 +

CD2

M
(1 + k)

= C(1 + k)
(

(1 + t)d2 +
D2

M

)
; (27)

for module B1: EB1 = E4 + E5 + E6 + E7 + E8 + E9:

EB1 = C(1 + k)
(

(1 + t)d2 +
D2

M

)
= EA1 ; (28)

for the other modules in cluster A: ECA = E2 + E11:

ECA =
CD2

M
(1 + k); (29)

for the other modules in cluster B: ECB = E5 + E8:

ECB =
CD2

M
(1 + k) = ECA. (30)

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Acta Polytechnica Vol. 52 No. 5/2012

In conclusion:

• The total energy needed per network:

Etot = 2C(1 + k)
(
(1 + t)d2 + D2

)
. (31)

• The energy for devices which are data sources
and sync sources:

Eactive = C(1 + k)
(

(1 + t)d2 +
D2

M

)
. (32)

• The energy for devices which only help transmis-
sion:

Epassive =
CD2

M
(1 + k). (33)

Case K. Let us take the same topology as in Case
J, but this time each device generates n data packets.
In this case, the average energy per device can be
calculated in the following manner:

• We start by counting the data packets in the
network: 2Mn.

• In one cluster, each device is active for n packets
(its own packets) and passive for the remaining
(M−1)n packets. In total, each cluster is respon-
sible for Mn packets (half of the total number of
packets).

Thus: the total energy per network becomes:

Etot = 2CMn(1 + k)
(
(1 + t)d2 + D2

)
; (34)

the energy per device is Emod = nEactive +
(M − 1)nEpassive:

Emod = nC(1 + k)
(

(1 + t)d2 +
D2

M

)
. (35)

Final conclusions. Let us compare the total en-
ergy requirements in cases K (general beamforming)
and I (general relay):

Etot,K
Etot,I

=
2CMn(1 + k)

(
(1 + t)d2 + D2

)
MnCD2(1 + k)

= 4
(

1 + (1 + t)
(
d

D

)2)
. (36)

If D � d, then Etot,K
Etot,I

→ 2, meaning that the overall
energy consumption beamforming presented in case
K is twice as inefficient as relay transmission of the
same order.

Let us now compare the energy requirements of
end devices in cases K (general beamforming) and I
(general relay):

Emod,K
Emod,I

=

nC(1 + k)
(
(1 + t)d2 + D

2

M

)
+ (M − 1)nCD

2

M
(1 + k)

1
4nCD

2(1 + k)

= 4
(

1 + (1 + t)
(
d

D

)2)
. (37)

If D � d, then Emod,K
Etot,I

→ 4. meaning that the end-
device energy consumption beamforming presented in
case K is four times as inefficient as relay transmission
of the same order.

Finally, let us now compare the energy requirement
of end devices in case K (general beamforming) and
the energy requirement of relays in case I (general
relay):

Emod,K
ER,I

=

nC(1 + k)
(
(1 + t)d2 + D

2

M

)
+ (M − 1)nCD

2

M
(1 + k)

Mn
2n CD

2(1 + k)

=
2N
M

(
1 + (1 + t)

(
d

D

)2)
. (38)

If D � d, then Emod,K
Etot,I

→ 2N
M

. In this case, if M = N
(the number of end-devices is equal to the number of
relays), the energy consumption in the case of beam-
forming per device is twice the energy consumption
on a relay.

Proposition. In a clustered network, relaying is at
limit twice more efficient for equivalent networks, per
total power consumption and per end device. In envi-
ronments in which relays cannot be installed or if the
graph cut (of the network) contains a number of relays
less than half of the number of end-devices, then the
network connected through phase-shift beamforming
will survive more than relaying

Proof. The proof has been already provided in a con-
structive way in this section.

Of course, the estimation here is an approximation,
because we have ignored the small distance differences
inside and outside the clusters. This however gives
a better understanding of the quantitative improve-
ments brought by phase-shift beamforming and in
this way give a maximum theoretical limit.

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Acta Polytechnica Vol. 52 No. 5/2012

Figure 6: The relay module position is varied along
the line uniting the centres of the two clusters.

Figure 7: Packets delivered between clusters in both
directions. The vertical axis represents the number
of packets, and the horizontal axis represents the
distance between the relay and the centre of cluster
A (in meters).

4 Experiments and Results
The simulations presented in this section are based
on the following assumptions:

• a free-space propagation model (no obstacles for
waves, no reflexions);

• battery capacity for each device: 200 mWh (larger
capacities are also permitted, but the simulation
will last longer);

• two clusters, each containing 4 modules;

• squared cluster areas;

• random placement of modules in the cluster area;

• Pmin = −75 dBm (minimal power);

• data rate DR = 115200 bps;

• antenna gain: 1.5 dBi isotropic (for the results
presented here, isotropic antennas were used
to show the contribution of the distributed
phase-shift beamforming in a separate manner —
anisotropic antennas can also be simulated);

• data packet size: 128 B (the size of a ZigBee
packet);

Figure 8: 1 to 4 relay nodes in between the clusters.

Figure 9: Packets delivered between clusters in both
directions. The vertical axis represents the number of
packets,and the horizontal axis is the number of tests
performed.

• acknowledgement size: 12 B;

• synchronization constant t = 2;

• random traffic is generated from each cluster to
the other cluster (random source module and
random destination module, where the source
and destination belong to different clusters);

• each presented result is the averaged value over
10 simulations;

• in the results, only the number of delivered pack-
ets is presented, because the time intervals are
proportional to the number of packets.

4.1 Experiment 1
Two clusters of 10 × 10 m, containing 4 modules each,
are placed 1000 m from each other. In between there
is a single relay module. The relay is moved along the
line which passes through the centres of each cluster
from the proximity of the first cluster to the proximity
of the second cluster (Fig. 6). The goal is to determine
the number of packets and the time interval in which
the network is functioning.

The result of this experiment is presented in Fig. 7,
and it shows that the best result (the longest uptime)
is achieved when the relay is placed in the middle
of the distance between the two clusters. In all the

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Acta Polytechnica Vol. 52 No. 5/2012

Figure 10: The B cluster moves away from cluster
A.

Figure 11: Packets delivered between clusters in
both directions. The vertical axis represents the num-
ber of packets, and the horizontal axis represents the
distance between the clusters (in meters).

tested cases, the clusters become disconnected due
to exhaustion of the relay battery. The fact that
the optimum is reached when the relay sits in the
middle of the distance has been theoretically shown;
the results match the prediction.

4.2 Experiment 2
Two clusters of 10 × 10 m, containing 4 modules each,
are placed 1000 m from each other. In between there
are 1 to 4 relay modules used in a round-robin fashion
(Fig. 8). The goal is to determine the number of
packets and the time interval in which the network is
functioning.
The results depicted in Fig. 9 show a dramatic

improvement as the number of relay modules increases.
In all the cases the clusters become disconnected due
to exhaustion of the relay battery. This leads to
one conclusion: if relays can be installed, this is the
preferred method.

4.3 Experiment 3
Two clusters of 10 × 10 m, containing 4 modules each,
are placed 450 m from each other. Cluster B is then
moved along the axis that connects the centres of

Figure 12: Increasing the cluster sizes.

Figure 13: The dependency of the number of deliv-
ered packets on cluster size. On the vertical axis, the
number of delivered packets; on the horizontal axis,
the size of the clusters in meters.

the two clusters, away from cluster A, up to 2000 m.
There are no relay nodes, only phase-shift beamformed
communication. The goal is to determine the number
of packets and the time interval in which the network
is functioning. (Fig. 10)
The results are depicted in Fig. 11, which shows

how distance affects the overall number of delivered
packets. The disconnection is caused by exhaustion
of the batteries of either the source node or the desti-
nation node.
What is really interesting in this graph (Fig. 11)

is that at a distance of 1000 m between the clusters,
the number of acknowledged packets is approximately
3.7 million. By comparison, the best-case scenario for
a single relay is just below one million. This proves
that phase-shift beamforming can outperform classic
relaying by a factor of 3 if the number of relays is
very low.

4.4 Experiment 4
Two clusters of 10 × 10 m, containing 4 modules each,
are placed 2000 m from each other. The size of each
cluster is increased (from 10 × 10 m to 10 × 10 m),
while its centre remains on the same coordinates. This
method proves the stability of phase-shift beamformed
communication between clusters (Fig. 12). The results

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Acta Polytechnica Vol. 52 No. 5/2012

are depicted in Fig. 13, and show that the number
of delivered packets is almost constant at around one
million, which corresponds to the result obtained in
Experiment 3 for the same distance between clusters.

5 Conclusions and future work
The work presented in this paper aimed to determine
the advantages and disadvantages of using distributed
phase-shift beamforming in comparison with classic
repeater techniques for interconnecting two distant
clusters of radio devices.
In this work certain energy consumptions were ig-

nored, e.q. for the data processing before the energy
is transmitted or after it is received. However, the
expected power needs are constant for each received
or processed data packet, depending only on the size
of the respective packet. Because the results are pre-
sented both in absolute form and in relative form
(beamformed towards a classic repeater), the influ-
ence of these constant power on the relative results is
minimal.

The previous section has shown that, by comparing
the worst result achievable through distributed phase-
shift beamforming with the best result obtainable by
installing repeaters, the technique presented in this
paper is about three times better than the classic
method. However, in cases where installing a repeater
is an option, it is the preferred method.
The power of this method is due to the fact that

it is scalable with the number of transmitters in each
cluster. This paper presents only the case of four
modules per cluster, because the algorithm that finds
the optimal phase combinations [5] has (for the mo-
ment) exponential complexity and, in order to achieve
results with a reasonable period of time and with rea-
sonable power consumption, the number of devices
must be limited. Work is in progress to provide a
faster algorithm of cluster discovery algorithm for this
technology.

The final note on the work presented in this paper
is that intra-cluster communications have been totally
ignored (with the exception of broadcasts — which
are however necessary due to inter-cluster communica-
tion). The reason for this is to avoid creating interfer-
ence between intra and inter cluster communications.
Inter-cluster communication requires much greater
resources, and must be protected better against inter-
ference. There are two ways to achieve this protection:
by dividing the time interval into separate time zones
or by using a new technique that we propose. From
the point of view of time separation, there are two
orthogonal time chunks for communication: an inter-
cluster chunk and an intra-cluster chunk. It can be
said that this paper details the inter-cluster chunk and
ignores the other chunk. However, our team is fully
confident that there is another solution: VCSMA/CA

(Virtual Carrier Sense Multiple Access With Colli-
sion Avoidance). This is work in progress, and it is
based on the fact that the problem of interference
has already been solved with individual devices by
RTS/CTS mechanisms or by busy-tone mechanisms
(BTMA — Busy Tone Multiple Access [2]). In our
case, instead of individual transmitters we have vir-
tual transmitters.

Acknowledgements
The research reported in this paper has been sup-
ported by the Ministry of Education, Youth and
Sports of the Czech Republic under research pro-
gram MSM 6840770014, and by the Grant Agency of
the Czech Technical University in Prague, grant No.
SGS11/158/OHK3/3T/13.

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