Actuator Cooperation (Joint Beamforming)

In this scenario, the actuators are assumed to be interconnected via high speed backhaul

links (wireline or wireless). After an initial handshake between a sensor and its associated

actuator (min. hop fashion, more details on this assignment are provided in Section 4.6),

each actuatortransmitsatrainingsequence. Theneachsensorestimatesthechannelbetween

itself and all the actuators, and it transmits this set of channel coecients to its associated

actuatorinamulti-hopfashion. Therefore,theTransmitterChannelStateInformation(CSIT)

is obtained. Furthermore, each actuator determines the schedules for its associated sensors.

Actuatorsexchange theirlocalCSITandtheir scheduling information viathebackhaullinks,

and jointly perform Maximal RatioCombining(MRC) beamforming inordertotransmit the

scheduling information to each sensor. Hence, actuators form a distributed antenna array.

Thetransmissionof the scheduling information isdone ina Round-Robin fashion andat the

same frequency. Each sensor has a channel vector h

i = [h _i1 , h _i2 , ..., h _iM ]

^{. In order for the}

per-actuator powerconstraint to be satised,each actuator

j

^{transmitsto sensor}

i A _ij = h ^∗ _ij

k h ij k

p P _j s _i

^(4.39)

Thereceived signalofthe sensornode

i

^isthen

y i = P M

j=1 h ij A ij + n ⇒ y _i = P M

j=1 k h _ij k p

P _j s _i + n

^(4.40)

where

i = 1, 2, ..., N

^and

s _i

^{is the schedule assigned to sensor node}

i

^{. It is assumed that}

E k s _i k ² = 1

^{. Thus theSNR of the sensornode}

i

^{inthe caseof equal power}transmission is

SN R _i =

P P M

j=1 k h _ij k 2

σ ²

^(4.41)

Joint beamformingenhances the received SNR dueto thearraygainand theexploitation

of macro-diversity which is inherent in a SANET. Therefore, this scheme provides a robust

way of minimizing sensor inactivity. This is achieved at the cost of CSIT at the actuators.

Furthermore,multipletimeslotsareneededinordertodeliverthescheduletoallsensornodes,

sinceactuators transmit to one sensornode at a time.

4.12 Simulation Results

In this section, we present our ns-2 [53] simulation results demonstrating the performance

of our actuator-selection, optimal ow routing, and TDMA MAC solution. As our analysis

is dierent from the related literature presented in this work, we only compare the results

given by the upper bound in (4.23) (optimal ow solution for the relaxed problem which is

independent of MAC) and the simulations performed inns-2 on top of a TDMA like MAC.

In our simulations, we consider dierent network sizes (varying the number of sensors and

actuators) with randomly deployed topologies. Also, we evaluate the lifetime only at level

one as the optimal lifetime solution at other levels can be interpreted in a similar fashion.

Further, in the existing network simulators e.g. [53, 52], there are no available means of

simulating a heterogeneous network consisting of sensors and actuators (as actuator have

dierenttransmissionand processingcapabilities). Therefore,wepost-processour ns-2based

tcl-scripts in order to simulate a heterogeneous sensor-actuator network. Some simulation

parameters are listed in Table 4.3. The simulations are run several times for each network

setting and the resultspresentedareaveraged over theseruns.

For each network setting, we calculate the upper bound on lifetime provided by (4.23)

throughMILPrelax. Wedenotethislifetimeas'LifetimefromAnalyticalBound'. Wedenote

the lifetime obtained with actual ns-2 simulation as'Lifetime from simulations'. The initial

energy at sensor

i

^{israndomly generated following auniform} distribution with

e _i ∈ [300, 500]

(kJ)

^{. Thedatagenerationrateateachsensor}

i

^,

g _i

^{,isalsouniformly}distributedwithin

[5, 10]

(kb/s)

^{. The}sensor-actuator routing modelunderconsideration isthesame asinSection 2.8.

At simulation start up, the nodes learn the network topology and built routes toward the

destination actuators (based on theoutcome of a cost-function). Inthis simulation-analysis,

actuators are also sensor nodes which have 0 sampling rate 4

. This learning process, which

dependson the network topology,can take upto

50 − 70

^seconds.

We simulated theADP, LEAD-RP andLEAD-MACin ns-2[53 ]. For sensor-sensor

coor-dination, the sensors only require one-hop neighbor identity through which it can reach the

actuator withlowercost ascompared to itsown. For sensor-actuator coordination, we

simu-lated topologies of various sizes (50-400 sensors). The considered packetsize is 50 bytes and

the transmission rate is 50kpbs. The average depth of theresulting routing trees is 4.4, 5.2,

and 7for20,30,and60sensorspercluster, respectively;correspondinglytheaveragenumber

of neighborsis 4.6, 5.0, and5.5. The resultsobtained from (4.23) and simulationsusing ns-2

arepresentedinFigure4.9. Itcan be easilyseenthatour approach (optimalrouting through

LEAD-RP,actuatorsearchthroughADP,andaTDMAMACthroughLEAD-MAC)can

pro-vide anetworklifetimeveryclose totheoptimalsolution. Theslight dierenceinthelifetime

obtained fromthesimulationsisduetotheenergy expenditureduringinitialnetworklearning

and route discovery toward actuators. The simulated lifetime lies exceptionally close to the

analytical bound (forrelaxedow-problem)due to thefollowing reasons: 1) we have built an

aggregation treetoward each actuator inthe network and calculate theoptimal ow routing

solution. 2)Theschedulinginformation issent tothesensorsbytheirmapped-actuatornodes

which correspondsto theoptimal ow solution. 3) The problem of synchronization is easily

solved asthe transmission schedule is calculated by the actuator ineach cluster. 4) There is

no extra energy expenditure as a result of collisions and successive retransmissions. 5) The

nodesare sent to sleep mode, whennot transmitting, and also no information is expected to

arrive froma sensor'sdownlink tree.

0 10 20 30 40 50

0 10 20 30 40 50 60 70 80 90 100

Randomly generated network topologies

Network Lifetime (in Days)

Lifetime from simulations Lifetime from Analytical Bound

Figure4.9: Network lifetimeunderanalytical and simulation results

Directed Diusion [1] and anycast [65] is chosen as the routing protocol for comparison.

4

Atrun-time,thesenodesaremodiedtoactuators(i.e.,dierentcommunicationcapabilitiescomparedto

sensors)sothatanaggregation treecouldbebuilttowardtheseactuatorsforeachcluster.

Figure4.10 shows the end-to-end latency asa function of network size. The delayincreases

with the increase in the network size, but the increase is signicantly less for ADP. This

gradual increase isthe resultofsmallermean-path lengthfor ADPasthecost-functionisset

to min-hoprouting and forwarding queuesatthesensors arenotsaturated atthegiven load.

Figure 4.11 show the mean energy consumption as a function of time. ADP energy savings

are more signicant due to the existence of multiple dened routing paths toward optimal

actuators, wheredependingontheremainingenergyoftheforwardingsensors,asourcesensor

can choose between several available paths to eciently route its data. In Figure 4.12, the

mean pathlength isshownasafunctionof networksize. Again themeanpath length(which

is related to the end-to-end latency) increases with the network size. However, the increase

is more gradual with the ADP ascompared to anycast and directed diusion. Using ADP,

sensors always transmit their data to the nearestactuator (because we set thecost-function

to min-hop routingfor actuator discovery during initial deployment).

0 500 1000 1500 2000

50 100 150 200 250 300 350 400

Delay (msec)

Sensors in the network Directed Diffusion

Anycast ADP

Figure 4.10: Mean end-to-endtransmission delays

A comparison with the analytical model of PEDAMACS [103 ] is presented for

delay-energyconsumptionanalysisatMAClayer. WecompareLEAD-MAConlywithPEDAMACS,

because this work hasalready been shown to perform better compared to other listed MAC

proposals for WSNs. Themaximumdelay observed bya network can be seeninFigure 4.13.

Theend-to-enddelayislessduetothedepth-rstschedulingpolicyofend-to-endroutesinthe

hybrid-schedule. Finally,we present acomparison fortheenergyconsumption inFigure4.14,

wheresensors consumesless energydue to an adaptive duty cycleandlonger sleep periods.

Theperformanceof theaforementioned transmissionschemes is evaluated intermsofthe

number of isolated sensors thatresults from each transmission scheme. A numberof sensors

isdeployeduniformlyinahexagonwitharadiusof1km. Threeactuatorsareassumedatthe

three vertices of the hexagon separatedbyan angle of120°. Actuator antennas areconsider

tohavea gainof12dB, whereas, sensornodeantennashave againof0 dB.Through

0 20 40 60 80 100

0 200 400 600 800 1000

Energy Consumption (joules)

Simulation time (in sec) Directed Diffusion - 100-sensors - 2-sinks

Anycast - 100-sensors - 2-sinks ADP - 100-sensors - 2-actuators

Figure4.11: Mean energy consumption asafunction of timefor anetwork of100 sensors

Carlo simulation the average number of isolated sensors is calculated for each transmission

schemeasafunctionoftheactuator transmitpower. Averagingisperformedoversensornode

positions and channel realizations. A sensor is assumed to be isolated if its received SNIR

or SNR isbelow thethreshold of 1 Watt. In Figure 4.15it is plotted the average number of

isolated sensors versusthe actuator transmit powerfor 1200 deployed sensors. Itcan beseen

that for thepower of -12 dBw isolated sensor zones arealmost completely eliminated inthe

caseofMRCbeamforming. InthecaseofReuseFactor3(RF3),isolatedzonesareeliminated

when the transmit power is approximately 0 dBw and in the case of Reuse Factor 1 (RF1)

the average numberof isolatedsensors saturates approximately at 0dBw.

0 5 10 15 20

50 100 150 200 250 300 350 400

Number of hops

Sensors in the network Directed Diffusion

Anycast ADP

Figure4.12: Mean numberoftransmissions perend-to-end path (meanpath length)

−30 0 −20 −10 0 10 20 30

200 400 600 800 1000 1200

Transmit Power [dBw]

Average Number of Inactive Sensors

1200 Deployed Sensors Overall

BC RF1 BC RF3 Joint MRC

Figure4.15: Average Numberofisolated Sensorsvs. Transmit Power.

InFigure4.16itisplottedtheaveragenumberofisolatedsensorsagainstthetotalnumber

of deployed sensorsfor a dierent numberofdeployed sensornodes, whenactuatorstransmit

0 0.5 1 1.5 2 2.5 3

10 15 20 25 30 35 40 45 50 55 60

Average Delay Observerd by Transmissions (Sec)

Average Number of Nodes in One Cluster

PEDAMACS LEAD-MAC

Figure4.13: Averagedelay inacluster

→

^{increasing# ofnodes}

poweris-12dBw. ItcanbeclearlyseenthatthejointMRCbeamformingschemeoutperforms

the simple Reuse 3 broadcasting, as the average number of isolated sensors is almost 0 for

that powerlevel.

100 200 300 400 500 600 700 800

10 15 20 25 30 35 40 45 50 55 60

Average Energy Consumed during one transmission schedule (mA)

Average Number of Nodes in One Cluster

PEDAMACS LEAD-MAC

Figure4.14: Average energy consumption inacluster

→

^{increasing #ofnodes}

300 400 500 600 700 800 900 1000 1100 1200

0 50 100 150 200 250 300 350 400 450 500

Total Number of Deployed Sensors

Average Number of Inactive Sensors

Transmit Power = −12.00 dBw

BC RF1 BC RF3 Joint MRC

Figure4.16: Average Numberof isolated SensorsVs. Total Numberof Deployed Sensors.

InFigures4.17,4.18and4.19,theprobabilityofinactivitycanbeseeninthedierentareas

ofthehexagon forthethreedierenttransmissionschemes considered, whenactuators

trans-mitpoweris-12 dBw. In thecases ofRF1 andRF3 schedulebroadcasting, thecenter ofthe

topology experiences a signicant probability of inactivity. In a realsystem implementation,

this would result to an important loss of information. On the contrary, Joint beamforming

almost eliminates isolated areas in the sensing eld at this power level. This turns out to

bea veryeective actuator transmissionscheme thatgreatlyreduces theamount oftransmit

powerneeded to ensure very low sensorinactivity. This isbecause of thebeamforming SNR

gainsandthemacro-diversitygainsthatareprovided bythespatiallydistributedtransmitting

actuators.

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

Broadcasting, Reuse Factor 1. Transmit Power = −12 dBw

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Figure 4.17: Probability of Sensor Inactivity in the areas of thesensing eld for the case of

ReuseFactor 1Schedule BroadcastTransmission.

−1 −0.5 0 0.5 1

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

Broadcasting, Reuse Factor 3. Transmit Power = −12 dBw

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Figure 4.18: Probability of Sensor Inactivity in the areas of thesensing eld for the case of

ReuseFactor 3Schedule BroadcastTransmission.

−1 −0.5 0 0.5 1

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

Maximal Ratio Combining Beamforming. Transmit Power = −12 dBw

0.01 0.02 0.03 0.04 0.05 0.06 0.07

Figure 4.19: Probability of Sensor Inactivity in the areas of thesensing eld for the case of

jointMaximal Ratio CombiningBeamforming.

Dans le document Cross layer optimization of wireless sensor and sensor-actuator networks (Page 133-143)