research article efficient cross-layer optimization...

Research ArticleEfficient Cross-Layer Optimization Algorithm forData Transmission in Wireless Sensor Networks

Chengtie Li Jinkuan Wang and Mingwei Li

School of Information Science and Engineering Northeastern University Shenyang Liaoning 110819 China

Correspondence should be addressed to Chengtie Li neuqlcthotmailcom

Received 23 June 2015 Accepted 13 October 2015

Academic Editor Jun Bi

Copyright copy 2015 Chengtie Li et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this paper we address the problems of joint design for channel selectionmedium access control (MAC) signal input control andpower control with cooperative communication which can achieve tradeoff between optimal signal control and power control inwireless sensor networks (WSNs)The problems are solved in two steps Firstly congestion control and link allocation are separatelyprovided at transport layer and network layer by supply and demand based on compressed sensing (CS) Secondly we propose thecross-layer scheme to minimize the power cost of the whole network by a linear optimization problem Channel selection andpower control scheme using the minimum power cost are presented at MAC layer and physical layer respectivelyThese functionsinteract through and are regulated by congestion rate so as to achieve a global optimality Simulation results demonstrate the validityand high performance of the proposed algorithm

1 Introduction

Wireless sensor networks find many applications in militaryareas detection habitat monitoring and so on Performancedegenerate analysis has gained much interest due to unbal-anced power allocation in physical layer excessive contentionwireless channel inMAC layer unfair link capacity allocationin network layer and the inappropriate transport protocol intransport layer WSNs suffer from several restrictions of thesink nodes and sensor nodes on account of the battery pow-ered computation complexity communication and storagecapabilities [1ndash3]

MAC (medium access control) which is critical technol-ogy concerning net performance [4] is in charge of allocationwireless communication resources for contention nodes inprotocol stack

Scheduling effectively achieves resource allocation forwireless communication To reach a satisfying schedulingscheme scheduling cost and scheduling objective regu-larly compromised the scheduling problem is transferredto multiobjective optimization Recently scholars integratedscheduling and power control for better performance andobtained certain achievements [5 6]

Reference [7] provided an in-depth analysis on theCS-based medium access control schemes and revealedthe impact of communication signal-to-noise ratio on thereconstruction performance Authors showed the process ofthe sensor data converted to the modulated symbols fortransmission and how the modulated symbols are recoveredvia compressed sensing Reference [8] studied the optimalflow control by a multiobjective linear programming prob-lem which achieved the optimization between utility andlifetime inWSNs Reference [9] jointly designed rate controlscheduling and power control with stochastic optimiza-tion problems to achieve cross-layer optimization protocoldesigning Reference [10] investigated optimal power controlrate adaptation and scheduling for an ultrawideband-basedIntravehicular Wireless Sensor Network for one-electronic-control-unit (ECU) and multiple-ECU cases These methodsare widely applied into many-to-one data transmission con-trol protocols and solved the problems in every aspect [11ndash14]However the above algorithms did not give a comprehensiveanalytic process for considering energy consumption chan-nel selection link capacity and congestion control to ensurebetter performance

Hindawi Publishing CorporationJournal of Electrical and Computer EngineeringVolume 2015 Article ID 545798 6 pageshttpdxdoiorg1011552015545798

2 Journal of Electrical and Computer Engineering

k

ji

CCH

Figure 1 Multihop routing cooperative communication model

In this paper cross-layer optimal design is presentedwhich considers the influence for congestion rate at physicallayerMAC layer network layer and transport layer to achieveminimum power cost in WSNs The algorithm coordinatescommunication protocols by congestion rate in the severallayers to solve lossy wireless channel excessive contentionand unfair access disabled bandwidth allocation and thefundamentally inappropriate mechanisms of TCP First wedesign a packet error rate control strategy based on conges-tion rate which makes the packet error rate in the domainof validity The power is exactly allocated on the basis of ldquotoeach according to his needsrdquo Second the optimal schemesof control input and link capacity with compressed sensingare discussedThird we construct minimum energy problemwith power control function congestion control functionlink allocation function and so on The optimum solutionsare the optimal power control and channel selection

2 Network and Node Model

For energy efficiency purpose the transmission power atevery node is assumed to be adjustable resulting in congestionprice when the congestion rate is bigger the power should beincreased for data transmitted successfully when the conges-tion rate is smaller the power is only satisfied for data trans-mitted regularly We assume that the sensor network consistsof119873 nodes of which the sink node is defined as node 119873

Communication from node 119894 to node 119895 contains directedcommunication hop (DCH) 119894 rarr 119895 [15] and cooperativecommunication hop (CCH) 119894 rarr 119896 rarr 119895 as shown inFigure 1 CCH consists of a sender a relay and a receiver(119894 119896 119895 in Figure 1 resp) such that both direct and relayedcopies of the information transmitted by the sender arereceived at the receiver

3 Cross-Layer Optimization Design ofCooperative Communication

In the wireline networks the protocols hold rigorous con-straint at each layer which is only responsible for oneselfnot being infiltrated Physical layer is mostly in charge ofpower allocation channel selection is achieved inMAC layerflow control is implemented in transport layer network layeris usually responsible for scheduling design However therequirement like this does not occur in WSNs Cooperative

communication is applied for protocols at each layer to makenet performance better

31 Power Control Define packet error rate with whiteGaussian noise [15] as follows

Ω119894119896DC = 1 minus (1 minus

1

2119890minus1205741198941198962)

119871

(1)

where 120574119894119896= (119875txtot119894119892119894119896119875119899) times (119861119899119877) is energy per bit to noise

power spectral density ratio 119875txtot119894 is the aggregated powerfor transmitting a packet at 119894 119861

119899is the noise bandwidth 119892

119894119896

is the path loss of link (119894 119896) in linear units 119875119899is the average

noise power 119877 is the maximum link data rate in bits persecond bitss and 119871 is the length of the packet The powerconsumption of a packet transmitted successfully is 119875txtot119894 =(1 + 119901

119894)119875tx119894 if congestion occurs in the WSNs 119875tx119894 denotes

transmitted power to a packet at ideal condition (congestiondoes not occur) and 119901

119894is the congestion rate at node 119894 the

average noise power 119875119899= (1 + 119901

119894)119875119899 where 119875

119899is the average

noise power at ideal condition the maximum link data rate119877 = (1+119901

119894)119877 where 119877 is the maximum link data rate at ideal

condition Thus

120574119894119896=(1 + 119901

119894) 119875tx119894119892119894119896

(1 + 119901119894) 119875119899

119861119899

(1 + 119901119894) 119877

=119875tx119894119892119894119896

(1 + 119901119894) 119875119899

119861119899

119877

(2)

We can conclude that 120574119894119896is adjusted to be smaller and

Ω119894119896DC is bigger when congestion rate is increased from

formula (2)The power appropriately adjusted by congestionrate makes the packet error rate constraint the domain ofvalidity The power is exactly allocated on the basis of ldquotoeach according to his needsrdquo which can extensively highlightpower efficiency

32 Congestion Control Recently lots of researchers haveaddressed the signal function with cross-layer optimal designto achieve better performance due to the characteristic ofhigher communication consumption and lower data processconsumption in WSNs [16ndash18] However almost all conges-tion control algorithms did not consider the data preprocess-ing before being transmitted [19] In this section we try toreduce the number of transmissions with a Toeplitz matrix incompressed sensing that enables the number of transmissionsto be extensively decreased in WSNs The transmission ofcompressed signal is not only relieving the congestion indata process overabundance but also economizing energy inthe transmission Compressed sensing model is expressed asfollows

119910 (119905) = Φ119909119894 (119905) + 120576 (3)

where 119909119894(119905) isin R119899times1 is input signal 119910(119905) isin R119898times1 is measure-

ment vector Φ isin R119898times119899 is sensing matrix 119898 ≪ 119899 and120576 isin R119898times1 is unknown vector formeasurement noise Supposethat the input signal is sparse and sensing matrix satisfiesrestricted isometry property (RIP) [20] To speed up con-gestion control we select Toeplitz matrix as sensing matrixmeeting Φ

2le 1

Journal of Electrical and Computer Engineering 3

The scheduling algorithm and signal control scheme arethe same in each link or at each node In this paper onlyconsider the scheduling in (119894 119896) and signal control at 119894 Thelinear function119860(119891

119894119896) of the link capacity 119891

119894119896in (119894 119896) denotes

the service capacity and the service requirement at node 119894by a linear function 119867(119909

119894(119905) 119909119894) of the control input signal

119909119894(119905) and original signal 119909

119894indicates the service requirement

Consider

119885 (119891119894119896 119909119894 (119905) 119909119894) = (1 minus 119901119894) 119860 (119891119894119896) minus 119867 (119909

119894 (119905) 119909119894) (4)

Formula (4) represents supply and demand function of theservice The valid service capacity achieves optimality ifand only if it is exactly satisfied with service requirementOtherwise it will bring unnecessary energy consumption

119909119894 (119905) = argmin

119909119885 (119891119894119896 119909119894 (119905) 119909119894) + 119901119894 (

120576

0) (5)

The most desired input feedback signal is argmin119909119885(119891119894119896

119909119894(119905) 119909119894) Considering congestion in the WSNs however

input signal should reach to expression in (5)

33 Scheduling Algorithm The adjustment of the transmittedpower in Section 31 being changed in the transmission rangeand the connectivity of the node causes the changes in therequirement of the link capacity In Section 32 the inputsignal satisfying supply and demand function minimum isgenerated On this basis we will discuss the link capacityallocation in the link (119894 119896) in this section From analysisthe network optimal condition is that supply and demandfunction attains minimum When function (4) is the actualminimum the link capacity 119891

119894119896is the optimal link capacity

In this scheduling on the one hand unnecessary energyconsumption with link capacity too big is effectively avoidedon the other hand the new congestion with link capacity toosmall is suppressed Thus 119891

119894119896can be denoted as follows

119891119894119896isin argmin119885 (119891

119894119896 119909119894 (119905) 119909119894) (6)

34 Channel Selection Power control is applied to dynam-ically adjust transmission power which can not only effec-tively reduce energy consumption in communication butalso prolong network lifetime in WSNs In addition powercontrol could remarkably influence the topology controlconnectivity throughput and real-time of message transmis-sion Moreover MAC layer or cross-layer design with powercontrol evidently optimizes network performance and high-lights QoS In this section we will discuss how to select chan-nel by cutting down unnecessary energy consumption [21]Energy is mainly expended at communications and compu-tation brings the energy to be neglected For a CCHwith relaynode 119896 power consumption chiefly includes three parts thefirst part is transmission power of a packet sent at node 119894

119862119878119896119894119895

= 119875tx119894tot (7)

the second part indicates that for relay node 119896 the poweraggregate to receive a packet from node 119894 and successfullytransmit a packet to node 119895 is

119862119877119896119894119895

= 119875rx119896cir + (1 minus Ω119894119896DC) 119875tx119894tot (8)

The third part indicates that for node 119895 the power aggregateto receive a packet from node 119894 and node 119896 is

119862119863119896119894119895

= 119875rx119895cir + (1 minus Ω119894119896cir) 119875rx119895cir (9)

Suppose that 119875rx119896 is the required power for receiving apacket for node 119896 at ideal condition Congestion should beconsidered for data valid transmission To achieve energyoptimization let

119862119878119896119894119895

= 119875tx119894tot = (1 + 119901119894) 119875tx119894

119862119877119896119894119895

= 119875rx119896cir + (1 minus Ω119894119896DC) 119875txtot119896

= (1 + 119901119896) 119875rx119896 + (1 minus Ω119894119896DC) (1 + 119901119896) 119875tx119896

119862119863119894119895119896

= 119875rx119895cir + (1 minus Ω119894119896DC) 119875rx119895cir

= (1 + 119901119895) 119875rx119895

+ (1 minus Ω119894119896DC) (1 minus Ω119896119895DC) (1 + 119901119895) 119875rx119895

(10)

From formula (10) the power aggregate is as follows

119862119894119895119896

= 119862119878119896119894119895

+ 119862119877119896119894119895

+ 119862119863119896119894119895

= (1 + 119901119894) 119875tx119894 + (1 + 119901119896) 119875rx119896

+ (1 minus Ω119894119896DC) (1 + 119901119896) 119875tx119896 + (1 + 119901119895) 119864rx119895


(11)

The energy for the packet transmitted or sent is consideredequal at each node (not considering congestion) thus (11)becomes119862119894119895119896

= 119862119878119896119894119895

+ 119862119877119896119894119895

+ 119862119863119896119894119895

= (1 + 119901119894) 119875119879+ (1 + 119901

119896) (119875119877+ (1 minus Ω

119894119896DC) 119875119879)

+ [(1 minus Ω119894119896DC) (1 minus Ω119896119895DC) + 1] (1 + 119901119895) 119875119877

(12)

Suppose that the desired packet error ratio at hop isΩobj andpower allocation constraint packet error ratio at hop can bedenoted

min 119862119894119895119896 forall119896 isin [2119873] 119896 = 119894 119895

st max (Ω119894119896DC Ω119896119895DC) le Ωobj

(1 minus 119901119906) 119860 (119891

119906V) minus 119867 (119909119906 (119905) 119909119906) ge 0

0 le 119901119906le 1

119909119906 (119905) = argmin

119909119885 (119891119906V 119909119906 (119905) 119909119906) + 119901119906 (

120576

0)

119891119894119896= 119891119906V isin argmin

119891

119885 (119891119906V 119909119906 (119905) 119909119906)

119901119906 (119905 + 1)

= 119901119906 (119905) + 120574119905 (119867 (119909

119906 (119905) 119909119906) minus 119860 (119891119906V))

(13)

Node 119896making (13) optimal is the optimal occupied node


35 Algorithm Design

Algorithm 1

Step 1 Initialization

Step 11 Initialize original signal 1199090isin 119877119899times1 and

select appropriate Φ isin 119877119898times119899 119898 ≪ 119899 calculate

119871Step 12 Given 119892

119894119896 119861119899 119901119899 119877

Step 2 Given the original 119901119906(0) and the expression of

119867(119909119906(119905) 119909119906) 119860(119891

119906V)

Step 21 forall119905 isin [0119873] calculate 119901119906(119905) 119909119906(119905) and

119891119906V

Step 22 Given ΩobjIf (1 minus 119901

119906)119860(119891119906V) minus 119867(119909119906(119905) 119909119906) ge 0

Then calculate Ω119894119896DC Ω119896119895DC

Else go to Step 1

Step 3

For 119891119906V isin argmin

119891119885(119891119906V 119909119906(119905) 119909119906)

If 0 le 119901119906(119905) le 1 max(Ω

119894119896DC Ω119896119895DC) le Ωobj

Then calculate 119862119894119895119896

Else if 0 le 119901119906(119905) le 1 max(Ω

119894119896DC Ω119896119895DC) gt Ωobj

Then go to Step 22Else if 119901

119906(119905) gt 1

Then go to Step 21End

End

End

End For

The performance analysis of the algorithm is presentedand proves its validity

Theorem 2 If 119909119906(119905) isin R119899times1 is sparse signal satisfying formula

(5) measurement vector with noise is expressed to 119910119906(119905) =

Φ119909119906(119905) + 120576 where the optimal vector is 119910lowast

119906constrained by

119910lowast

119906minus119910119906(119905) le 120575

119906 Let sensingmatrixΦ isin R119898times119899 obey restricted

isometry property (RIP) then

1003817100381710038171003817119909119906 (119905) minus 119909lowast

119906

10038171003817100381710038172le

119901119906120575119906

1 minus 119901119906 Φ2

(14)

where 119909lowast119906is the optimal value of 119909

119906(119905)

Proof By formula (5) we have

1003817100381710038171003817119909119906 (119905) minus 119909lowast10038171003817100381710038172

=

1003817100381710038171003817100381710038171003817100381710038171003817

argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)

minus argmin119909119885 (119891119906V 119909lowast

119906 119909119906)

+ 119901119906(

119910 minus Φ119909119906 (119905) minus (119910

lowastminus Φ119909lowast

119906)

0)

10038171003817100381710038171003817100381710038171003817100381710038172

(15)

le100381710038171003817100381710038171003817argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)


119906 119909119906)1003817100381710038171003817100381710038172

+

1003817100381710038171003817100381710038171003817100381710038171003817

119901119906(

119910 minus Φ119909119906 (119905) minus (119910


119906)

0)

10038171003817100381710038171003817100381710038171003817100381710038172

(16)

le100381710038171003817100381710038171003817argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)


119906 119909119906)1003817100381710038171003817100381710038172+ 119901119906

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

+ 119901119906

1003817100381710038171003817Φ119909119906 (119905) minus Φ119909lowast

119906

10038171003817100381710038172

(17)

The optimal value 119909lowast119906is the minimum value of 119909

119906(119905)

formula (17) is transformed into100381710038171003817100381710038171003817argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)


119906 119909119906)1003817100381710038171003817100381710038172= 0

(18)

Thus formula (17) becomes

= 119901119906

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

+ 119901119906

1003817100381710038171003817Φ119909119906 (119905) minus Φ119909lowast

119906(119905)10038171003817100381710038172

le 119901119906

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

+ 119901119906 Φ2

1003817100381710038171003817119909119906 (119905) minus 119909lowast

119906(119905)10038171003817100381710038172

(19)

Therefore formula (15) becomes

1003817100381710038171003817119909119906 (119905) minus 119909lowast10038171003817100381710038172

le119901119906

1 minus 119901119906 Φ2

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

le119901119906120575119906

1 minus 119901119906 Φ2

(20)

Thus algorithm (5) converges statistically to within asmall neighborhood of the optimal values 119909lowast

Since 119901119906is continuous Theorem 2 implies that the input

signal approaches the optimal 119909lowast when 120575119906is small enough

4 Simulation Analysis

In this section we exhibit numerical examples and simula-tion results for the proposed algorithm (cross-layer optimaldesign CLOD) We conduct numerical experiments usingNS2 to confirm the efficiency of the proposed algorithm Wealso perform simulations using Lee and Lim [3] and DCH tovalidate our assumptions In our numerical examples we set


DCHLee

CLOD

50 100 150 200 250 3000Simulation time (ms)

0

01

02

03

04

05

06

07

08

Pack

et lo

ss ra

tio

Figure 2 Comparison of dropped packet

a net topology with 100 nodes placed randomly in a 10 times 10field where the distance of neighboring nodes is set to 20mThe buffers are 10ndash100 packets Packet size is 1024 bits andsimulation time is 300ms

Figure 2 indicates that the dropped packets of the Leealgorithm and CLOD algorithm are relatively lower Thisillustrates that the algorithms could relieve congestion ata certain extent However there are some differences inthe algorithms CLOD dropped packet is the lowest whennode-level congestion and link-level congestion are simul-taneously existing This verifies that the algorithm achievesbetter network control by signal compressed and channelselection the dropped packet is lower in CLOD algorithmthan Lee algorithmwhich is owing to only dispose node-levelcongestion and ignore link-level congestion in Lee algorithmDCHmakes the congestion stay at the top because the copingmechanism for congestion is weak

Figure 3 shows that CLOD makes transmitted packetremarkably increase per second for signal compressed andchannel selection strategy The other algorithms cannotachieve so high throughput for required transmitted data toolarge resulting in congestion In addition the Lee algorithmand DCH algorithm show incapability of channel contentiontriggered congestion

Figure 4 displays comparison with energy in three algo-rithms From Figure 4 it can be observed that the bestresults of CLOD can reach the lowest energy consumptionSuch a phenomenon implies that compressed data makes thetransmission traffic drastically decrease which can effectivelyreduce energy consumption and distinctly relieve node-level congestion Channel selection makes certain positivecontribution to save energy and link capacity allocation canbe used to take full advantage of limited energy The othersare to be considerably inferior to CLOD in this problem


95

10

105

11

115

12

125

13

Thro

ughp

ut (M

bps)

DCHLee

CLOD

Figure 3 Comparison of throughput

DCHLee

CLOD


9992

9993

9994

9995

9996

9997

9998

9999

10

10001

10002Re

mai

ning

ener

gy (J

)

Figure 4 Comparison of remaining energy

5 Conclusions

In this paper we propose a cross-layer optimal protocolby integrating using ldquocross-layer designrdquo ldquooptimal theoryrdquoand ldquocompressed sensingrdquo to achieve higher throughput andpower efficiency In the power control protocol by adjustingcongestion rate to the reduction of power we could attainlower power consumption than the former algorithms In theproposed input signal control algorithm the signal size isadjusted to stable state Link capacity allocation is presentedby supply and demand function of the service Channel isselected by energy minimum optimal Through the analysisaccuracy of signal transmission is guaranteed although signalis to be lossy compression In addition simulation resultsshow that the proposed algorithm offers better performancein terms of throughput and power consumption comparedwith the other protocols


Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work has been supported by the Fundamental ResearchFunds for the Central Universities of China no N142303013and the Program of Science and Technology Research ofHebei University no QN2014326

References

[1] J Cheng Q Ye H Jiang D Wang and C Wang ldquoSTCDG anefficient data gathering algorithm based on matrix completionfor wireless sensor networksrdquo IEEE Transactions on WirelessCommunications vol 12 no 2 pp 850ndash861 2013

[2] Y Li M Sheng C Wang X Wang Y Shi and J LildquoThroughput-delay tradeoff in interference-free wireless net-works with guaranteed energy efficiencyrdquo IEEE Transactions onWireless Communications vol 14 no 3 pp 1608ndash1621 2015

[3] H-J Lee and J-T Lim ldquoCross-layer congestion control forpower efficiency over wireless multihop networksrdquo IEEE Trans-actions on Vehicular Technology vol 58 no 9 pp 5274ndash52782009

[4] W Chen and I J Wassell ldquoOptimized node selection for com-pressive sleeping wireless sensor networksrdquo IEEE Transactionson Vehicular Technology 2015

[5] L Orihuela F Gomez-Estern and F R Rubio ldquoScheduledcommunication in sensor networksrdquo IEEE Transactions onControl Systems Technology vol 22 no 2 pp 801ndash808 2014

[6] D Liao and A K Elhakeem ldquoA cross-layer joint optimizationapproach for multihop routing in TDD-CDMA wireless meshnetworksrdquo European Transactions on Telecommunications vol23 no 1 pp 6ndash15 2012

[7] T Xue X D Dong and Y Shi ldquoMultiple access and data recon-struction in wireless sensor networks based on compressedsensingrdquo IEEE Transactions on Wireless Communications vol12 no 7 pp 3399ndash3411 2013

[8] J Chen S He Y Sun P Thulasiraman and X M ShenldquoOptimal flow control for utility-lifetime tradeoff in wirelesssensor networksrdquo Computer Networks vol 53 no 18 pp 3031ndash3041 2009

[9] S Y Xiang and L Cai ldquoTransmission control for compressivesensing video over wireless channelrdquo IEEE Transactions onWireless Communications vol 12 no 3 pp 1429ndash1437 2013

[10] Y Sadi and S C Ergen ldquoOptimal power control rate adaptationand scheduling for UWB-based intravehicular wireless sensornetworksrdquo IEEE Transactions on Vehicular Technology vol 62no 1 pp 219ndash234 2013

[11] S B He J M Chen D K Y Yau and Y X Sun ldquoCross-layeroptimization of correlated data gathering in wireless sensornetworksrdquo IEEE Transactions on Mobile Computing vol 11 no11 pp 1678ndash1691 2012

[12] Y B Wang M C Vuran and S Goddard ldquoCross-layeranalysis of the end-to-end delay distribution in wireless sensornetworksrdquo IEEEACM Transactions on Networking vol 20 no1 pp 305ndash318 2012

[13] X Zhang H V Poor and M Chiang ldquoOptimal power alloca-tion for distributed detection over MIMO channels in wireless

sensor networksrdquo IEEE Transactions on Signal Processing vol56 no 9 pp 4124ndash4140 2008

[14] G A Shah V C Gungor and O B Akan ldquoA cross-layer QoS-aware communication framework in cognitive radio sensornetworks for smart grid applicationsrdquo IEEE Transactions onIndustrial Informatics vol 9 no 3 pp 1477ndash1485 2013

[15] L Shi and A O Fapojuwo ldquoCross-layer optimization withcooperative communication forminimum power cost in packeterror rate constrained wireless sensor networksrdquo Ad Hoc Net-works vol 10 no 7 pp 1457ndash1468 2012

[16] M C Vuran and I F Akyildiz ldquoXLP a cross-layer protocolfor efficient communication in wireless sensor networksrdquo IEEETransactions on Mobile Computing vol 9 no 11 pp 1578ndash15912010

[17] P F Zhang and S Jordan ldquoCross layer dynamic resourceallocation with targeted throughput for WCDMA datardquo IEEETransactions on Wireless Communications vol 7 no 12 pp4896ndash4906 2008

[18] G Athanasiou T Korakis O Ercetin and L Tassiulas ldquoAcross-layer framework for association control in wireless meshnetworksrdquo IEEE Transactions on Mobile Computing vol 8 no1 pp 65ndash80 2009

[19] P Yang andB Chen ldquoTo listen or not distributed detectionwithasynchronous transmissionsrdquo IEEE Signal Processing Lettersvol 22 no 5 pp 628ndash632 2015

[20] HMamaghanian N Khaled D Atienza and P VandergheynstldquoCompressed sensing for real-time energy-efficient ECG com-pression on wireless body sensor nodesrdquo IEEE Transactions onBiomedical Engineering vol 58 no 9 pp 2456ndash2466 2011

[21] F Fazel M Fazel and M Stojanovic ldquoRandom access com-pressed sensing for energy-efficient underwater sensor net-worksrdquo IEEE Journal on Selected Areas in Communications vol29 no 8 pp 1660ndash1670 2011

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k

ji

CCH

Figure 1 Multihop routing cooperative communication model

In this paper cross-layer optimal design is presentedwhich considers the influence for congestion rate at physicallayerMAC layer network layer and transport layer to achieveminimum power cost in WSNs The algorithm coordinatescommunication protocols by congestion rate in the severallayers to solve lossy wireless channel excessive contentionand unfair access disabled bandwidth allocation and thefundamentally inappropriate mechanisms of TCP First wedesign a packet error rate control strategy based on conges-tion rate which makes the packet error rate in the domainof validity The power is exactly allocated on the basis of ldquotoeach according to his needsrdquo Second the optimal schemesof control input and link capacity with compressed sensingare discussedThird we construct minimum energy problemwith power control function congestion control functionlink allocation function and so on The optimum solutionsare the optimal power control and channel selection

2 Network and Node Model

For energy efficiency purpose the transmission power atevery node is assumed to be adjustable resulting in congestionprice when the congestion rate is bigger the power should beincreased for data transmitted successfully when the conges-tion rate is smaller the power is only satisfied for data trans-mitted regularly We assume that the sensor network consistsof119873 nodes of which the sink node is defined as node 119873

Communication from node 119894 to node 119895 contains directedcommunication hop (DCH) 119894 rarr 119895 [15] and cooperativecommunication hop (CCH) 119894 rarr 119896 rarr 119895 as shown inFigure 1 CCH consists of a sender a relay and a receiver(119894 119896 119895 in Figure 1 resp) such that both direct and relayedcopies of the information transmitted by the sender arereceived at the receiver

3 Cross-Layer Optimization Design ofCooperative Communication

In the wireline networks the protocols hold rigorous con-straint at each layer which is only responsible for oneselfnot being infiltrated Physical layer is mostly in charge ofpower allocation channel selection is achieved inMAC layerflow control is implemented in transport layer network layeris usually responsible for scheduling design However therequirement like this does not occur in WSNs Cooperative

communication is applied for protocols at each layer to makenet performance better

31 Power Control Define packet error rate with whiteGaussian noise [15] as follows

Ω119894119896DC = 1 minus (1 minus

1

2119890minus1205741198941198962)

119871

(1)

where 120574119894119896= (119875txtot119894119892119894119896119875119899) times (119861119899119877) is energy per bit to noise

power spectral density ratio 119875txtot119894 is the aggregated powerfor transmitting a packet at 119894 119861

119899is the noise bandwidth 119892

119894119896

is the path loss of link (119894 119896) in linear units 119875119899is the average

noise power 119877 is the maximum link data rate in bits persecond bitss and 119871 is the length of the packet The powerconsumption of a packet transmitted successfully is 119875txtot119894 =(1 + 119901

119894)119875tx119894 if congestion occurs in the WSNs 119875tx119894 denotes

transmitted power to a packet at ideal condition (congestiondoes not occur) and 119901

119894is the congestion rate at node 119894 the

average noise power 119875119899= (1 + 119901

119894)119875119899 where 119875

119899is the average

noise power at ideal condition the maximum link data rate119877 = (1+119901

119894)119877 where 119877 is the maximum link data rate at ideal

condition Thus

120574119894119896=(1 + 119901

119894) 119875tx119894119892119894119896

(1 + 119901119894) 119875119899

119861119899

(1 + 119901119894) 119877

=119875tx119894119892119894119896

(1 + 119901119894) 119875119899

119861119899

119877

(2)

We can conclude that 120574119894119896is adjusted to be smaller and

Ω119894119896DC is bigger when congestion rate is increased from

formula (2)The power appropriately adjusted by congestionrate makes the packet error rate constraint the domain ofvalidity The power is exactly allocated on the basis of ldquotoeach according to his needsrdquo which can extensively highlightpower efficiency

32 Congestion Control Recently lots of researchers haveaddressed the signal function with cross-layer optimal designto achieve better performance due to the characteristic ofhigher communication consumption and lower data processconsumption in WSNs [16ndash18] However almost all conges-tion control algorithms did not consider the data preprocess-ing before being transmitted [19] In this section we try toreduce the number of transmissions with a Toeplitz matrix incompressed sensing that enables the number of transmissionsto be extensively decreased in WSNs The transmission ofcompressed signal is not only relieving the congestion indata process overabundance but also economizing energy inthe transmission Compressed sensing model is expressed asfollows

119910 (119905) = Φ119909119894 (119905) + 120576 (3)

where 119909119894(119905) isin R119899times1 is input signal 119910(119905) isin R119898times1 is measure-

ment vector Φ isin R119898times119899 is sensing matrix 119898 ≪ 119899 and120576 isin R119898times1 is unknown vector formeasurement noise Supposethat the input signal is sparse and sensing matrix satisfiesrestricted isometry property (RIP) [20] To speed up con-gestion control we select Toeplitz matrix as sensing matrixmeeting Φ

2le 1




119894119896in (119894 119896) denotes





Consider

119885 (119891119894119896 119909119894 (119905) 119909119894) = (1 minus 119901119894) 119860 (119891119894119896) minus 119867 (119909

119894 (119905) 119909119894) (4)


119909119894 (119905) = argmin

119909119885 (119891119894119896 119909119894 (119905) 119909119894) + 119901119894 (

120576

0) (5)








119891119894119896isin argmin119885 (119891

119894119896 119909119894 (119905) 119909119894) (6)


119862119878119896119894119895

= 119875tx119894tot (7)


119862119877119896119894119895



119862119863119896119894119895



119862119878119896119894119895

= 119875tx119894tot = (1 + 119901119894) 119875tx119894

119862119877119896119894119895


= (1 + 119901119896) 119875rx119896 + (1 minus Ω119894119896DC) (1 + 119901119896) 119875tx119896

119862119863119894119895119896


= (1 + 119901119895) 119875rx119895


(10)


119862119894119895119896

= 119862119878119896119894119895

+ 119862119877119896119894119895

+ 119862119863119896119894119895

= (1 + 119901119894) 119875tx119894 + (1 + 119901119896) 119875rx119896

+ (1 minus Ω119894119896DC) (1 + 119901119896) 119875tx119896 + (1 + 119901119895) 119864rx119895


(11)


= 119862119878119896119894119895

+ 119862119877119896119894119895

+ 119862119863119896119894119895

= (1 + 119901119894) 119875119879+ (1 + 119901

119896) (119875119877+ (1 minus Ω

119894119896DC) 119875119879)


(12)


min 119862119894119895119896 forall119896 isin [2119873] 119896 = 119894 119895


(1 minus 119901119906) 119860 (119891

119906V) minus 119867 (119909119906 (119905) 119909119906) ge 0

0 le 119901119906le 1

119909119906 (119905) = argmin

119909119885 (119891119906V 119909119906 (119905) 119909119906) + 119901119906 (

120576

0)

119891119894119896= 119891119906V isin argmin

119891

119885 (119891119906V 119909119906 (119905) 119909119906)

119901119906 (119905 + 1)

= 119901119906 (119905) + 120574119905 (119867 (119909

119906 (119905) 119909119906) minus 119860 (119891119906V))

(13)



35 Algorithm Design

Algorithm 1




119871Step 12 Given 119892

119894119896 119861119899 119901119899 119877


119867(119909119906(119905) 119909119906) 119860(119891

119906V)


119891119906V


119906)119860(119891119906V) minus 119867(119909119906(119905) 119909119906) ge 0


Else go to Step 1

Step 3


119891119885(119891119906V 119909119906(119905) 119909119906)

If 0 le 119901119906(119905) le 1 max(Ω

119894119896DC Ω119896119895DC) le Ωobj

Then calculate 119862119894119895119896

Else if 0 le 119901119906(119905) le 1 max(Ω

119894119896DC Ω119896119895DC) gt Ωobj


119906(119905) gt 1


End

End

End For






119910lowast

119906minus119910119906(119905) le 120575



1003817100381710038171003817119909119906 (119905) minus 119909lowast

119906

10038171003817100381710038172le

119901119906120575119906

1 minus 119901119906 Φ2

(14)


119906(119905)


1003817100381710038171003817119909119906 (119905) minus 119909lowast10038171003817100381710038172

=

1003817100381710038171003817100381710038171003817100381710038171003817

argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)


119906 119909119906)

+ 119901119906(

119910 minus Φ119909119906 (119905) minus (119910


119906)

0)

10038171003817100381710038171003817100381710038171003817100381710038172

(15)

le100381710038171003817100381710038171003817argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)


119906 119909119906)1003817100381710038171003817100381710038172

+

1003817100381710038171003817100381710038171003817100381710038171003817

119901119906(

119910 minus Φ119909119906 (119905) minus (119910


119906)

0)

10038171003817100381710038171003817100381710038171003817100381710038172

(16)

le100381710038171003817100381710038171003817argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)


119906 119909119906)1003817100381710038171003817100381710038172+ 119901119906

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

+ 119901119906

1003817100381710038171003817Φ119909119906 (119905) minus Φ119909lowast

119906

10038171003817100381710038172

(17)


119906(119905)



119906 119909119906)1003817100381710038171003817100381710038172= 0

(18)


= 119901119906

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

+ 119901119906

1003817100381710038171003817Φ119909119906 (119905) minus Φ119909lowast

119906(119905)10038171003817100381710038172

le 119901119906

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

+ 119901119906 Φ2

1003817100381710038171003817119909119906 (119905) minus 119909lowast

119906(119905)10038171003817100381710038172

(19)


1003817100381710038171003817119909119906 (119905) minus 119909lowast10038171003817100381710038172

le119901119906

1 minus 119901119906 Φ2

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

le119901119906120575119906

1 minus 119901119906 Φ2

(20)







DCHLee

CLOD


0

01

02

03

04

05

06

07

08

Pack

et lo

ss ra

tio







95

10

105

11

115

12

125

13

Thro

ughp

ut (M

bps)

DCHLee

CLOD


DCHLee

CLOD


9992

9993

9994

9995

9996

9997

9998

9999

10

10001

10002Re

mai

ning

ener

gy (J

)


5 Conclusions





Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119894119896in (119894 119896) denotes





Consider

119885 (119891119894119896 119909119894 (119905) 119909119894) = (1 minus 119901119894) 119860 (119891119894119896) minus 119867 (119909

119894 (119905) 119909119894) (4)


119909119894 (119905) = argmin

119909119885 (119891119894119896 119909119894 (119905) 119909119894) + 119901119894 (

120576

0) (5)








119891119894119896isin argmin119885 (119891

119894119896 119909119894 (119905) 119909119894) (6)


119862119878119896119894119895

= 119875tx119894tot (7)


119862119877119896119894119895



119862119863119896119894119895



119862119878119896119894119895

= 119875tx119894tot = (1 + 119901119894) 119875tx119894

119862119877119896119894119895


= (1 + 119901119896) 119875rx119896 + (1 minus Ω119894119896DC) (1 + 119901119896) 119875tx119896

119862119863119894119895119896


= (1 + 119901119895) 119875rx119895


(10)


119862119894119895119896

= 119862119878119896119894119895

+ 119862119877119896119894119895

+ 119862119863119896119894119895

= (1 + 119901119894) 119875tx119894 + (1 + 119901119896) 119875rx119896

+ (1 minus Ω119894119896DC) (1 + 119901119896) 119875tx119896 + (1 + 119901119895) 119864rx119895


(11)


= 119862119878119896119894119895

+ 119862119877119896119894119895

+ 119862119863119896119894119895

= (1 + 119901119894) 119875119879+ (1 + 119901

119896) (119875119877+ (1 minus Ω

119894119896DC) 119875119879)


(12)


min 119862119894119895119896 forall119896 isin [2119873] 119896 = 119894 119895


(1 minus 119901119906) 119860 (119891

119906V) minus 119867 (119909119906 (119905) 119909119906) ge 0

0 le 119901119906le 1

119909119906 (119905) = argmin

119909119885 (119891119906V 119909119906 (119905) 119909119906) + 119901119906 (

120576

0)

119891119894119896= 119891119906V isin argmin

119891

119885 (119891119906V 119909119906 (119905) 119909119906)

119901119906 (119905 + 1)

= 119901119906 (119905) + 120574119905 (119867 (119909

119906 (119905) 119909119906) minus 119860 (119891119906V))

(13)



35 Algorithm Design

Algorithm 1




119871Step 12 Given 119892

119894119896 119861119899 119901119899 119877


119867(119909119906(119905) 119909119906) 119860(119891

119906V)


119891119906V


119906)119860(119891119906V) minus 119867(119909119906(119905) 119909119906) ge 0


Else go to Step 1

Step 3


119891119885(119891119906V 119909119906(119905) 119909119906)

If 0 le 119901119906(119905) le 1 max(Ω

119894119896DC Ω119896119895DC) le Ωobj

Then calculate 119862119894119895119896

Else if 0 le 119901119906(119905) le 1 max(Ω

119894119896DC Ω119896119895DC) gt Ωobj


119906(119905) gt 1


End

End

End For






119910lowast

119906minus119910119906(119905) le 120575



1003817100381710038171003817119909119906 (119905) minus 119909lowast

119906

10038171003817100381710038172le

119901119906120575119906

1 minus 119901119906 Φ2

(14)


119906(119905)


1003817100381710038171003817119909119906 (119905) minus 119909lowast10038171003817100381710038172

=

1003817100381710038171003817100381710038171003817100381710038171003817

argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)


119906 119909119906)

+ 119901119906(

119910 minus Φ119909119906 (119905) minus (119910


119906)

0)

10038171003817100381710038171003817100381710038171003817100381710038172

(15)

le100381710038171003817100381710038171003817argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)


119906 119909119906)1003817100381710038171003817100381710038172

+

1003817100381710038171003817100381710038171003817100381710038171003817

119901119906(

119910 minus Φ119909119906 (119905) minus (119910


119906)

0)

10038171003817100381710038171003817100381710038171003817100381710038172

(16)

le100381710038171003817100381710038171003817argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)


119906 119909119906)1003817100381710038171003817100381710038172+ 119901119906

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

+ 119901119906

1003817100381710038171003817Φ119909119906 (119905) minus Φ119909lowast

119906

10038171003817100381710038172

(17)


119906(119905)



119906 119909119906)1003817100381710038171003817100381710038172= 0

(18)


= 119901119906

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

+ 119901119906

1003817100381710038171003817Φ119909119906 (119905) minus Φ119909lowast

119906(119905)10038171003817100381710038172

le 119901119906

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

+ 119901119906 Φ2

1003817100381710038171003817119909119906 (119905) minus 119909lowast

119906(119905)10038171003817100381710038172

(19)


1003817100381710038171003817119909119906 (119905) minus 119909lowast10038171003817100381710038172

le119901119906

1 minus 119901119906 Φ2

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

le119901119906120575119906

1 minus 119901119906 Φ2

(20)







DCHLee

CLOD


0

01

02

03

04

05

06

07

08

Pack

et lo

ss ra

tio







95

10

105

11

115

12

125

13

Thro

ughp

ut (M

bps)

DCHLee

CLOD


DCHLee

CLOD


9992

9993

9994

9995

9996

9997

9998

9999

10

10001

10002Re

mai

ning

ener

gy (J

)


5 Conclusions





Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










35 Algorithm Design

Algorithm 1




119871Step 12 Given 119892

119894119896 119861119899 119901119899 119877


119867(119909119906(119905) 119909119906) 119860(119891

119906V)


119891119906V


119906)119860(119891119906V) minus 119867(119909119906(119905) 119909119906) ge 0


Else go to Step 1

Step 3


119891119885(119891119906V 119909119906(119905) 119909119906)

If 0 le 119901119906(119905) le 1 max(Ω

119894119896DC Ω119896119895DC) le Ωobj

Then calculate 119862119894119895119896

Else if 0 le 119901119906(119905) le 1 max(Ω

119894119896DC Ω119896119895DC) gt Ωobj


119906(119905) gt 1


End

End

End For






119910lowast

119906minus119910119906(119905) le 120575



1003817100381710038171003817119909119906 (119905) minus 119909lowast

119906

10038171003817100381710038172le

119901119906120575119906

1 minus 119901119906 Φ2

(14)


119906(119905)


1003817100381710038171003817119909119906 (119905) minus 119909lowast10038171003817100381710038172

=

1003817100381710038171003817100381710038171003817100381710038171003817

argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)


119906 119909119906)

+ 119901119906(

119910 minus Φ119909119906 (119905) minus (119910


119906)

0)

10038171003817100381710038171003817100381710038171003817100381710038172

(15)

le100381710038171003817100381710038171003817argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)


119906 119909119906)1003817100381710038171003817100381710038172

+

1003817100381710038171003817100381710038171003817100381710038171003817

119901119906(

119910 minus Φ119909119906 (119905) minus (119910


119906)

0)

10038171003817100381710038171003817100381710038171003817100381710038172

(16)

le100381710038171003817100381710038171003817argmin119909119885 (119891119906V 119909119906 (119905) 119909119906)


119906 119909119906)1003817100381710038171003817100381710038172+ 119901119906

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

+ 119901119906

1003817100381710038171003817Φ119909119906 (119905) minus Φ119909lowast

119906

10038171003817100381710038172

(17)


119906(119905)



119906 119909119906)1003817100381710038171003817100381710038172= 0

(18)


= 119901119906

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

+ 119901119906

1003817100381710038171003817Φ119909119906 (119905) minus Φ119909lowast

119906(119905)10038171003817100381710038172

le 119901119906

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

+ 119901119906 Φ2

1003817100381710038171003817119909119906 (119905) minus 119909lowast

119906(119905)10038171003817100381710038172

(19)


1003817100381710038171003817119909119906 (119905) minus 119909lowast10038171003817100381710038172

le119901119906

1 minus 119901119906 Φ2

1003817100381710038171003817119910 minus 119910lowast10038171003817100381710038172

le119901119906120575119906

1 minus 119901119906 Φ2

(20)







DCHLee

CLOD


0

01

02

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05

06

07

08

Pack

et lo

ss ra

tio







95

10

105

11

115

12

125

13

Thro

ughp

ut (M

bps)

DCHLee

CLOD


DCHLee

CLOD


9992

9993

9994

9995

9996

9997

9998

9999

10

10001

10002Re

mai

ning

ener

gy (J

)


5 Conclusions





Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










DCHLee

CLOD


0

01

02

03

04

05

06

07

08

Pack

et lo

ss ra

tio







95

10

105

11

115

12

125

13

Thro

ughp

ut (M

bps)

DCHLee

CLOD


DCHLee

CLOD


9992

9993

9994

9995

9996

9997

9998

9999

10

10001

10002Re

mai

ning

ener

gy (J

)


5 Conclusions





Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article efficient cross-layer optimization...

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