www.ietdl.org

1&

Published in IET CommunicationsReceived on 3rd June 2013Accepted on 2nd January 2014doi: 10.1049/iet-com.2013.1079

104The Institution of Engineering and Technology 2014

ISSN 1751-8628

Optimised resource allocation under impulsive noisein power line communicationsAbir Chaudhuri, Manav R. Bhatnagar

Department of Electrical Engineering, Indian Institute of Technology – Delhi, Hauz Khas, New Delhi 110016, India

E-mail: manav@ee.iitd.ac.in

Abstract: Power lines render very harsh and hostile environment for electronic data communication. The key characteristics ofthe power line channel are time varying nature, frequency selective attenuation and presence of impulsive noise because ofrandom switching of power appliances. The impulsive nature of the additive noise has been ignored so far in the literature forresource allocation in power line communication system because this assumption results in intractable solutions. In this study,an approach of efficient resource allocation is introduced in order to maximise the throughput and achieve tolerable bit errorrate of the power line system, by adapting power transmitted in each cycle, under additive Middleton class A impulsive noise(MCAIN). The proposed resource allocation technique utilises sub-channel ordering to obtain a higher throughput; andprovides improvement as compared to the existing zero forcing based resource allocation technique under additive MCAIN.

1 Introduction

High speed communications over power lines have received agrowing interest in the past few years because of the poweroutlet ubiquity inside home. The channel attenuation isspecifically high and because of the various loads that areconnected to the indoor power outlets, the power linecommunication (PLC) channel impedance may varyrandomly [1]. The noise present in PLC is a mixture ofcoloured background noise, narrowband noise andimpulsive noise. Impulsive noise is generally caused byload switching transients in the network (capacitor bank,thermostat, refrigerator, air conditioner etc.) and forms themajor disturbance in the channel. During occurrence ofsuch impulses, the noise power is perceptibly higher andmay cause a significant increase in error rate [2]. Moreover,the topology of the PLC networks which usually consists ofseveral electrical branches and joints, inevitably leads toelectromagnetic reflections. Such reflections are alsogenerated by impedance mismatches between the channeland the connected electrical appliances thereby creating amultipath scenario [1].Orthogonal frequency division multiplexing (OFDM) has

been considered as robust adaptive modulation scheme thathas many advantages over other modulation types such aslow complexity, channel equalisation, good resistance overnarrowband and impulsive noises and the ability to achieveapproximate value of Shannon limit for channel capacityusing simple coding techniques [3]. However, the dataspread OFDM suffers degradation due to varying andfrequency selective attenuation in the channel. A bit andpower loading technique can be adopted to manage thepower and bits loaded to each sub-carrier depending onthe prevalent channel condition [4–6]. However, most of

the aforementioned works during optimisation assume thatthe noise present in PLC is additive white Gaussian noise(AWGN) for simplifying the analysis; although Middletonclass A impulsive noise (MCAIN) accurately realises theimpulsive noise [7, 8]. Hence, the existing techniques donot perform the resource allocation, in a realistic manner.In this paper, we present a resource allocation technique for

PLC, where the best sub-channel selection is done based onthe channel condition and they are appropriately bit loadedand power controlled to meet the required quality of service(QoS) parameters and at the same time maximising thethroughput, under MCAIN. This technique providesimprovement as compared to the existing zero forcing basedresource allocation technique under additive MCAIN. In thecase of zero forcing based resource allocation, afterselection of sub-channels, power of few of the highlyattenuated carriers are forced to zero and the availablepower is redistributed among the useful sub-channels.Although the proposed scheme distributes the sub-channelsby taking the fairness for the users into account.

2 System model

We consider an OFDM system consisting of N users utilisingK sub-channels in a power line channel. The alternatingcurrent (AC) line cycle is divided into T temporal slots andeach time slot is indexed by j, sub-channels are denoted byi and users are represented by n. Each user is assumed tohave a single transmitter and a receiver. Equal number ofsub-channels are allocated to each user to incorporatefairness. We assume that the duration of a time slot is lessthan the channel coherence time so that the channel gainremains constant in a single time slot; although they vary

IET Commun., 2014, Vol. 8, Iss. 7, pp. 1104–1108doi: 10.1049/iet-com.2013.1079

www.ietdl.org

among different time slots because of the time varying natureof the channel.We assume that M-ary quadrature amplitude modulation

(M-QAM) is used in each transmit period and for eachsub-channel with constellation size 2mijn , where mijn is thenumber of bits loaded on subcarrier i at time slot j for usern. The PLC transmitters are assumed to be able to adapt thenumber of bits transmitted at each time slot as a function ofthe channel state, that is, mijn =mijn(Gijn), where Gijn is thesignal-to-noise ratio (SNR) for the subcarrier i at time j foruser n. At time j for user n, a symbol is transmitted atpower level pjn. The bits mijn and power pjn are loaded ontothat subcarrier such that they maintain the requisite bit errorrate (BER). For each individual time slot, the parametersmijn and pjn are optimised.Further, we assume that the envelope of the additive noise

follows the MCAIN probability distribution function [2]

Pj(j) = e−A∑1m=0

Amj

m!sm2exp

−j2

2sm2

( )(1)

where s2m = s2 (m/A)+ G

( )/(1+ G), σ2 is the total noise

power and can be defined as s2 = s2g + s2

I , where s2g,

where s2g is the Gaussian noise power and s2

I is theimpulsive noise power, Γ is the mean power ratio of theGaussian noise component to non-Gaussian noisecomponent present in the PLC channel, ξ is the noiseenvelope and A is the impulsive index. The phase of theadditive noise is assumed to be uniformly distributedbetween − π and π. The symbol error probability ofM-QAM under MCAIN is given as [9] (see (2))

where Gijn·pjn is the effective SNR. Further, the channelcapacity of the power line channel for the subcarrier i at timej for user n, in the presence of the MCAIN, is given as [10]

Cijn(Gijn, p jn) = B∑1m=0

e−A Am

m!log2 1+ Gijn.p jn

( )(3)

where B is the bandwidth of a single sub-channel.The transmission rate of the nth user, n = 1, 2, …, N,

depends upon the sub-channel that is allocated to it. Let usassume cni be the sub-channel allocation index that takesthe value 1 when sub-channel i is allocated to user n, else itbecomes 0. Let Mj be the set of possible bits loaded ontothe sub-channel when the channel state is given by Gijn

Mj := {(mj1, mj2, . . . , mjN )T|mjn ≤

∑Ki=1

Cijncni

BER Gijn, p jn, mijn

( )= 4

mijn1− e−A

∑1m=0

Am

m!4erfc

− ��3

√ ��G

√��2

√ �����mijn −

√({⎡

⎣

+4 ����mijn

√ − 2( )

mijn1− e−A

∑1m=0

Am

m!21

({[

+mijn − 4 ����mijn

√ − 1( )mijn

1− e−A∑1m=0

Am

m

⎧⎨⎩

IET Commun., 2014, Vol. 8, Iss. 7, pp. 1104–1108doi: 10.1049/iet-com.2013.1079

∑Nn=1

cni ≤ 1, ∀n = 1, . . . , N , ∀i = 1, . . . , K} (4)

Mj is a convex closed and bounded set and the possible bitloading on sub-channels can be defined as

M := {�m|mjeMj, ∀jeT} (5)

where �m is a vector containing bits loaded onto sub-channelfor all users in each time slot. Similarly, for the case ofpower loading, let Pj be the set of possible values for powerloaded onto the sub-channel when the channel state is givenby Gijn

Pj := {(p j1, . . . , p jN )T|Pmin ≤ p jn ≤ Pmax, ∀n} (6)

where Pj is a convex closed and bounded set; the possiblepower loading on sub-channels can be defined as

P := {p|pj e Pj, ∀jeT} (7)

where �p is a vector contains power loading values for all usersin each time slot. The proposed algorithm selects the bit andpower loading of sub-channels depending on the channel stateconditions and constraints imposed on the system.

3 Adaptive resource allocation policy

The proposed resource allocation algorithm primarily aims tomaximise the throughput of the system and at the same timemeeting the QoS requirements that constitute of power andBER constraints.

3.1 QoS requirements

The QoS requirements ensure that the optimisation techniquehas specified system boundaries. The system power of N usersis constrained within a value as specified by the systemoperator

E∑Nn=1

p jn(Gijn)

[ ]≤ NPavg (8)

where E[·] represents the expectation and Pavg denotes the peruser average transmit power. The total BER for N users is alsoconstrained by a tolerable value, BERmax and is calculated,

������ijn.p jn����1sm

)}2⎤⎦

− erfc− ��

3√ ��������

Gijn.p jn

√��2

√ ���������mijn − 1

√sm

( )). erfc

− ��3

√ ��������Gijn.p jn

√��2

√ ���������mijn − 1

√sm

( )( )}]

!. 1− erfc

− ��3

√ ��������Gijn.p jn

√��2

√ ���������mijn − 1

√sm

( )( )2⎫⎬⎭

(2)

1105& The Institution of Engineering and Technology 2014

www.ietdl.org

according to the equation given in (2), as

E∑Nn=1

BER(Gijn, mijn, p jn)

[ ]≤ BERmax (9)

3.2 Optimisation problem formulation

The proposed resource allocation algorithm solves thefollowing optimisation problem to maximise the throughputwhile satisfying the QoS requirements

Maximise:∑Nn=1

∑Ki=1

mijn

s.t. E∑Nn=1

p jn(Gijn)

[ ]≤ NPavg

E∑Nn=1

BER(Gijn, mijn, p jn)

[ ]≤ BERmax

mijn ≤ Cijn ∀i, j, n

(10)

where mijneMj∀jeT . From (10), the Lagrangian can beformulated as (see (11))

where un, vn, wn are the Lagrange multipliers and x = [u1, u2,…, uN, v1, v2, …, vN, w1, w2, …, wN]

T.The Lagrangian can be further simplified and the

multipliers and optimal values can be computed for eachtime slot from (11). At optimality, the values for the nthuser and jth instant are �m∗, �p∗ and the Lagrange multiplieris x*. These obtained values satisfy the saddle pointcondition such that for (�m, �p, x)

L(�m∗, �p∗, x) ≥ L(�m∗, �p∗, x∗) ≥ L(�m, �p, x∗) (12)

Our algorithm iteratively generates estimates that converge tothe optimal set �ml, �pl, xl

( ) � �m∗, �p∗, x∗( )

where l is theiteration index. In this manner, our approach shall learn theoptimal values.

3.3 Proposed optimised ordering algorithm

The proposed algorithm is summarised as follows:Proposed resource allocation algorithm

† Step 1: InitialisationInitialise maximum and minimum limit of transmitted

power and tolerable BER for the link.† Step 2: Sub-channel ordering

For each transmitting node n in the link, the sub-channelsare sorted in descending order according to channel stateinformation Gijn which is a reflection of the SNR.

L(�m, �p, x) :=∑Nn=1

∑Ki=1

mijn −∑Nn=1

un∑Ki=

(

−∑Nn=1

vn(p jn(Gijn)− Pavg

1106& The Institution of Engineering and Technology 2014

† Step 3: Sub-channel allocationFor each transmitting node n, the sub-channels facing the

lowest attenuation are allocated to them from the orderedones.† Step 4: Bit and power loading

Then bit (mijn) and power (pjn) loading is done onto theallocated sub-channels to maximise the throughput andminimise power and at same time achieving the BER. Thisis accomplished using the optimisation technique.† Step 5: Contention resolution

During allocation of sub-channels a matrix is maintainedwhich resolves contention issues between two nodes tryingto send data using the same sub-channel at the same time.† Step 6: This iteration procedure is continued for all nodestill maximum throughput is obtained with minimal powerloading.

The proposed algorithm utilises the best possible availablesub-channels in the medium for transmission therebyensuring a high quality link between the transmitter andreceiver. The sub-channel allocation matrix resolvescontention issues among the sub-channels to ensure that thesame sub-channel is not allocated to two different user.During the next time slot, each user is re-allocatedsub-channels which takes care of the time varying nature ofthe medium due to change of topology of the network. Thisallows the user to have access to sub-channels with lowerattenuation compared to other techniques. Minimal powerloading refers to the minimum amount of power transmittedby a user to attain the tolerable BER.It is to be noted that a sub-channel facing higher attenuation

for a node might face a comparatively lower attenuation foranother node at a different location since they are spatiallydistributed and electromagnetic interference might addconstructively or destructively depending on the distanceand phase. This iterative method ensures that we takeadvantage of such a situation rather than zero forcing sucha sub-channel.

3.4 Complexity and convergence of the algorithm

The channel ordering is done for every user and in each timeslot. If N users and K sub-channels are ordered for T time slotsin a single AC cycle then the complexity comes to O(NTK).This is done to ensure that we take the maximum advantage ofthe time varying behaviour of the channel. Also, due tospatially separated users, the channel condition at eachuser’s end varies and hence it becomes essential to performchannel ordering for each user, thereby ensuring a betterperformance. The algorithm converges to an optimalsolution iteratively constrained by the boundary conditionsgiven in the paper.In the numerical experiments, we observe that the proposed

algorithm always converges and the optimal values of powerand bit loading is unique. We have experimented with manydifferent initialisation and never experienced any divergenceof the proposed algorithm.

1

BER(Gijn, mijn, p jn)− BERmax

)

)−∑Nn=1

wn

∑Ki=1

|mijn − Cijn|( )

(11)

IET Commun., 2014, Vol. 8, Iss. 7, pp. 1104–1108doi: 10.1049/iet-com.2013.1079

Fig. 2 Variation of BER with SNR at tolerable BER of the order10−5 using proposed sub-channel ordering, randomised orderingand zero forcing scheme, under M-QAM modulation

www.ietdl.org

4 Numerical results

In this section we compare the performance of the proposedoptimised sub-channel selection with random sub-channelselection and zero forcing (ZF) technique for PLC.In the simulations, 512 sub-channels are used in the

frequency range 1.8–16 MHz. The simulations are carriedout by setting the tolerable BER of the order 10−4 and10−5, for SNR values from 0 to 30 dB. During this durationthe channel transfer function is supposed to remainconstant. Simulations are carried out in the presence ofimpulsive Middleton class A noise using MATLAB; thevalue of impulsive index A = 0.9, in this model. Thecalculation at each SNR value is averaged over differentchannel realisations. Throughput is defined as the numberof bits loaded on the sub-channels per time slot duration.The analytical BER is calculated using the formula, asgiven in (2) (Table 1).In Fig. 1, it can be observed that the proposed resource

allocation method achieves higher throughput compared tothe random ordering of sub-channels method, in thepresence of impulsive noise. In addition, an existingalgorithm using zero forcing of heavily attenuatedsub-channels has an overall poor performance compared tothe proposed sub-channel selection scheme. For example,the proposed scheme achieves a throughput of 40 Mbpscompared to 32 and 15 Mbps achieved by the ZF andrandom ordering schemes, respectively, for BER = 10−4 at30 dB SNR. In all the cases, the BER of the system arekept within the tolerable limit. The BER variation withincreasing SNR can be observed in Figs. 2 and 3. It can be

Fig. 1 Variation of throughput with SNR using proposedsub-channel ordering, randomised ordering and zero forcingscheme, under M-QAM modulation

Table 1 Simulation parameters

no. of sub-channels 512frequency range 1.8–16 MHzSNR range 0–30 dBimpulsive index (A) 0.9tolerable BER 10−4, 10−5

coherence time 40.96 μs

IET Commun., 2014, Vol. 8, Iss. 7, pp. 1104–1108doi: 10.1049/iet-com.2013.1079

observed from Figs. 2 and 3 that the BER performance ofthe PLC system does not improve with increasing SNRafter a certain level under the proposed and existingresource allocation schemes. This behaviour is observeddue to the presence of inter-symbol interference (ISI) andinter-carrier interference (ICI) in the PLC system; increasinglevel of signal power also increases the power of ISI andICI. Since PLC channel experiences multipath effect due toreflection of transmitted signals that happen because ofmismatching of impedence in the network. Owing tomismatching of impedence, many signals superimpose atthe receiver having differential delay causing ISI. ICI arisesdue to loss of orthogonality of the sub-carriers. The BERperformance of the considered PLC system can be further

Fig. 3 Variation of BER with SNR at tolerable BER of the order10−4 using proposed sub-channel ordering, randomised orderingand zero forcing scheme, under M-QAM modulation

1107& The Institution of Engineering and Technology 2014

www.ietdl.org

improved by expanding the symbol duration or utilisingadaptive cyclic prefix.From the simulations it can be observed that the

sub-channel ordering performs significantly better comparedto other techniques at all SNR levels. It can be inferredfrom the throughput plots that zero forcing of highlyattenuated sub-channels and redistributing the power on theavailable ones does not ensure improvement in theperformance of the PLC system, in the presence ofimpulsive noise. The proposed sub-channel ordering on theother hand utilises the entire bandwidth of the PLC channelin more efficient manner; thereby enhancing the overallperformance of the PLC system.

5 Conclusion

In this paper, we propose a technique to enhance thethroughput and minimise power requirement in the PLCchannel, using sub-channel ordering. The system usesM-QAM modulation scheme along with adaptivetechniques. This paper discusses the techniques to enhancethe throughput and minimise power requirement in the PLCchannel, using sub-channel ordering in the presence ofimpulsive noise. To highlight the effectiveness of thetechnique, we have compared our method to the otherprevalent techniques such as random ordering and zeroforcing. These simulations are performed in the presence ofimpulsive noise and channel varying conditions whichduplicate the actual channel conditions of PLC. Thesimulations have been performed for a wide range of SNRvalues (0–30 dB) and at different tolerable BER valuesthereby validating the claim of enhanced throughput atvarying conditions. Contrary to most of the existing

1108& The Institution of Engineering and Technology 2014

resource allocation schemes for PLC systems, the proposedalgorithm improves the throughput of a PLC system, in thepresence of impulsive noise.

6 References

1 Zimmermann, M., Dostert, K.: ‘A multipath model for the powerlinechannel’, IEEE Trans. Commun., 2002, 50, (4), pp. 553–559

2 Di Bert, L., Caldera, P., Schwingshackl, D., Tonello, A.M.: ‘On noisemodeling for power line communications’. IEEE Int. Symp. on PowerLine Communications and Its Applications, 3–6 April 2011,pp. 283–288

3 Heggo, M., El Ramly, S.H., El Badawy, H.M.: ‘A novel method forthroughput enhancement of adaptive OFDM in attenuated power linechannels’. 2010 Int. Computer Engineering Conf., 27–28 December2010, pp. 44–49

4 Firouzabadi, S., O’Neill, D., Goldsmith, A.J.: ‘Optimal power linecommunications control policies using stochastic optimization’. 2010IEEE Int. Symp. on Power Line Communications and ItsApplications, 28–31 March 2010, pp. 96–101

5 Papandreou, N., Antonakopoulos, T.: ‘Resource allocation managementfor indoor power-line communications systems’, IEEE Trans. PowerDeliv., 2007, 22, (2), pp. 893–903

6 Chung, S.T., Goldsmith, A.J.: ‘Degrees of freedom in adaptivemodulation: a unified view’, IEEE Trans. Commun., 2001, 49, (9),pp. 1561–1571

7 Middleton, D.: ‘Statistical-physical models of electromagneticinterference’, IEEE Trans. Electromagn. Compat., 1977, EMC-19,(3), pp. 106–127

8 ‘IEEE standard for broadband over power line networks: medium accesscontrol and physical layer specifications’. IEEE Std. 1901–2010, 30December 2010

9 Miyamoto, S., Katayama, M., Morinaga, N.: ‘Performance analysis ofQAM systems under class A impulsive noise environment’, IEEETrans. Electromagn. Compat., 1995, 37, (2), pp. 260–267

10 Wiklundh, K.C., Stenumgaard, P.F., Tullberg, H.M.: ‘Channel capacityof Middleton’s class A interference channel’, Electron. Lett., 2009, 45,(24), pp. 1227–1229

IET Commun., 2014, Vol. 8, Iss. 7, pp. 1104–1108doi: 10.1049/iet-com.2013.1079