Unitary Matrix Frequency Modulated OFDM for Power

Line Communications over Impulsive Noise Channels

Chang-Jun Ahn†, Hiroshi Harada, Satoshi Takahashi‡National Institute of Information and Communications Technology (NICT)†

3-4 Hikarino-oka, Yokosuka, 239-0847, Japanjunny700@nict.go.jp

Faculty of Information Science, Hiroshima City University‡

3-4-1 Ozuka-Higashi, Asa-Minami, Hiroshima, 731-3194 Japantaka@ce.hiroshima-cu.ac.jp

Abstract. Power line channel is the time-frequency variant channel with impulsive noise. Therefore,power line communication makes performance degradation due to time-frequency variant and impulsivenoise. To overcome performance degradation, we consider the unitary signal constellation scheme andinvestigate the performance improvement of unitary matrix frequency modulated orthogonal frequency-division multiplexing(OFDM) for power line communication(UMFM-PLC/OFDM) over a PLC channel,and evaluate the BER performance. The proposed UMFM-PLC/OFDM system outperforms comparedwith the conventional PLC/OFDM.

Key words: Unitary signal constellation, impulsive noise, PLC, OFDM

1 Introduction

Power line communication (PLC) systems have manyadvantages and are assumed to be one of prospectivesolutions for short distance or in-home communica-tion networks [1]-[3]. PLC takes the advantage of usein everyplace at home without additional network line.However, power line channel is the time-and-frequencyvariant and exhibits remarkable difference between lo-cations, according to its network topology, the typesof wire lines. Moreover, many electrical appliancesfrequently cause man-made electromagnetic noise onpower line channels. Such man-made noise has theimpulsive characteristics. These are technically criti-cal problems to realize the power line communicationswith high rate and high reliability [4].

In such channels, impulsive noise and inter-symbol-interference (ISI) due to the frequency selective chan-nel cause an unacceptable degradation of the error per-formance. OFDM is an efficient scheme to mitigate theeffect of multi-path channel, since it eliminates ISI byinserting guard interval longer than the delay spreadof the channel [5],[6]. Therefore, OFDM is generallyknown as an effective technique for high data rate ser-vices over the PLC channel.

Recently the combination of PLC/OFDM andspace-time processing are employed to overcome theimpulsive noise and multipath effect [7],[8]. Thesecombination schemes exhibit better system perfor-

mance than the conventional PLC/OFDM in channelcorrupted by impulsive noise. However, these combi-nation systems are required the multi-wire power linecable for achieving a space-diversity. Therefore, theusage of space-time processing for PLC/OFDM is verylimited for in-home communications network.

To overcome the above-mentioned problems, inthis paper, we consider the unitary signal constella-tion scheme. Unitary signal constellation scheme hasbeen proposed to perform space-time diversity in wire-less communications system. Marzetta and Hochwaldproposed and investigated unitary space-time modula-tion(USTM) as a mean of achieving capacity [9],[10].These unitary signal constellations may be viewed asa multiple antenna extension. A unitary signal con-stellation is a matrix, whose columns are transmittedfrom multiple antenna elements and mutually orthog-onal to each other. Such constellations have been de-signed and shown to perform well for uncoded trans-mission [11]. In this paper, we consider the diagonalcode as an unitary signal constellation [12]. For a diag-onal code, the components except for diagonal compo-nents in unitary signal constellation are 0. Since thiscode achieves a diversity with only diagonal compo-nents of unitary signal constellation, in this paper, weconsider the unitary signal constellation with only di-agonal component non-zero for simulation. Note thatwe do not claim the optimality of the unitary signalconstellation, but rather, we argue that the unitary

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Proceedings of the 5th WSEAS Int. Conf. on Electronics, Hardware, Wireless and Optical Communications, Madrid, Spain, February 15-17, 2006 (pp45-49)

signal constellation with its flexible scalability, andhigh performance in this paper.

In the PLC channel, the channel response at a par-ticular subcarrier frequency is not supposed to be to-tally different from its neighboring frequencies, andhence, they must have correlation which depends onthe coherence bandwidth of the channel Bc. When weassign the diagonal components of the diagonal codeas an unitary signal constellation on neighboring fre-quencies. In this case, the diagonal components do notachieve the frequency diversity. However, we split thediagonal components over the coherence bandwidth,the detected signal can achieve the frequency diversity.In this paper, we propose the diagonal components ofunitary signal constellation with splitting over the co-herence bandwidth, and evaluate the system perfor-mance for PLC/OFDM over impulsive noise channels.The system model is described in Section 2. In Sec-tion 3, we show the simulation results. Finally, theconclusion is given in Section 4.

2 System model

2.1 Channel model

In PLC/OFDM systems, the channel response of fre-quency domain at the k-th subcarrier can be expressedas

H(k) =L−1∑

l=0

hl(k)ej2πkl/K = H(k)Hα(k) (1)

where H = [h0, h1, ..., hL−1]H is L-sized vector con-taining the time responses, L is the number of channelpaths, and α(k) is FFT coefficient. Moreover, in thispaper, we introduce Middleton’s Class A noise model[13] into a statistical model of impulsive noise environ-ment. This model is widely applicable by adjustingparameters, and provides fine closeness to experimen-tal values. Middleton’s noise model is composed ofsum of Gaussian noise and impulsive noise. The ClassA model is defined that the bandwidth of the noise isnarrower than the bandwidth of the receiving system,i.e., the noise pulses do not produce transients in thefront end of the receiver. According to the Class Anoise model, the PDF (Probability Density Function)of the noise amplitude z is as follows,

pa(z) =∞∑

m=0

e−AAm

m!· 1√

2πσ2m

exp(− z2

2σ2m

) (2)

where σ2m = σ2 · (m+A)+Γ

1+Γ , A is the impulsive index,Γ = σ2

G/σ2I is the GIR (Gaussian-to-impulsive noise

power ratio) with Gaussian noise power σ2G and im-

pulsive noise power σ2I , and σ2 = σ2

G + σ2I is the to-

tal noise power. The noise amplitude z followed by

Eq.(2) always includes the background Gaussian noisewith power σ2

G. On the other hand, sources of im-pulsive noise are distributed with Poison distribution(e−AAm)/m!. One impulsive noise source generatesnoise which is characterized by the Gaussian PDF withvariance σ2

I/A. The parameter A is defined as the aver-age number of impulses on the receiver in unit durationtimes the mean duration of them. The larger A, theimpulsive noise will be more continuous, and then theClass A noise is led to be more likely to the Gaussiannoise. Conversely, the smaller A, the Class A noisewill be more impulsive. In particular, if A is nearlyequal to 10, the statistical feature of the Class A noiseis almost similar to that of the Gaussian noise. As theGaussian noise power σ2

G is comparatively larger in thetotal noise power σ2, that is, Γ is larger, the Class Anoise will approach to the Gaussian noise. Conversely,the smaller Γ, the Class A noise will be more impul-sive.

2.2 A Class of Unitary Space-Time SignalConstellations

Unitary space-time signal is a matrix, whose rows aretransmitted from the transmitted elements and mutu-ally orthogonal to each other in wireless communica-tion systems. Let L ≥ 2 denotes the size of a unitarysignal constellation. We define θL = 2π

L . For any givenintegers η1, η2, η3 ∈ Z, we define the following unitarysignal constellation of size L

ν = ν(η1, η2, η3) = ξ(lη1, lη2, lη3) | l ∈ ZL (3)

where ZL = (0, 1, · · · , L − 1), and, ξ(lη1, lη2, lη3) isgiven by

ξ(lη1, lη2, lη3) =( ejθL 0

0 ejη1θL

)l

(4)

·( cos(η2θL) sin(η2θL)− sin(η2θL) cos(η2θL)

)l

·(

eiη3θL 00 e−jη3θL

)l

.

For any given constellation size L ≥ 2, we will find aunitary signal constellation from the following class

ΩL ≡ ν(η1, η2, η3) | η1, η2, η3 ∈ ZL (5)

such that the unitary signal constellation has thelargest diversity product in the constellation class asEq. (5). The above unitary signal constellation is builtfrom the parametric form of 2 × 2 unitary matrices.We therefore call the signal constellation as Eq. (4)parametric code. It is seen that when η2 = η3 = 0 isimposed in the constellation class as Eq. (5), the para-metric code as Eq. (4) is exactly the diagonal code inthe case M = 2. There have been several classes of

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Proceedings of the 5th WSEAS Int. Conf. on Electronics, Hardware, Wireless and Optical Communications, Madrid, Spain, February 15-17, 2006 (pp45-49)

2× 2 unitary space-time constellation which were pro-posed in the previously. A diagonal code cyclic groupcode for a general M was introduced. A main dif-ference between the diagonal code and the parametriccode is that the diagonal code is in general a non-groupsignal constellation.

2.3 UMFM-PLC/OFDM

Here, we employ the diagonal code for achieving a di-versity gain in the PLC channel. The data stream isdivided into bit sequences that consist of R ·M bits,where R and M denote information bits per parallelsymbol to be transmitted, and the number of diagonalelement. Each R ·M bit sequence is mapped into theconstellation ν(l) (l ∈ ZL) selected from L = 2RM .The constellation of unitary matrix for UMFM can bewritten as

diagν(l) =[ejlθL , · · · , ejlθL

], (l ∈ ZL) (6)

where ν(l) is M × M unitary matrix, diag· is thediagonal operator, respectively. For example, in thecase of M = 2 and R = 1, which is equal to BPSKmodulation. In this case, one of 2 × 2 unitary matrixν(l) is assigned.

In the PLC channel as Eq. (1), the channel re-sponse at a particular subcarrier frequency is not sup-posed to be totally different from its neighboring fre-quencies, and hence, they must have correlation whichdepends on the coherence bandwidth of the channelBc. When we assign the diagonal components of theunitary signal constellation on neighboring frequen-cies. In this case, the diagonal components do notachieve the frequency diversity. However, we split thediagonal components over the coherence bandwidth,the detected signal can achieve the frequency diver-sity. In this paper, we employ the diagonal code andsplit diagonal components of the selected code overthe coherence bandwidth. Hereafter, we call this pro-cessing as an unitary matrix frequency modulation forPLC/OFDM (UMFM-PLC/OFDM). In the UMFM-PLC/OFDM systems, the diagonal components of theselected unitary signal constellation are splitting overthe coherence bandwidth and are transmitted to thereceiver. In this case, the received signal Y(k) of thek-th subcarrier at receiver side is given by

Y(k) = H(k)X(k) + N(k) k = 1, · · · · ·,K (7)

where X(k) is the splitted diagonal component ofunitary signal constellation over the coherence band-width, and N is an impulsive noise. After de-splittingof the received signals and channel estimation, thefrequency domain signals Y are divided into M bits.Here, we consider the same structure of unitary signalconstellation for M × M as Eq. (6). Each M bit of

frequency domain signals is demodulated by ML esti-mator. The ML decision rule of the signal model asEq. (1) is given by

ν = arg min

K∑

k=1

∣∣∣Y(k)−H(k) (8)

·L∑

l=1

diag(ν)mod(k,M)+1(l)∣∣∣2

where∑L

l=1 diag(ν)mod(k,M)+1(l) is the diagonal com-ponent of unitary signal constellation. The neigh-boring signals of

∑Ll=1 diag(ν)mod(k,M)+1(l) without

splitting must have correlated channel responses, how-ever, the split signals over the coherence bandwidthachieve totally different channel responses. It meansthat UMFM-PLC/OFDM systems can achieve a fre-quency diversity gain.

3 Computer simulated results

In this section, the system performance of the pro-posed UMFM-PLC/OFDM system is compared withthe conventional PLC/OFDM when the power linechannel is corrupted by impulsive noise. Fig. 1 showsthe simulation model of UMFM-PLC/OFDM for Nc =128 subcarriers over the impulsive noise and multi-path PLC channel. In the transmitter, data stream isserial-to-parallel(S/P) transformed, and the diagonalcomponents of unitary signal constellation are splittedover the coherence bandwidth. The OFDM time sig-nal is generated by an IFFT and is transmitted overthe frequency selective and time variant PLC chan-nel after the cyclic extension has been inserted. Thetransmitted signals are subject to 2-path quasi-staticchannel. In this model, L = 2 path as an independentidentically distributed (i.i.d.) complex random vari-able according to Middleton’s Class A noise model.This case causes a severe frequency selective channel.Maximum delay spread is 0.5µ. In our simulations,we consider two different impulsive noise scenarios [8].The first one corresponds to a power line channel that

Table 1: Simulation parameters.Data Modulation BPSK

Demodulation Coherent ML detectionData rate 4 Msymbol/s

OFDM Symbol duration 65 µsecNumber of carriers 128

Channel 2 path quasi-staticMaximum path delay 0.5 µsec

Noise model Additional white Class A

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Proceedings of the 5th WSEAS Int. Conf. on Electronics, Hardware, Wireless and Optical Communications, Madrid, Spain, February 15-17, 2006 (pp45-49)

Input DataSerial

toparallel

Unitary mod

IFFTParallel

toserial

OFDMsignal

Guardinterval

OFDMsignal Serial

toparallel

FFTParallel

toserial

Output Data

Guardinterval Coherent ML

detection

Channel estimation

De-split

split

(a) Transmitter

(b) Receiver

Unitary mod

Unitary mod

Figure 1: Proposed UMFM-PLC/OFDM system.

is heavily disturbed by impulsive noise because theinter-arrival times between strong impulses are veryshort. The second one corresponds to a power linechannel that is weakly disturbed by impulsive noisebecause the inter-arrival times between impulses arevery long. We simulate this situation by consideringthe complete summation in Eq. (2). In the receiver,the received signals are S/P converted and Nc parallelsequences are passed to a FFT operator, which con-verts the signal back to the frequency domain. Thisfrequency domain signals are de-split and coherentlydemodulated by using ML detection. The simulationparameters are listed in Table 1.

Fig. 2 shows the BER performance of UMFM-PLC/OFDM and the conventional PLC/OFDM sys-tem for power line channels heavily distributed by im-pulsive noise. From Fig. 2, it is clear that the UMFM-PLC/OFDM system outperforms the conventionalPLC/OFDM over the entire range of energy per bit-to-noise spectral density ratio (Eb/N0) values. At BER of10−3, the proposed UMFM-PLC/OFDM system per-forms better than the conventional PLC/OFDM by 6dB. This is because UMFM-PLC/OFDM systems canachieve a diversity with splitting the diagonal compo-nents over the coherence bandwidth for a frequencydiversity.

Fig. 3 shows the BER performance of UMFM-PLC/OFDM and the conventional PLC/OFDM sys-tem for power line channels weakly distributed byimpulsive noise. BERs of the proposed UMFM-PLC/OFDM and the conventional PLC/OFDM withweak noise achieve better than those of with strongnoise. At BER of 10−3, the proposed UMFM-

10-6

10-5

10-4

10-3

10-2

10-1

100

-5 0 5 10 15 20 25

Conventional PLC/OFDMProposed USFM-PLC/OFDM

BE

R

Eb/No [dB]

Figure 2: BER performance of UMFM-PLC/OFDMand the conventional PLC/OFDM system for powerline channels heavily distributed by impulsive noise.

10-6

10-5

10-4

10-3

10-2

10-1

100

-5 0 5 10 15 20 25

Conventional PLC/OFDMProposed USFM-PLC/OFDM

BE

R

Eb/No [dB]

Figure 3: BER performance of UMFM-PLC/OFDMand the conventional PLC/OFDM system for powerline channels weakly distributed by impulsive noise.

PLC/OFDM system performs better than the conven-tional PLC/OFDM by 8 dB.

4 Conclusion

We have investigated the performance improvementof UMFM-PLC/OFDM over the multipath and im-pulsive noised PLC channel, and evaluated the BERperformance. The proposed UMFM-PLC/OFDM sys-tem can achieve 6 and 8dB gains compared with theconventional PLC/OFDM for heavily and weakly dis-tributed impulse noise channel, respectively.

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Proceedings of the 5th WSEAS Int. Conf. on Electronics, Hardware, Wireless and Optical Communications, Madrid, Spain, February 15-17, 2006 (pp45-49)

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