A Comparative Study of MFSK and CDMA for Power Line Communication with Background

Nakagami Noise

Aniruddha Chandra and Raihan Hazarika Electronics and Communication Engineering Department

National Institute of Technology, Durgapur WB, India-713209

aniruddha.chandra@ieee.org, raihan.hazarika@gmail.com

Abstract— Direct sequence code division multiple access (DS-CDMA) and M-ary frequency shift keying (MFSK) are two viable modulation schemes for broadband power line communication (PLC) channels, for multi-carrier and single carrier cases respectively. In this paper, we study the bit error rate (BER) performance of a synchronous DS-CDMA system and an MFSK system employing coherent detection for a PLC channel. The background noise present in PLC channel is assumed to follow Nakagami-m distribution as suggested by earlier works. Thereafter a comparison is drawn between the two modulation schemes. In order to draw the comparison at an equal level, we analyse the BER performances of the two systems having the same degree of transmitter/ receiver complexity along with the criteria of same bandwidth occupation, same transmission power as well as the same PLC channel characteristics. The study provides an insight as to how a small change in the parameter of a random variable (RV) describing the background power line noise has a marked influence on the BER performances of the two modulation schemes mentioned above. Also from the simulation results obtained it is quite evident that for a single user case, the MFSK system outperforms the DS-CDMA system at similar data rates.

Keywords-Bit Error Rate; CDMA; MFSK; Background Noise; Power Line Communication

I. INTRODUCTION In the recent years, the use of existing power lines for

the transmission of data and voice has been receiving much interest [1-3]. The advantages of PLC are very obvious, the ubiquity of power lines world wide and low cost of installation. In order to follow the demands, high speed communication over power line networks with data rates in the range of several megabits per second have to be established. However as power lines are not specifically designed for data communication, there are inevitably some effects, such as signal distortion due to frequency dependent cable loss, multipath propagation and noise, which provides a challenge to researchers for communication over power lines.

In contrast to the wireline telephone lines or Ethernet cables, noise in PLC channels cannot be modelled as simple additive white Gaussian noise (AWGN) [4-6]. Characterization of PLC channel noise is rather involved

and was categorized into five types in [6]. Out of the five, three types of noise (coloured background noise, narrow-band noise, and periodic impulsive noise asynchronous to the mains frequency) usually remain stationary and are summarized as background noise. The remaining two types (periodic impulsive noise synchronous to the mains frequency and asynchronous impulsive noise) are time variant and are classified as impulsive noise. The impulsive noise has a short duration with random occurrence and a high power spectral density. In this paper we focus on the average PLC system performance. Hence, we consider only the background noise encountered in PLC channels. Results in [7] reveal that the noise amplitude spectrum of the background power line noise follows a Nakagami-m distribution. The Nakagami model is often used to represent wireless fading signals in a multipath scattering environment with relatively large delay time spreads and with different clusters of reflected waves. The power lines, with many loops and joints, are likely to exhibit such multipath behaviour with substantial reflections.

Considerable amount of research work has been done in determining the optimum modulation techniques best suited for PLC channels. Single carrier modulation schemes such as frequency shift keying (FSK) [8-9] and phase shift keying (PSK) [10] have been tested extensively under the hostile conditions of PLC channels. Significant amount of work has also been done regarding the BER performances of multi-carrier modulation such as CDMA [11] and OFDM [12] based systems in PLC channels and their performances were compared in [13] and [14]. While single carrier modulation schemes such as FSK are a good solution for a low cost and a low data rate PLC system, multi-carrier schemes such as CDMA and OFDM are logical choices for medium data rate and high data rate PLC systems, due to their inherent robustness to multipath propagation and their ability to manage difficult noise conditions present in a hostile PLC channel. During the comparison between CDMA and OFDM systems for PLC channels, it has been shown [13] that while OFDM is a faster system compared to CDMA; the latter can support greater number of users. However till date no comparisons between MFSK and DS-CDMA have been made regarding their BER performance in a PLC system.

2010 IEEE Symposium on Industrial Electronics and Applications (ISIEA 2010), October 3-5, 2010, Penang, Malaysia

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In this paper, based on the noise model derived in [7], the BER performances of synchronous DS-CDMA and coherent MFSK systems is analysed through Monte Carlo simulations. Thereafter a comparison is made between the two modulation schemes based on their BER performances. During the comparison we ensured same bandwidth, bit rate and transmit power for both the systems. The channel characteristics were also kept fixed. The synchronous version for DS-CDMA and coherent type MFSK were chosen so that both systems have equivalent implementation complexity, i.e. in both the cases synchronizing blocks are required.

The paper is organized as follows. In Section II, a general baseband equivalent PLC system model is presented along with the characterization of background channel noise. This is followed by a discussion on the synchronous DS-CDMA and coherent MFSK system model used in the paper. In Section III the performances of the two modulations schemes over the given PLC channel model are discussed and a comparison is drawn between the two systems. Finally, a summary of results, some concluding remarks, and some possible future scopes of the work are presented in Section IV.

II. SYSTEM MODEL Fig. 1 shows a general baseband system model for a

PLC network with the transmitter part comprising of a DS-CDMA transmitter/ MFSK modulator and the receiver part consisting of a DS-CDMA receiver/ MFSK demodulator.

Figure 1. Baseband equivalent PLC system model.

In response to an input binary sequence { }jb the transmitter produces ( )ts~ which is either spread and modulated with binary PSK (for the DS-CDMA case) or frequency modulated (for the MFSK case). For an baseband transmitted signal , the baseband received signal

( )tr~ is given by

( ) ( ) ( )tntstr ~~~ += ; ∞<<−∞ t (1)

where )(tn is the complex background Nakagami noise at baseband. A detailed characterization of the noise process is presented in the next sub-section. The receiver reverses the action of the transmitter i.e. it either de-spreads and demodulates (in case of DS-CDMA) or simply demodulates (for MFSK case) to produce an estimate { jb̂ } of the original binary sequence. In order to ensure similar receiver complexity in both cases we have

considered coherent detection and perfect synchronisation between the users.

A. Power Line Background Noise As mentioned before, contrary to most other well

designed communication channels, PLC channels do not represent AWGN channels. The propagation scenario is rather complicated, as not only coloured background noise, but also narrowband interference and different types of impulsive disturbances occur. Attenuation and noise characteristics of the specific PLC channel dictate the actual channel frequencies used and as a result frequent channel calibration can be the norm with PLC. A review of the PLC channel characteristics can be found in [4-6].

Common buildings and residential electronic equipments is the main cause of background noise in PLC channels. To model the background noise characteristics of a typical PLC channel, long term measurements were carried out from 1 to 30 MHz [7]. An extensive study into the noise amplitude spectrum of the above PLC channel has shown that the probability distribution of the time domain noise amplitudes resembles the Nakagami-m distribution function. In other terms, the samples of the noise process ( )tn~ form a complex RV QI jnnn += ,

whose amplitude 22QI nnr += is distributed as

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛Ω

−⎟⎠⎞

⎜⎝⎛

ΩΓ= −

212 exp2 mrrm

mrf m

m

n ; 0≥r (2)

where ( ).Γ is the Gamma function [15, (8.310.1)], m is the shaping parameter of the Nakagami-m distributed RV while { }2rE=Ω denotes the power of the same. The argument ( )IQ nnarctan=θ is also random and is uniformly distributed over the complex phase plane, i.e.

( )ππ−θ ,~ U .

The Nakagami-m distribution is determined by the two parameters, m and Ω . It is well known that when 1=m , the Nakagami-m PDF reduces to the Rayleigh PDF

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛Ω

−Ω

=2

exp2 rrrf n ; 0≥r (3)

When 1>m , the Nakagami-m PDF has a smaller variance and a larger mean than the Rayleigh PDF while the reverse is true for 1<m . It has been shown in [7] that at low frequencies, the noise variance becomes larger (i.e.

1<m ) while at higher frequencies 1≈m and ( )tn~ becomes a complex Gaussian process, { } ( )2,0~, ΩNnn QI , with the amplitude following the Rayleigh PDF given in (3).

In the following sections, the noise model mentioned above is used for evaluating the BER performances of DS-CDMA and MFSK modulation schemes in PLC channels. As the focus of this paper is on the average PLC

Nakagami-m distributed noise

( )ts~ ( )tr~

( )tn~

{ }jb { }jb̂ DS-CDMA transmitter

/ MFSK modulator

DS-CDMA receiver / MFSK

demodulator

196

channel performance, only the background noise is included in this study. However, if there are some electrical appliances connected close to the power line transceiver, the noise encountered by the receiver can be quite different from the general background noise.

B. Synchronous DS-CDMA System Model We consider a general binary DS-CDMA system that

supports K active users, each transmitting with a data rate bb TR 1= and a chip rate of cc TR 1= where Tb, Tc are the

bit and chip durations respectively. The transmitted signal from kth user, { }Kk ,,2,1 ⋅⋅⋅∈ , is described by [16]

( ) ( ) ( ){ }tfjtsts ckk πℜ= 2exp~ (4)

where

( ) ( ) ( )tatbPts kkkk 2~ = (5)

is the baseband equivalent signal, fc is the common carrier frequency and Pk, bk(t), and ak(t) represent the transmitted power, input binary data, and the unique spreading code for the kth user. Further we assume that all the users are transmitting with same average power, i.e. kPPk ∀= ; . The data sequence bk(t)

( ) ( )∑∞

−∞=

−=j

bTjkk jTtCbtbb, (6)

is spread by a faster sequence ak(t)

( ) ( )∑∞

−∞=

−=j

cTjkk jTtCatac, (7)

and binary PSK (BPSK) modulated before it is fed to the channel. The coefficients { }jkb , for data signal are samples of an independent, identically distributed RV with a probability of 1/2 of being ± 1 and ( )⋅TC denotes unit amplitude rectangular pulse of duration T. The code sequence { }jka , is assumed to be periodic with one period equal to the processing gain

cb TTN = (8)

A larger processing gain allows for greater robustness against severe multipath and narrowband noise but with the trade-off of greater transmitter/receiver complexity and an increase in the transmission bandwidth.

For a general DS-CDMA system, there are K asynchronous simultaneous transmitted signals and the composite received signal at ith receiver is given by

( ) ( ) ( )tntstrK

kkiki +τ−=∑

=1, (9)

In (9), ki ,τ is the time delay for the communication link between the kth transmitter and the ith receiver. The process n(t) represents the background Nakagami noise present in the PLC channel. Assuming perfect synchronisation, i.e. if interfering signals are chip and phase aligned ( )kiki ,;0, ∀=τ , the received signal may be expressed as

( ) ( ) ( ) ( ) ( )tntftatbPtrK

kckki +π=∑

=1

2cos2 (10)

At the receiver, the received signal given in (10) is first demodulated and then de-spread with the corresponding signature sequence ai(t).

C. Coherent MFSK System Model In any M-ary modulation, the input binary stream is

divided into n-tuples of Mn 2log= bits where M is the constellation size. If the modulator is following an MFSK scheme then it converts every such n bit message to one of the M possible signals differing in frequency [17]. The ith signal { }Mi ,,2,1 ⋅⋅⋅∈ may be represented as

( ) ( ) ( ){ }tfjmTtsts csii π−ℜ= 2exp~ ; ( ) ss TmtmT 1+≤≤ (11)

where

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛ψ+π=

ss

si T

ihtjTEts exp2~ ; sTt ≤≤0 (12)

is the low-pass complex envelope of the ith signal, fc is the carrier frequency, and ( )bs nEE = , Eb and ( )bs nTT = , Tb pairs denote the energy and duration of a symbol and a bit respectively. The initial phase ψ can be arbitrary but in order to maintain orthogonality h should be an integer, i.e. the minimum separation between two adjacent frequencies should be ( )sT21 .

The transmitted signal passes through a non-ideal channel corrupted by background Nakagami noise and reaches the receiver. Let us denote the received signal as

( ) ( ) ( ){ }tfjmTtrtr cs π−ℜ= 2exp~ ; ( ) ss TmtmT 1+≤≤ (13)

where

( ) ( ) ( )tntstr ~~~ += ; sTt ≤≤0 (14)

is the corresponding baseband equivalent and ( )tn~ denotes a Nakagami-m distributed complex valued noise process.

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_________________________________________________________________________________________________

Figure 2. Block diagram of the Monte Carlo simulation model.

_________________________________________________________________________________________________

The task of the receiver is to decide, with the help of a demodulator, which signal was originally sent by the transmitter. A coherent demodulator is made of a bank of M correlators and the jth correlator produces an output

( ) ( )∫= sT

jj dttstrr0

, proportional to the likeliness of r(t)

with sj(t). At sampling times smTt = it compares the M decision variables { }Mjrj ,,2,1; ⋅⋅⋅∈ and decides on the hypothesis corresponding to the largest of them.

III. PERFORMANCE EVALUATION - SIMULATION RESULTS

Monte Carlo simulations were performed to obtain the BER values of the two systems under study. The BER is estimated by counting the erroneous bits at the receiver and then dividing the count by the total number of bits passed through the system. The simulation model was realized through Matlab and its various component blocks are described in Fig. 2.

The first block randomly generates binary digits with equal probability. Next, for DS-CDMA, the generated bits are spread with a pseudo noise (PN) sequence and modulated with BPSK. The receiver, on the other hand, demodulates the signal first and then de-spreads. In case the transmitter/ receiver use MFSK instead, the signal flow is through the dotted line. The simulations were performed in the baseband level and thus the modulation process does not involve any frequency translation. Before reception, the signal is perturbed with Nakagami-m distributed noise samples, which are generated by taking square root of samples of a gamma distributed RV. The output of the demodulator is compared with the original bits and subsequently the BER is computed.

Usually the number of bits examined at a SNR point is at least 10 times higher than the inverse of the expected error rate, i.e. to test a BER of 10-4, 105 bits were examined. Further, an average of 20 individual runs was taken to smooth the variation about the mean.

A. Performance of Synchronous DS-CDMA System A significant number of advantages are provided by

DS-CDMA over other modulation schemes such as resistance to multipath effect, multi-user capability, secure communication and some inherent narrowband

interference suppression. Fig. 3 shows the BER performance of a DS-CDMA system in a PLC channel corrupted by background Nakagami noise for two different processing gains of N = 16 and 64 when the number of users is fixed at K = 4. Although we have tested both Walsh and Gold codes as the spreading codes, as their performances are almost similar, only the results for Walsh codes are shown here. In a low frequency PLC channel, the Nakagami shaping parameter takes a value of less than one (m < 1). For our simulation runs, we have taken m = 0.5 and 1.

Figure 3. BER performance of DS-CDMA system with background Nakagami noise for K = 4.

The simulations show that for a DS-CDMA system with lower processing gain (N), the variation in the Nakagami shaping parameter (m) has a marked influence on the BER performance, especially at higher SNR values. However for higher processing gains (N), variations in m do not affect the BER performance much. When N is high, the error rates become identical to the BER values in presence of Gaussian noise.

In Fig. 4, the effect of increasing the number of simultaneous users accessing the DS-CDMA system has been analysed. The shaping parameter (m) and the processing gain (N) have been kept fixed at 0.5 and 31 respectively. As the number of simultaneous users (K) increase to 4, 7 and further to 13, the multiple access

Noise

BER

Generate random

binary data

Generate Nakagami RV

BPSK demodulator

BPSK modulator

MFSK demodulator

MFSK modulator

Generate PN sequence

Comparator (⋅) / total no. of bits

198

interference (MAI) causes severe degradation in BER performance.

Figure 4. BER performance of DS-CDMA system for different number of users with m = 0.5.

B. Performance of Coherent MFSK System Fig. 5 shows the BER performances of coherent

MFSK modulation over a PLC channel corrupted by background Nakagami noise for different modulation order (M = 4 and 16) and noise parameter (m = 0.5 and 1) values. As expected, the BER performance of the 16-FSK system is significantly better compared to the 4-FSK system. However, the variations in the shaping parameter (m) of the background Nakagami noise influence both the modulation schemes in a similar fashion. It can be seen that at m = 0.5, the performance of the MFSK system is the worst, while at m = 1, which is basically the Gaussian noise case, the BER performance improves slightly but only towards the higher SNR range.

Figure 5. BER performance of MFSK system with background Nakagami noise.

C. Comparison Between Single User DS-CDMA and MFSK The required transmission bandwidth (BW) for BPSK,

like every other passband digital communication, is infinite. However, as the amplitude spectrum falls rapidly

with frequency, generally the minimum required BW is calculated from data rate using a spectral efficiency value of 1bits/s/Hz. Thus in a CDMA system the relationship between the bandwidth (BW), processing gain (N) and the data rate (R) is given by [13]

NBWR = (15)

In this paper, Walsh codes are used for spreading the transmitted data. For a given processing gain (N), the length of Walsh codes (L) are given by an upper limit of N, rL 2= , where ⎡ ⎤Nr 2log= and ⎡ ⎤⋅ denotes ceiling function.

For an MFSK system employing coherent detection, the minimum separation between adjacent carrier frequencies should be sTh 2 , where h is an integer [18]. Although the minimum value of h is unity, as the band pass filters (at receiver front end) are never available with brick wall shaped cutoff characteristics, generally a larger value of h is considered to avoid adjacent channel interference (ACI). In our comparative study we have assumed nh = , where Mn 2log= , to account for the increasing ACI for larger M. To make room for M orthogonal carriers, the BW requirement is thus

sTMnBW 2= . Using the relation between symbol duration and data rate, RnnTT bs == , we may write

MBWR 2= (16)

Figure 6. Comparison in the BER performance of a single user DS-CDMA and MFSK system for m = 0.5.

From (15) and (16), it can been seen that in order to achieve a comparable data rate (R) between the two modulation schemes, the number of the orthogonal frequencies (M) has to be two times of the value of the processing gain (N), i.e. M = 2N. Provided that the BW is kept fixed, increasing N or M leads to lower data rates and vice-versa.

Fig. 6 brings out the comparison of the BER performance between a single user synchronous DS-CDMA and a coherent MFSK system, for two different

199

data rates. The bandwidth for the two systems has been kept fixed and the data rates are varied by changing the values of processing gain (N) for the DS-CDMA system and the number of orthogonal frequencies (M) for the MFSK system. The ratio RBW is set to an integer power of 2 so that { } { }MNnr ,log, 2= may have realistic integer values. The shaping parameter (m) of the background Nakagami noise for the PLC channel has been kept fixed at 0.5 for all the simulation runs and the transmission power is normalized to unity.

From the above simulation result, it can be seen that in order to achieve a BER of 10-3 the single user MFSK system requires SNR values of 4.92 dB and 3.87 dB for M = 32 and M = 128 respectively. However, the same BER performance is achieved by the single user DS-CDMA system at relatively higher SNR values of 7 dB and 6.73 dB, for N = 16 and N = 64. Thus, the BER performance of MFSK with coherent detection is significantly better compared to a synchronous DS-CDMA scheme, when the total data rate is considered for only a single user.

IV. CONCLUSIONS AND FUTURE SCOPE In this paper, we analyze the BER performance for

two modulation schemes, DS-CDMA and MFSK, for a broadband PLC channel having a Nakagami-m distributed background noise as the primary source of channel distortion. The BER performances of the two modulation schemes are analyzed with the help of simulation results. From the results, it can be concluded that for changes in the value of the shaping parameter (m) of the background Nakagami noise, the performance of MFSK modulation scheme is affected markedly. However for the DS-CDMA modulation scheme, when the processing gain (N) is high, such variations are not noticeable and its performance is almost similar to that of in presence of white Gaussian noise. For lower processing gain values, changes in the shaping parameter (m) influence the BER performance to a noticeable extent, but only for higher values of SNR. We also compared the BER performances of a single user DS-CDMA system and an MFSK system considering same bandwidth occupancy, same transmission power and the same PLC channel. From the simulation result, it can be concluded that for end-to-end transmissions (like trunk lines) MFSK system performs better than a single user DS-CDMA system in a PLC channel corrupted by background Nakagami noise. However a DS-CDMA system has multiple access capability, and for a local area network (LAN) type application, the performance metrics for the two systems change drastically and comparisons have to be drawn at a different level.

In the present work, both the receivers are considered to be ideal. When a RAKE receiver is used for DS-CDMA and practical filters are implemented for MFSK, the comparison may be more realistic. Also the comparison between an asynchronous DS-CDMA and a non-coherent MFSK system in PLC channel may yield

interesting results. Finally, if impulsive noise in addition to the background noise is considered, the comparison would be more decisive for the design engineers.

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