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Performance Analysis of Phase Noise Impaired

OFDM SysteminaMultipath Fading Channel

Joseph Gladwin S.

Assistant Professor

Department of Electronics and Communication

SSN College of Engineering

Kalavakkam–603110, India.

[email protected]

Mangayarkkarasi M.

PG Scholar

Department of Electronics and Communication

SSN College of Engineering

Kalavakkam–603110, India.

[email protected]

Abstract—OrthogonalFrequency Division Multiplexing

(OFDM)is becoming the chosen modulation technique for

wireless communications. Multicarrier modulation shows a

significant sensitivity to the phase noise present in the

oscillator used for frequency down-conversion at the portable

receiver. For this reason, it is important to evaluate the impact

of the phase noise on the system performance.In this paper, the

performance of phase noise impaired OFDM system over a

multipath frequency selective and time varying fading

channelis analyzed,in terms of Mean Square Error (MSE)and

Bit Error Rate (BER). The analysis shows a degradation of the

MSE and BER caused by the addition of phase noise at the

transmitter and receiver end of the OFDM communication

link. This performance degradation is evaluated from the

graphs of MSE and BER against Signal to Noise Ratio (SNR).

The simulation is performed using MatLab and the results

show a good agreement with analytical expressions.

IndexTerms—OFDM,phase noise,multipath Rayleigh fading

channel, MSE, BER.

I. INTRODUCTION

Orthogonal Frequency Division Multiplexing (OFDM) is a

multicarrier modulation technique,which divides the available

spectrum into several parallel data streams or channels, one for

each subcarrier. It is a multicarrier transmission technique

where the data bits are modulated by orthogonal

subcarriers.The main advantage of OFDM is to split the

available signal bandwidth intoa large number of independent

narrow-band subchannels.It also has many advantages over

single carrier systems, including its resistanceto frequency

selective fading [1].

Orthogonal frequency division multiplexing has been

widely adopted andimplemented in wire and wireless

communications,European Digital Audio Broadcasting (DAB),

Digital Video Broadcasting-Terrestrial (DVB-T) and its

handheld version DVB-H,and IEEE 802.11a/g standards for

Wireless Local AreaNetworks (WLANs)[2]-[3]. OFDM is a

best approach to mitigate the effect of multipath in a fading

channel. The disadvantage of OFDM, however, is that it is

sensitive to both carrier frequenciesoffset and phase noise [4]-

[5].OFDM is incorporated in numerous standards [6].However

the reliability of systems and services that are outcome of these

standards is heavily lessened by impairments such as frequency

offset, phase noise, IQ imbalance and power amplifier

nonlinearities [7].This paper is an attempt to address the effect

of phase noise on OFDM systems.Phase Noise (PN) results due

to space the imperfections of the Local Oscillators (LO) used

for theconversion of a baseband signal to a passband (or

viseversa).Because of the compactness of the subcarriers and

the high sensitivityto synchronization errors, phase noise

destroys the orthogonalitybetween adjacent subcarriers. With

respect to OFDM,PN shows itself in the form of a Common

Phase Error (CPE) and InterCarrier Interference (ICI)[8].Some

analysis of the effect of phase noise in OFDM systems has

been presented in [9]. The real time channel is highly frequency selective and

sophisticated equalization techniques are required to achieve

high bit rate transmissions. Wireless channel is modeled as

Rayleigh channel is used as a medium for data transmission.

Fig.1. Oscillator Phase Noise Impaired OFDM

System(Basic Block Diagram)

Rayleigh distribution best describe the stastical time varying

nature of the receivedenvelope of a flat fading signal[10].In

this paper, the Bit Error Rate (BER) and Mean Square Error

(MSE) performances of a OFDMsystem over Rayleigh fading

channelsis evaluated considering the influence of the phase

noise impairment.Phase noise impaired OFDM system is

shown in Fig.1.

The input signal is modulated by either Quadrature Phase

Shift keying (QPSK) or Binary Phase Shift Keying

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(BPSK)modulation. The modulated signal is converted to time

domain by Inverse Fast Fourier Transform (IFFT) operation.

Cyclic prefix is added to combat Inter Symbol Interference

(ISI) followed by the parallel to serial conversion. This signal

is called OFDM signal and it is converted to RF signal by the

transmit oscillator where is the

transmitter phase noiseand is the carrier frequency [8]. The

transmitted signal passes through the multipath fading channel

and is converted back by the receiver oscillator

where is the receiver phase noise. Fast

Fourier Transform (FFT) operation is performed and the signal

is demodulated to obtain the originaldata.

The paper is organized as follows: In SectionII, phase

noise process is reviewed and the OFDM system model is

given in thepresence of phase noise overRayleigh fading

channel. In Section III, the BER expression is derived. Section

IVgives the results of system performance analysis andfinally

Section V concludes the paper.

II. SYSTEM MODEL

A. Phase Noise Model

For autonomous oscillators, as , the PN ( ) becomes

asymptotically a Gaussian process with variance = that

linearly increases with time, being the rate of the variance

whose value depends on the kind of oscillator used[11].

Sampling the continuous time counterpart ( ), a discrete

Wiener process ( ) is obtained.It is typically given as

(1)

where, by definition of the Wiener PN process, (0) =

(0) = 0 and ( ) = ( ) ( 1) are the

independentincrements drawn from a zero mean Gaussian

distribution with variance[5].

(2)

B. Fading Channel Model

The transmitted OFDM signals are assumed to propagate

througha multipath fading channel.There are two types

multipath fading channels; frequency selective fading channel

and time varying fading channel. Rayleigh model best

approximates a practical multipath fading channel.

1)Frequency selectivefading channel model and estimation:

In frequency selective fading channel,the bandwidth of

the signal is greater than the coherence bandwidth of the

channel or delay spread is greater than the symbol period[12]. The Rayleigh channel has the function of sampling time

of the transmitted signal, maximum Doppler shift, delay

vector and gainvector. Then white Gaussian noise is added to

the OFDM signal.A discrete time filter is used to retrieve

useful signal from the degraded signal coming through the

channel.

2) Time varying fading channel model and estimation:

The time varying fading channel is also called flat fading

channel where the bandwidth of the signal is less than the

coherence bandwidth of the channel or delay spread is less

than the symbol period[12]. FIR (Finite Impulse Response) filter with response of a

multipath fading channelcan be modeled as:

(3)

where the time varying impulse response of the multipath

fading channel is and the multipath is denoted as L.

and denote the time varying complex gain and

excess delay of the i-th path.Here four multipaths are

used.Figure 2 shows a typical FIR implementation of the

filter.

A flat fading channel is considered in this paper.For

simplicity, the excess delays are fixed in the above

equation and is generated that follows Rayleigh equation

and is generated that follows Rayleigh distribution.

Clarke’s Rayleigh fading model [13] is used in simulation.

Fig.2. Multipath Fading Phenomena-Modeled as a time

varying FIR Filter

a)Theory of Rayleigh Fading

The complex impulse response of the flat fading channel

is

(4)

Where and are zero mean gaussian distributed.

The fading envelope is given by

(5)


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b) Clarke’s Rayleigh Fading model:

The sum-of-sinusoid method described for the random

process of flat Rayleigh fading with M multipathis

(6)

(7)

where , m and m are uniformly distributed over (0,2 )for all

n and mutually distributed. Here, is the maximum Doppler

spread and Tsis the sampling period and is the sample index

and is the number of multipath in the channel. Then m is

distributed over (1,M).

III.BER

A. QPSK Modulation

Quadrature Phase Shift Keying (QPSK) can be interpreted

as two independentBPSK systems (one on the I-channel and

one on the Q-channel), and thus exhibits the sameperformance

but twice the bandwidth (spectrum) efficiency. The data

source can be modulated using QPSK modulation. QPSK

modulation isthe PSK modulation of the data source with

mapping order four (M=4). So the data source is quantized to

four. In order to detect the real(inphase arm) and imaginary

part (quadrature arm), two threshold detectors are employed

by the QPSK receiver. The detected signals are then passed

through a parallel to serial converter.

1) BER:

Bit error rate is computed using the relation

(8)

Where is the Signal to Noise Ratio(SNR) and Q is the

quadratic function. This can also be expressed as follows:

(9)

Then the BER for phase noise impaired OFDM system is

calculated using QPSK demodulated data with phase noise.

B. BPSK Modulation

The data source can be modulated using BPSK

modulation. BPSK modulation isthe PSK modulation of the

data source with mapping order two (M=2). So the data source

is quantized into two levels.PSK is a digitalmodulation

scheme that conveys data by modulating the phase of the data

source.QPSK possesses two orthogonal BPSK systems which

do not interfere with each other. So, the BER for QPSK and

BPSK are identical.

IV.PERFORMANCE ANALYSIS

The BER performance of the OFDM system for different

digital modulation schemes (QPSK and BPSK) over a

multipath Rayleigh fading channel is investigated by means of

a computer simulation using MatLab.The performance of a

data transmission system is usually analysed and measured in

terms ofBER andMSEVsSNR.The various parameters of an

OFDMsystem were varied and tested by modeling it using

MatLab. The following parameters are used for computation

in this section:

TABLE I

SYSTEM AND CHANNEL PARAMETERS FOR SIMULATION

Number of samples 11264

Modulation QPSK and BPSK

Constellations M=4 for QPSK and M=2 for

BPSK

length of cyclic prefix 1408

Channel Type

Multipath Rayleigh fading

channel(four path)

(both frequency selective and

time varying)

Input SNR [0 0.6 1.2 1.8] in dB

A. Performance analysis over a Frequency selective fading

channel

Fig. 3BER performance-QPSK.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

10-0.303

10-0.302

10-0.301

SNR vs BER for QPSK Modulation with Phasenoise

SNR in dB

Bit E

rror

Rate

(BE

R)

in d

B


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Fig. 4 MSE performance - QPSK.

Fig. 5 Theoretical BER performance - QPSK

Fig. 6 BER performance - BPSK.

The BER and MSE performance of phase noise impaired

OFDM system over a multipath frequency selective Rayleigh

fading channel for QPSK and BPSK are shown in Fig. 3-5 and

Fig.6-8 respectively. In the presence of phase noise over

frequency selective fading channel, the BER and MSE were

analyzed for different SNR values.Figure 3 and Fig. 6 shows

that if the SNR value increases, the BERwill decrease.

Fig. 7 MSE performance - BPSK.

Fig. 8 Theoretical BER performance - BPSK

Figure 4 and Fig. 7 shows that the MSE performance of

an OFDM system over QPSK demodulation and a frequency

selective fading channel decreases as the SNR value increases.

The theoretical performance of QPSK and BPSK are shown in

Fig.5 and Fig.8.

B. Performance analysis over a time varying fading

channel

Fig. 9 BER performance of - QPSK.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.81.645

1.65

1.655

1.66

1.665

1.67

1.675

1.68

1.685x 10

-4

SNR in dB

Mean S

quare

Err

or (M

SE

)in d

B

SNR Vs MSE with phasenoise

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

10-1.3

10-1.2

SNR vs BER Theoritical for QPSK Modulation

SNR in dB

Bit E

rror

Rate

(BE

R)

in d

B

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

10-0.3

10-0.299

10-0.298

10-0.297

SNR vs BER for BPSK Modulation with Phasenoise

SNR in dB

Bit E

rro

r R

ate

(BE

R)

in d

B

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.84.445

4.45

4.455

4.46

4.465

4.47

4.475

4.48

4.485

4.49x 10

-5

SNR in dB

Mean S

quare

Error (M

SE

)in d

B


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

10-1.3

10-1.2

SNR vs BER Theoritical for BPSK Modulation

SNR in dB

Bit E

rror Rate

(BER) in

dB

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

10-0.302

10-0.301

10-0.3

10-0.299

10-0.298

10-0.297

SNR vs BER for QPSK Modulation with Phasenoise

SNR in dB

Bit E

rror

Rate

(BE

R)

in d

B


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Fig. 10 MSE performance - QPSK.

Fig. 11 Theoretical BER performance - QPSK

Fig. 12 BER performance - BPSK.

Fig. 13 MSE performance - BPSK.

Fig. 14 Theoretical BER performance - BPSK

The BER and MSE performance for QPSK and BPSK

over a time varying fading channel are shown in Fig. 9-11 and

Fig.12-14 respectively. In the presence of phase noise over

time varying fading channel, the BER and MSE were analyzed

with input SNR values. Figure 9 and Fig. 12 shows that if the

SNR value increases, the performance of BER will decrease in

the presence of phase noise. Figure 10 and Fig. 13 shows that

the MSE performance of an OFDM system over QPSK

demodulation and a time varying fading channel decreases as

the SNR value increases. The theoretical performance of

QPSK and BPSK are shown in Fig.11 and Fig.14.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.81.63

1.635

1.64

1.645

1.65

1.655

1.66x 10

-4

SNR in dB

Me

an

Sq

ua

re E

rro

r (M

SE

)in

dB


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

10-1.3

10-1.2

SNR vs BER Theoritical for QPSK Modulation

SNR in dB

Bit

Err

or

Ra

te(B

ER

) in

dB

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

10-0.318

10-0.317

10-0.316

10-0.315

10-0.314

10-0.313

SNR vs BER for BPSK Modulation with Phasenoise

SNR in dB

Bit E

rror R

ate

(BE

R) in

dB

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.82.08

2.09

2.1

2.11

2.12

2.13

2.14

2.15

2.16

2.17x 10

-4

SNR in dB

Me

an

Sq

ua

re E

rro

r (M

SE

)in

dB


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

10-1.3

10-1.2

SNR vs BER Theoritical for BPSK Modulation

SNR in dB

Bit

Err

or

Ra

te(B

ER

) in

dB


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TABLE II QUANTITATIVE VALUES OF SIMULATION RESULTS

MODULATION PERFORMANCE

PARAMETER

FREQUENCY SELECTIVE FADING

CHANNEL TIME VARYING FADING CHANNEL

QPSK

BER

BER(theoretical)

MSE

0.5007 0.4982 0.4972 0.4968

0.0786 0.0648 0.0522 0.0409

1.0e-003 *( 0.1680 0.1667 0.1664 0.1650)

0.5051 0.5017 0.4993 0.4984

0.0786 0.0648 0.0522 0.0409

1.0e-003 *( 0.1656 0.1648 0.1643 0.1631)

BPSK

BER

BER(theoretical)

MSE

0.5054 0.5053 0.5033 0.5008

0.0786 0.0648 0.0522 0.0409

1.0e-004 * (0.4487 0.4486 0.4468 0.4446)

0.4873 0.4862 0.4832 0.4800

0.0786 0.0648 0.0522 0.0409

1.0e-003 *( 0.2152 0.2139 0.2126 0.2085)

The theoretical values for the Bit Error Rate (BER) of

the frequency selective fading and time varying fading

channelof both QPSK and BPSK are the same, while their

practical values happens to differ in Table II. For QPSK the

BER of the Frequency Selective fading channel appears to

decrease gradually from 0.5007 to 0.4968 which is lesser in

comparison to the time varying fading channel, which

decreases from 0.5051 to 0.4984. Both QPSK and BPSK,

reveals that, the MSE of the frequency selective fading

channel is less when compared with the time varying fading

channel. For BPSK the BER of the Frequency Selective

fading channel appears to decrease gradually from 0.5054 to

0.5008 which is greater in comparison to the time varying

fading channel, which decreases from 0.4873 to 0.4800. In

general, the BER of Frequency selective fading channel is

more in BPSK than in QPSK, while it is the vice versa for

the time varying fading channel.

V.CONCLUSION

Phase noise causes significant degradation of

theperformance of OFDM systems. The effects of

phasenoise on the performance of OFDM systems havebeen

analytically evaluated. In this paper, the BER and MSE

performance of an OFDM system over multipath fading

channel was analyzed.It is computationally efficient due to

its use of FFT techniques for implementing modulation and

demodulation functions.Simulation results show that the

methodology presented in this work is accurate.

REFERENCES

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[9] T. Pollet, M. Van Bladel, and M. Moeneclaey,“BER

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[10] T. Schenk, RF Imperfections in High-Rate Wireless

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[11] Songping Wu and Yeheskel Bar-Ness, OFDM Systems in

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