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VOL. 3, NO. 3, March 2012 ISSN 2079-8407

Journal of Emerging Trends in Computing and Information Sciences©2009-2012 CIS Journal. All rights reserved.

http://www.cisjournal.org

344

Performance Evaluation of an OFDM System under RayleighFading Environment

1 Gurpreet Kaur, 2 Partha Pratim Bhattacharya

Department of Electronics and Communication Engineering, Faculty of Engineering and TechnologyMody Institute of Technology & Science (Deemed University), Lakshmangarh , Dist. Sikar, Rajasthan,

Pin – 332311, India

[email protected],

[email protected]

ABSTRACT

The performance of an OFDM system is affected by parameters such as carrier frequency offset and phase noise. In the

presence of such parameters the performance of OFDM system degrades. Under Rayleigh fading environment the performance

fluctuates depending on the signal strength. In this paper the performance of an OFDM system is studied in the presence of

Rayleigh fading channel. Results show that the SINR of the overall system fluctuates due to the effect of Rayleigh fadingchannel.

Keywords: OFDM Wireless communication system, carrier frequency offset (CFO), Phase noise, signal to interference plus noise ratio(SINR), Rayleigh fading channel.

1. ORTHOGONAL FREQUENCY DIVISION

MULTIPLEXING (OFDM)

OFDM (Orthogonal Frequency Division

Multiplexing) has been developed to combat multipath

effects and make better use of the system.

An important parameter that should be carefullyconsidered while dealing with OFDM system is phase noise

because an accurate prediction of the tolerable phase noise

can allow the system to relax specifications. Theconsideration of phase noise in OFDM systems is important

with frequencies above 25 GHz, as suggested in some

European ACTS projects dealing with LMDS (Local-

Multipoint Distribution Systems) [1]. The effect of phase

noise in OFDM and the degradation caused by it have been

analyzed by several authors [2]–[5].

Carrier frequency offset (CFO) exist between user

terminals and the base station. OFDM systems are very

sensitive to CFO, which leads to performance degradation

by introducing inter-carrier-interference (ICI) [6]. The purpose of this paper is to analyze the performance of an

OFDM wireless communication system in the combined

effect of carrier frequency offset and phase noise in Rayleighfading environment.

OFDM is a block modulation scheme where a

block of N information symbols is transmitted on N

subcarriers in parallel. The time duration of an OFDM

symbol is N times larger than that of a single-carrier system.

An OFDM modulator can be implemented as an inversediscrete Fourier transform (IDFT) on a block of N

information symbols which is then followed by an analog-

to-digital converter (ADC). In order to mitigate the effects of

inter symbol interference (ISI) caused by channel time

spread, each block of N IDFT coefficients is typically

preceded by a cyclic prefix (CP) or a guard interval

consisting of G samples, such that the channel length is at

least equal to the length of CP. In this condition, a linear

convolution of the transmitted sequence and the channel is

converted to a circular convolution. As a result, the effectsof the ISI are easily and completely eliminated. This

approach enables the receiver to use fast signal processing

transforms such as a fast Fourier transform (FFT) for OFDM

implementation [7]. Similar techniques can be employed in

single-carrier systems as well, by preceding each transmitted

data block of length N by a CP of length G, while using

frequency domain equalization at the receiver.

One of the best ways to mitigate the effect of

multipath is to use OFDM communication systems. A

combination of OFDM and coding associated with

interleaving in the frequency domain (COFDM) can take

advantage from the diversity associated to multipath [8].

The following equation gives the N point complex

modulation sequence transmitted by OFDM signal for the

ℎ symbol:

() = () 2

−1

=0

(1)

where n ranges from 0 to + − 1.

2. PHASE NOISE AND CARRIER

FREQUENCY OFFSET

Phase noise must be carefully considered when

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dealing with any of these communication systems since an

accurate prediction of the tolerable phase noise can allow thesystem and RF designers to relax specifications. A

theoretical analysis of phase noise effects in OFDM signals

is carried out by many authors. The complex envelope of thetransmitted OFDM signal for a given OFDM symbol,

sampled with sampling frequency = , is:

() = . 2

−1

=0

(2),

where n=0, 1, …, N-1.

This symbol is actually extended with a Time

Guard in order to cope with multipath delay spread.

Assuming that the channel is flat, the signal is only affected by phase noise at the receiver:

(

) =

(

).

() (3)

The received signal is an Orthogonal Frequency

Division De-multiplexed (OFDD) signal by means of a

Discrete Fourier Transform. For the purpose of separating

the signal and noise terms, let us assume that Φ(n) is small,

so that:

() ≈ 1 + (). (4)

In this case, the de multiplexed signal is given as:

() ≈ +

−1

=0

(). 2 (− )

−1

=0

(5)

() ≈ + (6)

Thus we have an error term for each sub-carrier

and which results from some combination of all of them and

is added to the useful signal. The signal to noise ratio

degradation ( ) caused by phase noise is the same inOFDM and signal carrier systems, given that phase noise

variance is small (2 ≪ 1) it follows the expression [9] :

= 10. log1 + 2 0

. (7)

In this equation represents the symbol energy

and 0 is the power spectral density of additive whiteGaussian noise. One way to characterize oscillator’s phase

noise is the single-side-band phase noise power density

function ( ), which represents the ratio (in dBc; ‘c’ stands

for carrier) between the single-side-band noise power in a 1

Hz bandwidth at a distance from the carrier and thecarrier power.

This characterization is normally performed by

using a spectrum analyzer which provides the power spectral

density of the equipment’s phase noise ( 0) in relation to

the carrier power (C). Given that the phase noise has a zero

mean and that extends up to a frequency b (either because

phase noise is band-limited or due to the presence of

filtering in the receiver), its variance can be found as [10]:

2 = � (20

0

). (8)

The absolute value of the actual CFO ɛ , is either

an integer multiple or a fraction of △ , or the sum of them.

If ɛ is normalized to the subcarrier spacing △ , then the

resulting normalized CFO of the channel can be generallyexpressed as:

ɛ =

ɛ

△ = + є (9)

where δ is an integer and |є | ≤ 0.5. The impact of aninteger CFO on OFDM system is different from the

influence of a fractional CFO. In the event that δ≠0 and ε=0,

symbols transmitted on a certain subcarrier, e.g., subcarrier

k, will shift to another subcarrier , = + −1. As the ICI effect is focused, normalized CFO is

considered as given below,

ɛ =

ɛ

△ = є (10)

Since no ICI is caused by an integer CFO, relative

CFO (ε) to assumed to be a Gaussian process, statistically

independent of the input signal, with zero mean and

variance ɛ

2.

3. FORMULATION OF SINR

In the presence of CFO, phase noise, timing jitter

and Rayleigh fading the OFDM system performance can be

expressed by the following SINR expression [10]:

(ɛ, 2,, )

≥ 2 (1 − ){2(ɛ)}

1 + 2(1 − )[0.5947(sinɛ)2 + {22 2(ɛ) ∑ 1

2 ( )

}] + 2−1=1

; |ɛ|

≤0.5,|

|

≤1. (11)

where ɛ is the normalized CFO, 2 is the variance of phase

noise, denotes timing jitter and corresponds to the channelattenuation/gain parameter in Rayleigh fading environment.

is the input SNR, N is the number of sub-carriers in the

channel.

When the impulse response (; ) is modeled as a

zero mean complex valued guassian process, the envelope

|(; )| at any instant is Rayleigh distributed. In this case thechannel is said to be Rayleigh fading channel. In the event that

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there are fixed scatterers or signal reflectors in the medium in

addition to randomly moving scatterers (; ) can no longer be modeled to have zero mean.

SINR expression in the presence of phase noise and

CFO without timing jitter and considering a Rayleigh fading

environment can be expressed as:

(ɛ,2,)

≥ 2{2(ɛ)}

1 + 2[0.5947(sin ɛ)2 + {22 2(ɛ)∑ 1

2 ( )

}]−1=1

; |ɛ| ≤ 0.5 (12)

Table 1: System and channel parameters for simulation

Number of sub carriers (N) 64

Channel typeRayleigh fading

channel

Input SNR values 10 dB.

Channel attenuation/gain

parameter (α)

0.2,0.4,0.6,0.8,1,1.2,

1.4,1.6,1.8

Normalized CFO 0.05

Variance of phase noise 0.33

4. RESULT AND DISCUSSION

Simulation has been carried out using MATLAB.

Figure 1 and 2 shows the plot of SINR versus variance of

phase noise (2) for various values of attenuation/gain parameter, normalized CFO being 0.05. Results are plotted

for input SNR () of 10 dB.

Figure 1: SINR versus variance of phase noise as a function

of attenuation/gain parameter (CFO=0.05)

Figure 2: SINR versus variance of phase noise as a function

of attenuation/gain parameter (CFO=0.05)

Figure 3 and 4 show the variation of SINR versus

normalized CFO, for various values of attenuation/gain parameter. Variance of phase noise and input SNR () areconsidered to be 0.33 and 10 dB respectively.

Figure 3: SINR versus normalized CFO as a function of

attenuation/gain parameter (variance of phase noise=0.33)

Figure 4: SINR versus normalized CFO as a function of

attenuation/gain parameter (variance of phase noise=0.33)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-8

-6

-4

-2

0

2

4

6

8

10

variance of phase noise

S I N R

( i n d

B )

SINR versus variance of phase noise (CFO=0.05 and attenuation/gain parameter<=1)

attenuation/gain parameter=0.2




attenuation/gain parameter=1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-6

-4

-2

0

2

4

6

8

10

12

14

variance of phase noise

S I N R

( i n

d B )

SINR versus variance of phase noise (CFO=0.05 and attenuation/gain parameter>=1)






0.02 0.04 0.06 0.08 0.1 0.12 0.14

-8

-6

-4

-2

0

2

Normalized CFO

S I N R

( i n d B )

SINR versus normalized CFO (variance of phase noise=0.33 and attenuation/gain parameter<=1)






0. 012 0. 014 0. 016 0. 018 0. 02 0. 022 0.024 0. 026 0. 028 0. 03 0. 032

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

Normalized CFO

S I N R

( i n d B )

SINR versus normalized CFO(variance of phase noise=0.33 and attenuation/gain parameter>=1)






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It can be seen from Figure 1, that for an input SNR

of 10 dB as attenuation/gain parameter is decreased from 1to 0.2, the SINR values decreases and the gain parameter 1

indicates zero fading. Figure 2 show that for an input SNR

of 10 dB as attenuation/gain parameter increases from 1 to1.8, the SINR values increase and is highest for gain

parameter of 1.8. It can also be seen from Figure 3, that for an input SNR of 10 dB as attenuation/gain parameter

decreases from 1 to 0.2, the SINR values decreases. Figure 4

show that for an input SNR of 10 dB as attenuation/gain

parameter increases from 1 to 1.8 the SINR values increases.

So the SINR value increases or decreases from its value

when there is no fading depending on constructive or

destructive interference of the signals from multipath.

5. CONCLUSION

In this paper, performance evaluation of an OFDM

communication system is studied by taking normalized CFO

and variance of phase noise under consideration in Rayleigh

fading environment (α≠1). An SINR expression is taken intoconsideration for evaluating the same. Results show that as

compared to an ideal channel (attenuation/gain parameter=1)the SINR is less for an OFDM system under Rayleigh fading

environment when attenuation/gain parameter<1 whereas theSINR is more for an OFDM system under Rayleigh fading

environment when attenuation/gain parameter>1.

REFERENCES

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[8] B. Le Floch, M. Alard, and C. Berrou, “Coded

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