WorldAcademics

World Academics Journal of Engineering Sciences ______World Acad. J. Eng. Sci. 01 2006 (2014) ISSN: 2348-635X doi:10.15449/wjes.2014.2006

Performance Evaluation of OFDM system with FEC in Rayleigh, Rician and AWGN channel

Smita Jolania1, Amol Kumbhare2 and Sandeep Toshniwal1

1Dept. of Electronics and Comm, KITE, Affiliated to RTU, Jaipur, India. 2Dept. of Electronics and Comm, MITM, RGPV, Indore, India. Email: [email protected], [email protected], [email protected]

Abstract: Orthogonal Frequency Division Multiplexing(OFDM) technique is a multi-carrie r transmission technique which is being recognized as an excellent method for high speed bi-directional wire less data communication. In OFDM the data is modulated using multiple number of sub-carriers that are orthogonal to each other because of which the problems associated with other schemes such as Inter Symbol Interference (ISI) and Inter Carrier Interference (ICI) are reduced. High bit error rates of the wireless communication system require employing forward error correction (FEC) methods on the data transferred to reducing the error in transmission. This paper shows the working of a forward error correction (FEC) coding technique using convolutional encoding with Viterbi decoding. This paper deals with the analysis of OFDM System with 16- QAM modulation technique over Rayleigh, Rician and Additive White Gaussian Noise (AWGN) environments with the channel coding and finally the results are conveyed.

Keywords: AWGN, QAM, Ray leigh Fad ing, Ric ian Fad ing.

transmission by means of frequency division Introduction multiplexing (FDM) with overlapping . It was found to be an efficient scheme for bandwidth

utilization and to mitigate the effect of multipath Orthogonal frequency division multiplexing propagation. It also eliminated the requirement of (OFDM) is regarded widely as the key underlying high-speed equalization technique. Firstly OFDM- air interface technology for wireless systems such as based WLAN standard, IEEE 802.11, was released WiMAX, 3GPP long-term evolution (LTE), and which can support a data rate up to 2 Mbps. Than 3GPP2 ultra-mobile broadband (UMB). Multicarrier IEEE approved an OFDM based standard 802.11a techniques, including OFDM-based wireless for supporting a data rate up to 54 Mbps. systems, will provide the solution for future- Each has a different frequency and generation wireless communications. OFDM is a the frequencies chosen so that an integral number of parallel trans mission scheme, where a high-rate cycles in a symbol period so the signals are serial data stream is split up into a set of low-rate mathematically orthogonal. But the BER (Bit Error substreams, each of which is modulated on a Rate) value of the wireless medium is relatively separate single carrier (SC-FDM). By selecting a high. This drawback sometimes introduce special set of (orthogonal) carrier frequencies, high destructive effects on the wireless data transmission spectral efficiency is obtained because the spectra of performance. the SCs overlap, while mutual influence among the As a result, error control is necessary in these SCs can be avoided. By introducing a cyclic prefix applications. During digital data transmission and as the gaurd interval(GI), the orthogonality can be storage operations, performance criterion is maintained over a dispersive channel. commonly determined by BER which is simply: The concept of multicarrier communication was Number of error bits / Number of total bits. So we first introduced by Chang [3]. He suggested a implemented the forward error correction using the multicarrier scheme utilizing the parallel data

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method convolution coding at transmitter side and S’(t)= Viterbi decoding at the receiver section. Another major problems of OFDM is that the peak amplitude of the emitted signal can be (3) considerably higher than the average amplitude. This With the cyclic extension, the actual OFDM Peak-to-Average Ratio (PAR) issue originates from symbol duration is increased from Ts to T = Ts+Tg. the fact that an OFDM signal is the superposition of N sinusoidal signals on different subcarriers.On Error correcting code average the emitted power is linearly proportional to N.So we have used the PAPR reduction method hat Channel coding and modulation provide the is iterative clipping and filtering the OFDM signal. means of mapping information into waveforms such that the receiver (with an appropriate demodulator OFDM system and cyclic prefix and decoder) can recover the information in a reliable manner. convolutional encoding is one way OFDM modulation divides the entire frequency of performing channel coding. selective fading channel into many narrow band flat A convolutional encoder accepts a sequence of fading subchannelsl in which high-bit-rate data are message symbols and produces a sequence of code transmitted in parallel and do not undergo IS1 due to symbols. Its computations depend not only on the the long symbol duration. Each data stream is current set of input symbols but, on some of the subsequently modulated onto different carrier previous input symbols as well. The input bits are (subcarrier). Due to the orthogonality between stored in fixed length shift register and they are individual subcarriers, the higher spectral efficiency combined with the help of mod-2 adders. An input than in the pure FDM can be obtained. The binary sequence and contents of shift registers perform data at the modulator input are first serial to parallel modulo-two addition after information sequence is converted. The data stream in each parallel branch is sent to shift registers, so that an output sequence is then mapped according to the selected constellation obtained. This operation is equivalent to binary and subsequently transformed into the time domain convolution and hence it is called convolutional via the IFFT operation. coding. The ratio R=k/n is called the code rate for a Mathematically OFDM(modulated) signal can convolutional code where k is the number of parallel be represented as input bits and n is the number of parallel decoded output bits, m is the symbolized number of shift Let be the complex symbols to be registers. Viterbi decoding algorithm is mostly transmitted by OFDM modulation,so OFDM signal applied to convolutional encoder and it uses can be expressed as maximum likelihood decoding technique

Channel model S(t) = Wireless systems generally use air or space for transmit the signal, this is called propagation so the signal is received in distorted form may be due to reflection, diffraction and scattered distortion. = for 0 ≤ t ≤ Ts (1) By the above three phenomenon we can see that the receiver received signal by different path having Where fk = f0 + kΔf delay or low strength, this is called Multipath Fading. Different type of channel that can be used for = (2) the Modulation and Propagation of radio signal are AWGN, Rayleigh and Rician Fading Channel. for k = 0, 1,. . . , N - 1. T and f are called the s symbol duration and subchannel space of OFDM, A. AWGN channel respectively. In order for receiver to demodulate Additive White Gaussian Noise (AWGN) is a OFDM signal, the symbol duration must be long channel model in which only impairment to enough such that Ts. f = 1, wh ich is also called communication is a linear addition of wideband or orthogonality condition. white noise with a constant spectral density and a To deal with delay spread of wireless channels, Gaussian distribution of amplitude. In the case of a cyclic extension is usually used in OFDM systems. white Gaussian noise the values at any pair of times OFDM signal s(t), can be extended into S’(t) by are identically distributed and statistically independent on each other. Signal amplitude frequency response is flat, means signal pass through channel without any amplitude loss and having

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infinity bandwidth and phase frequency response is The PAPR of OFDM signal with N subcarriers linear, so no phase distortion of frequency sampled at symbol rate is upper-bounded by the components. It is just the noise that is added to the value N. OFDM modulated signal when it is travelling The clipping is surely the simplest method for through the channel given as: the PAPR reduction. In its basic form, this method r(t) = s(t) + n(t) simp ly clips the signal s(t) at instant t in the Where r(t) is received signal and n(t) is the transmitter to the desired maximal level A. Additive White Gaussian Noise. S (t) = (7) B. channel clip As the clipping represents the nonlinear In mobile radio channels, the Rayleigh function, the PAPR of the signal will be reduced at distribution is commonly used to describe the the expense of signal distortions resulting in adjacent statistical time varying nature of the received channel emissions and BER increase. The idea of envelope of a flat fading signal, or the envelope of adjacent channel emissions filtering after clipping an individual multipath component which is the has been applied but the filtering of clipped signals specialized model for stochastic fading when there is results in new peaks creation, the method of iterative no line of sight signal. If there is no dominant clipping and filtering has been subsequently done. component to the scatter, then such a process will This method is based on the zero padding of the have zero mean and phase evenly distributed signal in the frequency domain and frequency between 0 and 2π radians. The envelope of the domain filtering of clipped signal at the output of channel response will therefore be Rayleigh IFFT. distributed which is the magnitude of the sum of two equal independent orthogonal Gaussian random variables and the probability density function is Simulation model given as There are several parameters to objectively measure the performance of communication systems P(r) = , r > 0 (4) and the influence of nonlinearities on their signals. The statistical properties of signals are well Where is the time-average power of the described using the PAPR CCDF described above. received signal. A. System Parameters B.Rician fading channel OFDM system parameters used in the When there is a dominant stationary signal simulation are indicated in Table I. Simulations are component present, such as a line-of-sight carried out for d ifferent signal-to noise (SNR) ratios propagation path, the smallscale fading envelope and for each value of the Bit Error Rate (BER) is distribution is Ric ian. This type of signal is calculated. In our paper we have simulated the code approximated by Rician distribution in which the using MATLAB 7.0 for different channels. dominating component run into more fade the signal characteristic goes from Rician to Rayleigh Table I distribution. Rician Fading channel can be defined Parameters Specification the parameter K called the Rice Factor which is the FFTsize 64 ratio between the power in the direct path and the Nu mber of subcarriers 52 power in the other, scattered, paths. If the Rice Factor is 0 then the Rician Faded Envelope reduces down to Rayleigh faded Envelope. Cyclic prefix length 16(25%) Power density function for Rician distribution is Signal constellation 16-QAM given by: Nu mber of frames 100 Channel model AWGN,Rayle igh,Ric ian Coding technique Convolution coding P(r) = ,for(A≥0,r≥0) (5) Decoding technique Viterbi decoding Here A is the peak amplitude of the dominant signal and I0 is the modified Bessel function of the Filter window Hamming window first kind and zero-order. PAPR reduction ICF(Iterative clipping V.PAPR REDUCTION SCHEME method and filtering) The envelope dynamic of signal s(t) can be objectively measured using the parameter called B. Simulation Results and Discussions Peak to Average Power Ratio (PAPR) defined as: The Rayleigh Fading channel is constructed using in MATLAB the rayleighchan () function with PAPR{S(t)}= (6) sampling period of 100μs and Doppler Frequency

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shift of 10. Then the signal is passed through this Communications Systems”, London, United channel using the filter () function. The same is done Kingdom: Artech House, 2004, pp. 117-122. for Rician Fading channel with the channel is [2] S. Kaiser, “On the performance of different constructed using ricianchan () function with the detection techniques for OFDM-CDMA in same sampling period and Doppler Frequency shift fading channels”, In proceedings of IEEE as above and the Rician Factor k varying.We have Global Telecommunication Conference, Vol. 3, generated the BER v/s SNR graph for various Issue 11, pp 2059-2063, 1995. channels. Here we can see clearly that the BER is [3] X. Li and L. J. Cimini, Jr., “Effects of clipping reduced as we increase the SNR. and filtering on the performance of OFDM,” in For uncoded OFDM signal following output has Proc. VTC’97, May 1997, pp. 1634–1638. been observed: [4] Dennis silage, “Dig ital Co mmunication Systems Using MATLAB and Simulink”, Bookstand Table II Publishing, 2009. Channel PAPR [5] J. Armstrong, “Peak-to-average power reduction A W GN 6.9817 for OFDM by repeated clipping and frequency Rayle igh 6.9572 domain filtering”, Electronics Letters, 28TH Rician 7.2079 February 2002, Vol. 38, No. 5, pp. 246-247. [6] A. J. Viterbi, “Convolutional Codes and their Table III Performance in Communication Systems”, Rice factor PAPR IEEE Transactions on information Theory, Vol. K=1 7.4337 IT-19, No. 5, PP 751-772, Oct 1971. K=3 7.3283 [7 ] Abdi, A. and Tepedelenlioglu, C. and Kaveh, M. K=5 6.9129 and Giannakis, G., "On the estimation of the K K=7 7.0421 parameter for the Rice fading distribution", IEEE Communications Letters, March 2001, p. K=10 6.9715 92 -94.

[8] Vineet Sharma, Anuraj Shrivastav, Anjana Jain, PAPR for Uncoded OFDM sinal=6.9033 Alok Panday "BER Performance of OFDM- PAPR for Coded OFDM signal=7.2259 BPSK,-QPSK,-QAM over AWGN channel

using forward Error correcting code", Conclusion International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 , In this paper we compare the performance in terms vol. 2, no. 3, May-Jun 2012, pp.1619-1624. of BER using 16-QAM modulation scheme on [9] L. Wang, Ch. Tellambura, “A Simplified Rayleigh, Rician and AWGN Channel. The Clipping and Filtering Technique for PAR simulation results are provided and from which we Reduction in OFDM Systems”, IEEE Signal can evidently conclude that the QAM gives better Processing Letters, Vol. 12, No. 5, June 2005, performance under AWGN channel compared to PP.453-456. other propagation channels.On increasing the value [10]”Performance evaluation of OFDM system with of the SNR, the effect of the distortions introduced Rayleigh,Rician and AWGN Channel” Sai by the channel will also goes on decreasing, as a Krishna Borra,Suman Krishna Chaparala, result of this, the BER will a lso decreases at higher International Journal of Emerging Technology values of the SNR. Also the BER can be controlled and Advanced Engineering ISSN 2250-2459, by help of using channel coding. We can also Volume 3, Issue 3, March 2013 conclude by the above graph that AWGN channel is [11] Ali Calhan, Celal Ceken and Ismail Ertruk, best among all the above channels. “Comparative Performance Analysis of Forward Error correction Techniques used in References Wireless Communications”, Proceedings of the third International Conference on wireless and Mobile Communications,0-7695-2796-5/07. [1] Ramjee Prasad ―”Basics of OFDM and Synchronization‖ in OFDM for Wireless

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Figure 1: System Model of OFDM using QAM mapping and Cyclic prefix

0 10

-1 10 BER

AWGN Rayleigh Rician -2 10 0 2 4 6 8 10 12 14 16 18 SNR

Fig.2.BER V/s SNR for uncoded OFDM in different channels

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BER varying in rician channel with different rice factor

-0.5 10 BER

k=1 -0.6 10 k=3 k=5 k=7 k=10

0 2 4 6 8 10 12 14 16 18 SNR

Fig.3.Rician channel performance With different rice factors(k)

BER for Coded and Uncoded signal in AWGN channel 0 10 uncoded OFDM Coded OFDM

-1 10 BER

-2 10 0 2 4 6 8 10 12 14 16 18 SNR

Fig.4.Performance of AWGN channel for coded and uncoded OFDM

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