Performance Analysis of OFDM System in Multipath Fading Environment

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3 samples x 0 to x. Assuming the incoming complex data is random it follows that the IFFT is a set of N independent random complex sinusoids summed together. The samples, x 0 to x are then converted back into a serial data stream producing a baseband OFDM transmit symbol of length T = N. T s. A Cyclic Prefix (CP), which is a copy of the last part of the samples is appended to the front of the serial data stream before Radio Frequency (RF) up conversion and transmission. The CP combats the disrupting effects of the channel which introduce Inter Symbol Interference (ISI). In the receiver the whole process is reversed to recover the transmitted data, the CP is removed prior to the FFT which reverses the effect of the IFFT. The complex symbols at the output of the FFT, Y 0.. Y are then demodulate and the original bit steam recovered. Mathematically the demodulation process (assuming no CP and no channel impairments) using the FFT is equation (1), Y m,k = FFT{x m,n } n=0 = 1 N x m,ne j2πnk N n=0 d=0 = 1 N X m,de j2πn(d k) N = 1 X N d=0 m,d e j2πn(d k) n=0 N = 1 X N d=0 m,d Nδ[d k] = X m,k (1) Cyclic Prefix The Cyclic Prefix or Guard Interval is a periodic extension of the last part of an OFDM symbol that is added to the front of the symbol in the transmitter, and is removed at the receiver before demodulation. Figure 2: Cyclic Prefix The cyclic prefix has to two important benefits The cyclic prefix acts as a guard interval. It eliminates the inter-symbol interference from the previous symbol. It acts as a repetition of the end of the symbol thus allowing the linear convolution of a frequency selective multipath channel to be modelled as circular convolution which in turn maybe transformed to the frequency domain. This approach allows for simple frequency domain processing such as channel estimation and equalization. Channel Estimation Based On Block-Type Pilot Arrangement In block-type pilot based channel estimation, the pilot is sent in all sub-carriers with a specific period. Assuming the channel is constant during the block, it is insensitive to frequency selectivity. Since the pilots are sent at all carriers, there is no interpolation error. The estimation can be performed by using either LS or MMSE. The LS estimate is represented by: h LS = X 1 y (2) Where, X = diag{x 0, x 1, x }, y = [ y 0... y ] Where x i is the pilot value sent at the i th subcarrier and y i is the value received at the i th sub-carrier. If the time domain channel vector g is Gaussian and uncorrelated with the channel noise, the frequencydomain MMSE estimate of g is given by: Where, F = [ h MMSE = FR gy R yy y (3) 00 W N 00() W N ()() W N ] and W N ()0 W N nk = 1 N e j2πn N k Where R gy and R yy is cross covariance matrix between g and y and the auto-covariance matrix of y respectively. When the channel is slow fading, the channel estimation inside the block can be updated using the decision feedback equalizer at each subcarrier. Decision feedback equalizer for the k th subcarrier can be described as follows: The channel response at the k th sub-carrier estimated from the previous symbol {H e (k)} is used to find the estimated transmitted signal {X e (k)}. X e (k) = Y(k) H e (k) k = 0,1, N 1 (4) X e (k) is mapped to the binary data through signal demapper and then obtained back through signal mapper as X pure (k). The estimated channel {H e (k)} is updated by: H e (k) = Y(k) X pure (k) k = 0,1, N 1 (5) Since the decision feedback equalizer has to assume that the decisions are correct, the fast fading channel will cause the complete loss of estimated channel

4 parameters. Therefore, as the channel fading becomes faster, there happens to be a compromise between the estimation error due to the interpolation and the error due to loss of channel tracking. For fast fading channels, as will be shown in simulations, the comb-type based channel estimation performs much better. Communication Channel This is the channel through which the data is transferred. Presence of noise in this medium affects the signal and causes distortion in its data content. BER(dB) Ofdm simulation LS LMMSE RANK-MMSE PSEUDO CODE Define needed variables like number of bits per symbols, Number of symbols, FFT length and SNR value; { Generate Binary data form randint according to No. of symbols and No. of bits per symbols; Convert serial data to parallel streams according to number of sub channels; Calculate Inverse Fast Fourier transform and convert data into frequency domain; Add cyclic prefix to IFFT data; Insert pilot carrier in parallel streams of data; Until SNR loop expires Pass data through Rayleigh Multipath channel; Remove cyclic prefix; Convert data into time domain by performing Fast Fourier transform; Remove Pilot carriers; Convert data into serial bit stream; Compare generated data and demodulated data to find Bit Error rate; } } III. SIMULATION AND RESULTS BER(dB) Ofdm simulation 2 delay path 5 delay path 8 delay path SNR(dB) Figure 3: BER v/s. SNR graph for multipath delay in Rayleigh channel SNR(dB) Figure 4: BER vs. SNR performance comparison for different methods IV. CONCLUSION The work is undertaken in this paper firstly discusses the OFDM system and fading channel. The implementation of OFDM model is presented with the analysis of the capabilities of OFDM in Rayleigh fading channel. The simulation uses MATLAB and the effect of different modulation schemes has been evaluated over OFDM system. On comparing the variations of the BER for different SNR in the MATLAB simulation, it is observed that the BER performance of LMMSE is better than LS and RANK-MMSE schemes. At 30 db SNR, the BER performance of LMMSE scheme is 4% better than the LS and far better than RANK-MMSE scheme. Finally it is concluded that the OFDM system with LMMSE scheme is suitable for low capacity short distance applications. While the OFDM with LS and RANK-MMSE techniques are useful for large capacity and long distance applications which slightly increase the BER. The OFDM promises to be a suitable multiplexing technique for high capacity wireless communication application. REFERENCE [1] A. D. S. Jayalath, C. Tellambura and H. Wu, Reduced complexity PTS and new phase sequences for SLM to reduce PAPR of an OFDM signal, IEEE, Vehicular Technology Conference Proceedings, VTC Tokyo, [2] W. G. Jeon, K. H. Paik, and Y. S. Cho, Twodimensional pilot-symbol-aided channel estimation for OFDM systems with transmitter diversity, IEICE Transactions on Communications, vol. E85B, pp , Apr [3] M. L. Doelz, E. T. Heald, and D. L. Martin, Binary Data Transmission Techniques for Linear Systems, IEEE, Proc. IRE, vol. 45, pp , May [4] R. W. Chang, Synthesis of Band Limited Orthogonal Signals for Multichannel Data Transmission, Bell Syst. Tech. Journal., vol. 45, pp. 1,7751,796, Dec 1966.

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