Root Raised Cosine Pulse Shape Based ICI Suppression in OFDM System for Rayleigh Multipath Channel

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; 0 … . 1 1 Where X k represents complex symbol transmitted over k th sub carrier and N is the number of subcarriers used in the system. Figure (1) shows the basic blocks of the transmitter and receiver in an OFDM scheme. At transmitter, with the help of mapper block input information is mapped into complex symbols and transformed into a parallel form using serial to parallel block. Symbols obtained at the output of serial to parallel block are modulated over an individual subcarrier by IDFT block. The output of IDFT/IFFT block is first transformed into a serial form and with the help of DAC it is changed into analog form. In the receiver side first information is obtained in digital form using ADC and it is demodulated using DFT/FFT operation. The demodulated symbols are de mapped into original information. The difference in the power of an OFDM symbol affected by CFO and the power of an OFDM symbol not affected by CFO is equal to the total ICI present in that symbol. Average ICI over the entire transmitted and received OFDM symbols gives the total ICI present in the system. This paper suggests the use of Root raised cosine pulse shape based filter to reduce ICI. Further optimized value of roll off factor is obtained for minimum value of ICI.
IV. PULSE SHAPING Pulse shaping filters are used to confine the signal bandwidth, to enhance the data rate and to reduce transmission errors such as ISI (Inter Symbol Interference) [5] [8]. Pulse shaping filter reduces the side lobes of individual subcarrier, which is the main cause of ICI, when the orthogonality of subcarriers get lost due to the carrier frequency offset. The two important properties of the perfect pulse shaping filter are, a large stop-band attenuation to diminish ICI and minimized ISI to attain low bit error rate (BER). According to the Nyquist criteria, the impulse response of the shaping filter should have null crossings at multiples of the symbol duration to achieve ISI free transmission and to assist in timing recovery [5] [8]. The filter that satisfies Nyquist criterion has a sinc pulse in the time domain with a brick wall frequency response. This type of filter is difficult to realize in practice and basically the impulse response of perfect continuous filter is sampled to obtain a realizable filter. For this the sampling rate should be double than the symbol rate of the message, i.e. the filter must interpolate the data by a minimum factor of two or more. The raised cosine filter satisfies Nyquist criteria and it is band-limited to (1+β) R/2, where β is the roll-off factor and R is the data rate. Its impulse response is specified by sin / with zero crossings once every T b seconds.

V. ROOT RAISED COSINE FILTER
The raised cosine filtering operation can be split and implemented at the transmitter and receiver both. The transfer functions of these filters are such that their multiplication is equal to the transfer function of a single raised cosine pulse shaping filter. To optimize signal to noise ratio at the receiver, the transfer function of the raised cosine filter, P (f) is split equally between the transceiver, thus giving (6) This is called 'square root raised cosine filter' having impulse response of The pulse shaping filter at the transmitter performs up-sampling of the signal whereas, the matched filter at the receiver performs down-sampling. This approach provides better stop band attenuation than using a single raised cosine filter at the transmitter and a down-sampler at the receiver. It also reduces Inter symbol Interference (ISI) among the symbols. The matched filter detects a pulse with a known shape p (t) in the received symbol Y(t) which is of the form p(t)+N(t). N (t) is additive, stationary noise with zero mean.

VI. ADAPTIVE PULSE SHAPING
The roll-off factor (β) of the pulse shaping function determines the width of the transition band of the pulse. As β increases from 0 to 1, the pulse period decreases and also there is an increase in the side lobe attenuation. Thus the restriction of signal over time domain causes expansion in frequency domain and signal will consume excess bandwidth. So there must be a compromise between value of β and the bandwidth in order to achieve undistorted transmission of a pulse over a narrowband channel. Realistic communication systems utilize a roll off factor between 0.1 and 0.5.In adaptive pulse shaping the authors vary the roll off factor from 0.1 to 0.5 and obtained the ICI power at these values. The value of β which gives minimum ICI is the optimized roll off factor.

VII. SIMULATION RESULTS
Implemented OFDM system for QPSK modulation scheme is shown in Figure 4. System is implemented for 64 subcarriers and channel is modelled as a Rayleigh multipath channel with 2 discrete paths. The time domain symbols available at the output of IDFT/IFFT block are given to the Root Raised Cosine (RRC) pulse shaping filter. The matched filter used at the receiver is also a Root Raised Cosine filter. From Figure 5 it is understood that error performance of QPSK modulated OFDM system gets degraded in the presence of frequency offset. Figures 6 and 7 compare ICI and C/I with respect to CFO for pulse shaped OFDM symbols with that of without shaped symbols in Rayleigh multipath channel. It is observed that at a value of 0.1 frequency offset the ICI for original system (without using pulse shaping) is approximately -41dB(close to 10 -4 ) and after using RRC filtering it will be approximately -47dB (close to 10 -5 ). Also C/I ratio is enhanced from 4 dB (above 10 0 ) to 10 dB (close to 10 1 ). Thus due to the use of Root Raised Cosine filter ICI get reduced and C/I ratio gets improved. Figure 8 helps to obtain optimum roll off factor (β) to achieve minimum ICI.

VIII. CONCLUSION
In this paper, the authors have implemented the OFDM system with QPSK mapping scheme for Rayleigh faded multipath channel. It can be analyzed that with increase in frequency offset, Inter carrier interference power (ICI) and BER increases while Carrier to interference ratio decreases.ICI is responsible for degradation of OFDM system performance, so pulse shaping techniques are found to be good for reducing ICI in all existing ICI reduction techniques. Approximately 6 dB reduction in ICI and 6 dB increase in C/I ratio at a value of 0.1 frequency offset is obtained after using RRC type of pulse shaping. Also, through adaptive pulse shaping, the authors have obtained optimum roll off factor of 0.43 at which minimum ICI value of 8x10 -5 approximately is obtained. Thus the reduction of ICI by using an RRC pulse shaping technique decreases the susceptibility of OFDM system with the Carrier frequency offset.