Inter symbol interference (ISI) is avoided by assuming the duration of cyclic long enough and furthermore the channel is assumed to be stationary within one symbol period ( h(k)=hr ).
The frequency domain channel response at subcarrier k is given by
H_k=∑_r▒〖h_r e^(-j2π (τ_r k)/(T_s N)) (5)〗
Where Ts is the sample interval. Frequency-domain received baseband data then becomes
Z_k=X_k H_k+W(k) (6)
Due to the time domain sampling effect, the discrete time channel impulse response is given by g(n)=1/N ∑_(k=(-N)/2)^(N/2-1)▒〖H(k) e^(j2π nk/N) (7)〗 the received*…show more content…*

Z=XF_g+W=X h+W (8) Now the channel response at all data subcarrier are estimated using pilot subcarriers and are denoted as H ̂_k k= (-N)/2,-,0,-,N/2-1 and the received data can then be equalized*…show more content…*

This method is used for initial channel estimation at pilot subcarrier without using any statistical knowledge of the channel, so it’s very less commutative complexity. Proposed algorithm Algorithm is proposed for data aided channel estimation in multipath fading channel using 16-QAM modulation technique for time varying OFDM system. Any rectangular QAM constellation is equivalent to superimposing two ASK signals on quadrature carriers (I & Q components). For 16-QAM modulation, the symbol size is 4 bits. Based upon the Karnaugh maps first two bits is considered as the two bits ASK modulated on the in-phase arm and next two bits is considered as the two bits of ASK modulated on the quadrature arm. Let PQRS be the four bits thus the respective values for each index in the array are taken as PQ+iRS. Proposed array indices (PQ+jRS) are the input to 16-QAM modulator and corresponding array values are the 16-QAM modulator output that are gray coded and mapped to constellation points. Let the variables PQ and RS with the four amplitude level {-3,-1.+1,+3}.Now the different pilot symbol bits are

Z=XF_g+W=X h+W (8) Now the channel response at all data subcarrier are estimated using pilot subcarriers and are denoted as H ̂_k k= (-N)/2,-,0,-,N/2-1 and the received data can then be equalized

This method is used for initial channel estimation at pilot subcarrier without using any statistical knowledge of the channel, so it’s very less commutative complexity. Proposed algorithm Algorithm is proposed for data aided channel estimation in multipath fading channel using 16-QAM modulation technique for time varying OFDM system. Any rectangular QAM constellation is equivalent to superimposing two ASK signals on quadrature carriers (I & Q components). For 16-QAM modulation, the symbol size is 4 bits. Based upon the Karnaugh maps first two bits is considered as the two bits ASK modulated on the in-phase arm and next two bits is considered as the two bits of ASK modulated on the quadrature arm. Let PQRS be the four bits thus the respective values for each index in the array are taken as PQ+iRS. Proposed array indices (PQ+jRS) are the input to 16-QAM modulator and corresponding array values are the 16-QAM modulator output that are gray coded and mapped to constellation points. Let the variables PQ and RS with the four amplitude level {-3,-1.+1,+3}.Now the different pilot symbol bits are

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