Sunday, May 23, 2010
Tuesday, December 29, 2009
1536 FFT Implementation in LTE
Transmission BW | 1.4 MHz | 2.5 MHz | 5 MHz | 10 MHz | 15 MHz | 20 MHz |
Sampling Frequency | 1.92 MHz | 3.84 MHz | 7.68 MHz | 15.36 MHz | 20.34 MHz | 30.72 MHz |
FFT size | 128 | 256 | 512 | 1024 | 1536 | 2048 |
The FFT reduces the number of computations of DFT from O(N2) to O(NlogN) by decomposition in time or frequency domain. The DFT of a sequence x(n) is given by
In the current design, the transform length, N, is 1536. Using the decimation in time method, the first step is to divide the input sequence into three sequences. Each sequence goes through the 512-point FFT computation. The last step combines the three sequences to get a final output result.
For N=1536, we have
Where mod() denote the modular operation. The following flowchart describes the steps to calculate 1536 FFT for LTE downlink.
Following Matlab script implements the 1536 FFT.
N=1536;
N1 = 1536/3;
for i=1:N1
y1(i) = x(3*i-2);
y2(i) = x(3*i-1);
y3(i) = x(3*i);
end
FFT_y1 = fft(y1,512);
FFT_y2 = fft(y2,512);
FFT_y3 = fft(y3,512);
for n=1:N
FFT_y(n) = FFT_y1(mod((n-1),512)+1)+FFT_y2(mod((n-1),512)+1)*exp(-j*2*pi*(n-1)/1536);
FFT_y(n) = FFT_y3(mod((n-1),512)+1)*exp(-j*2*2*pi*(n-1)/1536)+FFT_y(n);
End