OFDMA_Part9 - gives a useful relationship between the DFTs...

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9 Figure 3. OFDM Receiver Equations E7, E8 and E9 shed some light on another subtle advantage of the circular symmetry introduced by the CP. To compute the Discrete-Time Fourier Transform (DTFT) of y [ n ], we require an infinite number of time samples. In a real-world OFDM system, one cannot acquire an infinite number of time samples and hence cannot compute the DTFT of y [ n ]. However, the DFT of y [ n ] doesn’t require an infinite number of time samples; it is simply equivalent to the circular convolution of h and x . This is because the convolution of equation E7 can be written as the circular convolution of equation E8 due to the circular symmetry of { x CP + OFDM } (as was shown in E6). On the same lines as DTFT, DFT has the property that circular convolution in the time- domain transforms into multiplication in the frequency domain; thus E9 follows from E8. E9
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Unformatted text preview: gives a useful relationship between the DFTs of y [ n ], x [ n ] and h [ n ]. When y [ n ] is passed through the CP block of Figure 3, the CP of y [ n ] (for n < 0) gets removed. This results in N time-domain symbols whose DFT is Y [ k ] = H[ k ]X[ k ] in the absence of noise (as was explained in the previous paragraph). These time-domain symbols are sent through the serial-to-parallel converter and then passed through an FFT block. The outputs of the FFT block are the Y [ k ] samples, which are nothing but the scaled versions of the original symbols X [ k ] (over here, the scaling is H [ k ] because Y [ k ] = H[ k ]X[ k ] according to equation E9). Since H [k] is the channel gain associated with the k th subcarrier, each H [ k ] can be estimated...
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