The questions below are for OFDM, IFFT, FFT operations.

Example 1

In OFDM modulation, a stream of parallel symbols are input to an IFFT operation of size $M$ for example and the output is time domain samples of size $M$.

My question is:

Let us take for example, the fact that the input symbols to the FFT operation are QAM symbols. Then, at the output of IFFT I receive $M$ samples. Each sample is weighted sum of modulated subcarriers.

Does it mean that each QAM symbol (input of IFFT) is sent out on ONE subcarrier?

Example 2

I have seen a paper that take the time domain samples of an impulse response of channel of length $T_{CH}$ puts them into M-FFT operation and the result was $H(k)$ for $k\in[1:M]$ which the authors state are the frequency response of the $k$th subcarrier. Why is that the FFT generated the subcarrier frequency response? According to Example 1, each sample should be weighted sum of all input ?

Can anyone explain to me whats the connection between two examples?

Thanks and looking forward for your clarification.


1 Answer 1


To your first question, yes, each symbol is sent on a separate subcarrier; that's the basic idea of OFDM.

I'm not sure where your confusion lies with your second question. It's well-known that the Fourier transform of a system's impulse response gives its frequency response. In this case, the system is the communication channel. If you choose the sample rate of your impulse response measurement properly, and use the appropriately-sized FFT, you can get a frequency response measurement whose bins line up with the subcarrier frequency grid. This can be used for equalizing the channel.


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