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I'm trying to implement an sound card-based OFDM modem. A paper says:

...A serial to parallel converter is applied and the IFFT operation is performed on the parallel complex data.

Say I have a stream $S$ of complex numbers, then after serial-to-parallel (S/P) conversion, it becomes $S_1$ and $S_2$. But as far as I'm concerned, OFDM requires the sub-carriers to be orthogonal to each other. So can I just perform IFFT twice directly on the streams without defining the frequencies of sub-carriers? I'm quite puzzled. Any help on this will be greatly appreciated. Thanks.

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The serial/parallel converter shown in most OFDM transmitter block diagrams is required in a hardware implementation but not very meaningful for software implementation. Because in software there is no IFFT block that actually works with parallel inputs, it's all serial processing in reality.

Let $S(k)$ be your input stream of complex numbers and $N$ be the number of subcarriers, i.e. the IFFT size. Then you have to calculate the IFFT of every $N$ samples in $S(k)$, i.e. of the vectors $[S(iN),\ldots,S((i+1)N - 1)]$, with symbol index $i=0,1,2,\ldots$. The result is the OFDM modulated time domain signal. If I understand your example correctly you have to apply the IFFT to both $S_1$ and $S_2$, yes.

The output of the IFFT operation is also complex, in general. Unless you use two audio channels followed by an Inphase/quadrature mixer that shifts the signal to a carrier frequency the vectors defined above have to exhibit a complex conjugate symmetry in order to obtain a real-valued time domain signal. (So-called discrete multitone (DMT))

The allocation of data to subcarriers happens through the IFFT algorithm you're using. The FFTW library, for example, allocates $S(0)$ to frequency zero and $S(N-1)$ to "frequency" $-N/2$. What physical frequency this corresponds to in turn depends on the sampling frequency of the digital-to-analog converter you're using. Orthogonality is inherent to the (I)FFT algorithm, you don't have to apply any further processing to obtain it.

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  • $\begingroup$ This is an awesome answer! Thanks a lot. But there is still one thing I don't quite understand. What does the IFFT size mean here? Why is it the same thing as the number of sub-carriers? In my understanding, I want 4 sub-carriers so I collect 256 complexes from the stream, then divide them into 4 groups and perform IFFT four times. Thus I have 4 carriers and an IFFT size of 64. Could you tell me where am I wrong? $\endgroup$ – babel92 Jan 16 '14 at 15:15
  • $\begingroup$ The IFFT size is always equal to the number of subcarriers. If you do a 64-IFFT, you're modulating 64 subcarriers. Note that, due to guard interval insertion, OFDM using a small number of subcarriers (like 4) is highly inefficient. $\endgroup$ – Deve Jan 16 '14 at 16:07

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