2.2 Symbols-to-fft (transmitter) (labview)

Input/outputs and help

This function (shown above in Figure 1) implements the most important and often the most confusing part of the OFDM transmitter chain: converting the parallel group of symbols to a continuous time-domain signal. Note that this module requires the Digital-to-Analog coverter Rate (D/A Rate) and the fundamental frequency of the subcarriers. Both of these parameters were not needed until now, because we've been discretely preparing our OFDM data.

The most frequently asked question about OFDM is "Why IFFT?" To those unfamiliar, IFFT stands for "Inverse Fast Fourier Transform." This is simply an efficient algorithm for performing the Inverse Discrete Fourier Transform, the sampled version of the IDTFT (Inverse Discrete Time Fourier Transform) which is the Fourier Transform for discretized signals. Confused yet? Don't worry. Simply understand the IFFT's function is to take the frequency-domain representation of a signal, and produce the time-domain equivalent.

So again you ask, why are we performing this step? Aren't we already in the time domain? Well, it's all rather relative. We know for OFDM the 'O' stands for Orthogonality. This attractive feature of OFDM signals makes the subcarriers insensitive to spectral overlap, much like Quadrature Multiplexing where we mix signals with cosine and sine of the same frequency. Thus as long as we modulate a variety of carriers all orthogonal to one another, we can neglect overlap of their spectra and still always recover each carrier separately without distortion. The orthogonality for OFDM comes from finding a fundamental frequency (lowest), and mixing all the other carriers with multiples of this fundamental, or harmonics. So how do we implement this?

Okay, let's look at a 32-subcarrier OFDM signal. We could modulate 32 frequencies with our 32 symbols and add them up, but this is extremely inefficient. Instead, we can start in the frequency domain, and place our symbols in adjacent samples. By doing this, because the samples are periodic, we're guarunteed to have all the frequency samples orthogonal to the first non-DC frequency. Then, since we can use Quadrature Multiplexing later on, we can simply place 15 symbols in the first 15 samples after DC, insert a bunch of zeros, and then place the last 15 symbols in the last 15 spots. So we now have 32 subcarriers modulated: +-fo, our fundamnetal, +-2fo, ... , +-14fo in the frequency domain. Essentially what we've done is build our signal from the spectrum. Because we have done this without any kind of conjugate symettry (at least not planned any), we will get a complex time-domain signal when the inverse FFT is taken. This is okay! We eventually will modulate cosine at our intermediate frequency with the real part of our baseband signal, and the imaginary part with sine.