Suppose an OFDM transmitter with four subcarriers is implemented using the structure shown below.
If the serial data input rate is 40 bps, each parallel stream will run at 10 bps. Theoretically, the spectrum (assuming BPSK modulation for each subcarrier) of the IFFT output $x$ should look like shown below (the subcarrier carrier frequencies were chosen arbitrarily).
Each channel occupies a bandwidth from -10 Hz to +10 Hz around the subcarrier, resulting in a total OFDM null-to-null bandwidth of 50 Hz, as shown in the spectrum above.
However, the simulated spectrum of the IFFT output $x$ is shown below. Each input bit is represented by one sample (there is no reason to use more samples before the DAC).
One difference between the theoretical and simulated spectra is the difference in bandwidth. The theoretical spectrum has a bandwidth of 50 Hz, whereas the simulated spectrum has a bandwidth of 40 Hz. This can be explained by setting all IFFT inputs to zero, except one, and calculating the resulting spectrum. This process can then be repeated for each of the parallel inputs numbered 0 to 3 in the transmitter structure above. The four spectra are shown below.
Clearly, each parallel stream contributes a bandwidth of 20 Hz, spaced at 10 Hz. This corresponds to the theoretical BPSK OFDM spectrum, except that stream 2 is located at 20 Hz which mirrors back to -20 Hz, with the result that the total bandwidth is 40 Hz and not 50 Hz.
In order to transmit the OFDM signal on a carrier, more samples are required per IFFT output value. The DAC should therefore employ a sample-and-hold strategy, of which the simplest is probably just repeating every IFFT output value $K$ times. The spectrum of the sample-and-hold signal $x_r$ with $K=8$ is shown below.
The bandwidth has now increased to 80 Hz, which can again be explained by looking at the individual contributions of each of the parallel streams, shown below.
The spectrum between -20 Hz and 20 Hz in each of the subfigures above corresponds to each respective stream shown in the OFDM streams (before resampling) figure. The harmonics caused by resampling however cause the bandwidth to increase from 40 to 80 Hz.
What should the bandwidth of the BPSK OFDM signal be after resampling? Is it 50 Hz (according to theoretical graph shown), 40 Hz (simulated before resampling) or 80 Hz?
Should a filter be used to achieve the correct bandwidth?
How is OFDM typically implemented to ensure the correct bandwidth; should some subcarriers be set to zero? Should another DAC approach be used?