On the design and use principles of ofdm

Written in front: personal study record, please criticize and correct me.

OFDM, as its name implies, is orthogonal frequency division multiplexing. In short, it is to use multiple orthogonal subcarriers to carry information for transmission. (The definition of orthogonality and the transformation in time-frequency domain will not be repeated here. )

Question 1: In short, what should the spectrum of OFDM look like? I think so:

Right? A plurality of orthogonal subcarriers are transmitted simultaneously. You can see that this picture meets the definition. (Note that this is the amplitude spectrum and the phase spectrum is not drawn, but in fact, if the signal is PSK modulated in OFDM, the phase spectrum carries the symbol information. Keep an eye here, talk about it later)

But, in fact, the phase spectrum in the textbook is like this:

Ha ha ha, so complicated. Why did the impulse function become the Sa function? Because the subcarriers are windowed. OFDM signals are limited to a time period of (0, t). See the figure below.

It can be seen that this is an OFDM signal, which has four subcarriers in the time domain, the fifth highest synthesis, and the period time window length is 1. (Note that the amplitudes of the subcarriers are the same here, which means that the information is not within the amplitude. The frequency domain of time window is Sa function, which explains the frequency spectrum of OFDM. ) As soon as the problem was solved, this picture actually bothered me for a long time. Maybe I didn't listen carefully in class:)

So, question 2: I know the principle of OFDM, so what is the OFDM signal like (essentially a modulation problem)?

In fact, this question has been answered above, but I think it is not enough. Even if the frequency spectrum of OFDM symbols and the time domain waveform of symbols are known. I want to see symbolic information. That is, how is it modulated? According to textbooks, OFDM symbols are composed of a group of subcarriers carrying PSK or QAM modulation signals. Stop and think, PSK and QAM signals. Come on, how simple it is, PSK, phase modulation, QPSK For complex points, the symbol set (1, 2, 3, 4) corresponds to four phases (45, 135, 225, 3 15). The constellation diagram and time domain waveform are not shown here. The following table is combined with Figure 3. It is assumed that different phases on subcarriers carry different signal information.