From the Wikipedia article: "An inverse FFT is computed on each set of symbols, giving a set of complex time-domain samples. These samples are then quadrature-mixed to passband in the standard way. The real and imaginary components are first converted to the analogue domain using digital-to-analogue converters (DACs); the analogue signals are then used to modulate cosine and sine waves at the carrier frequency, f{c}, respectively. These signals are then summed to give the transmission signal, s(t)."
So, information is added to a pure sine (or cosine) wave. This causes the wave to have not just one frequency, but a range of frequencies within a bandwidth that can be seen in the frequency domain of the signal. Having found out about this only yesterday, there are a number of questions. I've added an image of a regular time domain OFDM signal found somewhere on the internet.
- Does the modulated signal really pass through the very narrow (ideally, 20 MHz in regular LTE) bandpass filter at the receiver? At a center frequency of 2 GHz that would mean to bandpass only what is within 1.99 GHz and 2.01 GHz, which sounds impressive to me.
- Wouldn't even the slightest distortion from the emitter move the frequency of the signal out of the passband?
- At 2 GHz operating frequency (analog time domain signal, at the LNA), there are 2*10^9 cycles in a second. If the number of carriers is 2048, and a symbol is a string of 2048 cycles or slightly more including the cyclic prefix, doesn't it mean that the theoretical maximum symbol rate is (2*10^-9)/(2048+prefix length)? This would mean that the signal is transmitted continuously. This is not true, however, since the symbol rate is a function of the sampling time, Ts, which is 32.552 ns. So, I don't really understand what FFT samples has to do with the 2 GHz analog signal that is present at the receiving LNA. My reasoning is that I could digitize the signal with any number of samples, get a plot for each 2048-cycle sequence then apply FFT.
If the graph below is the LNA signal of 2 GHz LTE, what would the period of a cycle be in nanoseconds? There are about 20 cycles from what I understand. How many cycles of this type would a symbol take?
Later edit: Regarding the third question, I've found an answer. Digital processing of the signal is done in the baseband, which is independent of carrier frequency. It needs to be converted into the passband. These links have more information: IFFT and OFDM upconversion
baseband and passband modulation
Later edit 2: it seems that there are many ways to convert the baseband OFDM into the passband. Constant Envelope OFDM is one interesting way to do it, the baseband OFDM signal is phase modulating the carrier. This is in contrast to regular OFDM where the baseband is somesort of amplitude modulating the carrier. More info at "Constant Envelope OFDM Phase Modulation", for example.