# Constellation Mapping In OFDM

If i am not mistaken, the two following hold :

a. In OFDM Conceptualization, the constellation mapping at Tx (or de-mapping at Rx) is done in Frequency domain

b. However the basic theory (Including the math) of constellation mapping, example PSK/QAM, is always in Time Domain. I have not found any explanation in the frequency domain.

So :

1. Is there a way to convert between the two domains ? (To at least understand the underlying math and the ready-easy-see connection between the two domains ?)

2. Or is there something else going on ? Am i missing something ?

Basically : If i am writhing a MATLAB/Python code...do i do the Modulation (Demodulation) in Time (As per Constellation Mapping concept) Domain or the Frequency (As per OFDM Concept Formulation and usage ) Domain

My concerns arise due to the following :

a. https://en.wikipedia.org/wiki/File:OFDM_transmitter_ideal.png (Constellation Mapping/Modulaton is clearly in Frequency domain.)

b. https://electronicscoach.com/phase-shift-keying.html (PSK concepts are explained in time domain)

So the input bit stream, which could be random data, or say audio-video data is in time domain, it is first modulated by say QPSK. Second, the modulated data is converted to frequency domain ( by dft) , then the mapping to each subcarrier...and then the entire mapped data at transmitter ( in frequency domain) is converted back to time domain using idft, for transmission through the air? Correct? And then finally the same is done in reverse order at receiver ..correct ?

So a given frame would be four samples in the frequency domain taking on one of four values: $$X_k \in (\frac{1}{\sqrt{2}}(1+j, 1-j, -1+j, -1-j))$$ depending on the data. The 4 samples in frequency would become four samples in time through an inverse FFT, resulting in the same 4 samples in time that we would expect to have if we created 4 QPSK waveforms on four closely spaced frequencies and summed them together...which is what gets transmitted over the air as a time domain signal. OFDM is basically a massively parallel implementation of QAM modulations spaced at frequencies where (with proper timing and synchronization) each carrier is orthogonal to the other carriers.