OFDM Visual Lab: QPSK
Quadrature Phase Shift Keying (2 bits/symbol)
Step 1: Mapping 2 Bits per Subcarrier
QPSK uses four points. Each subcarrier $k$ carries two bits $(b_{2k}, b_{2k+1})$.
$$X_k = \frac{1}{\sqrt{2}} \left[ (2b_{2k}-1) + j(2b_{2k+1}-1) \right]$$
Step 2: Frequency to Time (IFFT)
Step 3: Received Constellation
Note how the points cluster around $(\pm 0.7, \pm 0.7)$ due to the $1/\sqrt{2}$ normalization.