OFDM Visual Lab: BPSK Modulation
A complete visual walkthrough of the Multiplexing and Demultiplexing process.
Step 1: Information Bit Generation
We start with raw binary data. For BPSK, each bit represents one symbol.
$$\text{Data Vector: } \mathbf{b} = [b_0, b_1, \dots, b_{N-1}], \quad b_i \in \{0, 1\}$$
Step 2: BPSK Constellation Mapping
Bits are mapped to complex voltages. 0 becomes -1 and 1 becomes +1.
$$X_k = (2b_k - 1) + 0j$$
Step 3: Inverse Fast Fourier Transform (IFFT)
This is where the magic happens. We transform 16 parallel subcarriers into one continuous time-domain signal. Each subcarrier is orthogonal to the others.
$$x[n] = \frac{1}{\sqrt{N}} \sum_{k=0}^{N-1} X_k e^{j \frac{2\pi nk}{N}}$$
Step 4: Adding Cyclic Prefix (CP)
We copy the last few samples of the symbol and put them at the start. This prevents Inter-Symbol Interference (ISI).
Step 5: Receiver - FFT & Demultiplexing
At the receiver, we remove the CP and use the FFT to convert the signal back into the frequency domain to recover our subcarriers.
$$Y_k = \frac{1}{\sqrt{N}} \sum_{n=0}^{N-1} y[n] e^{-j \frac{2\pi nk}{N}}$$