Simulation of BER vs. SNR for OFDM Modulation with BPSK
BER Results Log
| SNR (dB) | BER |
|---|
Transmitted Bits (Partial)
Received Bits (Partial)
Mathematical Logic of the Simulation
1. Bit-to-Symbol Mapping (BPSK)
Each bit \(b_i \in \{0, 1\}\) is mapped to a bipolar complex value:
If bit = 1, \(X_k = 1 + 0j\)
If bit = 0, \(X_k = -1 + 0j\)
If bit = 0, \(X_k = -1 + 0j\)
2. Orthogonal Multiplexing (IFFT)
The frequency-domain symbols \(X_k\) are converted to discrete time-domain samples \(x[n]\) using the Inverse Fast Fourier Transform:
\(x[n] = \frac{1}{N} \sum_{k=0}^{N-1} X_k e^{j \frac{2\pi nk}{N}}\)
3. Noise Scaling (AWGN)
To ensure the BER curve is accurate, noise is calculated based on the measured power of the time-domain signal.
\(SNR_{linear} = 10^{(SNR_{dB}/10)}\)
\(\sigma_{noise} = \sqrt{\frac{Power_{signal}}{2 \cdot SNR_{linear}}}\)
\(\sigma_{noise} = \sqrt{\frac{Power_{signal}}{2 \cdot SNR_{linear}}}\)