Theoretical BER Simulation Code for DFT-S OFDM over Gaussian Channels

In wireless communication systems, DFT-S OFDM (Discrete Fourier Transform Spread Orthogonal Frequency Division Multiplexing) technology is widely adopted for uplink transmission due to its low Peak-to-Average Power Ratio (PAPR) characteristics. This paper discusses theoretical BER simulation methodologies for DFT-S OFDM systems operating in Gaussian channel environments. The simulation framework comprises three core modules: signal generation, channel transmission, and receiver detection. The implementation begins with generating random binary information data, followed by mapping the bit stream to complex symbols using modulation schemes like QAM/PSK through constellation mapping functions. The key differentiator from conventional OFDM is the DFT pre-spreading operation, implemented using FFT algorithms to enhance frequency-selective fading resistance through frequency-domain spreading. Channel modeling employs Additive White Gaussian Noise (AWGN) channels, where SNR parameters are adjusted programmatically to simulate varying channel conditions. The receiver performs symmetric inverse processing including cyclic prefix removal, FFT transformation, equalizer application (using zero-forcing or MMSE algorithms), and IDFT de-spreading operations. BER calculation is implemented through bit-wise comparison between transmitted and received data streams using error counting algorithms. Critical analysis focuses on three aspects: 1) Verifying the logarithmic relationship between SNR and BER against theoretical expectations using curve fitting techniques 2) Performance comparison with conventional OFDM through parallel simulation implementations 3) Investigating the impact of different modulation orders (QPSK, 16QAM, 64QAM) on system performance using parameterized modulation functions. This system-level simulation validation visually demonstrates the noise resistance capabilities of DFT-S OFDM technology, providing theoretical references for practical communication system design through MATLAB-based Monte Carlo simulations and statistical performance analysis.