Orthogonal Frequency Division Multiplexing (OFDM)

The cyclic prefix ensures that each OFDM symbol period encompasses the entire channel impulse response. This makes the circular convolution property of the DFT applicable, allowing simple one-tap equalization per subcarrier. Without it, linear convolution would spread a symbol across multiple OFDM symbol periods, causing inter-symbol interference.

By dividing the wideband channel into narrowband subcarriers, each subcarrier experiences approximately flat (frequency-flat) fading. This replaces a complex frequency-selective equalization problem with simpler per-subcarrier gain correction, dramatically reducing receiver complexity.

Synchronization errors (timing or frequency offset) destroy the orthogonality between subcarriers, causing inter-carrier interference. Timing offset shifts the FFT window and loses the cyclic prefix benefit; frequency offset rotates subcarrier phase differently and leaks energy across carriers. Both must be estimated and corrected before symbol detection.

Techniques include clipping (crude but simple), companding, tone reservation, tone injection, and selected mapping (SLM). Each trades off computational cost, PAPR reduction, and data overhead. Most practical systems use a combination; 5G allows filter bank multi-carrier variants that inherently reduce PAPR.