Chapter Summary

Chapter Summary

Key Points

• 1.

  OFDM = IFFT at TX, FFT at RX. The IFFT modulates $N$ data symbols onto orthogonal subcarriers. The cyclic prefix converts linear convolution to circular, enabling one-tap equalization: $\hat{X}[k] = Y[k]/H[k]$.

• 2.

  The CP must exceed the maximum channel delay. If $N_{\text{CP}} < L-1$, ISI breaks the circular convolution property and creates an irreducible BER floor. In 5G NR, the CP is about $N/16$ of the symbol duration.

• 3.

  Channel estimation from pilots is critical. Estimate $H[k]$ at pilot positions and interpolate to data positions. MMSE estimation exploits channel statistics and outperforms LS, especially at low SNR.

• 4.

  MMSE equalization beats ZF at low SNR. ZF amplifies noise on deeply faded subcarriers. MMSE balances noise suppression and channel inversion: $\hat{X} = H^*Y/(|H|^2 + 1/\text{SNR})$.

• 5.

  OFDM enables joint communication and sensing. The same OFDM signal provides radar capability: IFFT across subcarriers gives range, FFT across symbols gives Doppler. This JCAS capability is central to 6G.