Chapter Summary

Chapter Summary

Key Points

• 1.

  OFDM parallel-channel decomposition. Given cyclic prefix $\ge$ delay spread, the $N_{\rm sc}$-point FFT turns a frequency- selective channel with $L$ paths into $N_{\rm sc}$ parallel scalar flat-fading sub-channels. Uncoded OFDM per-subcarrier detection loses the intrinsic $L$-fold diversity.

• 2.

  BICM-OFDM recovers frequency diversity. By spreading coded bits across subcarriers with an ideal interleaver, BICM-OFDM achieves diversity $\min(d_H, L)$ — the code's Hamming distance capped by the channel's resolvable paths.

• 3.

  BICM-OFDM-STBC: three dimensions multiply. The Akay-Ayanoglu- Caire (2006) theorem: BICM-OFDM combined with Alamouti STBC achieves diversity $d = \min(d_H, L) \cdot n_t n_r$. Space and frequency diversity do not add — they multiply. This is the architectural template of LTE, Wi-Fi 6/7, and DVB-T2.

• 4.

  OFDM's mobility ceiling. Subcarrier orthogonality breaks when the channel varies within an OFDM symbol. Doppler-induced ICI has power $(\nu/\Delta f)^2$, imposing an SNR ceiling. Mitigation: 5G NR flexible numerology scales subcarrier spacing up to 120 kHz for mmWave FR2.

• 5.

  OTFS as the delay-Doppler alternative. OTFS maps a doubly- selective channel to a sparse 2D channel on the delay-Doppler grid. BICM over the OTFS grid achieves $\min(d_H, P)$ diversity without ICI — smaller raw diversity than OFDM but robust to 500+ km/h mobility.

• 6.

  Production systems. BICM-OFDM-STBC underpins LTE-V2X, NR-V2X, Wi-Fi 6/7, and DVB-T2. OTFS is proposed for 6G HSR and NTN scenarios; 3GPP NTN (Rel-17) uses extended OFDM with enhanced Doppler tracking.

• 7.

  The Caire contribution. Akay-Ayanoglu-Caire 2006 (IEEE Trans. Commun.) is the seventh and final CommIT-affiliated paper tagged in this book. It established the diversity formula $d = \min(d_H, L) \cdot n_t n_r$ that every modern high-mobility wireless design uses as its performance yardstick.