Chapter 21: Coded Modulation for High-Mobility Channels

Learning Objectives

• Derive the OFDM parallel-channel decomposition: given a cyclic prefix $N_{\rm cp}$ longer than the channel's delay spread, show that the $N_{\rm sc}$-point FFT turns a frequency-selective channel with $L$ resolvable paths into $N_{\rm sc}$ parallel flat-fading scalar channels, one per subcarrier
• State and prove the Akay-Ayanoglu-Caire diversity formula: the BICM-OFDM-STBC system achieves diversity $d = \min(d_H, L) \cdot n_t n_r$, where $d_H$ is the binary code's minimum Hamming distance, $L$ is the number of resolvable paths, and $n_t, n_r$ are the transmit and receive antenna counts
• Identify the delay-Doppler representation of a time-varying channel, define the Zak transform, and explain why OTFS modulation converts a doubly-selective channel into a quasi-static 2D channel that supports BICM over the delay-Doppler grid
• Quantify the ICI (inter-carrier interference) penalty of OFDM under Doppler: derive the approximate SNR loss $\Delta\mathrm{SNR} \approx \nu_{\rm max}^2 / (2 \Delta f^2)$ as a function of normalised Doppler, and identify the operational mobility ceiling of current OFDM deployments
• Map the results onto modern standards: 5G NR FR1 OFDM for pedestrian and vehicular speeds, LTE-V2X and NR-V2X sidelink for 500 km/h relative velocities, and OTFS research for 1000 km/h high-speed rail and non-terrestrial networks (NTN)
• Connect the BICM theory of Ch. 5-6 and the STBC theory of Ch. 10-11 into a single high-mobility architecture and recognise it as the landmark Akay-Ayanoglu-Caire (2006) design that defined the 802.11n / LTE / DVB-T2 transmit chain