Prerequisites & Notation

Before You Begin

This chapter brings together BICM (Ch 5-6), STBC (Ch 10-11), and OFDM (Telecom book Ch 14) to analyse coded modulation on high-mobility, frequency-selective channels.

BICM capacity and the bit-metric PEP (Ch 5, 6)(Review ch05)
Self-check: Can you write the BICM capacity as a sum of binary sub-channel capacities?
Space-time block codes: Alamouti and rank/determinant criteria (Ch 10, 11)(Review ch10)
Self-check: Do you know why Alamouti achieves full diversity $n_t n_r$ with linear decoding?
OFDM modulation and the cyclic prefix (Telecom Ch 14)
Self-check: Can you describe why a cyclic prefix $\ge$ delay spread eliminates ISI?
Fading channels: coherence time, coherence bandwidth (Telecom Ch 6)
Self-check: What determines the coherence bandwidth of a multipath channel?
Diversity order as the asymptotic slope of log-BER vs log-SNR(Review ch06)
Self-check: Can you extract the diversity order from a BER-vs-SNR plot?

Notation for This Chapter

Symbols used in the high-mobility coded-modulation chapter.

Symbol	Meaning	Introduced
$N_{\rm sc}$	Number of OFDM subcarriers	s01
$N_{\rm cp}$	Cyclic prefix length	s01
$L$	Number of resolvable channel paths (delay taps)	s01
$\Delta f$	OFDM subcarrier spacing	s01
$\tau_{\max}$	Channel delay spread (max delay)	s01
$\nu_{\max}$	Channel Doppler spread (max Doppler)	s04
$d_H$	Minimum Hamming distance of the outer binary code	s02
$d = \min(d_H, L) \cdot n_t n_r$	BICM-OFDM-STBC diversity order (Akay-Ayanoglu-Caire)	s02
$X[k, \ell]$	OTFS symbol at Doppler index $k$ , delay index $\ell$	s03
$T_c, B_c$	Channel coherence time and coherence bandwidth	s04

← Ch 20 BICM-OFDM: Harvesting Frequency Diversity