Chapter 20: Coded Modulation for Massive MIMO

Learning Objectives

• State the additive quantisation noise model for a uniform $b$-bit ADC, derive the quantisation-SNR rule $\mathrm{SNR}_q = 6.02\, b + 1.76$ dB from Bennett's theorem, and identify the two regimes in which the model breaks down (low $b$, low input SNR)
• Derive the single-input 1-bit-quantised AWGN capacity $C_{1\text{-bit}} = 1 - h_2(Q(\sqrt{\text{SNR}}))$ as a binary-symmetric channel with Gaussian-informed crossover probability, and explain the $2/\pi \approx -1.96$ dB low-SNR loss relative to the unquantised Shannon capacity
• Construct a Spatial Modulation (SM) transmitter (Mesleh 2008) that embeds $\log_2 n_t + \log_2 M$ bits per channel use by activating one of $n_t$ antennas and transmitting one of $M$ QAM symbols, and analyse its BER as a mixture of antenna-index errors and symbol errors
• Generalise SM to Generalised Spatial Modulation (GSM) with $n_a$ active antennas, derive the rate $\lfloor \log_2 \binom{n_t}{n_a} \rfloor + n_a \log_2 M$ bits, and prove that $n_a^* = n_t/2$ maximises the log-binomial contribution
• Connect massive-array channel hardening (MIMO book Ch. 18) to coded-modulation design: explain why the BICM-vs-CM gap narrows on hardened channels and why hybrid (digital + analogue) beamforming plus low-resolution ADCs is the mmWave 5G NR and emerging 6G architecture
• Identify the three deployment settings where these techniques matter — mmWave 5G NR FR2 (low-res ADCs + hybrid beamforming), 802.11ay 60 GHz WiGig (beamforming + index modulation research), and 6G cell-free massive MIMO (1-bit uplink sensing) — and recognise the engineering trade-offs that motivated each choice