Summary

Chapter 23 Summary: RF and Hardware Aspects

Key Points

• 1.

  Transceiver architecture choices fundamentally shape system performance. Direct-conversion receivers enable high integration but introduce I/Q imbalance, modelled as $\hat{x} = \alpha_1 x + \alpha_2 x^*$ with image rejection ratio $\text{IRR} \approx 4/(\epsilon^2 + \Delta\phi^2)$. For 256-QAM, IRR $> 30$ dB is required, demanding amplitude imbalance $< 3$% and phase imbalance $< 3^{\circ}$.

• 2.

  Power amplifier nonlinearity creates in-band EVM degradation and out-of-band spectral regrowth. The Rapp model with smoothness parameter $p$ characterises the AM/AM compression. The fundamental EVM--efficiency trade-off requires input back-off comparable to the signal PAPR, reducing PA efficiency to single digits for OFDM signals. Digital pre-distortion (DPD) recovers 2--4 dB of back-off, roughly doubling efficiency.

• 3.

  ADC quantisation imposes a resolution--bandwidth--power trade-off with $P_{\text{ADC}} \propto 2^b \cdot f_s$. The SQNR follows the 6 dB/bit rule. For massive MIMO, 5--6 bit ADCs suffice at typical operating SNRs. The extreme case of 1-bit ADCs, analysed via the Bussgang decomposition, imposes a hard per-user capacity ceiling of $\approx 2.47$ bits/s/Hz regardless of antenna count.

• 4.

  Phase noise from local oscillators degrades OFDM through common phase error (CPE, correctable) and inter-carrier interference (ICI, residual). The Lorentzian model gives $\text{SIR}_{\text{ICI}} = \Delta f_{\text{SCS}}/(2\pi\beta_{3\text{dB}})$, showing that ICI improves linearly with subcarrier spacing. This is a primary motivation for wider SCS at mmWave frequencies in 5G NR.

• 5.

  Hybrid beamforming factors the precoder as $\mathbf{F} = \mathbf{F}_{\text{RF}}\mathbf{F}_{\text{BB}}$ with $N_{\text{RF}} < N_{\text{ant}}$ RF chains. The OMP algorithm exploits mmWave channel sparsity to design the analog precoder. With $N_{\text{RF}} \geq 2K$ RF chains and sparse channels, hybrid beamforming closely approaches fully digital performance while reducing RF power by 50--75%.