Prerequisites

Before You Begin

• Large-scale propagation and path-loss models(Review ch05)

  Self-check: Can you apply the log-distance path-loss model $PL(d) = PL(d_0) + 10n\log_{10}(d/d_0) + X_\sigma$ and interpret the path-loss exponent $n$ for different environments?

• Small-scale fading and multipath channel models(Review ch06)

  Self-check: Can you describe Rayleigh and Rician fading, define coherence bandwidth $B_c$ and coherence time $T_c$, and explain the tapped-delay-line channel model?

• Antenna arrays and beamforming fundamentals(Review ch07)

  Self-check: Can you compute the array factor for a uniform linear array (ULA), derive the half-power beamwidth $\theta_{3\text{dB}} \approx 0.886\lambda/(Nd)$, and explain how phased arrays steer their beams?

• OFDM waveform structure and resource grid(Review ch14)

  Self-check: Can you describe the OFDM signal model, define the cyclic prefix length relative to the channel delay spread, and explain subcarrier spacing and numerology in 5G NR?

• MIMO spatial multiplexing and precoding(Review ch15)

  Self-check: Can you write the MIMO signal model $\mathbf{y} = \mathbf{H}\mathbf{x} + \mathbf{n}$, explain SVD-based precoding, and compute the achievable rate with water-filling power allocation?

• Multi-user MIMO and beamforming(Review ch16)

  Self-check: Can you explain zero-forcing and MMSE precoding for the multi-user MIMO downlink and describe how spatial degrees of freedom are shared among users?

• RF hardware impairments: phase noise, PA nonlinearity, ADC quantisation(Review ch23)

  Self-check: Can you model phase noise as a Wiener process, describe the impact of PA nonlinearity on OFDM signals (PAPR, EVM), and quantify the effect of low-resolution ADCs on receiver performance?