Prerequisites

Before You Begin

• Complex baseband representation and digital modulation(Review ch04)

  Self-check: Can you express a passband signal $s(t) = \text{Re}[x(t)\,e^{j2\pi f_c t}]$ in terms of its complex baseband equivalent $x(t) = x_I(t) + jx_Q(t)$ and explain the role of I and Q branches in a modulator?

• MIMO channel model and spatial multiplexing(Review ch07)

  Self-check: Can you write the MIMO signal model $\mathbf{y} = \mathbf{H}\mathbf{x} + \mathbf{n}$ and explain how spatial multiplexing achieves a multiplexing gain of $\min(N_t, N_r)$?

• OFDM modulation, PAPR, and the frequency-domain signal model(Review ch14)

  Self-check: Can you derive the PAPR of an OFDM signal with $N$ subcarriers and explain why PAPR grows as $O(N)$ in the worst case? Can you state the per-subcarrier model $Y_k = H_k X_k + W_k$?

• Massive MIMO beamforming and channel estimation(Review ch18)

  Self-check: Can you explain how a base station with $M \gg K$ antennas achieves array gain of $M$ and describe the favourable propagation condition $\mathbf{H}^{H}\mathbf{H}/M \to \mathbf{I}_K$ as $M \to \infty$?