Prerequisites

Before You Begin

• Vectors, norms, and inner products(Review ch01)

  Self-check: Can you compute the norm $\|\mathbf{h}\|$ of a complex channel vector $\mathbf{h} \in \mathbb{C}^L$ and express $\|\mathbf{h}\|^2$ as $\sum_{l=1}^{L} |h_l|^2$?

• Random variables, expectation, and independence(Review ch02)

  Self-check: Can you compute $E[\sum_{l=1}^{L} X_l]$ when $X_1, \ldots, X_L$ are independent and identically distributed random variables?

• Chi-squared and exponential distributions(Review ch02)

  Self-check: Do you know the PDF of a sum of $L$ independent exponential random variables (Erlang distribution) and its connection to the chi-squared distribution with $2L$ degrees of freedom?

• Rayleigh and Rician fading models(Review ch06)

  Self-check: Can you state the PDF of the instantaneous SNR $\gamma$ for a single Rayleigh fading link and compute $P(\gamma < \gamma_0)$?

• Coherence time, coherence bandwidth, and fading correlation(Review ch06)

  Self-check: Can you explain when two channel realisations are approximately independent based on the coherence time $T_c$ and coherence bandwidth $B_c$?

• BER in AWGN and Rayleigh fading(Review ch08)

  Self-check: Can you state the BER for BPSK in AWGN ($P_b = Q(\sqrt{2E_b/N_0})$) and in Rayleigh fading ($P_b \approx 1/(4\bar{\gamma})$ at high SNR)?

• Detection and estimation in fading channels(Review ch09)

  Self-check: Can you explain the difference between coherent detection (requires CSI) and non-coherent detection, and state the pairwise error probability in fading?