Chapter Summary

Chapter Summary

Key Points

• 1.

  The cache-aided MIMO broadcast channel replaces the error-free shared link of Chapters 1–4 with a noisy Gaussian BC, one $L$-antenna transmitter to $K$ single-antenna users, each with cache $M$. The natural figure of merit is degrees of freedom (high-SNR slope).

• 2.

  The headline result (Lampiris-Caire 2017): $\mathrm{DoF} = \min(t + L, K)$ where $t = KM/N$ is the caching gain and $L$ is the antenna count. Matches the information-theoretic upper bound for this class under perfect CSIT.

• 3.

  Gains are ADDITIVE, not multiplicative. Coded caching contributes $t$ extra DoF on top of the classical MIMO BC DoF of $L$. The two mechanisms — XOR cancellation via cached side info and zero-forcing beamforming — operate at different layers of the signal; they do not compound into $(t+1)L$.

• 4.

  The Lampiris-Caire scheme retains the MAN placement unchanged, but replaces delivery groups of size $(t+1)$ with groups of size $(t+L)$. Each group uses $L$ linearly independent beams, each carrying a coded-XOR message that simultaneously benefits $t+1$ users of the group via cached side information, and is nulled at the remaining $L-1$ users via ZF.

• 5.

  Finite-SNR behavior. Sum-rate scales as $(t+L)\log_2(1 + \beta\rho)$, with $\beta < 1$ capturing the interference-leakage penalty from imperfect ZF. The DoF advantage translates into finite-SNR rate gains at all operationally relevant SNRs.

• 6.

  CSIT is the practical bottleneck. Perfect CSIT yields $\mathrm{DoF} = t+L$; no CSIT degrades to $\mathrm{DoF} = t+1$ (cache gain survives; spatial gain lost). Coded caching partially substitutes for CSIT — a design lever for CSIT-expensive regimes like mmWave and FDD.

• 7.

  Subpacketization grows to $\binom{K}{t+L-1}$. The multi-antenna scheme inherits MAN's subpacketization problem and adds a factor of $L$. Polynomial-subpacketization multi-antenna schemes are an active research frontier.