Chapter Summary

Chapter Summary

Key Points

• 1.

  MIMO detection separates spatially multiplexed streams. ZF ($\mathbf{H}^\dagger\mathbf{y}$) eliminates interference but amplifies noise. MMSE adds regularization ($N_0/E_s \cdot \mathbf{I}$) to prevent noise blow-up. ML is optimal but has $O(M^{N_t})$ complexity.

• 2.

  SVD precoding diagonalizes the MIMO channel. With $\mathbf{W} = \mathbf{V}$ and $\mathbf{G} = \mathbf{U}^H$, the MIMO channel becomes $r$ parallel scalar channels with gains $\sigma_k$. Water-filling power allocation achieves capacity.

• 3.

  ZF precoding enables multi-user MIMO. ZF precoding $\mathbf{W} = \mathbf{H}^H(\mathbf{H}\mathbf{H}^H)^{-1}$ nulls inter-user interference at the cost of a power penalty. It requires $N_t \ge K$ (more TX antennas than users).

• 4.

  Massive MIMO makes simple processing optimal. With $M \gg K$, channel hardening ($\frac{1}{M}\mathbf{H}^H\mathbf{H} \to \mathbf{I}$) and favorable propagation make conjugate beamforming near-optimal. No matrix inversion needed.

• 5.

  Pilot contamination is the massive MIMO bottleneck. Reuse of pilot sequences across cells causes estimation errors that do not vanish with more antennas. This motivates pilot decontamination and large-scale MIMO research.