Summary

Chapter 16 Summary: MIMO II — Space-Time Coding and Transceiver Architectures

Key Points

• 1.

  Space-time code design is governed by the rank and determinant criteria: the rank of the codeword difference matrix $\Delta\mathbf{C}$ determines the diversity order ($r \cdot N_r$), while $\det(\Delta\mathbf{C}\,\Delta\mathbf{C}^H)$ controls the coding gain. Orthogonal STBCs (including Alamouti) enable single-symbol ML decoding but are limited to rate $R \leq 3/4$ for $N_t > 2$ with complex constellations.

• 2.

  Spatial multiplexing (V-BLAST/D-BLAST) transmits independent data streams from each antenna, achieving throughput that scales linearly with $\min(N_t, N_r)$. V-BLAST uses ordered successive interference cancellation at the receiver, detecting the strongest layer first to minimise error propagation.

• 3.

  MIMO receivers span a performance-complexity hierarchy: ML detection (optimal, $O(M^{N_t})$) achieves diversity order $N_r$; linear ZF and MMSE ($O(N_t^2 N_r)$) achieve diversity $N_r - N_t + 1$; MMSE-OSIC ($O(N_t^3 N_r)$) recovers diversity approaching $N_r$ through successive cancellation and optimal ordering.

• 4.

  MMSE-SIC achieves MIMO capacity. With Gaussian codebooks and perfect cancellation, the sum of individual MMSE-SIC stream rates equals $\log_2\det(\mathbf{I} + \frac{\text{SNR}}{N_t}\mathbf{H}\mathbf{H}^{H})$ regardless of the decoding order. This is the MIMO analogue of successive decoding for the multiple-access channel.

• 5.

  Precoding with CSIT enables the transmitter to shape signals before transmission: MRT maximises single-stream SNR, ZF precoding nulls inter-user interference, MMSE precoding balances interference suppression and power efficiency, and dirty paper coding achieves the broadcast channel capacity region.

• 6.

  Limited feedback quantises the channel to $B$ bits using a codebook. Grassmannian packings optimise worst-case quantisation. The rate loss scales as $2^{-B/(N_t-1)}$, and maintaining a fixed rate gap as SNR grows requires adding $(N_t - 1)$ feedback bits per 3 dB — a fundamental scaling law that motivates TDD reciprocity for massive MIMO.