Chapter Summary

Chapter 7 Summary: Joint Spatial Division and Multiplexing

Key Points

• 1.

  Spatial correlation as a resource. In massive MIMO, the covariance eigenspace of each user's channel is low-dimensional ($r_k \ll N_t$) and stable over time. JSDM exploits this structure by grouping users with similar spatial signatures and designing a pre-beamformer per group.

• 2.

  Two-stage precoding. The pre-beamforming matrix $\mathbf{B}_g$ (based on long-term covariance) projects onto the group's eigenspace, reducing the effective channel dimension from $N_t$ to $r_g$. The inner precoder $\mathbf{P}_g$ (based on the $r_g$-dimensional effective channel) handles multi-user interference within the group using standard MU-MIMO techniques.

• 3.

  Massive CSI overhead reduction. JSDM reduces CSI feedback from $K \cdot N_t$ to $\sum_g |\mathcal{S}_g| \cdot r_g$ complex scalars per coherence interval — typically a 10-20$\times$ reduction. Pilot overhead is similarly reduced, making FDD massive MIMO practical.

• 4.

  Asymptotic optimality. The sum rate of JSDM-ZF converges to that of full-CSI ZF as $N_t \to \infty$, because inter-group interference decays as $O(1/N_t)$ and the pre-beamformer captures an increasing fraction of the channel energy.

• 5.

  Inter-group interference management. When group eigenspaces are approximately orthogonal (non-overlapping angular supports), the pre-beamformer suppresses inter-group interference without any instantaneous CSI. Groups can even reuse the same pilot sequences.

• 6.

  Connection to 5G NR. The two-stage structure of JSDM directly influenced the design of the 5G NR Type II codebook, where wideband beam selection (pre-beamformer) is combined with subband coefficient feedback (inner precoder).