Chapter 15: MIMO I: Channel Modeling and Capacity

Learning Objectives

• Construct the MIMO channel matrix $\mathbf{H}$ and write the input-output relationship $\mathbf{y} = \mathbf{H}\mathbf{x} + \mathbf{n}$ for an $n_r \times n_t$ system
• Relate channel rank and condition number to the spatial multiplexing capability of a MIMO link
• Apply the Kronecker and Weichselberger correlation models to generate realistic spatially correlated MIMO channels
• Decompose a deterministic MIMO channel into parallel sub-channels via SVD and compute capacity with water-filling power allocation
• State and apply Telatar's formula for ergodic MIMO capacity under Rayleigh fading
• Distinguish ergodic capacity from outage capacity and explain when each metric is appropriate
• Define degrees of freedom and multiplexing gain, and show that $\mathrm{DoF} = \min(n_t, n_r)$
• State the Zheng-Tse diversity-multiplexing tradeoff $d^*(r) = (n_t - r)(n_r - r)$ and interpret its implications for MIMO system design