Chapter 16: Random Matrix Theory for Estimation

Learning Objectives

• Apply the Marchenko-Pastur law to predict the spectrum of large sample covariance matrices
• Derive the deterministic equivalent of the MMSE SINR for MIMO detection in the large-system limit
• State and interpret the Donoho-Tanner phase transition for $\ell_1$ minimization
• Use Stieltjes transforms to compute the spectral distribution of sums and products of random matrices
• Explain the role of free probability in analyzing iterative receivers with multiple random matrix components