Chapter 21: Introduction to Random Matrix Theory

Learning Objectives

• Explain why the empirical spectral distribution of large random matrices converges to a deterministic limit and why this matters for MIMO communications
• State and derive the Marchenko-Pastur law for i.i.d. Gaussian matrices and compute its density, support, and moments
• Define the Stieltjes transform and use it to characterize limiting spectral distributions via fixed-point equations
• Apply deterministic equivalents to compute ergodic MIMO capacity with spatially correlated channels without Monte Carlo simulation