Distribution of the Scaled Condition Number of Single-spiked Complex Wishart Matrices

2021/05/11 by Dissanayake, Pasan, Dharmawansa, Prathapasinghe, Chen, Yang
#15B52 #60B20 #62H10 #65F35 #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #G.1.3 #G.3 #Information Theory (cs.IT) #Probability (math.PR) #Signal Processing (eess.SP) #Statistics Theory (math.ST) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2105.05307

Abstract

Let X∈ℂ^{n× m} (m≥ n) be a random matrix with independent columns each distributed as complex multivariate Gaussian with zero mean and \it single-spiked covariance matrix I_n+ ηuu^*, where I_n is the n× n identity matrix, \colorblueu∈ℂ^{n× 1} is an arbitrary vector with unit Euclidean norm, η≥ 0 is a non-random parameter, and (⋅)^* represents the conjugate-transpose. This paper investigates the distribution of the random quantity κ_SC²(X)=∑_k=1ⁿ λ_k/λ₁, where \colorblue0≤ λ₁≤ λ₂≤ …≤ λ_n

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