How much does transmit correlation affect the sum-rate scaling of MIMO Gaussian broadcast channels?
IEEE Transactions on Communications
Transient analysis of data-normalized adaptive filters
IEEE Transactions on Signal Processing
Distribution of noncentral indefinite quadratic forms in complex normal variables
IEEE Transactions on Information Theory
Exact performance analysis of the ε-NLMS algorithm for colored circular Gaussian inputs
IEEE Transactions on Signal Processing
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In this work, we propose a transparent approach to evaluating the CDF of indefinite quadratic forms in Gaussian random variables and ratios of such forms. This quantity appears in the analysis of different receivers in communication systems and in various applications in signal processing. Instead of attempting to find the pdf of this quantity as is the case in many papers in literature, we focus on finding the CDF. The basic trick that we implement is to replace inequalities that appear in the CDF calculations with the unit step function and replace the latter with its Fourier transform. This produces a multi-dimensional integral that can be evaluated using complex integration. We show how our approach extends to nonzero mean Gaussian real/complex vectors and to the joint distribution of indefinite quadratic forms.