MIMO Wireless Networks, 2nd Edition

Appendix B

Complex Gaussian Random Variables and Matrices

B.1 Some Useful Probability Distributions

Consider that h is a complex Gaussian variable, i.e., a circularly complex variable with zero mean and variance . This means that both the real and imaginary parts of h are zero mean Gaussian variables of variance . In this case, follows a Rayleigh distribution,

(B.1)

with the following properties:

(B.2)

(B.3)

The CDF of s is given by

(B.4)

The random ...