riecovest.random_matrices.sample_complex_t_distribution

riecovest.random_matrices.sample_complex_t_distribution(mean, covariance, rng, num_samples, degrees_of_freedom)

Sample from a complex t-distribution with given mean, covariance matrix and degrees of freedom.

See equation (21) and then Section IV. A in [ollilaComplex2012]

Parameters:

  • mean (complex ndarray of shape (dim,)) – Mean of the complex Gaussian distribution.

  • cov (complex ndarray of shape (dim, dim)) – Covariance matrix of the complex Gaussian distribution.

  • rng (numpy.random.Generator) – Random number generator.

  • num_samples (int) – Number of samples to draw.

  • degrees_of_freedom (int) – Specifies which distribution from the t-family to sample from. Converges to Gaussian as degrees of freedom goes to infinity.

Returns:

sample – Samples from the specified distribution

Return type:

ndarray of shape (dim, num_samples)

References

[ollilaComplex2012] E. Ollila, D. E. Tyler, V. Koivunen, and H. V. Poor, “Complex elliptically symmetric distributions: survey, new results and applications,” IEEE Transactions on Signal Processing, vol. 60, no. 11, pp. 5597–5625, Nov. 2012, doi: 10.1109/TSP.2012.2212433.