Exact Simulation of Noncircular or Improper Complex-Valued Stationary Gaussian Processes using Circulant Embedding

Abstract
This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding literature. The method can be performed in operations, where n is the length of the desired sequence. The method is exact, except when eigenvalues of prescribed circulant matrices are negative. We evaluate the performance of the algorithm empirically, and provide a practical example where the method is guaranteed to be exact for all , with an improper fractional Gaussian noise process.
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