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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 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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