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This paper is concerned with the study of the embedding circulant matrixmethod to simulate stationary complex-valued Gaussian sequences. The method is,in particular, shown to be well-suited to generate circularly-symmetricstationary Gaussian processes. We provide simple conditions on the complexco-variance function ensuring the theoretical validity of the minimal embeddingcirculant matrix method. We show that these conditions are satisfied by manyexamples and illustrate the algorithm. In particular, we present a simulationstudy involving the circularly-symmetric fractional Brownian motion, a modelintroduced in this paper.

Fast and exact simulation of complex-valued stationary Gaussian processes through embedding circulant matrix