Widely Linear Simulation of Continuous-Time Complex-Valued Random Signals

An approach to the simulation of continuous-time complex-valued random signals under widely linear processing is investigated. The technique is based on a version of the Karhunen-Loève expansion for improper stochastic signals defined on any interval of the real line which takes into account the full statistical information of the signal, i.e., the correlation and complementary correlation functions. It is especially designed for simulating approximately a broad class of signals including complex Gaussian or transformation of complex Gaussian signals and it can be accommodated to simulate any widely linear operations of the signal of interest. Its feasibility and accuracy is examined numerically by considering an example in which the technique devised is compared with the classical approach that ignores the complementary correlation information.