Blind source separation (BSS) techniques are required for various signal decomposing issues. Independent component analysis (ICA), assuming only a statistical independence among stochastic source signals, is one of the most useful BSS tools because it does not need a priori information on each source. However, there are many requirements for decomposing multiple deterministic signals such as complex sinusoidal signals with different frequencies. These requirements may include pulse compression or clutter rejection. It has been theoretically shown that an ICA algorithm based on maximizing non-Gaussianity successfully decomposes such deterministic signals. However, this ICA algorithm does not maintain a sufficient separation performance when the frequency difference of the sinusoidal waves becomes less than a nominal frequency resolution. To solve this problem, this paper proposes a super-resolution algorithm for complex sinusoidal signals by extending the maximum likelihood ICA, where the probability density function (PDF) of a complex sinusoidal signal is exploited as a priori knowledge, in which the PDF of the signal amplitude is approximated as a Gaussian distribution with an extremely small standard deviation. Furthermore, we introduce an optimization process for this standard deviation to avoid divergence in updating the reconstruction matrix. Numerical simulations verify that our proposed algorithm remarkably enhances the separation performance compared to the conventional one, and accomplishes a super-resolution separation even in noisy situations.

ICA (Independent Component Analysis) has a remarkable capability of separating mixtures of stochastic random signals. However, we often face problems of separating mixtures of deterministic signals, especially sinusoidal signals, in some applications such as radar systems and communication systems. One may ask if ICA is effective for deterministic signals. In this paper, we analyze the basic performance of ICA in separating mixtures of complex sinusoidal signals, which utilizes the fourth order cumulant as a criterion of independency of signals. We theoretically show that ICA can separate mixtures of deterministic sinusoidal signals. Then, we conduct computer simulations and radio experiments with a linear array antenna to confirm the theoretical result. We will show that ICA is successful in separating mixtures of sinusoidal signals with frequency difference less than FFT resolution and with DOA (Direction of Arrival) difference less than Rayleigh criterion.