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The Fourth Order Cumulant-Based MUSIC Algorithm for Harmonic Retrieval in Colored Noise

The MUSIC algorithm is well known for its high resolution capability and various aspects of its statistical performance have been investigated. In this paper, a general fourth order cumulant matrix which conforms with the structure of MUSIC algorithm is introduced. Because the fourth order cumulant is insensitive to Gaussian noise, The MUSIC-type method can be reformulated using the fourth-order cumulant matrices instead of autocorrelation matrices when additive noise is colored Gaussian. By doing so, the additive colored Gaussian noise can be suppressed. So fourth order cumulant-based MUSIC algorithm provides better resolution and estimation performance when noise is color. Firstly,the theory of MUSIC algorithm is studied; additionally,the relation between fourth order cumulant and autocorrelation function is analyzed. Simulation results demonstrate the effectiveness of the cumulant-based MUSIC algorithm, and it can restrain effectively the effect of coloured noise comparing with its equivalent second-order statistics-based version. Moreover, it has higher resolution probability and low SNR scenario in direction of arrival estimation.