This paper mainly deals with the problem of direction-of-arrival (DOA) estimation for the ultra sparse nested (USN) MIMO array by operating on two co-prime frequencies. The USN MIMO array consists of a sparse uniform (SU) transmitting array and a more SU receiving array with nested relationship, which generates a SU sum coarray. In this case, the DOA estimation is aliasing because the difference coarray of the sum coarray (DCSC) of the USN MIMO array is also SU for the reference operation frequency. To remove the aliasing, an additional operation frequency with coprime relationship is utilized to form an extra SU sum coarray where the spacing of two adjacent virtual sensors is coprime with that of reference frequency(RF). As a result, two coprime spacings of sum coarrays are combined into a coprime sum coarray which provides a desired DCSC with a majority of contiguous virtual sensors. Finally, with respect to these contiguous virtual DCSC sensors, an augmented correlation matrix with contiguous correlation lags is obtained to calculate MUSIC spectrum. Simulation results demonstrate the resolvable ability for more targets than physical sensors and the performance comparison under both cases of proportional and nonpropotional target spectra.

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