Gridless wideband DOA estimation in nonuniform noise with increased DOFs

This paper presents gridless schemes for direction finding of wideband sources using sparse array with nonuniform noise. According to the frequencies relationship, we obtain multiple equivalent scaled difference coarrays, which are combined later to formulate synthetic virtual array when sources share the same normalized power spectrum in different subbands. After treating the term affected by nonuniform noise as hole, an atomic norm optimization problem to recover the noise-free signal of interpolated synthetic uniform linear array (ULA) is designed. We analyze the estimation error distribution of the noise-independent terms in synthetic virtual array and based on this, impose a constraint to avoid tuning process and effect of noise. Furthermore, it extremely increases the number of detectable sources, even making it possible to exceed the degree of freedoms of difference coarray. For the general case when sources have arbitrary powers, a multi-snapshot atomic norm optimization problem is formulated, where signal from scaled coarrays is considered as partial observation of synthetic ULA for different snapshots. Similarly, a newly constructed constraint is added, with which most of the above advantages are sustained. Besides, we give the semidefinite programming form and the Cramer-Rao bounds. The superiority of the proposed algorithms is demonstrated by simulations.