31 research outputs found
A New Restriction on Low-Redundancy Restricted Array and Its Good Solutions
In array signal processing, a fundamental problem is to design a sensor array
with low-redundancy and reduced mutual coupling, which are the main features to
improve the performance of direction-of-arrival (DOA) estimation.
For a -sensor array with aperture , it is called low-redundancy (LR) if
the ratio is approaching the Leech's bound for ; and the mutual coupling is often
reduced by decreasing the numbers of sensor pairs with the first three smallest
inter-spacings, denoted as with . Many works have
been done to construct large LRAs, whose spacing structures all coincide with a
common pattern with the
restriction . Here denote the spacing between adjacent
sensors, and is the largest one. The objective of this paper is to find
some new arrays with lower redundancy ratio or lower mutual coupling compared
with known arrays. In order to do this, we give a new restriction for to be , and obtain 2 classes of -type arrays, 2 classes
of -type arrays, and 1 class of -type arrays for any .
Here the -Type means that . Notably, compared with
known arrays with the same type, one of our new -type array and the new
-type array all achieves the lowest mutual coupling, and their uDOFs are
at most 4 less for any ; compared with SNA and MISC arrays, the new
-type array has a significant reduction in both redundancy ratio and
mutual coupling.
We should emphasize that the new -type array in this paper is the first
class of arrays achieving and for any
Sharp sufficient conditions for stable recovery of block sparse signals by block orthogonal matching pursuit
In this paper, we use the block orthogonal matching pursuit (BOMP) algorithm to recover block sparse signals x from measurements y = Ax + v, where v is an β2-bounded noise vector (i.e., kvk2 β€ Η« for some constant Η«). We investigate some sufficient conditions based on the block restricted isometry property (block-RIP) for exact (when v = 0) and stable (when v , 0) recovery of block sparse signals x. First, on the one hand, we show that if A satisfies the block-RIP with Ξ΄K+1 1 and β2/2 β€ Ξ΄ < 1, the recovery of x may fail in K iterations for a sensingmatrix A which satisfies the block-RIP with Ξ΄K+1 = Ξ΄. Finally, we study some sufficient conditions for partial recovery of block sparse signals. Specifically, if A satisfies the block-RIP with Ξ΄K+1 < β2/2, then BOMP is guaranteed to recover some blocks of x if these blocks satisfy a sufficient condition. We further show that this condition is also sharp