Chun-Lin Liu – Topics – Super Nested Arrays (1D)

• Toolkit for coarray MUSIC and coarray interpolation

• Sparse array design with reduced mutual coupling

  • Super nested arrays (1-D)

  • Hourglass arrays (2-D)

• Cramér-Rao bounds for sparse arrays

• Others

Super Nested Arrays

2D representations of the nested array and the super nested array. (View larger)

In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). While there are methods to counteract this through appropriate modeling and calibration, they are usually computationally expensive, and sensitive to model mismatch. On the other hand, sparse arrays, such as nested arrays, coprime arrays, and minimum redundancy arrays (MRAs), have reduced mutual coupling compared to uniform linear arrays (ULAs). With denoting the number of sensors, these sparse arrays offer freedoms for source estimation because their difference coarrays have -long ULA segments. But these well-known sparse arrays have disadvantages: MRAs do not have simple closed-form expressions for the array geometry; coprime arrays have holes in the coarray; and nested arrays contain a dense ULA in the physical array, resulting in significantly higher mutual coupling than coprime arrays and MRAs.

The super nested array has all the good properties of the nested array, and at the same time achieves reduced mutual coupling. There is a systematic procedure to determine sensor locations. For fixed , the super nested array has the same physical aperture, and the same hole-free coarray as does the nested array. But the number of sensor pairs with small separations (, , etc.) is significantly reduced. The last property helps to reduce mutual coupling effects. Simulations demonstrate the superior performance of super nested arrays in the presence of mutual coupling.

Interactive Interface for Super Nested Arrays

This interactive interface assists users to understand the basics of super nested arrays and to create new array configurations of their own. With this interface, users can place the sensors arbitrarily on the 2D representation, show the associated difference coarray, and calculate the weight functions.

The interactive interface (left) and some information about the difference coarray (right). (View larger)

• Click here or the above image to download the interactive interface (MATLAB m-files). Please read README.pdf for instructions. (Last update: August 15, 2016)

Our Papers

1. C.-L. Liu and P. P. Vaidyanathan, ‘‘Super Nested Arrays: Linear Sparse Arrays with Reduced Mutual Coupling – Part I: Fundamentals,’’ IEEE Trans. on Signal Processing, vol. 64, no. 15, pp. 3997-4012, Aug. 2016.

   1. DOI and Full text

   2. Sample code for Fig. 4. Please execute main_Fig_4.m for the plots.

   3. Sample code for Fig. 9. Please execute main_practical_example.m for the plots.

2. C.-L. Liu and P. P. Vaidyanathan, ‘‘Super Nested Arrays: Linear Sparse Arrays with Reduced Mutual Coupling – Part II: High-Order Extensions,’’ IEEE Trans. on Signal Processing, vol. 64, no. 16, pp. 4203-4217, Aug. 2016.

   1. DOI and Full text

   2. Supplementary document.

3. C.-L. Liu and P. P. Vaidyanathan, ‘‘Super Nested Arrays: Sparse Arrays with Less Mutual Coupling than Nested Arrays,’’ in Proc. of 2016 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP 2016), pp. 2976-2980, Shanghai, China, Mar. 2016.
   (Best Student Paper Award)
   (DOI) (Full text) (Slides)

4. C.-L. Liu and P. P. Vaidyanathan, ‘‘High Order Super Nested Arrays,’’ in Proc. of the Ninth IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2016), pp. 1-5, Rio de Janeiro, Brazil, Jul. 2016.
   (Best Student Paper Award)
   (DOI) (Full text) (Slides)