Optimizing Minimum Redundancy Arrays for Robustness

Sparse arrays have received considerable attention due to their capability of resolving $\mathrm{O}(N^{2})$ uncorrelated sources with N physical sensors, unlike the uniform linear array (ULA) which identifies at most $N -1$ sources. This is because sparse arrays have an $\mathrm{O}(N^{2}) -$long ULA segment in the difference coarray, defined as the set of differences between sensor locations. Among the existing array configurations, minimum redundancy arrays (MRA) have the largest ULA segment in the difference coarray with no holes. However, in practice, ULA is robust, in the sense of coarray invariance to sensor failure, but MRA is not. This paper proposes a novel array geometry, named as the robust MRA (RMRA), that maximizes the size of the hole-free difference coarray subject to the same level of robustness as ULA. The RMRA can be found by solving an integer program, which is computationally expensive. Even so, it will be shown that the RMRA still owns $\mathrm{O}(N^{2})$ elements in the hole-free difference coarray. In particular, for sufficiently large N, the aperture for RMRA, which is approximately half of the size of the difference coarray, is bounded between $0.0625 N^{2}$ and $0.2174 N^{2}$.11This work was supported in parts by the ONR grants N00014-17-1-2732 and N00014-18-1-2390, the NSF grant CCF-1712633, the California Institute of Technology, the Ministry of Education, Taiwan, R.O.C, under Yushan Young Scholar Program (Grant No. NTU-107V0902), and National Taiwan University.