Composite Singer Arrays with Hole-free Coarrays and Enhanced Robustness

In array processing, minimum redundancy arrays (MRA) can identify up to $\mathcal{O}\left( {{N^2}} \right)$ uncorrelated sources (the $\mathcal{O}\left( {{N^2}} \right)$ property) with N physical sensors, but this property is susceptible to sensor failures. On the other hand, uniform linear arrays (ULA) are robust, but they resolve only $\mathcal{O}(N)$ sources. Recently, the robust MRA (RMRA) was shown to possess the $\mathcal{O}\left( {{N^2}} \right)$ property and to be as robust as ULA. But finding RMRA is computationally difficult for large N. This paper proposes a novel array geometry called the composite Singer array, which is related to a classic paper by Singer in 1938, and to other results in number theory. For large N, composite Singer arrays could own the $\mathcal{O}\left( {{N^2}} \right)$ property and are as robust as ULA. Furthermore, the sensor locations for the composite Singer array can be readily computed by the proposed recursive procedure. These properties will also be demonstrated by using numerical examples.