Higher order direction finding from rectangular cumulant matrices: The rectangular 2q-MUSIC algorithms

- The 2q-th order data statistics are arranged into arbitrary rectangular matrices.
- The rectangular 2q-MUSIC algorithms exploit these matrices for direction finding.
- Rectangular arrangements permit to adjust the identifiability-performance trade-off.
- Non-redundant arrangements of the data statistics further improve the performance.

Fourth-order (FO) high resolution direction finding methods such as 4-MUSIC have been developed for more than two decades for non-Gaussian sources mainly to overcome the limitations of second order (SO) high resolution methods such as MUSIC. In order to increase the performance of 4-MUSIC in the context of multiple sources, the MUSIC method has recently been extended to an arbitrary even order 2q (q≥2), for square arrangements of the 2qth-order data statistics, giving rise to the 2q-MUSIC algorithm. To further improve the performance of 2q-MUSIC, the purpose of this paper is to extend the latter to rectangular arrangements of the data statistics, giving rise to rectangular 2q-MUSIC algorithms. Two kinds of rectangular arrangements, corresponding to redundant and non-redundant arrangements are considered. In particular, it is shown that rectangular arrangements of the higher order (HO) data statistics achieve a trade-off between performance and maximal number of sources to be estimated. These rectangular arrangements also lead to a complexity reduction for a given level of performance, which is still increased by non-redundant arrangements of the statistics. These results, completely new, open new perspectives in HO array processing.