Almost sure identifiability of constant modulus multidimensional harmonic retrieval

In a recent paper by Jiang et al. in this Transactions, it has been shown that up to ⌊K/2⌋ ⌈L/2⌉ two-dimensional (2-D) exponentials are almost surely identifiable from a K × L mixture, assuming regular sampling at or above Nyquist in both dimensions. This holds for damped or undamped exponentials. As a complement, in this correspondence, we show that up to ⌈K/2⌉ ⌈L/2⌉ undamped exponentials can be uniquely recovered almost surely. Multidimensional conjugate folding is used to achieve this improvement. The main result is then generalized to N > 2 dimensions. The gain is interesting from a theoretical standpoint but also for small 2-D sensor arrays or higher dimensions and odd sample sizes.