Almost sure identifiability of constant modulus multidimensional harmonic retrieval

In a previous paper by Jiang et al. (see ibid. vol.49, p.1849-59, 2001) 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 article, 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.