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 /spl lfloor/K/2/spl rfloor/ /spl lceil/L/2/spl rceil/ two-dimensional (2-D) exponentials are almost surely identifiable from a K/spl times/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 /spl lceil/K/2/spl rceil/ /spl lceil/L/2/spl rceil/ 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.