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Almost sure identifiability of constant modulus multidimensional harmonic retrieval

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2 Author(s)
Xiangqian Liu ; Dept. of Electr. & Comput. Eng., Minnesota Univ., Minneapolis, MN ; N. D. Sidiropoulos

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.

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IEEE Transactions on Signal Processing  (Volume:50 ,  Issue: 9 )