Almost sure identifiability of constant modulus multidimensional harmonic retrieval

  • Authors:
  • Xiangqian Liu;N.D. Sidiropoulos

  • Affiliations:
  • Dept. of Electr. & Comput. Eng., Minnesota Univ., Minneapolis, MN;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2002

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Abstract

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 N2 dimensions. The gain is interesting from a theoretical standpoint but also for small 2-D sensor arrays or higher dimensions and odd sample sizes.