Almost sure identifiability of constant modulus multidimensional harmonic retrieval

Xiangqian Liu, Nicholas D. Sidiropoulos

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2366-2368
Number of pages3
JournalIEEE Transactions on Signal Processing
Issue number9
StatePublished - Sep 2002

Bibliographical note

Funding Information:
Manuscript received December 11, 2001; revised June 1, 2002. This work was supported by NSF/Wireless under Grant CCR-0096164, subcontract participation in the ARL Communications and Networks CTA, and DARPA/ATO under Contract MDA 972-01-0056. The associate editor coordinating the review of this paper and approving it for publication was Dr. Olivier Cappe.


  • Array signal processing
  • Frequency estimation
  • Harmonic analysis
  • Multidimensional signal processing
  • Spectral analysis


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