Structured Nyquist Correlation Reconstruction for DOA Estimation with Sparse Arrays

Chengwei Zhou, Yujie Gu, Zhiguo Shi, Martin Haardt

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Sparse arrays are known to achieve an increased number of degrees-of-freedom (DOFs) for direction-of-arrival (DOA) estimation, where an augmented virtual uniform array calculated from the correlations of sub-Nyquist spatial samples is processed to retrieve the angles unambiguously. Nevertheless, the geometry of the derived virtual array is dominated by the specific physical array configurations, as well as the deviation caused by the practical unforeseen circumstances such as detection malfunction and missing data, resulting in a quite sensitive model for virtual array signal processing. In this paper, we propose a novel sparse array DOA estimation algorithm via structured correlation reconstruction, where the Nyquist spatial filling is implemented on the physical array with a compressed transformation related to its equivalent filled array to guarantee the general applicability. While the unknown correlations located in the whole rows and columns of the augmented covariance matrix lead to the fact that strong incoherence property is no longer satisfied for matrix completion, the structural information is introduced as <italic>a prior</italic> to formulate the structured correlation reconstruction problem for matrix reconstruction. As such, the reconstructed covariance matrix can be effectively processed with full utilization of the achievable DOFs from the virtual array, but with a more flexible constraint on the array configuration. The described estimation problem is theoretically analyzed by deriving the corresponding Cram&#x00B4;er-Rao bound (CRB). Moreover, we compare the derived CRB with the performance of the virtual array interpolation-based algorithm. Extensive simulations are conducted to demonstrate the effectiveness of the proposed DOA estimation algorithm in terms of achievable DOFs, resolution, and estimation accuracy.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalIEEE Transactions on Signal Processing
StateAccepted/In press - 2023
Externally publishedYes

Bibliographical note

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  • Array signal processing
  • Correlation
  • Covariance matrices
  • Direction-of-arrival estimation
  • Direction-of-arrival estimation
  • Estimation
  • Nyquist spatial filling
  • Sensor arrays
  • Sensors
  • sparse arrays
  • structured correlation reconstruction


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