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An \(\ell _p\)-norm Based Method for Off-grid DOA Estimation

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Abstract

The sparse signal recovery-based direction of arrival (DOA) estimation has received a great deal of attention over the past decade. From the sparse representation point of view, \(\ell _0\)-norm is the best choice to evaluate the sparsity of a vector. However, solving an \(\ell _0\)-norm minimization problem is non-deterministic polynomial hard (NP-hard). Thus, The common idea for many sparse DOA estimation methods is to use the \(\ell _1\)-norm as the sparsity metric. However, its sparse solution may not coincide with the solution resulting from the \(\ell _0\)-norm thus deteriorating the DOA estimation performance. In this paper, we propose a new sparse method based on \(\ell _p\) (\(0<p<1\)) regularization for DOA estimation to achieve a sparser solution than \(\ell _1\) regularization. In particular, we use the Taylor expansion to convert the \(\ell _p\)-norm minimization problem to a weighted \(\ell _1\)-norm problem. Then, a two-step iterative method is employed to achieve the DOA estimate. The \(\ell _p\) (\(0<p<1\)) regularization is able to improve the angle resolution, leading to an improved performance in low SNR and correlated signal scenarios. Numerical results show that our proposed method has better estimation performance than many other methods do.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) (61671144, 61471205, 61771256), and by the Regroupement Strategique en Microelectronique du Quebec (ReSMiQ).

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Authors and Affiliations

  1. The Key Lab of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Nanjing, 210003, People’s Republic of China

    Zeyun Zhang & Xiaohuan Wu

  2. School of Information Science and Engineering, Southeast University, Nanjing, People’s Republic of China

    Chunguo Li

  3. Department of Electrical and Computer Engineering, Concordia University, Montreal, Canada

    Wei-Ping Zhu

Authors
  1. Zeyun Zhang
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  2. Xiaohuan Wu
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  3. Chunguo Li
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  4. Wei-Ping Zhu
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Correspondence to Zeyun Zhang.

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Zhang, Z., Wu, X., Li, C. et al. An \(\ell _p\)-norm Based Method for Off-grid DOA Estimation. Circuits Syst Signal Process 38, 904–917 (2019). https://doi.org/10.1007/s00034-018-0892-7

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  • DOI: https://doi.org/10.1007/s00034-018-0892-7

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