Circuits, Systems, and Signal Processing

, Volume 38, Issue 2, pp 904–917 | Cite as

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

  • Zeyun ZhangEmail author
  • Xiaohuan Wu
  • Chunguo Li
  • Wei-Ping Zhu
Short Paper


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.


Direction of arrival (DOA) estimation Off-grid model \(\ell _p\)-norm Sparse signal recovery (SSR) 



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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Zeyun Zhang
    • 1
    Email author
  • Xiaohuan Wu
    • 1
  • Chunguo Li
    • 2
  • Wei-Ping Zhu
    • 3
  1. 1.The Key Lab of Broadband Wireless Communication and Sensor Network TechnologyNanjing University of Posts and TelecommunicationsNanjingPeople’s Republic of China
  2. 2.School of Information Science and EngineeringSoutheast UniversityNanjingPeople’s Republic of China
  3. 3.Department of Electrical and Computer EngineeringConcordia UniversityMontrealCanada

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