Fast and Efficient 2-D and K-D DFT-Based Sinusoidal Frequency Estimation

Solak V., Aldirmaz-Colak S., SERBES A.

IEEE TRANSACTIONS ON SIGNAL PROCESSING, cilt.70, ss.5087-5101, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 70
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1109/tsp.2022.3216929
  • Dergi Adı: IEEE TRANSACTIONS ON SIGNAL PROCESSING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.5087-5101
  • Anahtar Kelimeler: 2-D frequency estimation, QSE, Multi-dimensional frequency estimation, DFT interpolation, MSE, OF-ARRIVAL ESTIMATION, PARAMETER-ESTIMATION, MASSIVE MIMO, INTERPOLATION, ESPRIT
  • Kocaeli Üniversitesi Adresli: Evet

Özet

Frequency estimation of a 2-D complex sinusoid under white Gaussian noise is a significant problem having a wide range of applications from signal processing, radar/sonar to wireless communications. This paper proposes two novel and fast DFT-based algorithms for the frequency estimation of 2-D complex sinusoids. The proposed algorithms employ q-shifted DFT coefficients of the signal that correspond to interpolating the signal by a factor of 1/vertical bar q vertical bar without actually performing zero-padding, where q is an element of [-0.5, 0.5]. We show that the first algorithm is asymptotically efficient since it achieves the asymptotic Cramer-Rao bound (CRB) when the DFT shift parameter and the number of iterations are selected appropriately for large signal size. We propose strict bounds on the selection of these parameters for overall asymptotic efficiency. Then, based on the first algorithm, we propose a second algorithm which also performs on the CRB for both small and large signal lengths. The total computational cost of both of the proposed algorithms is in the order of O(N1Na2 log N-1 log N-2), where N-1 and N-2 are the size of the signal. Finally, we generalize the second algorithm to K-dimensions, where K is any integer larger than one. Comprehensive simulation results confirm all of our theoretical derivations, and also show that our algorithms outperform existing algorithms.