Low complexity subspace approach for unbiased frequency estimation of a complex single-tone

• Published in: Digital signal processing Vol. 145; p. 104304
• Main Authors: Pourafzal, Alireza, Skrabanek, Pavel, Cheffena, Michael, Yildirim, Sule, Roi-Taravella, Thomas
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.02.2024
• Subjects: Complex single-tone; Frequency estimation; Short observation interval; Subspace method; Subspace method; Short observation interval; Complex single-tone; Frequency estimation
• ISSN: 1051-2004; 1095-4333
• DOI: 10.1016/j.dsp.2023.104304

We propose a single-tone frequency estimator of a one-dimensional complex signal in complex white Gaussian noise. The estimator is based on the subspace approach and the unitary transformation. Due to its low space and time-complexity, we name the estimator as Low complexity Unitary Principal-singular-vector Utilization for Model Analysis (LUPUMA). Regardless of the observation length, LUPUMA provides a uniform estimation variance over the whole frequency range, while achieving the lowest time-complexity among subspace methods. The proposed estimator asymptotically reaches the Cramér-Rao Lower Bound. For short observations, the signal-to-noise ratio threshold of LUPUMA corresponds to the threshold of the maximum likelihood estimator. The low space and time-complexity along with the stable and state-of-the-art estimation performance for short observations make LUPUMA an ideal candidate for applications with a limited number of signal samples, limited computational power, limited memory, and for applications that require rapid processing time (low latency).