Coprime beamforming: fast estimation of more sources than sensors

• Published in: IET radar, sonar & navigation Vol. 13; no. 11; pp. 1956 - 1962
• Main Authors: Baxter, William, Nosrati, Hamed, Aboutanios, Elias
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 01.11.2019
• Subjects: array signal processing; computational complexity; computational cost; coprime beamforming; coprime‐pair configuration; degrees of freedom; direction‐of‐arrival estimation; DOA; estimation performance; fast estimation; fast Fourier transform; fast Fourier transforms; fast iterative interpolated beamformer; FIIB; high‐fidelity frequency estimates; high‐resolution subspace‐based methods; interpolation; iterative methods; lag estimates; Research Article; sensing array; significant hardware computational savings; single estimate; source separation; spatial smoothing; subspace techniques; subspace‐based algorithms; virtual array; fast Fourier transforms; iterative methods; single estimate; coprime-pair configuration; subspace techniques; virtual array; direction-of-arrival estimation; high-resolution subspace-based methods; DOA; array signal processing; lag estimates; computational cost; degrees of freedom; subspace-based algorithms; VA; estimation performance; fast estimation; fast Fourier transform; source separation; spatial smoothing; interpolation; fast iterative interpolated beamformer; coprime beamforming; sensing array; FIIB; significant hardware computational savings; computational complexity; high-fidelity frequency estimates
• ISSN: 1751-8784; 1751-8792; 1751-8792
• DOI: 10.1049/iet-rsn.2018.5647

In radar, the minimisation of redundancies within the sensing array can lead to significant hardware computational savings. Arrays with a coprime-pair configuration enjoy increased degrees of freedom and can detect more sources than sensors. To achieve this, a virtual array (VA) consisting of the full complement of lags is usually constructed and subspace-based algorithms are then employed to obtain the direction-of-arrival (DOA) or frequency estimates. However, the application of the subspace techniques to the VA incurs a significant computational cost and requires spatial smoothing. The authors propose and analyse the application of the fast iterative interpolated beamformer (FIIB) to the coprime DOA estimation problem. The FIIB enjoys a computational complexity of the same order as the fast Fourier transform and does not require spatial smoothing. They consider two implementations that construct the VA differently with the first selecting a single estimate for each lag and the other employing averaged values of the lag estimates. They present a comprehensive study of the estimation performance as a function of signal-to-noise ratio, number of snapshots and source separation. The results clearly show that the FIIB delivers high-fidelity frequency estimates that consistently outperform the high-resolution subspace-based methods.