Conventional Beamforming (CBF), One-Dimensional DOA Estimation

Conventional Beamforming (CBF) is a classical spatial signal processing technique primarily used for one-dimensional Direction of Arrival (DOA) estimation. The core principle involves applying weighted summation to signals received by a sensor array to enhance signals from specific directions while suppressing interference from other directions, thereby achieving precise estimation of target directions. In code implementation, this typically involves creating steering vectors that represent phase delays for different arrival angles.

For one-dimensional DOA estimation, uniform linear arrays (ULA) or vector arrays are commonly employed as receiving arrays. The beamforming process consists of two main steps: First, calculating time delays or phase differences between array elements based on the array's geometric structure using mathematical formulas involving element spacing and signal wavelength. Second, performing weighted accumulation of output signals from all array elements to form beams oriented toward specific directions. Beam steering is achieved by adjusting weight values through algorithms that compute complex weights for each angular sector, with target DOA ultimately determined through peak detection in the spatial spectrum. A typical implementation would involve scanning through angles from -90° to 90° with 1° increments while computing the array response for each angle.

In multi-target scenarios, conventional beamforming can estimate DOAs for different targets through time-division or frequency-division scanning techniques. However, its resolution is limited by the array aperture and signal frequency, with better performance under high signal-to-noise ratio (SNR) conditions. Importantly, as the number of array elements increases, the main beam becomes narrower and sidelobe levels decrease, thereby improving DOA estimation accuracy and interference rejection capability. The relationship between element count and beamwidth can be mathematically modeled using array factor equations.

In practical applications, selecting appropriate operating frequencies and optimizing SNR are crucial considerations. Higher frequencies result in narrower beam widths but may be constrained by propagation losses, while improved SNR helps distinguish weak targets from strong interference. Although conventional beamforming offers low computational complexity and simple implementation, its performance in multi-target and low-SNR scenarios may be inferior to super-resolution algorithms like MUSIC or ESPRIT. The computational advantage makes CBF suitable for real-time systems where rapid DOA estimation is required, often implemented using efficient matrix multiplication operations in signal processing libraries.