Common Beamforming Algorithms and Simulation Collection

Beamforming is a core technology in array signal processing, primarily used to enhance signals from target directions while suppressing interference and noise. This article introduces several common beamforming algorithms and their simulation implementation approaches with code-related descriptions.

### 1. Conventional Beamforming (CBF) CBF is the most fundamental beamforming method that adjusts weighting coefficients of array elements to steer the main lobe toward the target direction. The core principle involves time alignment (or phase compensation) to ensure signals from the target direction add coherently during superposition, thereby enhancing the output signal. In simulation implementation, key steps include calculating steering vectors using MATLAB's `phased.SteeringVector` function and plotting beam patterns with `pattern` methods. The weighting vector is typically computed as w = a(θ)/N, where a(θ) is the steering vector toward direction θ.

### 2. Minimum Variance Distortionless Response (MVDR) The MVDR algorithm minimizes total output power (i.e., suppresses interference and noise) while maintaining distortionless response in the target direction. Compared to CBF, MVDR offers superior interference rejection capability but requires higher computational complexity due to covariance matrix estimation and inversion operations. In simulation implementation, proper covariance matrix estimation (using sample covariance matrix with `x*x'/N` computation) and regularization techniques (like diagonal loading) are crucial for numerical stability. The weight calculation follows w = R⁻¹a(θ)/(aᴴ(θ)R⁻¹a(θ)), where R is the estimated covariance matrix.

### 3. Least Mean Square (LMS) Adaptive Beamforming LMS is an adaptive algorithm that iteratively adjusts weights to minimize the mean square error between array output and desired signal. Its advantages include computational simplicity and suitability for dynamic environments, but convergence speed and steady-state performance are significantly influenced by the step size parameter. In MATLAB simulation, implement weight update using w(n+1) = w(n) + μx(n)e*(n), where μ is the step size, x(n) is the input vector, and e(n) is the error signal. Tuning the step size parameter is essential for observing convergence characteristics and interference suppression performance.

### Simulation Implementation Approach When simulating these algorithms in MATLAB, the following steps are typically required: Array Modeling: Define parameters such as number of elements, element spacing, and signal wavelength using `phased.ULA` or `phased.URA` objects. Signal Synthesis: Simulate target and interference signals with specified arrival angles and SNR ratios using `phased.IsotropicAntennaElement` and signal generation functions. Algorithm Implementation: Code the core computation logic for CBF, MVDR, and LMS algorithms, utilizing MATLAB's array processing toolbox functions for efficient implementation. Performance Analysis: Plot beam patterns using `pattern` function or evaluate algorithm performance through metrics like SINR (Signal-to-Interference-plus-Noise Ratio) with quantitative comparison scripts.

By comparing beam patterns and interference rejection capabilities of different algorithms, one can gain intuitive understanding of their advantages, limitations, and suitable application scenarios through visual and quantitative analysis.