Robust Adaptive Beamforming for Sparse Arrays

ObjectiveThe rapid development of modern communication technologies, such as 5G networks and Internet of Things (IoT) applications, increases the complexity of signal processing in wireless communication and radar systems. Adaptive beamforming is widely used because it extracts the signal of interest in the presence of interference and noise. Traditional robust adaptive beamforming methods address steering vector mismatch, which may result from environmental nonstationarity, Direction-Of-Arrival (DOA) estimation errors, imperfect array calibration, antenna deformation, and local scattering. However, they do not leverage the advantages of the Sparse Array (SA), which reduces hardware complexity and system cost. They also often fail to suppress SideLobe Levels (SLLs) under interference conditions, limiting their effectiveness in complex electromagnetic environments. To address these issues, a robust adaptive beamforming algorithm is proposed that incorporates SA and low-SLL constraints.MethodsUnlike conventional sparse approaches that place the l0 norm penalty in the objective function, the proposed method introduces the l0 norm into the constraint. This formulation ensures that the optimized array configuration meets the pre-specified number of active sensors and avoids the uncertainty associated with sparse-weight tuning in multi-objective optimization models. In addition to the sparsity constraint, an SLL suppression constraint is incorporated to impose an upper bound on array response in interference and clutter directions. By integrating these constraints into a unified optimization framework, the method achieves a robust Minimum Variance Distortionless Response (MVDR) beamforming scheme that exhibits sparsity, adaptivity, and robustness. To address the nonconvexity of the formulated optimization problem, a convex relaxation strategy is used to convert the nonconvex constraint into a convex one. Based on this formulation, robust adaptive beamforming methods are developed to generate a sparse weight solution from a Uniform Linear Array (ULA). Although the method is derived from a ULA, the sparse weight solution provides practical advantages. By assigning zero weights to selected sensors, the number of active elements is reduced, lowering hardware cost and computational burden while preserving desirable beamforming performance. The main contribution of this work lies in establishing a unified framework that enables collaborative optimization of robustness, beam performance, SLL, and array sparsity.Results and DiscussionsA series of simulation experiments were conducted to evaluate the performance of the proposed sparse robust beamforming algorithm under multiple scenarios, including multi-interference environments, steering vector mismatch, Angle-Of-Arrival (AOA) mismatch, low Signal-to-Noise Ratio (SNR) conditions, and complex electromagnetic environments based on practical antenna arrays. The results show that the algorithm maintains stable mainlobe gain in the desired signal direction while forming deep nulls in interference directions. First, in the presence of steering vector mismatch, conventional MVDR beamformers often exhibit reduced mainlobe gain or beam pointing deviation, which compromises desired-signal reception. By contrast, the proposed method maintains a stable, distortionless mainlobe direction under mismatch conditions, ensuring high gain in the desired signal direction (Fig. 2(a), Fig. 3(a)). Second, with the introduction of an SLL constraint, clutter is suppressed effectively and peak SLLs are reduced markedly (Fig. 2(b)). Third, under low-SNR conditions, the method shows strong noise resistance. Even in heavily noise-contaminated scenarios, it maintains effective interference suppression and achieves high output Signal-to-Interference-plus-Noise Ratio (SINR), demonstrating adaptability to weak-target detection and cluttered environments. Moreover, the optimized SA configuration achieves beamforming performance close to that of a ULA while activating only part of the sensors (Fig. 2). Finally, experimental validation using real antenna arrays further confirms the method’s effectiveness (Fig. 3). Stable performance is maintained, and high gain is achieved in the desired direction even under AOA estimation mismatch (Fig. 4). Overall, the results indicate that the proposed method enhances robustness and hardware efficiency and provides reliable performance in complex electromagnetic environments.ConclusionsA robust adaptive beamforming algorithm for sparse arrays is proposed. The central innovation is the construction of a joint optimization model that integrates array sparsity, robustness to steering vector mismatch, and low SLL constraints within a unified framework. Compared with approaches such as MVDR, which emphasizes interference suppression, Covariance Matrix Reconstruction (CMR), which enhances robustness, and Non-Adjacent Constrained Sparsity (NACS), which achieves array sparsity, the proposed method attains a balanced improvement across these dimensions. Simulation results show that in scenarios featuring steering vector errors, AOA estimation mismatches, and low-SNR conditions, the method maintains satisfactory beamforming performance with reduced hardware cost, demonstrating strong practical engineering utility and application potential.