This paper presents a differentiable optimization framework for the design of constrained Linear Differential Microphone Arrays (LDMAs). The proposed method leverages a non-uniform delay-and-sum beamformer as a light-weight base system model, proving its ability to achieve the optimal beampattern of LDMAs by jointly optimizing microphone positions and filter weights. The formulation enables the optimized design of a filter with a distortion-free constraint in the desired sound direction, while also imposing constraints on microphone positioning to ensure consistent performance. Through evaluation on multiple metrics, including Mean Squared Error (MSE), Directivity Index (DI), White Noise Gain (WNG), and computation time, and comparison with state-of-the-art methods, this approach demonstrates a flexible, directive, robust, and hardware-efficient design.

翻译：本文提出了一种用于约束线性差分麦克风阵列（LDMA）设计的可微优化框架。所提出的方法采用非均匀延迟求和波束形成器作为轻量级基础系统模型，通过联合优化麦克风位置和滤波器权重，证明了其能够实现LDMA的最优波束方向图。该公式允许在期望声源方向上设计具有无失真约束的滤波器，同时施加麦克风定位约束以确保性能一致性。通过在多种指标（包括均方误差（MSE）、指向性指数（DI）、白噪声增益（WNG）和计算时间）上进行评估，并与最新方法进行比较，该方法展示了一种灵活、定向、鲁棒且硬件高效的设计方案。