大规模通信系统的发展对传统滤波器设计提出了更高的要求，稀疏有限脉冲响应（FIR）滤波器具有低计算复杂度与低实现成本的特点，但常规凸松弛近似设计方法会产生额外的逼近误差，稀疏性也不理想，并且求解过程复杂。针对FIR滤波器在设计中由于乘法器个数多而导致实现成本高的问题，该文提出了一种基于加权最小二乘准则的稀疏FIR滤波器设计方法。首先，根据不同范数性质对初始稀疏表示的L_{\mathrm{0}}范数进行替换，即对目标函数进行改进，从而在保持稀疏性的基础上，解决非凸函数难以直接求解的问题；然后，将目标问题转化为2个凸子问题差的形式，根据迭代规则构造形式更为简单的子问题，采用交替求解方法求解子问题，以进一步提高求解效率并降低求解复杂度；最后，在确定0系数的位置后，通过求解一个加权最小二乘问题来进一步减小近似误差。仿真实验结果显示：与已有的稀疏滤波器求解方法相比，所提方法能够提高FIR滤波器的系数稀疏性，降低乘法器个数，并且在稀疏性增强的情况下获得较为折中的均方根误差与最大误差，同时计算机求解时间更少，求解效率更高。

The development of large-scale communication systems puts higher requirements on traditional filter design. Sparse finite impulse response (FIR) filters have the characteristics of low computational complexity and low implementation cost, but conventional convex relaxation approximation design methods produce additional approximation errors, exhibit suboptimal sparsity, and involve complex solving processes. To address the issue of high implementation costs caused by the large number of multipliers in FIR filter design, this paper proposed a sparse FIR filter design method based on a weighted least squares criterion. Firstly, the norm of the initial sparse representation is replaced based on the properties of different norms, thereby improving the objective function. This modification maintains sparsity while addressing the challenge of directly solving non-convex functions. Next, the target problem was reformulated as the difference between two convex sub-problems. Simplified sub-problems were constructed according to iterative rules, and an alternating solution method was adopted to further enhance solving efficiency and reduce complexity. Finally, after determining the positions of zero coefficients, a weighted least squares problem was solved to further reduce approximation errors. The simulation results show that compared with the existing sparse filter solving methods, the proposed method can improve the coefficient sparsity performance of FIR filters, reduce the number of multipliers and obtain a compromise between root-mean-square error and maximum error in the case of sparsity enhancement. Meanwhile, the computational solving time is significantly reduced, and solving efficiency is notably improved.