This paper addresses the challenge of spatially sparse precoding in millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems, which suffer from significant path loss due to their high carrier frequency. The authors propose a method to design hybrid RF/baseband precoders that leverage the spatial structure of mmWave channels, formulating the problem as a sparse reconstruction task. By using basis pursuit, they develop algorithms to approximate optimal unconstrained precoders and combiners, which can be implemented in low-cost RF hardware. The proposed approach is shown to approach the performance limits of unconstrained mmWave systems, even when practical transceiver constraints are considered. The paper also includes a detailed system model, channel model, and numerical results demonstrating the effectiveness of the proposed methods.This paper addresses the challenge of spatially sparse precoding in millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems, which suffer from significant path loss due to their high carrier frequency. The authors propose a method to design hybrid RF/baseband precoders that leverage the spatial structure of mmWave channels, formulating the problem as a sparse reconstruction task. By using basis pursuit, they develop algorithms to approximate optimal unconstrained precoders and combiners, which can be implemented in low-cost RF hardware. The proposed approach is shown to approach the performance limits of unconstrained mmWave systems, even when practical transceiver constraints are considered. The paper also includes a detailed system model, channel model, and numerical results demonstrating the effectiveness of the proposed methods.