Intelligent reflecting surface (IRS) is envisioned as a promising solution for controlling radio propagation environments in future wireless systems. In this paper, we propose a distributed intelligent reflecting surface (IRS) assisted multi-user millimeter wave (mmWave) system, where IRSs are exploited to enhance the mmWave signal coverage when direct links between base station and users are unavailable... First, a joint active and passive beamforming problem is established for weighted sum-rate maximization. Then, an alternating iterative algorithm with closed-form expressions is proposed to tackle the challenging non-convex problem, thereby decoupling the active and passive beamforming variables. Moreover, we design a constraint relaxation technique to address the unit modulus constraints pertaining to the IRS. Numerical results demonstrate that the distributed IRS can potentially enhance the communication performance of existing wireless systems. (read more)