Recently, the radio access network (RAN) has been reimagined through open RAN (O-RAN) architecture to overcome the limitations of the traditional monolithic, black-box design philosophy and to leverage emerging technologies such as cloud computing, machine learning, and artificial intelligence. Although O-RAN disaggregates the base station (BS) into independent components to enable modular deployment, this paradigm introduces new challenges in signal processing and beamforming. In particular, beamforming in O-RAN must account for fronthaul link (FHL) capacity constraints, coordinated operation of multiple radio units (possibly from different vendors), and resource management, including transmit power allocation. To address these challenges, this work proposes novel beamforming techniques for a downlink multiuser hybrid massive multiple-input multiple-output system, in which hybrid architectures are deployed at both the users and at each BS radio unit. We formulate a sum-rate maximization problem incorporating transmit-power, unit-modulus, and FHL capacity constraints. The proposed algorithm integrates gradient descent and the Lagrange multiplier method to design analog beamformers and digital precoders, respectively, whereas digital combiners are designed to render the received streams parallel to each other. By avoiding computationally intensive operations such as eigenvalue and singular value decompositions, the proposed approach, as evidenced by simulation results, achieves superior performance with moderate computational complexity compared to existing benchmark schemes.

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