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1. Introduction In 5G NR, precoding is the mathematical operation that converts the spatial layers of PDSCH data into signals for the available transmit antenna ports / RF chains. Beamforming is what those weighted signals ultimately produce in space. The key relationship is x=Ws where: s∈C^(N_L×1) is the vector of data symbols on the PDSCH layers, W∈C^(N_TX×N_L ) is the precoding matrix, and x∈C^(N_TX×1) contains the signals transmitted through the antenna ports/RF chain

1. Introduction The exponential growth in mobile data traffic, driven by 4K/8K video, cloud gaming, AR/VR, industrial IoT, and private 5G networks, has forced wireless systems to evolve beyond traditional antenna systems. One of the most transformative technologies enabling 5G performance is Massive MIMO (Multiple Input Multiple Output). Unlike conventional MIMO (2x2, 4x4, 8x8), Massive MIMO scales antenna elements to tens or even hundreds at the base station, enabling spatia