## 4 Results and Discussion
This is notable because the EGC upper bound is typically achievable only in a beamforming setup with perfect CSI and continuous phase shifters. In contrast, the proposed approach uses only a partial, imperfect uplink CSI estimated at the base station as a fingerprint of the channel and a marker of the UE's position, along with RSRP for reward modeling. This demonstrates the practicality and effectiveness of the proposed method, even with limited and imperfect channel information. This advantage is particularly evident in scenarios with blockages, where user signals rely on reflections to reach the access point. The proposed solution demonstrates its adaptability to the propagation environment by adjusting the beam pattern, thereby capturing signals from multiple directions and gaining more power. This ability to dynamically adjust and optimize the beam pattern in response to environmental conditions not only improves the performance in nLOS scenarios but also highlights the potential of MARL-based hybrid beamforming in real-world applications where blockages and reflections are common. By leveraging the capabilities of MARL, the system can efficiently manage complex and variable propagation environments, ensuring high data rates and reliable connectivity even under challenging conditions. Figure 8: Comparison of average beamforming gain versus number of beams in the learned codebook in nLOS with 32-element ULA. The performance of MARL is contrasted against various hybrid precoding techniques including manifold optimization (MO) [19], sparse orthogonal matching pursuit (SOMP) algorithm [5], and the two-stage hybrid beamforming (TS-HB) algorithm [4]. Notably, MO and SOMP were initially proposed for single-user scenarios, but for comparison, these algorithms are adjusted to the multi-user context by adopting the interference cancellation strategy outlined in [9]. In the simulation plot for no interference, the outcomes of fully-digital beamforming and combining are traced. This approach effectively eliminates interference, serving as a reference point in the evaluations. Figure 9 shows a comparative analysis of the achievable sum-rate performance of the algorithms across various SNR levels, assuming the perfect knowledge of CSI and the available array response. The system parameters are set as follows: each BS has 32 antennas (\(N_{BS}=32\)), each UE has 4 antennas (\(N_{M}=4\)), synthetic noise with an SNR of 20 dB, and phase shifter quantization is performed with 3 bits (\(r=3\)). The multiuser environment consists of four simultaneous UEs (\(M=4\)), each with five paths (\(L=5\)). This consistent configuration is maintained across all algorithms to ensure a fair comparison. For reference, fully digital beamforming and the MO algorithm, known for their near-optimal analog and baseband precoders, have been included. Notably, the performance of the proposed MARL approach closely matches that of the MO algorithm, consistently achieving the highest sum-rate among all the algorithms. As evident from the simulation results with perfect CSI shown in Figure 9, in a typical hybrid beamforming scenario with ideal channel conditions and minimal interference, the sum-rate begins to plateau as the system nears its maximum spatial multiplexing capability. At this point, the effects of quantization noise and hardware imperfections become more pronounced. Additionally, the \(\log_{2}(1+\text{SNR})\) term grows more slowly, approaching a logarithmic limit. This indicates that the incremental gain in capacity (and thus sum-rate) diminishes as SNR increases. A perfect CSI and array response data are typically unavailable. To assess the impact of corrupted CSI and array response data on the performance of the proposed system,  
Figure 9: SNR vs. sum-rate comparison for perfect CSI and array response (\(N_{BS}=32\), \(N_{M}=4\), \(r=3\), \(M=4\), \(L=5\)). complex AWGN noise was added to both the array response and channel matrix.