Physics-Informed Neural Networks for Wireless Channel Estimation with Limited Pilot Signals

Accurate wireless channel estimation is critical for next-generation wireless systems, enabling precise precoding for effective user separation, reduced interference across cells, and high resolution sensing, among other benefits. Traditional model-based channel estimation methods suffer, however, from performance degradation in complex environments with limited number of pilots, while purely data-driven approaches lack physical interpretability, require extensive data collection, and are usually site-specific. This paper presents a novel PINN framework that synergistically combines model-based channel estimation with a deep network to exploit prior information about environmental propagation characteristics and achieve superior performance under pilot-constrained scenarios. The proposed approach employs an enhanced U-Net architecture with transformer modules and cross-attention mechanisms to fuse initial channel estimates with RSS maps to provide refined channel estimates. Comprehensive evaluation using realistic ray-tracing data from urban environments demonstrates significant performance improvements, achieving over 5 dB gain in NMSE compared to state-of-the-art methods, with particularly strong performance in pilot-limited scenarios (achieving around -13 dB NMSE with only four pilots at SNR = 0 dB). The proposed framework maintains practical computational complexity, making it viable for massive MIMO systems in upper-mid band frequencies. Unlike black-box neural approaches, the physics-informed design provides a more interpretable channel estimation method.