Mitigating Group Delay Mismatch in Terahertz Hybrid Beamforming Systems: A Frequency-Selective Joint Analog-Digital Framework

Terahertz (THz) hybrid analog-digital beamforming systems face significant performance degradation due to group delay mismatch in phase shifters, which distorts beam patterns and significantly reduces the array gain. This paper presents a comprehensive framework to model, analyze, and mitigate group delay mismatch in THz hybrid analog-digital beamforming systems, addressing a critical oversight in existing research. We first establish a theoretical model for group delay mismatch in THz hybrid analog-digital beamforming systems, revealing its frequency-dependent Gaussian distribution and its cascading impact on beam squint and capacity degradation. Our analysis explicitly incorporates spatial group delay gradients, ultra-wideband channel characteristics, and hardware non-idealities, deriving closed-form expressions for beam misalignment and capacity loss. These results demonstrate that group delay-induced degradation scales quadratically with center frequency and is insensitive to bandwidth or array size, redefining THz system design priorities. We then propose a robust frequency selective hybrid analog-digital beamforming algorithm that jointly optimizes analog and digital beamformers to counteract group delay distortions. The analog beamformer, designed via Riemannian manifold optimization, minimizes spatial group delay gradients under the constant modulus constraints, while the digital precoders employs minimax optimization to compensate residual phase errors across subcarriers. Simulations under realistic THz channel conditions validate the accuracy of our analysis and the effective of our proposed design. Specially, our algorithm achieves 33.91 bps/Hz spectral efficiency at 10 dB SNR, outperforming conventional methods by 31.5% without requiring additional expensive analog lines.