Tradeoffs in Avoiding Truncation in Hierarchical Time Delay Beamforming Networks

This letter examines truncation errors in hierarchical beamforming networks (BFNs) using layered time delay units (TDUs). While quantization errors are assumed to be bounded by half the least significant bit (LSB/2), this assumption breaks down at low resolution, leading to delay truncation and significant phase errors. A revised framework is proposed which introduces a scaling factor to account for cumulative quantization error propagation and to derive the required delay range for each layer. Closed-form expressions and simulations illustrate how bit allocation affects truncation risk and phase error growth. The results provide design tools to balance resolution, scan range and phase performance in efficient wideband BFNs.