Tirza Routtenberg

Mixed-resolution architectures, combining high-resolution (analog) data with quantized data, are widely employed in emerging communication and radar systems to balance accuracy, power consumption, and hardware cost. However, quantization introduces nontrivial information losses in estimation tasks that complicate performance analysis and system design. In this paper, we derive the weighted Bayesian Crame´[jls-end-space/]r-Rao bound (WBCRB) for complex-valued parameter estimation from mixed-resolution data consisting of analog and 1-bit quantized measurements. We present three special cases of the WBCRB: (i) the classical BCRB; (ii) the WBCRB based on the Bayesian Fisher information matrix inverse weighting; and (iii) the Aharon-Tabrikian tightest WBCRB with an optimal weight. Furthermore, we propose a novel regime-aware mean-squared-error (MSE) approximation method that leverages the WBCRB in informative regions and analytically transitions to the theoretical saturation floor to capture the non-monotonic MSE behavior across signal-to-noise ratio regimes. Closed-form results for the bounds and MSE approximation are derived for the widely-used linear Gaussian orthonormal model. Simulation results demonstrate that the proposed WBCRB variants capture the non-monotonic MSE behavior, in contrast to the BCRB. Moreover, the MSE approximation method provides a significantly more insightful performance analysis than the bounds, thus offering a robust tool for the design and optimization of mixed-resolution systems.