2024/07/01 by Benedikt Fesl, Fesl, Benedikt, Wolfgang Utschick +1 · 2 citations
Computer Science · Engineering · #Analog and Mixed-Signal Circuit Design #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Electrical engineering #Information Theory (cs.IT) #Photonic and Optical Devices #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2407.01305
openalex publication_date 2024/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present new fundamental results for the mean square error (MSE)-optimal conditional mean estimator (CME) in one-bit quantized systems for a Gaussian mixture model (GMM) distributed signal of interest, possibly corrupted by additive white Gaussian noise (AWGN). We first derive novel closed-form analytic expressions for the Bussgang estimator, the well-known linear minimum mean square error (MMSE) estimator in quantized systems. Afterward, closed-form analytic expressions for the CME in special cases are presented, revealing that the optimal estimator is linear in the one-bit quantized observation, opposite to higher resolution cases. Through a comparison to the recently studied Gaussian case, we establish a novel MSE inequality and show that that the signal of interest is correlated with the auxiliary quantization noise. We extend our analysis to multiple observation scenarios, examining the MSE-optimal transmit sequence and conducting an asymptotic analysis, yielding analytic expressions for the MSE and its limit. These contributions have broad impact for the analysis and design of various signal processing applications.