Harmonic Suppression and Weak Signal Generation Method for DAC with Stochastic Quantization

Echo simulation is crucial in radar hardware-in-the-loop simulations. The dynamic range of echo power is extremely large owing to factors such as target distance variation and the radar antenna main-to-side lobe ratio. Modern radars can process echoes with wide dynamic ranges through their hardware design and signal processing， requiring the radar echo simulation system to possess the ability to generate echoes with large dynamic ranges. At present， the control of echo simulation signal power is primarily accomplished through two components： digital attenuation and analog attenuation. Digital attenuation is achieved by adjusting the amplitude of the digital signals and constrained by the quantization bits and signal quality of the digital-to-analog converter （DAC）. In contrast， analog attenuation is implemented via digitally controlled radio-frequency attenuators， and limited by signal isolation requirements， resulting in higher hardware costs and increased design complexity to achieve large dynamic range power control. This study focuses on the dynamic range extension of digital attenuation. Quantization-induced noise harmonics in DACs constitute the predominant bottleneck restricting digital attenuation. The prevailing approach for mitigating such harmonics involves dithering techniques， in which an intentionally introduced dithering signal prior to quantization disrupts the coherence between the quantization noise and input signals， thereby suppressing harmonic generation. This study proposes a stochastic quantization model that formalizes the quantization process as a stochastic mapping from real numbers to integers. We theoretically prove that conventional dither-based quantization represents a subset of stochastic quantization and derive an optimal stochastic quantization scheme. Building on this framework， we develop a novel echo power control strategy that synergistically integrates analog and digital attenuation. Under the operational constraints of limited analog attenuation， the proposed scheme achieves wide-dynamic-range signal power control and weak signal generation through the systematic incorporation of stochastic quantization techniques.