Compressive PLL Tracking for Sub-Nyquist Signal Estimation
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Solution Overview
Problem
Conventional phase-locked loops (PLLs) face challenges in efficiently tracking and estimating parameters of sinusoidal signals, especially in large bandwidths, due to limitations in sampling rates and computational complexity, particularly when dealing with sparse or compressible signals.
Innovation Solution
The development of compressive sensing-based phase-locked loops (CS-PLL) and quadrature compressive sensing phase-locked loops (QCS-PLL) that utilize compressive samplers and random demodulation to track oscillating signals, allowing for sub-Nyquist sampling rates and reduced computational complexity while maintaining performance through inner product preservation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional phase-locked loops (PLLs) are used for tracking and estimating parameters of sinusoidal signals, then parameter estimation can be performed, but sampling rates must be at or above the Nyquist rate which increases device complexity and computational load
Solution Approach 1:
The patent changes the fundamental parameter of sampling rate from Nyquist rate or above to sub-Nyquist rates. By using compressive sensing techniques, the system can accurately estimate signal parameters (frequency, phase, amplitude) while sampling at rates below the traditional Nyquist threshold, thereby reducing device complexity and computational requirements while maintaining measurement precision
Solution Approach 2:
The patent replaces the traditional mechanical sampling approach (uniform sampling at Nyquist rate) with a compressive sensing-based measurement system. This substitution uses random demodulation and compressive samplers that project the signal onto a lower-dimensional space, eliminating the need for high-rate uniform sampling while preserving parameter estimation accuracy
2Reliability
If conventional PLLs operate at Nyquist sampling rates, then complete signal information is captured, but computational complexity increases significantly
Solution Approach 1:
The patent extracts only the essential signal parameters (frequency, phase, amplitude) directly from compressive measurements without requiring complete signal reconstruction. By using phase-locked loop techniques operating on compressed data, the system obtains reliable parameter estimates while avoiding the computationally intensive process of full signal recovery, thus maintaining reliability with reduced complexity
Solution Approach 2:
The patent performs parameter estimation directly in the compressed domain before any potential reconstruction step. By designing the PLL to operate on compressive measurements directly, the system obtains signal parameters in advance without needing to fully reconstruct the signal, thereby reducing computational complexity while maintaining information completeness for the specific task of parameter estimation
3Device complexity
If sub-Nyquist sampling rates are used, then device complexity and computational load are reduced, but measurement precision may deteriorate
Solution Approach 1:
The patent introduces compressive sensing techniques and random demodulation as intermediary processes between the signal and the parameter estimation algorithm. These intermediaries transform the signal into a compressed representation that preserves the essential information needed for accurate parameter estimation, allowing sub-Nyquist sampling without sacrificing measurement precision
Solution Approach 2:
The patent employs phase-locked loop feedback mechanisms that continuously adjust the estimated parameters based on the compressed measurements. The feedback loop refines frequency, phase, and amplitude estimates by comparing expected signal behavior with actual compressive measurements, thereby maintaining high measurement precision even at reduced sampling rates
Data Source
AI summary
A method for estimating and tracking locally oscillating signals. The method comprises the steps of taking measurements of an input signal that approximately preserve the inner products among signals in a class of signals of interest and computing an estimate of parameters of the input signal from its inner products with other signals. The step of taking measurements may be linear and approximately preserve inner products, or may be non-linear and approximately preserves inner products. Further, the step of taking measurements is nonadaptive and may comprise compressive sensing. In turn, the compressive sensing may comprise projection using one of a random matrix, a pseudorandom matrix, a sparse matrix and a code matrix. The step of tracking said signal of interest with a phase-locked loop may comprise, for example, operating on compressively sampled data or by operating on compressively sampled frequency modulated data, tracking phase and frequency.