Spectrally Sparse Signal Reconstruction With Time-Modulated Subsampling
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Solution Overview
Problem
Existing compressed signal acquisition methods for multi-band RF signals require high-speed and expensive A/D converters to analyze wideband signals, which are costly and have limited dynamic range.
Innovation Solution
A method involving non-uniform bandpass subsampling with time-modulated pulse repetition frequency, allowing for signal acquisition and reconstruction without the need for high-rate A/D converters, using Morlet wavelets, Haar wavelets, or Gabor functions, and modulating the repetition frequency within an acquisition frame to reduce the required sampling rate.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If non-uniform bandpass subsampling is used to acquire wideband signals, then the sampling rate can be reduced below Nyquist frequency, but high-speed and expensive A/D converters are still required to maintain signal quality
Solution Approach 1:
The patent applies dynamics by making the pulse repetition frequency time-modulated rather than constant. The PRF varies over time within an acquisition frame, creating a dynamic sampling pattern that spreads spectral replicas across different frequency positions. This time-varying approach allows use of lower-rate A/D converters while maintaining wideband signal acquisition capability, as the dynamic PRF prevents spectral overlap that would occur with fixed-rate sampling.
Solution Approach 2:
The patent changes the parameter of pulse repetition frequency from a fixed value to a time-modulated variable. By modulating the PRF parameter over time, the system achieves spectral spreading that enables compressed sensing with lower sampling rates. The PRF modulation creates a mapping between time and frequency domains that allows reconstruction of wideband signals from subsampled data using algorithms like ISTA or FISTA.
2Measurement precision
If high sampling rates are used to avoid spectral aliasing, then signal quality is maintained, but energy consumption increases
Solution Approach 1:
The patent uses periodic action through time-modulated pulse repetition within acquisition frames. Instead of continuous high-rate sampling, the system employs periodic pulse trains with time-varying repetition frequencies. This periodic structure, combined with compressed sensing reconstruction algorithms, maintains signal quality while dramatically reducing the average sampling rate and associated energy consumption of the A/D converter.
3Ease of operation
If uniform sampling is used to simplify the acquisition process, then implementation is easier, but spectral leakage and aliasing occur in wideband signals
Solution Approach 1:
The patent replaces uniform static sampling with dynamic time-modulated sampling. The pulse repetition frequency varies over time according to a modulation pattern, creating a dynamic sampling grid that adaptively maps different frequency components to different time instances. This dynamic approach prevents spectral aliasing while maintaining implementation feasibility through structured modulation patterns that can be synchronized and tracked.
Solution Approach 2:
The patent introduces time modulation as an additional dimension to the sampling process. By varying the PRF over time, the system transforms a one-dimensional frequency sampling problem into a two-dimensional time-frequency problem. This dimensional expansion allows the use of lower sampling rates while preserving spectral information through the time-varying mapping, which can be inverted during reconstruction using compressed sensing algorithms.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables efficient acquisition and reconstruction of wide RF bands with reduced energy consumption and converter costs by utilizing lower average sampling rates, while maintaining signal quality and avoiding spectral aliasing.
Implementation Method 1
mixed by means of a multiplier 120, with a pulse train (for example Morlet wavelets), pNUWBS(t)
Data Source
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AI summary
The present invention relates to a compressed acquisition method for a spectrally sparse signal within a given spectral band. The received signal is mixed (820) during an acquisition frame with a train of pulses following one another with a repetition frequency linearly modulated in time within that frame. The resulting mixture is filtered (830) using a low-pass filter and sampled (840) at a non-uniform rate equal to the repetition frequency, to provide complex samples representative of the received signal. The spectrum of the received signal can be estimated by weighting the spectral values of a pulse into a plurality of frequencies equally distributed in the band using the complex samples, and summing these weighted values for each of these frequencies. An estimate of the received signal is thus obtained by inverse Fourier transform. The spectral band can also be scanned from the spectrum thus estimated.