Compressed Sensing of Spectrally Sparse Signals Without ADC Overlap
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Solution Overview
Problem
Existing compressed sensing methods for wide RF bands require expensive and inefficient high-rate analog-to-digital converters to analyze signals, as they rely on non-uniform wavelet band-pass sampling with fixed pulse repetition frequencies, leading to high energy consumption and spectral overlap.
Innovation Solution
A method of modulating the repetition frequency of pulse trains over time within a sensing frame, allowing for lower average sampling rates by ensuring spectral sub-bands do not overlap, thus enabling the use of less expensive converters and reducing energy consumption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Use of energy by moving object
If non-uniform wavelet band-pass sampling with fixed pulse repetition frequencies is used, then signal reconstruction is achieved, but high-rate analog-to-digital converters are required leading to high energy consumption
Solution Approach 1:
The patent applies dynamics by making the pulse repetition frequency variable rather than fixed. The pulse train's repetition frequency is modulated over time according to a modulation signal, allowing the sampling rate to adapt dynamically. This dynamic approach enables the system to use lower average sampling rates while still capturing spectrally-sparse signal information effectively, thereby reducing energy consumption without sacrificing reconstruction quality.
Solution Approach 2:
The patent changes the parameter of pulse repetition frequency from a fixed value to a time-varying parameter. By modulating the repetition frequency according to a modulation signal, the system transforms the static sampling approach into a dynamic one. This parameter change allows the sampler to operate at lower rates on average while maintaining the ability to reconstruct spectrally-sparse signals, resolving the contradiction between energy consumption and measurement precision.
2Device complexity
If fixed pulse repetition frequency is used for compressed sensing, then signal sampling is simplified, but spectral overlap occurs reducing sensing efficiency
Solution Approach 1:
The patent resolves the spectral overlap issue by dynamically varying the pulse repetition frequency over time through modulation. This dynamic adjustment ensures that spectral replicas do not overlap, maintaining reliable spectral separation. The modulation approach adds minimal complexity to the sampling system while effectively preventing spectral overlap, thus improving reliability without significantly increasing device complexity.
3Measurement precision
If high-rate analog-to-digital converters are used to analyze wide RF bands, then signal analysis accuracy is improved, but cost and energy consumption increase
Solution Approach 1:
The patent changes the operating parameters of the sampling system by modulating the pulse repetition frequency. This allows the use of lower-rate, less expensive analog-to-digital converters while maintaining signal analysis accuracy for spectrally-sparse signals. The parameter modulation enables cost-effective hardware implementation without sacrificing measurement precision, as the time-varying sampling rate captures sufficient signal information for accurate reconstruction.
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 reconstruction of spectrally-sparse signals without high-rate converters, achieving reduced energy consumption and effective signal analysis across wide RF bands.
Implementation Method 1
the received signal is first amplified in a low-pass amplifier (LNA), 110, then mixed by means of a multiplier 120, with a pulse train (for example Morlet wavelets), pNUWBS(t)
Implementation Method 2
the result of mixing is filtered and amplified by an automatic gain control amplifier, 130, before being sampled
Data Source
AI summary
A method is provided for performing compressed sensing of a spectrally-sparse signal within a given spectral band. The received signal being mixed over a sensing frame with a pulse train scrolling with a repetition frequency linearly modulated over time within this frame. The result of mixing is filtered by low-pass filtering and sampled at a non-uniform rate equal to the repetition frequency, to result in complex samples representative of the received signal. The spectrum of the received signal can be estimated by weighting, using the complex samples, the spectral values of a pulse into a plurality of frequency equidistributed in the band, and by summing up these weighted values for each of these frequencies. An estimate of the received signal is thereby deduced by inverse Fourier transform. The spectral band can be scanned based on the spectrum thus estimated.