Wideband frequency-hopping measurement is crucial for the stable operation of frequency-hopping communication systems. Traditional digital signal processing methods based on the Nyquist-Shannon sampling theorem are limited by bandwidth. Although compressed sensing reduces the sampling rate for analog-to-digital converters, its reliance on high-speed pseudo-random sequences restricts practical applications. In this paper, we propose a wideband frequency-hopping measurement method based on quantum compressed sensing, which enables dynamic capture of wideband frequency-hopping signals. By utilizing coherent state as quantum resources and mapping frequency-hopping signal onto photonic wave functions via an electro-optical modulator, a compressive measurement system is constructed that leverages the inherent randomness of coherent photon measurement collapse, and successfully achieved measurement and reconstruction of a frequency-hopping signal with 5 GHz bandwidth and a hopping rate of 100 kHop/s. A high data compression ratio of 2.1 × 10 3 was attained at a frequency-hopping rate of 1 kHop/s. By integrating time-frequency analysis methods with Bayesian optimization algorithm for frequency-hopping parameter estimation, a time estimation accuracy of 1 μs is achieved. Our research offers what we believe to be a new solution for wideband frequency-hopping measurement and can be extended to various fields such as radar and cognitive radio.
Wideband frequency-hopping measurement is crucial for the stable operation of frequency-hopping communication systems. Traditional digital signal processing methods based on the Nyquist-Shannon sampling theorem are limited by bandwidth. Although compressed sensing reduces the sampling rate for analog-to-digital converters, its reliance on high-speed pseudo-random sequences restricts practical applications. In this paper, we propose a wideband frequency-hopping measurement method based on quantum compressed sensing, which enables dynamic capture of wideband frequency-hopping signals. By utilizing coherent state as quantum resources and mapping frequency-hopping signal onto photonic wave functions via an electro-optical modulator, a compressive measurement system is constructed that leverages the inherent randomness of coherent photon measurement collapse, and successfully achieved measurement and reconstruction of a frequency-hopping signal with 5 GHz bandwidth and a hopping rate of 100 kHop/s. A high data compression ratio of 2.1 × 10 3 was attained at a frequency-hopping rate of 1 kHop/s. By integrating time-frequency analysis methods with Bayesian optimization algorithm for frequency-hopping parameter estimation, a time estimation accuracy of 1 μs is achieved. Our research offers what we believe to be a new solution for wideband frequency-hopping measurement and can be extended to various fields such as radar and cognitive radio.
Real-time sensing of ultra-wideband radio-frequency signal with high frequency resolution is challenging, which is confined by the sampling rate of electronic analog-to-digital converter and the capability of digital signal processing. By combining quantum mechanics with compressed sensing, quantum compressed sensing is proposed for wideband radio-frequency signal frequency measurement. By using an electro-optical crystal as a sensor which modulates the wave function of the coherent photons with the signal to be measured. The frequency spectrum could be recovered by detecting the modulated sparse photons with a low time-jitter single-photon detector and a time-to-digital converter. More than 50 GHz real-time analysis bandwidth is demonstrated with the Fourier transform limit resolution. The further simulation shows it can be extended to more than 300 GHz with the present technologies.
With the rapid development of radio frequency technology such as radar, electronic warfare and 5G communication, the measurement and real-time spectrum characterization of broadband radio frequency signals become increasingly important. The traditional radio frequency signal real-time measurement technology is limited by the sampling rate of analog-to-digital converter and the ability to process digital signals, and encounters the problems of narrow measurement band, large data volume, and susceptibility to electromagnetic interference. This work is to study a radio frequency signal measurement technology based on quantum compression sensing, which uses integrated electro-optical crystal as radio frequency sensor, and constructs a compression sensing machine by modulating the photon wave function of the measured radio frequency signal to realize the compression measurement of broadband radio frequency signal, significantly improving the spectrum sensing bandwidth. The experiment demonstrates the long-term spectrum monitoring of power frequency and intermediate frequency high voltage signals, and the real-time spectrum measurement of high frequency radio frequency signals. Under the Fourier limit spectrum resolution, the real-time spectrum analysis bandwidth of GHz magnitude is realized, and the data compression rate reaches 1.7×10–5, which can meet the needs of 5G wireless communication, cognitive radio and other applications for broadband radio frequency signal spectrum measurement, and provide a new technical path for developing the next-generation broadband spectrum sensing technology.
How many measurements are fundamentally required to capture a signal. Shannon's information theory established the bedrock of this question in 1948, the Nyquist Shannon theorem set the first answer, and compressed sensing (CS) rewrote it in 2006 by reducing the required measurement number to M = O(Klog(N/K)) for a K sparse signal. Here, we propose quantum compressed sensing (QCS), a paradigm that reframes signal acquisition as a unitary quantum evolution. By encoding high dimensional signal information into a single quantum probe state, then introducing domain-alignment evolution,a physically realizable unitary transformation that maps the sparse basis directly onto the measurement basis. QCS executes the support-set search at the quantum level without consuming measurement trials. The logarithmic penalty vanishes, compressing the required measurement number from the classical bound to M =O(K) and reducing reconstruction from ill posed optimization to linear estimation. We experimentally validate QCS using frequency and time domain sparse signals, confirming that the measurement number scales linearly with sparsity and decouples entirely from the signal dimension. Our work provides a physical pathway toward ultimate information acquisition efficiency, with broad implications for sensing, imaging, and communication.
We propose a novel, to the best of our knowledge, approach to realizing instantaneous frequency measurement with ultrahigh measurement bandwidth, which utilizes three-channel photonic compressive sensing (CS) with sub-Nyquist pseudo-random binary sequences (PRBSs). In each CS channel, an alias frequency is recovered due to the sub-Nyquist property of the applied PRBS. A frequency identification algorithm is employed to determine the frequency of the signal under measurement according to the three alias frequencies. The proposed approach significantly reduces the bit rate of the applied PRBSs and the sampling rate required by the digitizers in CS. A proof-of-concept experiment for measuring frequency in the Ku band is demonstrated using PRBSs at 1 Gb/s and digitizers with a sampling rate of 250 MS/s.
Compressive sensing is a novel approach that linearly samples sparse or compressible signals at a rate much below the Nyquist-Shannon sampling rate and outperforms traditional signal processing techniques in acquiring and reconstructing such signals. Compressive sensing with matrix uncertainty is an extension of the standard compressive sensing problem that appears in various applications including but not limited to cognitive radio sensing, calibration of the antenna, and deconvolution. The original problem of compressive sensing is NP-hard so the traditional techniques, such as convex and nonconvex relaxations and greedy algorithms, apply stringent constraints on the measurement matrix to indirectly handle this problem in the realm of classical computing. We propose well-posed approaches for both binary compressive sensing and binary compressive sensing with matrix uncertainty problems that are tractable by quantum annealers. Our approach formulates an Ising model whose ground state represents a sparse solution for the binary compressive sensing problem and then employs an alternating minimization scheme to tackle the binary compressive sensing with matrix uncertainty problem. This setting only requires the solution uniqueness of the considered problem to have a successful recovery process, and therefore the required conditions on the measurement matrix are notably looser. As a proof of concept, we can demonstrate the applicability of the proposed approach on the D-Wave quantum annealers; however, we can adapt our method to employ other modern computing phenomena -like adiabatic quantum computers (in general), CMOS annealers, optical parametric oscillators, and neuromorphic computing.
Quantum imaging based on entangled light sources exhibits enhanced background resistance compared to conventional imaging techniques in low-light conditions. However, direct imaging of dynamic targets remains challenging due to the limited count rate of entangled photons. In this paper, we propose a quantum imaging method based on quantum compressed sensing that leverages the strong correlation characteristics of entangled photons and the randomness inherent in photon pair generation and detection. This approach enables the construction of a compressed sensing system capable of directly imaging high-speed dynamic targets. The results demonstrate that our system successfully achieves imaging of a target rotating at a frequency of 10 kHz, while maintaining an impressive data compression rate of 10 −6 . This proposed method introduces a pioneering approach for the practical implementation of quantum imaging in real-world scenarios.