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IEEE Access

Quantum Two-Mode Squeezing Radar and Noise Radar: Correlation Coefficient and Integration Time

David Luong, Bhashyam Balaji, Sreeraman Rajan

Published Jan 1, 2020• 8 citations
Publisher

Abstract

Quantum two-mode squeezing (QTMS) radars and noise radars perform matched filtering of the received signal using a reference signal stored within the radar. Their target detection performance depends on the correlation between the received and reference signals, and the improved detection performance of QTMS radars over noise radars is due to the fact that it has an increased correlation. In this paper, we present a novel way of understanding how detection performance depends on the correlation by relating the correlation to the integration time. Concretely, we prove that increasing the correlation by a given factor is equivalent to increasing the integration time by the square of that factor. We apply this result to a recent QTMS radar experiment where the increase in correlation was approximately a factor of 3. This was found to be equivalent to increasing the integration time by a factor of 9, thus confirming the validity of our result and approximation.

DOI
10.1109/access.2020.3029473

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Quantum two-mode squeezing (QTMS) radars and noise radars perform matched filtering of the received signal using a reference signal stored within the radar. Their target detection performance depends on the correlation between the received and reference signals, and the improved detection performance of QTMS radars over noise radars is due to the fact that it has an increased correlation. In this paper, we present a novel way of understanding how detection performance depends on the correlation by relating the correlation to the integration time. Concretely, we prove that increasing the correlation by a given factor is equivalent to increasing the integration time by the square of that factor. We apply this result to a recent QTMS radar experiment where the increase in correlation was approximately a factor of 3. This was found to be equivalent to increasing the integration time by a factor of 9, thus confirming the validity of our result and approximation.
Quantum two-mode squeezing (QTMS) radars and noise radars detect targets by correlating the received signal with an internally stored recording. A covariance matrix can be calculated between the two which, in theory, is a function of a single correlation coefficient. This coefficient can be used to decide whether a target is present or absent. We can estimate the correlation coefficient by minimizing the Frobenius norm between the sample covariance matrix and the theoretically expected form of the matrix. Using simulated data, we show that the estimates follow a Rice distribution whose parameters are simple functions of the underlying, “true” correlation coefficient as well as the number of integrated samples. We obtain an explicit expression for the receiver operating characteristic curve that results when the correlation coefficient is used for target detection. This is an important first step toward performance prediction for QTMS radars.
For target detection, quantum two-mode squeezing (QTMS) radars and noise radars require estimation of a covariance matrix. A scalar function of the covariance matrix is then used for deciding the presence or absence of a target. In this paper, estimation of the covariance matrix is carried out by minimizing the Frobenius norm between the sample covariance matrix and the theoretically expected form of the matrix. Two scalars, a normalized correlation coefficient and an unnormalized cross-correlation, are used for detecting the target. Their performances are compared and found to be the same. Probability distributions are then fit to the histograms of these estimated correlations. Using these fitted distributions, expressions are obtained for receiver operating characteristic (ROC) curves that predict the performance of these functions in the task of deciding whether a target is present or not. This work is a first step toward understanding and modeling target detection performance of a QTMS radar or noise radar when using correlation-related measures as detector functions.
Recently, the authors have built and evaluated a prototype quantum radar in the laboratory which operates at microwave frequencies. This radar, which they call a quantum two‐mode squeezing radar (QTMS radar), generates a pair of entangled microwave signals and transmits one of them through free space, using the other signal as a reference to perform matched filtering. The specific type of entanglement is called a two‐mode squeezed vacuum, a type of continuous‐variable entanglement between two frequencies. Motivated by the success of these experiments, they try to better understand the entangled QTMS radar signals in this study. They do so by comparing it to a simpler, more conventional radar system, which they call a two‐mode noise radar (TMN radar). They also show how both types of radars are related to standard noise radars as described in the literature. They find that the signals for QTMS radar signals and TMN radar signals have the same mathematical form and that they are related to noise radar by a simple mathematical transformation. This shows that QTMS radar signals can be emulated by a fictional, idealised TMN radar and that it is possible to apply results from the noise radar literature to QTMS radar.
We analyze the signal-to-noise ratio (SNR) metric in the context of quantum two-mode squeezing (QTMS) radar and find that there are actually two SNRs associated with a QTMS radar, one for the received signal and another for a signal retained inside the radar. Definitions for these SNRs are proposed which are simpler than those hitherto used in the quantum radar literature. We plot receiver operating characteristic (ROC) curves for varying values of these two SNRs. These plots show that the quality of the matched filtering performed by the radar, as quantified by the SNR of the retained signal, can have a strong impact on detection performance.
In this paper, we provide a simple introduction to the enhancement achievable by quantum radars. We show that an important type of quantum radar, known as quantum two-mode squeezing (QTMS) radar, is mathematically connected to noise radars. The quantum advantage stems from QTMS radar’s ability to mitigate the effect of quantum noise, leading to greater contrast in the matched filter output between the target present and target absent cases. This reduced the integration time needed to detect a target. For imaging applications that rely on matched filtering, the quantum enhancement leads to a speedup in imaging as well.
Noise radars have the same mathematical description as a type of quantum radar known as quantum two-mode squeezing radar. Although their physical implementations are very different, this mathematical similarity allows us to analyze them collectively. We may consider the two types of radars as forming a single class of radars, called noise-type radars. The target detection performance of noise-type radars depends on two parameters: the number of integrated samples and a correlation coefficient. In this paper, we show that when the number of integrated samples is large and the correlation coefficient is low, the detection performance becomes a function of a single parameter: the number of integrated samples multiplied by the square of the correlation coefficient. We then explore the detection performance of noise-type radars in terms of this emergent parameter; in particular, we determine the probability of detection as a function of this parameter.