Quantum Radar Signal Processing
David Luong · 2023
Quantum radars use phenomena from quantum physics, such as quantum entanglement, to enhance detection performance compared with classical radars.This thesis presents an end-to-end analysis of an entanglement-based radar called quantum two-mode squeezing radar (QTMS radar).This type of radar is of particular interest because a QTMS radar experiment has actually been performed, and because QTMS radars are closely related to a type of classical radar known as noise radar (NR).As part of the analysis, we develop a mathematical theory of QTMS radars and show that QTMS radars and NRs can be united under a single probabilistic model.We then show how their signals are to be processed to determine the presence or absence of a target, and undertake an extensive analysis of the target detection performance of QTMS radars and NRs.These theoretical results are verified using data drawn from a QTMS radar experiment and a laboratory NR.One important conclusion, supported by both theory and experiment, is that the receiver operating characteristic curve for a QTMS radar is better than that of an NR with the same signal powers.Throughout the thesis, we emphasize the need to establish common ground between quantum physics and radar engineering, and it is hoped that the unified theory of QTMS radar and NR presented here will play a role in this. List of TablesCommon sense imagines that when it sees a table it sees a table.This is a gross delusion.Bertrand Russell The ABC of Relativity 2.1 A taxonomy of quantum sensors 11 5.1 System parameters for Wilson's QTMS radar experiment 104 6.1 QTMS radar variables and parameters 127 6.2 Rice distribution parameters fitted to simulated values of ρ ˆ145 6.3 Parameter estimates for Wilson et al.'s QTMS radar prototype 151 6.4 TVD between theoretical and experimental PDFs for the QTMS radar 152 6.5 Transmit powers and parameter values for the experimental NR 153 6.6 TVD between theoretical and experimental PDFs for the NR 156 7.1 Parameter values for the ROC curve plots 196 8.1 Correlation coefficient vs. transmit power: fit parameters 210 8.2 Correlation coefficient vs. range: fit parameters 218 8.3 Noise radar system parameters used in Example 8.10 232 8.4 QTMS radar system parameters used in Example 8.11 233 B.1 Relationships between probability distributions 281 xvi List of Figures As the Chinese say, 1001 words is worth more than a picture.John McCarthy 3.1 Time evolution of coherent states 64 3.2 Vacuum noise in a beam splitter 68 4.1 Target detection using a detector and a threshold 77 4.2 Probabilities of detection and false alarm for the envelope detector 78 4.3 ROC curves for the envelope detector 83 4.4 ROC curves for the NP detector (sinusoidal radar) compared with those for the envelope detector 92 5.1 Illustration of the basic QI protocol 95 5.2 Block diagram of Wilson's QTMS radar setup 102 5.3 Horn antennas used in the Wilson experiment 102 5.4 Interior and exterior of the dilution refrigerator 105 5.5 Interior of the can containing the JPA 106 5.6 Simplified diagram of a JPA 108 5.7 JPA mounted on a printed circuit board 109 5.8 Block diagram of the benchmark NR for the Wilson experiment 110 6.1 Correlation number line 135 6.2 Separable, entangled, and forbidden values of ρ as a function of σ 1 135 6.3 PDF of σ ˆ1 141 xvii LIST OF FIGURES xviii 6.4 Exact and approximate PDFs of ρ ˆ143 6.5 TVD between the exact and approximate PDFs of ρ ˆ146 6.6 Concentration parameter vs. Nρ 2 148 6.7 Exact and approximate PDFs of φ ˆ149 6.8 TVD between the exact and approximate PDFs of φ ˆ149 6.9 Theoretical and experimental PDFs for the QTMS radar 151 6.10 Theoretical and experimental PDFs for the experimental NR with transmit power -18.91 dBm 154 6.11 Theoretical and experimental PDFs for the experimental NR with transmit power -9.380 dBm 154 6.12 Theoretical and experimental PDFs for the experimental NR with transmit power 1.955 dBm 155 7.1 PDF of the NP detector (target present) 169 7.2 PDF of the NP detector (target absent) 170 7.3 LIST OF FIGURES xix 8.3 Correlation coefficient vs. range 8.4 ROC curves for the MF detector for various ranges 8.5 Correlation coefficient vs. range for an experimental NR 8.6 ROC curves for all detectors when ρ → 0 and N → ∞ 8.7 ROC curve for the MF detector when ρ → 0 and N → ∞: increasing ρ vs. increasing N 8.8 Probability of detection vs. Nρ 2 when ρ → 0 and N → ∞ 8.9 ROC curves for D MF and ρ ˆwhen ρ is large and N is small 8.10 ROC curves for the Wilson experiment, showing the increase in N required for the benchmark NR to match the QTMS radar 8.11 Maximum range vs. ρ 0 and N when p d = 0.9 and p fa = 10 -6 D.1 Simplified block diagram of the NR setup D.2 Photograph of the NR setup D.3 NR aimed at a wall D.4 Corner reflector used for the experiment in Section 8.2to x 0 in a given situation, without asserting that x = x 0 elsewhere.An index of symbols and abbreviations used in this thesis, together with the page at which each symbol or abbreviation is first defined, is included at page 262.The reader is encouraged to make liberal use of this index.