CounterInterception and CounterExploitation Features of Noise Radar Technology
Abstract
:1. Introduction
2. PseudoRandom Numbers Generators and Cryptography Security
3. Information Content of Radar Signals
3.1. Mutual Information of a Random Process
3.2. On the Significance of MIR and SFM in Radar
 (a)
 Linear Frequency Modulation (LFM) pulse with duration $T$ such that $B\xb7T\gg 1$.
 (b)
 Noise Radar operation emitting noise waveforms with three cases:
 (b_{1})
 “natural” PeaktoAverage Power Ratio, $PAPR\ge 10$ (Gaussian process for the components I and Q);
 (b_{2})
 “low $PAPR$”, e.g., $PAPR=1.5$ (nonGaussian process for I and Q);
 (b_{3})
 “unimodular” waveform, $PAPR=1$ (nonGaussian process for I and Q).
4. Estimation of Entropy and Mutual Information by Simulation
4.1. “Natural” PAPR (Gaussian Process)
4.2. Controlled PAPR (NonGaussian Process)
5. Conclusions, Recommendations and Perspectives for Future Research
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
Appendix A
Appendix A.1. Entropy and Negentropy
Appendix A.2. SelfInformation and MutualInformation
Appendix B
Definition of a SecondOrder Stationary (SOS) Process
 (i)
 it is WSS, i.e., $\forall iE\left[{Z}_{i}\right]$ is constant and the covariance function $R\left(i,i+m\right)=E\left[{Z}_{i+m}{Z}_{i}^{*}\right]$ only depends on the index difference $m$, i.e.,$R\left(i,i+m\right)=R\left(m\right)$;
 (i)
 $\forall i$ the pseudo covariance function $\tilde{R}\left(i,i+m\right)=E\left[{Z}_{i+m}{Z}_{i}\right]$ only depends on the index difference $m$, i.e., $\tilde{R}\left(i,i+m\right)=\tilde{R}\left(m\right)$.
Appendix C
function E = EntropyEstimationHist(X1)
 function E = EntropyEstimationHist2D(X1,X2)

h = histogram(X1);  h = histogram2(X,X2); 
x = h.BinEdges;  x = h.XBinEdges; 
BinCount = h.BinCounts;  y = h.YBinEdges; 
zero = find(BinCount == 0);  stepx = x(2) − x(1); 
for k = 1:length(zero)
 stepy = y(2) − y(1); 
BinCount(zero(k)) = 1e − 18;  BinCount = h.BinCounts; 
end
 zero = find(BinCount == 0); 
BinCount = BinCount/sum(BinCount);  for k = 1:length(zero)

step = x(2) − x(1);  BinCount(zero(k)) = 1e − 18; 
E = log(step) − sum(BinCount.*log(BinCount));  end

end
 BinCount = BinCount/sum(sum(BinCount)); 
E = log(stepx*stepy) − sum(sum(BinCount.*log(BinCount)));  
end

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Spectrum  MIR  SFM 

Uniform  0.00  1.00 
Hamming  0.272  0.580 
BlackNuttall  1.258  0.081 
Spectrum  ${\sigma}_{1\left(2\right)}^{2}$  $h\left(X\right)$  ${S}_{1}^{2}$  ${S}_{2}^{2}$  $\widehat{h}\left({X}_{1}\right)$ $\mathrm{by}{S}_{1}^{2}$  $\widehat{h}\left({X}_{2}\right)$ $\mathrm{by}{S}_{2}^{2}$  $\widehat{h}\left({X}_{1}\right)$ by histogram  $\widehat{h}\left({X}_{2}\right)$ by histogram 
Uniform  0.5  1.0724  0.5004  0.5013  1.0727  1.0737  1.0723  1.0732 
Hamming  0.5  1.0724  0.5002  0.4994  1.0725  1.0718  1.0722  1.0718 
BlackNuttall  0.5  1.0724  0.4974  0.4970  1.0697  1.0703  1.0692  1.0697 
Spectrum  ${\rho}_{12}$  ${\widehat{\rho}}_{12}$  $h\left({X}_{1},{X}_{2}\right)$  $\widehat{h}\left({X}_{1},{X}_{2}\right)$ $\mathrm{by}{\widehat{\rho}}_{12}$  $\widehat{h}\left({X}_{1},{X}_{2}\right)$ by 2D hist.  $I\left({X}_{1},{X}_{2}\right)$  $\widehat{I}\left({X}_{1},{X}_{2}\right)$ $\mathrm{by}{\widehat{\rho}}_{12}$  $\widehat{I}\left({X}_{1},{X}_{2}\right)$ by 2D hist. 
Uniform  0  5.3·10^{−5}  2.1447  2.1447  2.1345  0  1.4·10^{−9}  0.0111 
Hamming  0.4258  0.4267  2.0447  2.0443  2.0338  0.10002  0.1005  0.1099 
BlackNuttall  0.6727  0.6681  1.8435  1.8491  1.8366  0.3013  0.2956  0.3024 
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Galati, G.; Pavan, G.; Savci, K.; Wasserzier, C. CounterInterception and CounterExploitation Features of Noise Radar Technology. Remote Sens. 2021, 13, 4509. https://doi.org/10.3390/rs13224509
Galati G, Pavan G, Savci K, Wasserzier C. CounterInterception and CounterExploitation Features of Noise Radar Technology. Remote Sensing. 2021; 13(22):4509. https://doi.org/10.3390/rs13224509
Chicago/Turabian StyleGalati, Gaspare, Gabriele Pavan, Kubilay Savci, and Christoph Wasserzier. 2021. "CounterInterception and CounterExploitation Features of Noise Radar Technology" Remote Sensing 13, no. 22: 4509. https://doi.org/10.3390/rs13224509