Study On Target Detection Method In MIMO Radar Based On Free Probability Theory

MIMO (Multiple-Input Multiple-Output) radar has been concerned in recent yearsas a new type of radar system, and the target detection problem has receivedsignificant attention. While, traditional target detection for MIMO radar usuallyrequires the number of samples is greater than the number of sensors. If the number ofsamples and the the number of sensors are in the same order of magnitude, thetraditional method of signal processing that uses sample covariance matrix in asubstitute for statistical covariance matrix will no longer be suitable, as it will affactthe performance of the detection.As a hot research subject, nowadays, the random matrix theory has the naturaladvantages of processing the large dimensional matrix, its application in the field ofradar research has been focused by many international and domestic scholars. The freeprobability theory (FPT) is an important branch of random matrix theory, which hasbeen successfully applied in many fields.In this thesis, the FPT is creatively applied to target detection in MIMO radar,combining with related theory of random matrix, not only can it make a decision of“yes” or “no” to the target signal, but also count the number of target signals, andobtain the scattering coefficient of the radar target. In this thesis, the FPT is used tocalculate the eigenvalues of two mixed random matrix easily, to estimate the MIMOradar target scattering matrix. RCS is one of the most important indicators in thestealth and anti-stealth techniques, whose amplitude is the most basic parameter oftarget scattering characteristics. In this paper, we can obtain the number of targetsignals and accurately estimate the amplitude of the RCS at the same time, which issignificant for the further research on the radar target identification. In this paper, themain contributions are as follows:At first, the two calculation methods of the free convolution (including addictivefree convolution and multiplicative free convolution), i.e., the numerical calculationmethod and the non-numerical calculation method, are investigated in this thesis, andthe simulation experiments are carried out respectively. Also, the eigenvaluesdistribution of the sample covariance matrix is given and the reason of the error is the analyzed through the MMSE simulation of the moment of the sample covariancematrix.On this basis, the matrix model of the MIMO radar target detection is established.On the premise that random matrix is asymptotic freedom, the radar echo signal isrepresented by a large dimensional random matrix. The statistical covariance matrix isestimated according to the sample covariance matrix and the eigenvalues are extractedfrom the moment through Newton-Girard formula. Then, the detection of the RCSamplitudes of radar scattering for a single target or multiple targets is completed.This algorithm can be applied in the case of small samples. Using FPT, thestatistical covariance matrix is estimated based on its sample covariance matrix, whichis suitable for actual case. In addition, traditional detection methods usually requirethat noise power is known. However, this condition does not hold in practice. Underthe condition of unknown structure of received signal and unknown noise variance,we still can obtain the ideal results using the proposed method. Therefore, we come tothe conclusion that the algorithm can enhance the robustness of target detection forlarge scaled MIMO radars.