Research On Finite Random Matrix Methods For Target Detection In Transmit Diversity MIMO Radar

Transmit diversity multiple-input-multiple-output(MIMO)radar can transmit signals by multiple transmit diversity antennas and receive echo signals by a multi-antenna array.Due to the large spacing between the transmitting antenna elements and the fact that the signals are uncorrelated with each other,the radar cross section(RCS)of the target is approximately constant.It has obvious advantages in terms of target detection,and its signal processing method has received extensive attention.A series of traditional methods have been proposed to improve the performance of MIMO radar target detection.Although these methods improve the detection performance,they still have the following defects: The first is to know the priori information such as the target scattering matrix and noise variance,which belongs to the non-blind detection method.Second,it is necessary to assume that the number of snapshots is much greater than the number of array elements.When the numbers of array elements and snapshots are in the same order of magnitude,it is no longer applicable.In order to solve the above problems,in recent years,we have applied the random matrix theory(RMT)to MIMO radar target detection to achieve blind target detection without prior knowledge.However,since the RMT method is based on the asymptotic spectrum theory,it is suitable for the case that the number of snapshots and the number of elements are large enough.In practical applications,they are often limited.In this situation,there will be deviations in using the RMT method.In this thesis,the finite-dimensional random matrix theory(FRMT)is combined with the target detection of transmit diversity MIMO radar,and new target detection algorithms are proposed for the situation that both the number of snapshots and the number of array elements are seriously deficient.The main innovative work of this article is as follows:A target detection algorithm for transmit diversity MIMO radar is proposed based on finite dimensional random matrix theory-standard condition number(FRMT-SCN).This algorithm considers that the number of received array elements and the number of snapshots are both small and close to each other.It uses the SCN,which is the ratio of the maximum and minimum eigenvalues of the echo signal sample covariance matrix as the detection statistic,and uses the exact distribution expression of the Wishart matrix SCN in the FRMT to obtain the decision threshold.The simulation results verify the detection performance of the proposed FRMT-SCN algorithm and the influence of the number of transmit diversity on the detection probability is analyzed.The algorithm can solve the problem that the numbers of snapshots and array elements are in the same order of magnitude and are severely deficient,and the blind detection can be achieved.However,this algorithm is only applicable to the case that there are two received array elements.A target detection algorithm for transmit diversity MIMO radar is proposed based on finite dimensional random matrix theory-joint eigenvalue distribution(FRMT-JED).The algorithm uses the largest eigenvalue of the echo signal sample covariance matrix as the detection statistic.Based on the joint eigenvalue distribution(JED)of Wishart matrix in FRMT,the exact distribution expression of the maximum eigenvalue of the sample covariance matrix is derived.This method is suitable for more than two receiving array elements.However,when the number of array elements is relatively large,the computational complexity will also increase.Aiming at the large computational complexity of the FRMT-JED algorithm,a target detection algorithm for transmit diversity MIMO radar is proposed based on FRMT-dual extremes JED.In the algorithm,the average of the maximum and minimum eigenvalues of the sample covariance matrix is used as the test statistic,and applies the JED of dual eigenvalue extremes of Wishart matrix in FRMT is applied to derive its exact distribution expression to obtain the decision threshold.Since no matrix calculation is required,it can greatly reduce computational complexity and achieve blind detection.