Research On Statistical Resolution Limit Of Signals

In radar,sonar and communication fields,the receiver often needs to distinguish between multiple target signals which are very close at distance,angle or speed etc,this type of signals essentially correspond to very close at the parameters of time delay,phase or frequency etc.The SRL of signals is an important index to describe the distance between the interest parameter when the adjacent target signals can be correctly resolved.The research of the SRL has the important theoretical guiding significance and practical value.Firstly,this dissertation studies one dimensional SRL and two dimensional SRL of two adjacent deterministic far-field signals and one dimensional SRL of two adjacent deterministic far-field signals in the context of interference based on the GLRT and the CRB.Since the computation complexity of the SRL based on the GLRT is high and the SRL based on CRB exists the defect of model limitation,secondly,an analysis method on the basis of the Rao test is puts forward for the one dimensional SRL and two dimensional SRL of two adjacent deterministic far-field signals.The main works of this thesis are as follows:1.The research background and the research status of the SRL are systematically expounded first.2.One dimensional SRL of two adjacent deterministic far-field signals under two cases of known noise variance and unknown noise variance are analyzed by using the GLRT,the CRB and the Rao test,and the performance of these three algorithms are compared in terms of the complexity of the algorithm,the detection probability and the signal to noise ratio.The simulation results show that the SRL based on the asymptotic distribution of the GLRT is proportional to the SRL based on CRB.The computational complexity of the SRL based on the Rao test is lower than that of the SRL based on the GLRT,and the performance of the Rao test is better than that of the GLRT.3.One dimensional SRL of two adjacent deterministic far-field signals under two cases of known noise variance and unknown noise variance in the context of interference are analyzed by using the GLRT,the CRB and the Rao test,and the performance of these three algorithms are compared in terms of the complexity of the algorithm,the detection probability and the signal to noise ratio.The simulation results show that the SRL based on the asymptotic distribution of the GLRT is proportional to the SRL based on CRB.The performance of the Rao test is better than that of the GLRT,and the computational complexity of the SRL based on the Rao test is lower than that of the SRL based on the GLRT.4.Two-dimensional SRL of random signals in MIMO systems is analyzed by using the GLRT,the CRB and Rao test.The simulation results show that the SRL based on the asymptotic distribution of the GLRT is proportional to the SRL based on CRB.The performance of the Rao test is better than that of the GLRT.