Research On Mutual Information Of Radar Detection System

With the development of radar technology,radar target detection technology has received more and more attention and radar detection system plays an increasingly important role in national defense construction and national economic construction.At present,the research on the application of information theory to radar field mainly focuses on the design of radar signal waveforms.For describing the process of radar target detection with information theory,scholars at home and abroad have explored actively,however,a unified information theory system has not been formed yet.In this paper,we employ the thoughts and methodologies of Shannon's information theory to study radar target detection system and establish information of target detection through theoretical derivation.We research distance information and amplitude-phase information in which the scattering coefficient of the target is constant and obeys Rayleigh distribution and the target is distributed uniformly in the observation range.The main work and innovations are as follows:1.For two different target models,which are constant scattering coefficient target and Rayleigh scattering coefficient target,we derive the expression between detection statistics vector and position vector,amplitude-phase vector with the methodologies of Shannon's information theory,which explains that detection is the process of obtaining information of target and bit can be used to measure target information in theory.2.For a single target radar detection system,we derive the theoretical formula of distance information and amplitude-phase information under two different target models.If scattering coefficient of targets obeys Rayleigh distribution and phase of targets obeys uniform distribution,theoretical analysis shows that distance information is proportional to both logarithm of Time-Bandwidth Product(TBP)and Signal-to-Noise Ratio(SNR)and amplitude-phase information is proportional to the logarithm of SNR.The simulation results of maximum likelihood algorithm show that Cramér-Rao Bound is the upper bound of distance information in radar detection.3.For a multi-target radar detection system,we derive the theoretical expression of information for constant targets and Gaussian targets.Particularly,multi-target joint distance information and amplitude-phase information of radar system both are multiple of that in a single situation if there is no interference between any targets.While we also derive Cramér-Rao Bound of two Gaussian targets.What is different is that we redefine range resolution from the perspective of radar information theory and obtain upper bound of resolution at different SNR,which breaks through the limitations of bandwidth of traditional radar resolution.The simulation results show that distance information gradually reduces as the distance between targets decreases,the decrease rate in unit bandwidth is greater than that outside unit bandwidth and distance information reaches the minimum when two targets coincide.