New Theory Of Cramér-Rao Lower Bound For Gaussian Estimation And Applications To Wireless Communications

In order to meet the increasing demand of users for wireless communication services,improving the performance of communication system has become the goal of the new generation of wireless communication system.In different application scenarios,the complexity and diversity of wireless channels bring great challenges to the detection and estimation of signals.We need higher performance receivers to suppress the impact of various complex interference.In different application scenarios,the complexity and diversity of wireless channels bring great challenges to the detection and estimation of signals.We need higher performance receivers to suppress the impact of various complex interference.Among them,one of the core methods to solve the above problems is to build an accurate estimator to improve the accuracy of parameter estimation of noisy signals.The Cramér-Rao lower bound(CRLB),as the performance standard of the estimator,assists the optimization and design of the parameter estimation method,which is of great significance for the design of wireless communication system.The traditional time discrete CRLB depends on the strict independent hypothesis of the observation samples,but in the actual communication system,it is often unable to guarantee the possibility of obtaining the independent samples.In this thesis,based on CRLB of scalar parameter estimation,CRLB for vector parameter estimation in Gaussian white noise is proposed.The application of continuous CRLB expressed by the energy of derivative signal are analyzed in time delay parameter and amplitude parameter estimation.In the problem of signal pulse timing recovery,the performance is analyzed and the pulse is selected using the lower bound.At the same time,the Hybrid CRLB on Time Delay Estimation in Nakagami-m(m<1)fading channel is analyzed.The main research work of this thesis is summarized as follows:(1)CRLB analysis in Gaussian white noise and the construction of its vector form:This thesis first analyzes the filtering characteristics and autocorrelation function characteristics of three commonly used filters to prove that independent samples can not always be obtained from the observed noise signals.This shows that the sample independence assumption based on the traditional CRLB is difficult to meet in actual communication systems.In this thesis,in the Gaussian white noise environment,based on the traditional Cramér-Rao lower bound for scalar parameter estimation,a CRLB for signal vector parameter estimation is proposed,which expression is based on the energy of derivative signal.Then,by analyzing several application examples of CRLB of signal parameter estimation in Gaussian white noise,this thesis proves that CRLB with the ratio of the energy of derivative signal to the noise power spectral density can reflect the relationship between influence factors,the parameters in CRLB and CRLB more clearly than CRLB with the signal to noise ratio.(2)Application of continuous CRLB in pulse shaping:This thesis first introduces the better than raised cosine pulse based on the ideal low-pass characteristic pulse and raised cosine pulse.Then CRLB theory is applied to the analysis of the timing recovery performance of the signal pulse and the selection,which proves that the advantages of the improved raised cosine pulse compared to the ordinary raised cosine pulse in terms of distortion rate and bit error rate are not at the expense of timing recovery performance.When the excess bandwidth is less than 0.25,its timing recovery performance will be better than the ordinary raised cosine pulse signal.(3)Hybrid CRLB on Time Delay Estimation in Nakagami-m(m<1)fading channel:This thesis studies the estimation of time delay parameters in Nakagami-m(m<1)fading channel under Gaussian white noise,and proposes Hybrid CRLB for the joint estimation of time delay parameter(deterministic parameter)and channel gain(random parameter).