Lower Bound On Distributed Multi-antenna-varying Channel Characteristic Parameter Estimation

At the receiving side of distributed antenna systems, channel parameteracquisition is the key technology for synchronization and equalization. In general, thechannel characteristic parameters include fading, time delay and frequency offset.Nonlinear filtering method using sequential observation has been paid closeattention in such a challenging field. These filtering algorithms will be beneficial tothe design of receivers. Differed from the model that the three kinds of featureparameters are considered as quasi-static model in some symbol period, in this paper,according to the random time-varying parameters, it established two kinds ofchannel parameter lower bound based on the theory of nonlinear filtering lowerbound using known and unknown true values of the characteristic parameters,respectively. At first, when complex channel fading coefficients are known, frequencyoffsets show obviously nonlinear characteristics in its observation model, the lowerbound of frequency offsets are achieved. The specific method is to obtain thefirst-order Jacobi matrix at the real value, and then to calculate the Fisherinformation matrix using a recursive state transition probability density function andthe observation likelihood function. Afterwards, the lower bounds of complexchannel fading coefficients are obtained by the same way when the frequency offsetsare known. Next, a posterior lower bounds for joint estimation are built based onthree kinds of characteristic parameters. The simulation results show that the lowerbounds of all parameters are convergent with the increment of the number of theobserved values. When the three kinds of parameters are jointly estimated,frequency offsets have small effect on complex channel fading coefficients, and thelower bounds of frequency offsets are much smaller than complex channel fading.Process noise has much influence on the values of lower bounds. Moreover, whenthe variance of process noise magnitude exceeds to a certain value, filtering resultwill be divergent. Because the true values of the parameters cannot be achieved inthe process of filtering, on the assumption that the estimated value complex channelfading coefficients is known and frequency offsets estimated value is known, the approximate lower bound of channel parameters are built. The specific method is tospread the observation function into two orders Taylor series using Kalman estimates,then to obtain the Hessian matrix and conditional mean and the conditional variance.Next, the approximate lower bound can be achieved by a recursive state transitionprobability density function and the observation likelihood function. The simulationresults show that the approximate lower bound of channel fading is larger than theCramer-Rao lower bound because of the estimating error. The approximate lowerbound of frequency offsets is larger than the Cramer-Rao lower bound because ofthe additional part of the conditional variance.