Robust fading channel estimation under parameter and process noise uncertainty with risk sensitive filter and its comparison with CRLB

As an alternative to Kalman filtering, a risk-sensitive filtering is proposed for a linear time-varying fading channel estimation problem and its robustness against the parameter and process noise uncertainty in the channel model is explored. The time-varying channel estimation problem is formulated as time varying Finite Impulse Response (FIR) filter with a known rectangular pulse at input and Gaussian noise corrupted signal at output. In time-varying FIR filter, estimation of time varying coefficients with uncertain condition is an important and critical task. In literature, Kalman filter (KF) based fading channel estimation approach has been studied and it has limitations that lead to inaccurate estimation when there is a high level of uncertainty in initial conditions and bias in system model and/or noise covariance. To overcome the above limitation, the risk sensitive filter (RSF) is proposed. In this work, bias in channel is considered to investigate the effect of risk/cost performance of channel estimation problems. The special feature of risk sensitive filter is it uses a risk factor/parameter in the exponential cost function, so that the probability density function of variable of interest to be estimated and to be reshaped with proper tuning of risk factor, thus robustness again uncertainty can be achieved. In this paper, with KF and RSF the robustness against uncertainty in channel model parameter and process noise covariance is presented. Numerical simulation result has been carried out and the Root Mean Square error (RMSE) with Monte Carlo runs is studied. In order to estimate the Channel parameter under uncertain conditions, the performance of risk sensitive filter is improved than the conventional Kalman filter. To investigate the theoretical performance, Cramer-Rao Lower Bound (CRLB) is applied and its channel estimation performance is compared with performance obtained by the filters. When uncertainty is present in parameter, the risk sensitive filter's performance is comparatively close to that of CRLB performance than the performance of Kalman Filter.