Delayed-pilot sampling for mixture Kalman filter with application in fading channels

Sequential Monte Carlo (SMC) methods are powerful techniques for online filtering of nonlinear and non-Gaussian dynamic systems. Typically dynamic systems exhibit strong memory effects, i.e., future observations can reveal substantial information about the current state. Recently, the delayed-sample sampling method has been proposed in the context of mixture Kalman filter (MKF), which makes use of future observations in generating samples of the current state. Although this method is highly effective in producing accurate filtering results, its computational complexity is exponential in terms of the delay, due to the need to marginalize the future states. In this paper, we address this difficulty by developing two new sampling schemes for delayed estimation, namely, delayed-pilot sampling and hybrid-pilot sampling. The basic idea of delayed-pilot sampling is that instead of exploring the entire space of future states, we generate a number of random pilot streams, each of which indicates what would happen in the future if the current state takes a particular value. The sampling distribution of the current state is then determined by the incremental importance weight associated with each pilot stream. The delayed-pilot sampling can be used in conjunction with the delayed-sample method, resulting in a hybrid scheme. This new sampling technique is then applied to solve the problem of adaptive detection and decoding in flat-fading communication channels. Simulation results are provided to demonstrate the performance of the new low-complexity sampling techniques for delayed estimation and to compare with the delayed-sample method.