Joint Transmit and Receive Filter Optimization for Sub-Nyquist Wireless Channel Estimation

摘要

In this article a framework is presented for the joint optimization of theanalog transmit and receive filter with respect to a channel estimationproblem. At the receiver, conventional signal processing systems restrict thebandwidth of the analog pre-filter $B$ to the rate of the analog-to-digitalconverter $f_s$ in order to comply with the well-known Nyquist samplingtheorem. In contrast, here we consider a transceiver that by design violatesthe common paradigm $B\leq f_s$. To this end, at the receiver we allow for ahigher pre-filter bandwidth $B>f_s$ and study the achievable channel estimationaccuracy under a fixed sampling rate when the transmit and receive filter arejointly optimized with respect to the Bayesian Cram\'{e}r-Rao lower bound. Forthe case of a channel with unknown delay-Doppler shift we show how toapproximate the required Fisher information matrix and solve the transceiverdesign problem by an alternating optimization algorithm. The presented approachallows us to explore the Pareto-optimal region spanned by transmit and receivefilters which are favorable under a weighted mean squared error criterion. Wediscuss the complexity of the obtained transceiver design by visualizing theresulting ambiguity function. Finally, we verify the achievable performance ofthe proposed designs by Monte-Carlo simulations of a likelihood-based channelestimator.