Abstract
In this article, a framework is presented for the joint optimization of the analog transmit and receive filter with respect to a parameter estimation problem. At the receiver, conventional signal processing systems restrict the two-sided bandwidth of the analog pre-filter $B$ to the rate of the analog-to-digital converter $f_s$ to comply with the well-known Nyquist-Shannon sampling theorem. In contrast, here we consider a transceiver that by design violates the common paradigm $B\leq f_s$. To this end, at the receiver, we allow for a higher pre-filter bandwidth $B>f_s$ and study the achievable parameter estimation accuracy under a fixed sampling rate when the transmit and receive filter are jointly optimized with respect to the Bayesian Cram\'{e}r-Rao lower bound. For the case of delay-Doppler estimation, we propose to approximate the required Fisher information matrix and solve the transceiver design problem by an alternating optimization algorithm. The presented approach allows us to explore the Pareto-optimal region spanned by transmit and receive filters which are favorable under a weighted mean squared error criterion. We also discuss the computational complexity of the obtained transceiver design by visualizing the resulting ambiguity function. Finally, we verify the performance of the optimized designs by Monte-Carlo simulations of a likelihood-based estimator.
Highlights
T HE inference of unknown parameters is of interest in technical applications such as radar, sonar, image analysis, biomedicine or seismology
TRANSCEIVER OPTIMIZATION ALGORITHM In the following we focus on solving the transceiver design problem (18) with the approximate expected Fisher information matrix (EFIM) derived in the previous section
For the presented transceiver optimization framework we examine the Pareto-optimal set P = {(g(t), h(t))} of transmit and receive filters, for which the estimation of one parameter cannot be improved through the filter design without reducing the accuracy of the other parameter
Summary
T HE inference of unknown parameters is of interest in technical applications such as radar, sonar, image analysis, biomedicine or seismology. If a certain bandwidth B is available to the transmitter, fulfilling the Nyquist-Shannon theorem requires one to provide sufficiently large power and hardware resources at the receiver to perform sampling with fs ≥ B. Since high estimation accuracy rather than a low reconstruction error is the desired goal, compliance with the sampling theorem can be relaxed This leads to the fundamental question of how to design signal parameter estimation methods and systems when commonly used principles like the Nyquist-Shannon theorem are set aside
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