3 research outputs found
Joint Transmit and Receive Filter Optimization for Sub-Nyquist Delay-Doppler Estimation
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 to the rate of the
analog-to-digital converter to comply with the well-known Nyquist-Shannon
sampling theorem. In contrast, here we consider a transceiver that by design
violates the common paradigm . To this end, at the receiver, we
allow for a higher pre-filter bandwidth 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.Comment: 15 pages, 16 figure
Analog transmit signal optimization for Undersampled delay-Doppler estimation
In this work, the optimization of the analog transmit waveform for joint delay-Doppler estimation under sub-Nyquist conditions is considered. Based on the Bayesian Cramér-Rao lower bound (BCRLB), we derive an estimation theoretic design rule for the Fourier coefficients of the analog transmit signal when violating the sampling theorem at the receiver through a wide analog pre-filtering bandwidth. For a wireless delay-Doppler channel, we obtain a system optimization problem which can be solved in compact form by using an Eigenvalue decomposition. The presented approach enables one to explore the Pareto region spanned by the optimized analog waveforms. Furthermore, we demonstrate how the framework can be used to reduce the sampling rate at the receiver while maintaining high estimation accuracy. Finally, we verify the practical impact by Monte-Carlo simulations of a channel estimation algorithm