  Multiband sensing is a promising technology that utilizes multiple
non-contiguous frequency bands to achieve high-resolution target sensing. In
this paper, we investigate the fundamental limits and optimization of multiband
sensing, focusing on the fundamental limits associated with time delay. We
first derive a Fisher information matrix (FIM) with a compact form using the
Dirichlet kernel and then derive a closed-form expression of the Cramer-Rao
bound (CRB) for the delay separation in a simplified case to reveal useful
insights. Then, a metric called the statistical resolution limit (SRL) that
provides a resolution limit is employed to investigate the fundamental limits
of delay resolution. The fundamental limits of delay estimation are also
investigated based on the CRB and Ziv-Zakai bound (ZZB). Based on the above
derived fundamental limits, numerical results are presented to analyze the
effect of frequency band apertures and phase distortions on the performance
limits of the multiband sensing systems. We formulate an optimization problem
to find the optimal system configuration in multiband sensing systems with the
objective of minimizing the delay SRL. To solve this non-convex constrained
problem, we propose an efficient alternating optimization (AO) algorithm which
iteratively optimizes the variables using successive convex approximation (SCA)
and one-dimensional search. Simulation results demonstrate the effectiveness of
the proposed algorithm.
