# Uncertainty Principle in Distributed MIMO Radars

## TL;DR

This paper explores how the radar uncertainty principle influences waveform design in distributed MIMO radars to optimize target localization accuracy, proposing a novel optimization approach and demonstrating its effectiveness through numerical analysis.

## Contribution

It introduces a new waveform design method based on the uncertainty principle, utilizing non-convex optimization and swarm algorithms for improved target parameter estimation.

## Key findings

- Global optimization achieves solutions at bounding box vertices.
- Proposed waveform design improves CRLB for target position and velocity.
- Numerical results validate the effectiveness of the optimization approach.

## Abstract

Radar uncertainty principle indicates that there is an inherent invariance in the product of the time-delay and Doppler-shift measurement accuracy and resolution which can be tuned by the waveform at transmitter. In this paper, based on the radar uncertainty principle, a conceptual waveform design is proposed for a distributed multiple-input multiple-output (MIMO) radar system in order to improve the Cramer-Rao lower bound (CRLB) of the target position and velocity. To this end, a non-convex band constrained optimization problem is formulated, and a local and the global solution to the problem are obtained by sequential quadratic programming (SQP) and particle swarm algorithms, respectively. Numerical results are also included to illustrate the effectiveness of the proposed mechanism on the CRLB of the target position and velocity. By numerical results, it is also concluded that the global solution to the optimization problem is obtained at a vertex of the bounding box.