# On the Design of Constant Modulus Probing Waveforms with Good Correlation Properties for MIMO Radar via Consensus-ADMM Approach

## TL;DR

This paper develops a novel consensus-ADMM based method to design constant modulus MIMO radar waveforms with optimized correlation properties, ensuring convergence and computational efficiency.

## Contribution

It introduces a new non-convex consensus optimization framework and customized ADMM algorithms with theoretical convergence guarantees for waveform design.

## Key findings

- Proposed algorithms effectively optimize waveform correlation properties.
- Algorithms converge under proper parameter settings.
- Variants improve computational speed and efficiency.

## Abstract

In this paper, we design constant modulus probing waveforms with good correlation properties for collocated multi-input multi-output (MIMO) radar systems. The main content is as follows: first, we formulate the design problem as a fourth order polynomial minimization problem with constant modulus constraints. Then, by exploiting introduced auxiliary variables and their inherent structures, the polynomial optimization model is equivalent to a non-convex consensus minimization problem. Second, a customized alternating direction method of multipliers (ADMM) algorithm is proposed to solve the non-convex problem approximately. In the algorithm, all the subproblems can be solved analytically. Moreover, all subproblems except one subproblem can be performed in parallel. Third, we prove that the customized ADMM algorithm is theoretically-guaranteed convergent if proper parameters are chosen. Fourth, two variant ADMM algorithms, based on stochastic block coordinate descent and accelerated gradient descent, are proposed to reduce computational complexity and speed up the convergence rate. Numerical examples show the effectiveness of the proposed consensus-ADMM algorithm and its variants.