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MIMO Radar Meets Polarization-Reconfigurable Antennas: A BCRB Perspective

Jinpeng Xu, Shuowen Zhang

TL;DR

This work develops a PRA-aided MIMO radar framework that exploits polarization reconfigurability via phase shifter-based PRAs to sense an unknown angular location parameter with only prior distribution information. It derives the Bayesian Cramér-Rao bound (BCRB) for the angular location, then formulates a joint design of the transmit sample covariance ${m R}_X$ and the transmit/receive phase shifts to minimize the BCRB, solved efficiently by an alternating-optimization (AO) algorithm with closed-form updates. The proposed AO algorithm converges to a stationary point and demonstrates superior performance through simulations, achieving lower BCRB and better beampatterns than various benchmarks. The results illustrate the practical value of continuous polarization control for polarization diversity in low-complexity radar deployments.

Abstract

In this paper, we investigate a novel multiple-input multiple-output (MIMO) radar system aided by phase shifter based polarization-reconfigurable antennas (PRAs). Specifically, a base station (BS) equipped with multiple PRAs at both the transmitter and the receiver aims to sense the unknown and random angular location parameter of a point target via sending wireless signals and processing the received echo signals reflected by the target, where only prior distribution information about the location parameter is available for exploitation. Firstly, we characterize the sensing performance of this novel PRA-based MIMO radar system by deriving the Bayesian Cramér-Rao bound (BCRB) of the mean-squared error (MSE) in estimating the desired location parameter with prior distribution information. Then, to fully exploit the new design degrees-of-freedom (DoF) empowered by PRAs, we study the joint optimization of the transmit sample covariance matrix as well as the transmit and receive phase shift vectors to minimize the sensing BCRB subject to a transmit power constraint. This problem is non-convex and difficult to solve due to the coupling among optimization variables. To resolve this issue, we develop an alternating optimization (AO) based algorithm which iteratively obtains the closed-form optimal solution to each variable with the others being fixed at each time, thus being guaranteed to converge to at least a stationary point of the joint optimization problem. Numerical results validate the effectiveness of the proposed algorithm.

MIMO Radar Meets Polarization-Reconfigurable Antennas: A BCRB Perspective

TL;DR

This work develops a PRA-aided MIMO radar framework that exploits polarization reconfigurability via phase shifter-based PRAs to sense an unknown angular location parameter with only prior distribution information. It derives the Bayesian Cramér-Rao bound (BCRB) for the angular location, then formulates a joint design of the transmit sample covariance and the transmit/receive phase shifts to minimize the BCRB, solved efficiently by an alternating-optimization (AO) algorithm with closed-form updates. The proposed AO algorithm converges to a stationary point and demonstrates superior performance through simulations, achieving lower BCRB and better beampatterns than various benchmarks. The results illustrate the practical value of continuous polarization control for polarization diversity in low-complexity radar deployments.

Abstract

In this paper, we investigate a novel multiple-input multiple-output (MIMO) radar system aided by phase shifter based polarization-reconfigurable antennas (PRAs). Specifically, a base station (BS) equipped with multiple PRAs at both the transmitter and the receiver aims to sense the unknown and random angular location parameter of a point target via sending wireless signals and processing the received echo signals reflected by the target, where only prior distribution information about the location parameter is available for exploitation. Firstly, we characterize the sensing performance of this novel PRA-based MIMO radar system by deriving the Bayesian Cramér-Rao bound (BCRB) of the mean-squared error (MSE) in estimating the desired location parameter with prior distribution information. Then, to fully exploit the new design degrees-of-freedom (DoF) empowered by PRAs, we study the joint optimization of the transmit sample covariance matrix as well as the transmit and receive phase shift vectors to minimize the sensing BCRB subject to a transmit power constraint. This problem is non-convex and difficult to solve due to the coupling among optimization variables. To resolve this issue, we develop an alternating optimization (AO) based algorithm which iteratively obtains the closed-form optimal solution to each variable with the others being fixed at each time, thus being guaranteed to converge to at least a stationary point of the joint optimization problem. Numerical results validate the effectiveness of the proposed algorithm.

Paper Structure

This paper contains 14 sections, 28 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. PRA Model based on Phase Shifters
  4. MIMO Radar Model
  5. Characterization of Angular Location Estimation Performance via BCRB
  6. Problem Formulation
  7. Proposed Solution to Problem (P1)
  8. Optimization of $\bm{R}_X$ with Given $\bm\xi$ and $\bm\varphi$
  9. Optimization of $\varphi_m$ with Given $\bm{R}_X$, $\bm\xi$, $\{\varphi_\ell,\ell\neq m\}_{\ell=1}^M$
  10. Optimization of $\xi_n$ with Given $\bm{R}_X$, $\bm\varphi$, $\{\xi_\ell,\ell\neq n\}_{\ell=1}^N$
  11. Summary of the Proposed AO-based Algorithm
  12. Complexity Analysis
  13. Numerical Results
  14. Conclusions

Figures (4)

  • Figure 1: Illustration of a MIMO radar system with phase shifter based PRAs.
  • Figure 2: Convergence behavior of Algorithm \ref{['algo1']}.
  • Figure 3: Radiated power pattern and $p_\Theta(\theta)$ over different angles.
  • Figure 4: BCRB versus received SNR for proposed and benchmark schemes.