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Optimal Transmit Signal Design for Multi-Target MIMO Sensing Exploiting Prior Information

Jiayi Yao, Shuowen Zhang

Abstract

In this paper, we study the transmit signal optimization in a multiple-input multiple-output (MIMO) radar system for sensing the angle information of multiple targets via their reflected echo signals. We consider a challenging and practical scenario where the angles to be sensed are unknown and random, while their probability information is known a priori for exploitation. First, we establish an analytical framework to quantify the multi-target sensing performance exploiting prior distribution information, by deriving the posterior Cramér-Rao bound (PCRB) as a lower bound of the mean-squared error (MSE) matrix in sensing multiple unknown and random angles. Then, we formulate and study the transmit sample covariance matrix optimization problem to minimize the PCRB for the sum MSE in estimating all angles. Moreover, we propose a sum-of-ratios iterative algorithm which can obtain the optimal solution to the PCRB-minimization problem with low complexity. Numerical results validate our results and the superiority of our proposed design over benchmark schemes.

Optimal Transmit Signal Design for Multi-Target MIMO Sensing Exploiting Prior Information

Abstract

In this paper, we study the transmit signal optimization in a multiple-input multiple-output (MIMO) radar system for sensing the angle information of multiple targets via their reflected echo signals. We consider a challenging and practical scenario where the angles to be sensed are unknown and random, while their probability information is known a priori for exploitation. First, we establish an analytical framework to quantify the multi-target sensing performance exploiting prior distribution information, by deriving the posterior Cramér-Rao bound (PCRB) as a lower bound of the mean-squared error (MSE) matrix in sensing multiple unknown and random angles. Then, we formulate and study the transmit sample covariance matrix optimization problem to minimize the PCRB for the sum MSE in estimating all angles. Moreover, we propose a sum-of-ratios iterative algorithm which can obtain the optimal solution to the PCRB-minimization problem with low complexity. Numerical results validate our results and the superiority of our proposed design over benchmark schemes.
Paper Structure (12 sections, 1 theorem, 25 equations, 5 figures, 1 algorithm)

This paper contains 12 sections, 1 theorem, 25 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Multi-Target Sensing Performance Characterization Exploiting Prior Information
  4. Derivation of FIM from Observation, $\bm{F}_{\mathrm{O}}$
  5. Derivation of FIM from Prior Information, $\bm{F}_{\mathrm{P}}$
  6. Derivation of PCRB of MSE for Sensing $\bm{\theta}$
  7. Problem Formulation
  8. Optimal Solution Structure to Problem (P1)
  9. Optimal Solution to Problem (P1) via Interior-Point Method for Semi-Definite Program (SDP)
  10. Optimal Solution to Problem (P1) via Sum-of-Ratios Iterative Algorithm
  11. Numerical Results
  12. Conclusions

Key Result

Proposition 1

For Problem (P1), an optimal transmit sample covariance matrix is $\boldsymbol{R}_{X}^{\star}=\sum_{n=1}^N{P_n\boldsymbol{q}_n\boldsymbol{q}_{n}^{H}}$, where $\sum_{n=1}^N{P_n}=P$ and $\boldsymbol{q}_n$ is the eigenvector corresponding to the strongest eigenvalue of $\sum_{m=1}^M{\boldsymbol{H}^\sta

Figures (5)

  • Figure 1: Illustration of multi-target MIMO sensing with prior information.
  • Figure 2: Convergence behavior of Algorithm 1.
  • Figure 3: Computation time of solving $\hbox{(P1)}$ using different algorithms.
  • Figure 4: Radiated power pattern and PDF of the targets over different angles.
  • Figure 5: PCRB with different transmit signal designs.

Theorems & Definitions (1)

  • Proposition 1