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Joint Transmission and Compression Optimization for Networked Sensing with Limited-Capacity Fronthaul Links

Weifeng Zhu, Shuowen Zhang, Liang Liu

TL;DR

The paper addresses networked sensing in a cellular ISAC framework where multiple BSs compress and forward echoes over limited fronthaul to a central unit for joint localization of multiple random targets. It derives a posterior Cramér-Rao bound (PCRB) as a function of the BS transmit covariances ${oldsymbol{R}}_n$ and compression covariances ${oldsymbol{Q}}_n$, and casts a non-convex PCRB-minimization problem under per-BS power and fronthaul constraints. An alternating optimization strategy with successive convex approximation (SCA) solves the joint transmit and compression design (Algorithms I–III), and a novel estimate-then-beamform-then-compress (EBC) scheme reduces complexity when the receive antennas are large by projecting to a $2K$-dimensional subspace using beamforming matrices ${oldsymbol{C}}_n={oldsymbol{E}}_r(oldsymbol{ heta}_n)$. Numerical results confirm significant PCRB improvements over baselines and demonstrate the practical benefits and scalability of the EBC strategy in massive MIMO settings.

Abstract

This paper considers networked sensing in cellular network, where multiple base stations (BSs) first compress their received echo signals from multiple targets and then forward the quantized signals to the central unit (CU) via limited-capacity fronthaul links, such that the CU can leverage all useful echo signals to perform high-resolution localization. Under this setup, we manage to characterize the posterior Cramer-Rao Bound (PCRB) for localizing all the targets with random positions as a function of the transmit covariance matrix and the compression noise covariance matrix of each BS. Then, a PCRB minimization problem subject to the transmit power constraints and the fronthaul capacity constraints is formulated to jointly design the BSs' transmission and compression strategies. We propose an efficient algorithm to solve this problem based on the alternating optimization technique. Specifically, it is shown that when either the transmit covariance matrices or the compression noise covariance matrices are fixed, the successive convex approximation (SCA) technique can be leveraged to optimize the other type of covariance matrices locally optimally. Moreover, we also propose a novel estimate-then-beamform-then-compress strategy for the massive receive antenna scenario, under which each BS first estimates targets' angle-of-arrivals (AOAs) locally, then beamforms its high-dimension received signals into low-dimension ones based on the estimated AOAs, and last compresses the beamformed signals for fronthaul transmission. An efficient beamforming and compression design method is devised under this strategy. Numerical results are provided to verify the effectiveness of our proposed algorithms.

Joint Transmission and Compression Optimization for Networked Sensing with Limited-Capacity Fronthaul Links

TL;DR

The paper addresses networked sensing in a cellular ISAC framework where multiple BSs compress and forward echoes over limited fronthaul to a central unit for joint localization of multiple random targets. It derives a posterior Cramér-Rao bound (PCRB) as a function of the BS transmit covariances and compression covariances , and casts a non-convex PCRB-minimization problem under per-BS power and fronthaul constraints. An alternating optimization strategy with successive convex approximation (SCA) solves the joint transmit and compression design (Algorithms I–III), and a novel estimate-then-beamform-then-compress (EBC) scheme reduces complexity when the receive antennas are large by projecting to a -dimensional subspace using beamforming matrices . Numerical results confirm significant PCRB improvements over baselines and demonstrate the practical benefits and scalability of the EBC strategy in massive MIMO settings.

Abstract

This paper considers networked sensing in cellular network, where multiple base stations (BSs) first compress their received echo signals from multiple targets and then forward the quantized signals to the central unit (CU) via limited-capacity fronthaul links, such that the CU can leverage all useful echo signals to perform high-resolution localization. Under this setup, we manage to characterize the posterior Cramer-Rao Bound (PCRB) for localizing all the targets with random positions as a function of the transmit covariance matrix and the compression noise covariance matrix of each BS. Then, a PCRB minimization problem subject to the transmit power constraints and the fronthaul capacity constraints is formulated to jointly design the BSs' transmission and compression strategies. We propose an efficient algorithm to solve this problem based on the alternating optimization technique. Specifically, it is shown that when either the transmit covariance matrices or the compression noise covariance matrices are fixed, the successive convex approximation (SCA) technique can be leveraged to optimize the other type of covariance matrices locally optimally. Moreover, we also propose a novel estimate-then-beamform-then-compress strategy for the massive receive antenna scenario, under which each BS first estimates targets' angle-of-arrivals (AOAs) locally, then beamforms its high-dimension received signals into low-dimension ones based on the estimated AOAs, and last compresses the beamformed signals for fronthaul transmission. An efficient beamforming and compression design method is devised under this strategy. Numerical results are provided to verify the effectiveness of our proposed algorithms.
Paper Structure (19 sections, 3 theorems, 56 equations, 10 figures, 3 tables)

This paper contains 19 sections, 3 theorems, 56 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Main Contributions
  4. Organizations and Notations
  5. System Model
  6. Posterior Cramér-Rao Bound for Localization
  7. Optimizing Transmission and Compression Strategies for PCRB Minimization
  8. Optimization of Transmission Covariance Matrices
  9. Optimization of Compression Noise Covariance Matrices
  10. Computational Complexity Analysis
  11. An Estimate-Then-Beamform-Then-Compress Strategy When $N_r$ is Large
  12. Receive Beamforming and Compression Design
  13. Computational Complexity Analysis
  14. Numerical Results
  15. Performance Evaluation of Algorithm III
  16. ...and 4 more sections

Key Result

Proposition 1

Define $\boldsymbol{F}_1$, $\boldsymbol{F}_2$, and $\boldsymbol{F}_3$ as (equ:F1) -- (equ:F3) on the top of the next page, where with $\dot{\boldsymbol{A}}_n = \left[\frac{\partial \boldsymbol{a}(\theta_{n,1})}{\partial \theta_{n,1}},\ldots,\frac{\partial \boldsymbol{a}(\theta_{n,K})}{\partial \theta_{n,K}}\right] \in \mathbb{C}^{M_r \times K}$, $\dot{\boldsymbol{V}}_n = \left[\frac{\partial \bol

Figures (10)

  • Figure 1: System model for networked sensing with limited-capacity fronthaul.
  • Figure 2: Sensing performance versus BSs' transmit power.
  • Figure 3: Sensing performance versus BSs' fronthaul capacity.
  • Figure 4: Sensing performance versus targets' number $K$.
  • Figure 5: Diagram of the cellular system with $7$ hexagonal cells and target distributions.
  • ...and 5 more figures

Theorems & Definitions (4)

  • Proposition 1
  • Remark 1
  • Proposition 2
  • Theorem 1