Performance Bounds and Optimization for CSI-Ratio based Bi-static Doppler Sensing in ISAC Systems

TL;DR

This work tackles clock asynchronism in CSI-ratio based bi-static ISAC by deriving a closed-form CRB for Doppler estimation under high-SNR and a tractable approximated CRB that reveals how system parameters affect sensing accuracy. It then develops OFDM-symbol optimization strategies to minimize the Doppler CRB in both noise- and interference-limited regimes, supported by ML validation. The proposed designs yield substantial improvements in Doppler accuracy, especially for low-speed targets, and provide practical waveform tools for networked sensing scenarios. Overall, the results offer a rigorous performance bound and actionable waveform design for CSI-ratio based bi-static Doppler sensing in PMN-style ISAC systems.

Abstract

Bi-static sensing is crucial for exploring the potential of networked sensing capabilities in integrated sensing and communications (ISAC). However, it suffers from the challenging clock asynchronism issue. CSI ratio-based sensing is an effective means to address the issue. Its performance bounds, particular for Doppler sensing, have not been fully understood yet. This work endeavors to fill the research gap. Focusing on a single dynamic path in high-SNR scenarios, we derive the closed-form CRB. Then, through analyzing the mutual interference between dynamic and static paths, we simplify the CRB results by deriving close approximations, further unveiling new insights of the impact of numerous physical parameters on Doppler sensing. Moreover, utilizing the new CRB and analyses, we propose novel waveform optimization strategies for noise- and interference-limited sensing scenarios, which are also empowered by closed-form and efficient solutions. Extensive simulation results are provided to validate the preciseness of the derived CRB results and analyses, with the aid of the maximum-likelihood estimator. The results also demonstrate the substantial enhanced Doppler sensing accuracy and the sensing capabilities for low-speed target achieved by the proposed waveform design.

Figures (10)

• Figure 1: The definition of the mainlobe, exemplifying two cases. (a) $K_\text{all} = K = 140$, and $\varphi_k=k$. (b) $K_\text{all} = 140$ , $K = 64$, and $\varphi_k$ follows (\ref{['Optimization_K_even']}).
• Figure 2: Illustration of the structure of $\bm{\varphi}$ in optimization algorithm, with $K_\text{all} = 32$, $K = 18$, $K_F = 5$, and $K_B = 4$, where $K_F + K_B = {K}/{2}$.
• Figure 3: Doppler CRBs (\ref{['proposition_aldfikhajkldihf_first_formula']}) and the MLE results versus $R_\text{SN}$.
• Figure 4: Doppler CRBs and the MLE results versus radial velocity, comparing CRB results in (\ref{['proposition_aldfikhajkldihf_first_formula']}) and (\ref{['CRB_closed_form_single_text']}).
• Figure 5: Doppler CRBs (\ref{['proposition_aldfikhajkldihf_first_formula']}) for Doppler versus $\theta_d$. (a) Doppler CRBs versus $\theta_d$; (b) Results of (\ref{['corollary_CRB_infinite_FORMULA_c']}) versus $\left|{{h_{s, 1}}/{h_{s, 0}}}\right|$; (c) Doppler CRBs versus $\sin\left(\theta_d\right)$.

Theorems & Definitions (16)

• Lemma 1
• Proposition 1
• Proposition 2
• proof
• Corollary 1
• proof
• Corollary 2
• proof
• Remark 1
• Corollary 3