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Performance Bounds of Near-Field Sensing with Circular Arrays

Zhaolin Wang, Xidong Mu, Yuanwei Liu

Abstract

The performance bounds of near-field sensing are studied for circular arrays, focusing on the impact of bandwidth and array size. The closed-form Cramer-Rao bound (CRBs) for angle and distance estimation are derived, revealing the scaling laws of the CRBs with bandwidth and array size. Contrary to expectations, enlarging array size does not always enhance sensing performance. Furthermore, the asymptotic CRBs are analyzed under different conditions, unveiling that the derived expressions include the existing results as special cases. Finally, the derived expressions are validated through numerical results.

Performance Bounds of Near-Field Sensing with Circular Arrays

Abstract

The performance bounds of near-field sensing are studied for circular arrays, focusing on the impact of bandwidth and array size. The closed-form Cramer-Rao bound (CRBs) for angle and distance estimation are derived, revealing the scaling laws of the CRBs with bandwidth and array size. Contrary to expectations, enlarging array size does not always enhance sensing performance. Furthermore, the asymptotic CRBs are analyzed under different conditions, unveiling that the derived expressions include the existing results as special cases. Finally, the derived expressions are validated through numerical results.
Paper Structure (9 sections, 5 theorems, 32 equations, 6 figures)

This paper contains 9 sections, 5 theorems, 32 equations, 6 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Transmit Signal Model
  4. Receive Signal Model
  5. Performance Bounds and Analysis
  6. Cramér-Rao Bound
  7. Asymptotic CRBs
  8. Numerical Results
  9. Conclusion

Key Result

Lemma 1

If $N \gg 1$ and $R \le r$, the closed-form expressions of $u_{\theta}$, $u_r$, $c_{\theta}$, $c_r$, and $\eta$ can be derived as where $K(\alpha)$ is a transcendental function given by

Figures (6)

  • Figure 1: Geometry of the considered system.
  • Figure 2: The numerical results of function $\Xi(\frac{R}{r}, \frac{B}{f_c})$.
  • Figure 3: The numerical results of function $\Phi\left(\frac{R}{r}\right)$.
  • Figure 4: CRBs versus the number of subcarriers under the conditions of the fixed bandwidth of $B = 500$ MHz and the fixed subcarrier spacing of $1$ MHz, respectively.
  • Figure 5: CRBs versus the number of antennas under the conditions of the fixed aperture of $R = 0.5$ m and the fixed antenna spacing of $d = c/(2f_c)$, respectively.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Lemma 1
  • Theorem 1
  • Corollary 1
  • Corollary 2
  • Corollary 3