Approximation of the Range Ambiguity Function in Near-field Sensing Systems

TL;DR

This work addresses range-angle resolution in radiative near-field sensing with large NF arrays by deriving the matched-filter ambiguity function and proposing a separable approximation: $\mathcal{A}(\mathbf{p}',\mathbf{p}) \approx \chi_B(\mathbf{p}',\mathbf{p}) \mathrm{AF}_{\mathcal{M}}(\mathbf{p}',\mathbf{p}) \mathrm{AF}_{\mathcal{N}}(\mathbf{p}',\mathbf{p})$. It provides closed-form NF AF for four common geometries (ULA, UCA, URA, UPCA) and establishes a bandwidth-aperture product constraint that ensures the separation remains accurate. The analysis reveals geometry-dependent improvements in PSL and ISL from near-field beamfocusing, particularly at shorter ranges, and shows how bandwidth can compensate for poor NF sidelobe performance in bandwidth-limited regimes. The findings offer practical guidance for designing NF sensing systems and OFDM-based implementations to achieve uniform sidelobe performance while balancing aperture size and available bandwidth. Overall, the paper quantifies the trade-offs between near-field beamfocusing and bandwidth in shaping resolution, PSL, and ISL across array geometries, with gains diminishing as distance grows from the array.

Abstract

This paper investigates the range ambiguity function of near-field systems where bandwidth and near-field beamfocusing jointly determine the resolution. First, the general matched filter ambiguity function is derived and the near-field array factors of different antenna array geometries are introduced. Next, the near-field ambiguity function is approximated as a product of the range-dependent near-field array factor and the ambiguity function due to the utilized waveform and bandwidth. An approximation criterion based on the aperture-bandwidth product is formulated, and its accuracy is examined. Finally, the improvements to the ambiguity function offered by the near-field beamfocusing, as compared to the far-field case, are presented. The performance gains are evaluated in terms of resolution improvement offered by beamfocusing, peak-to-sidelobe and integrated-sidelobe level improvement for a few popular array geometries. The gains offered by the near-field regime are shown to be range-dependent and substantial only in close proximity to the array.

Figures (12)

• Figure 1: Array factor per geometry for $D=50 \lambda$ a target located at at $80 \lambda$.
• Figure 2: Comparison of the exact and approximated array factor per geometry for $D=50\lambda$ and target located at $d'_{\min} = 60\lambda$.
• Figure 3: Beamdepth as a function of distance for two array aperture sizes and selected array geometries.
• Figure 4: Comparison of the SIMO/MISO OFDM ambiguity function for different array geometries and values of $B_{\mathrm{f}} D_{\lambda}$ product, for $K=1024$, $D_{\lambda} = 50 \lambda$ and target at $d_{\min} = 60 \lambda$.
• Figure 5: Comparison of the MIMO OFDM ambiguity function for different array geometries and values of $B_{\mathrm{f}} D_{\lambda}$ product, for $K=1024$, $D_{\lambda} = 25 \lambda$ and target at $d_{\min} = 30 \lambda$.