Non-Contiguous Wi-Fi Spectrum for ISAC: Impact on Multipath Delay Estimation

TL;DR

The Cram\'er-Rao lower bound (CRLB) for delay separation is derived and analyzed, confirming the benefit of larger frequency aperture, while revealing pronounced, separation-dependent oscillations driven by gap geometry and inter-path coupling.

Abstract

Leveraging channel state information from multiple Wi-Fi bands can improve delay resolution for ranging and sensing when a wide contiguous spectrum is unavailable. However, frequency gaps shape the delay response, introducing sidelobes and secondary peaks that can obscure closely spaced multipath components. This paper examines multipath delay estimation for Wi-Fi-compliant multiband configurations using channel state information (CSI). For a two-path model with unknown complex gains and delays, the Cramér-Rao lower bound (CRLB) for delay separation is derived and analyzed, confirming the benefit of larger frequency aperture, while revealing pronounced, separation-dependent oscillations driven by gap geometry and inter-path coupling. Given the local nature of Cramér-Rao lower bound, the delay response is analyzed next. In the single-path case, the combined subband responses determine how delay-domain sidelobe levels are distributed. The dominant peak spacing is set primarily by the separation between subband center frequencies. In the two-path case, increased aperture sharpens the mainlobe but also intensifies sidelobes and leakage, yielding competing peaks and, in some regimes, a dominant peak shifted from the true delay. Finally, a normalized leakage metric is introduced to predict problematic separations and to identify regimes where local Cramér-Rao lower bound analysis does not capture practical peak-leakage behavior in delay estimation.

Figures (7)

• Figure 1: Illustration of Indoor Multipath Propagation for Multiband WiFi Sensing.
• Figure 2: Simulation scenarios A1-A3 and B1-B3 positioned within the European Wi-Fi channelization framework under ETSI regulations.
• Figure 3: Square-root CRLB of $\Delta\tau$ versus SNR for scenarios A1-A3 and B1-B3, shown for $\Delta\tau=1$ ns (top) and $\Delta\tau=10$ ns (bottom), with $\alpha_1=1$ and $\alpha_2=0.7e^{j\pi/3}$. Contiguous references are included for the gapped cases.
• Figure 4: Square-root CRLB of $\Delta\tau$ versus $\Delta\tau$ (ns) at SNR = 20 dB, with $\alpha_1=1$ and $\alpha_2=0.7e^{j\pi/3}$. Contiguous references are included for the gapped cases.
• Figure 5: Normalized single-path delay response $|g_s(\tau)|$ defined in \ref{['eq:gs_def']} for Groups A and B.