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

TL;DR

This paper investigates how non-contiguous Wi-Fi spectrum impacts multipath delay estimation, analyzing theoretical bounds and practical effects of frequency gaps on sensing accuracy and sidelobe behavior.

Contribution

It provides a detailed analysis of delay estimation in multiband Wi-Fi, deriving the CRLB for non-contiguous spectra and introducing a leakage metric to predict estimation challenges.

Findings

Larger frequency aperture improves delay resolution.

Frequency gaps cause sidelobes and secondary peaks.

A leakage metric predicts problematic delay separations.

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 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. Given the local nature of Cram\'er-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 Cram\'er-Rao lower bound analysis does not capture practical peak-leakage behavior in delay estimation.