On OFDM Ranging Performance Degradation in Multipath Scenarios

Abstract

Multipath propagation represents a dominant error source limiting the accuracy of radio-based ranging and positioning in urban environments. Conventional ranging estimators typically estimate only the range of the first arriving path while neglecting the multipath components. This introduces a bias and causes the estimator's variance to diverge from the Cramér-Rao Bound (CRB). While extensive research has established performance bounds for estimators that jointly estimate all paths, the specific impact on the variance of ignoring these components remains largely unexplored. This paper derives bounds on the bias, variance, and mean square error (MSE) for ranging in multipath channels for the purpose of positioning. We consider Orthogonal Frequency Division Multiplexing (OFDM) signals in multipath channels with deterministic path delays and gains. The paper focuses on time-delay estimation (TDE) in the mid-to-high signal-to-noise ratio (SNR) regime under two scenarios: (i) when the receiver jointly estimates all propagation paths, and (ii) when the receiver underestimates the number of paths. Specifically, for the latter case, we derive a semi closed-form expression for the variance of the time-delay estimator that considers a single-path when in reality there are L paths. This derivation is based on the misspecified Cramér-Rao bound (MCRB). Although unmodelled multipath has been traditionally viewed as detrimental to time-delay estimation, we reveal that in some cases the estimation variance improves. For a two-path channel we show that the variance depends on the relative gain, carrier phase, and separation of the paths. Additionally, the estimation bias is upper-bounded by constructive and destructive path interference. Finally, we empirically process a six-path simulated channel frequency response with fixed path delays and gains, to demonstrate that the derived MSE bound is tight for mid-to-high SNRs. This work characterizes the impact of multipath propagation on the variance of time-delay estimation, which is essential for designing accurate ranging signals and estimators in urban scenarios.