Optimizing Frequency Switching Pattern to Reduce Asynchronization Effect in MCPD Ranging Systems

Accurate distance estimation in two-way multi-carrier phase difference (MCPD) ranging systems is degraded by carrier frequency offset (CFO) and timing discrepancies caused by asynchronized clocks between nodes. In previous work, carrier frequencies were typically utilized in ascending order during the MCPD process, a method referred to as sequential switching (SS) frequency switching pattern (FSP). Under asynchronous conditions, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SS</i> FSP induces a linear phase trend across the frequency spectrum, resulting in systematic biasing. Existing works address this problem by estimating and compensating for the phase shifts caused by the asynchronization, but introduce additional computational complexity, latency, and power consumption. In this paper, we present a new signal model accounting for the relevant hardware imperfections, characterizing the effects of asynchronization on the phase measurements, and highlighting the limitations of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SS</i> FSP. Building on this analysis, we propose rearranging carrier frequencies in the FSP and introduce a set of novel FSPs that eliminate the linear phase trend across the frequency spectrum and reduce the estimation error without requiring estimation or correction procedure. The results of the simulation study show that the proposed FSPs outperform the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SS</i> FSP under different oscillator mismatches achieving sub-centimeter systematic error at high signal-to-noise ratios (SNR), with performance gain decreasing with decreasing SNR and performance variability occurring with different numbers of carriers. Real-world experimental validation confirms a strong agreement between simulated and measured channel impulse responses and that the proposed FSPs produce more robust distance estimates to CFO variations than the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SS</i> FSP.