Sensitivity of RMS Delay Spread Estimation to Power Delay Profile Thresholding in Time-Varying Channels at 33 GHz

I. INTRODUCTION

• RMS delay spread is the square root of the PDP delay distribution’s second central moment and helps assess frequency selectivity, intersymbol interference, and wideband-system performance.Mean delay is the first moment of the delay distribution.Source: §I · p. 1
• Estimated RMS delay spread depends both on physical multipath characteristics and on which PDP samples pass the adopted threshold.The relative cutoff is expressed in decibels against each individual PDP’s peak; it should remain above the estimated noise threshold to avoid noise-dominated samples.Source: §I · p. 1
• Prior experimental studies examined threshold sensitivity, noise removal, and estimation ambiguities, including recommendations for combined thresholding approaches.The introduction cites work on PDP dynamic range, UWB threshold levels, and consistency across mmWave measurement campaigns.Source: §I · pp. 1–2
• The paper investigates how relative PDP power thresholds affect RMS delay spread statistics in a time-varying mmWave channel at 33 GHz.It examines temporal evolution and empirical distributions for thresholds from −20 to −50 dB, focusing on the median, P90, and statistical convergence.Source: §I · p. 2

A. Measurement Setup

• The testbed uses separate Tx and Rx units built around a vector signal generator and a signal analyzer, supporting up to 1 GHz instantaneous bandwidth.The instruments operate at frequencies up to 44 GHz.Source: A. Measurement Setup · p. 2, Figure 1 · p. 2
• Identical directional horn antennas cover 26.5–40 GHz, with nominal 25 dBi gain and approximately 7° elevation and 9° azimuth half-power beamwidths.The setup uses one such antenna at each end of the link.Source: A. Measurement Setup · p. 2
• A 1 GHz FMCW chirp was sampled at 1.2 GSa/s, with 16 μs recordings every 25 ms for 30 seconds at a 33 GHz carrier frequency.This produced 1,200 recording windows and approximately 1,200 complete chirps for processing.Source: A. Measurement Setup · p. 2

B. Measurement Scenario

• The Tx was installed on a pedestrian footbridge and the Rx near the roadside, with antennas about 5 m and 1.5 m above road level, respectively.The investigated road section was along Hradecká Street near the Brno University of Technology campus.Source: B. Measurement Scenario · p. 2
• The aerial view identifies Tx and Rx locations and the monitored traffic direction along the investigated road section.The figure locates the deployment near BUT campus on Hradecká Street.Source: B. Measurement Scenario · p. 2, Figure 2 · p. 3
• The Tx and Rx antennas faced the nearest traffic lane; their geometry was quasi-monostatic, while the direct Tx–Rx path lay outside the main beams and vehicle-related components were treated as NLOS.Source: B. Measurement Scenario · p. 3
• Vehicles introduced time-varying scattering and reflection components into a setting with relatively few stationary scatterers, changing the PDP and associated temporal dispersion.Static contributors included street lighting poles, traffic signs, overhead road information boards, and metal safety barriers.Source: B. Measurement Scenario · p. 3

III. RESULTS

• The time-delay representation distinguishes nearly horizontal stationary or slowly varying traces from vehicle-related traces: approaching vehicles slope downward and receding vehicles upward.Approximately 16 approaching and 10 receding vehicles are distinguishable in the analyzed recording.Source: §III · p. 3, Figure 3 · p. 3
• Late-delay noise averages −46.6 dB in three example profiles and −43.2 dB across valid PDPs; −50 dB may include noise-dominated samples.The −40 dB cutoff remains above mean background power for most PDPs.Source: §III · p. 3, Figure 4 · p. 4
• For each PDP, the relative cutoff is set against its peak power, and samples below it are excluded before RMS delay spread is calculated.The threshold analysis initially considers −20, −30, and −40 dB.Source: §III · pp. 3–4
• Lower cutoffs generally yield higher time-varying RMS delay spreads because weak multipath components can contribute to the second moment, especially when far from the mean delay.The −20, −30, and −40 dB curves exhibit similar temporal trends.Source: §III · p. 4, Figure 5 · p. 4
• The −20 dB empirical CDF shifts toward lower delay spreads than the −30 and −40 dB CDFs, whose differences are considerably smaller.Threshold selection affects both individual estimates and their statistical distributions.Source: §III · p. 4, Figure 6 · p. 4
• From −20 to −50 dB, median RMS delay spread rises from approximately 140 to 168 ns and P90 from approximately 200 to 210 ns; approximately −40 dB is practical convergence for both.The median approaches its maximum below approximately −41 dB, while P90 stabilizes below approximately −35 dB.Source: §III · p. 4, Figure 7 · p. 4

• The analysis used empirical wideband measurements in a dynamic road environment where moving vehicles introduced significant multipath variations.Source: §IV · p. 5
• Lowering the cutoff from −20 to −50 dB raised median RMS delay spread from approximately 140 to 168 ns and P90 from 200 to 210 ns.Source: §IV · p. 5
• The median and P90 approached stable values below approximately −41 and −35 dB, respectively, making −40 dB a practical convergence level for these data.Source: §IV · p. 5
• The convergence level is specific to the propagation scenario and measurement conditions, and consistent thresholding matters when comparing campaigns.Source: §IV · p. 5