Ya.V. Aleksakina1, G.S. Voronkov2, A.Kh. Sultanov3, I.V. Kuznecov4

1-4 Ufa University of Science and Technology (Ufa, Russia)

1 alelsakinayv@uust.ru; 2 voronkov.gs@ugatu.su; 3 sultanov.ah@ugatu.su; 4 kuznecov.iv@ugatu.su

Ultra-wideband (UWB) communication and positioning systems employ nanosecond-duration impulse signals distributed across the 3–10 GHz frequency band according to the IEEE 802.15.4a standard. This approach provides nanosecond-level time resolution, enabling precise multipath channel resolution, low spectral power density to prevent interference with other systems, and excellent multipath resilience through time-domain path discrimination. The pulse shape selection is a critical design parameter determining overall system performance. While Gaussian pulses remain widely used due to their implementation simplicity and universal applicability, monopulses (first derivatives of Gaussian functions) offer significant advantages: zero DC spectral component, narrower bandwidth, superior low-frequency noise suppression, and superior matching with RC-filtering networks employed in modern transimpedance amplifier receivers. Despite these practical benefits, the available literature lacks rigorous mathematical comparison of these waveforms based on first principles. Most existing studies either employ simplified matched-filter models without accounting for receiver dynamics or resort to numerical simulation without deriving closed-form analytical expressions.

This paper addresses this gap by deriving complete analytical expressions for detection error probability of both Gaussian pulses and monopulses through rigorous solution of the Fokker-Planck equation, elucidating the physical mechanisms of monopulse superiority, and establishing optimal detector parameters for each waveform type. The receiver model consists of an RC-integrator with additive white Gaussian noise, corresponding to classical direct-amplification receiver architectures based on transimpedance amplifiers with capacitive feedback.

The comparative analysis based on stochastic receiver modeling yields analytical expressions for mean signal response, noise variance, and error probability under optimal detection conditions. Key findings include:

Signal-to-Noise Ratio Advantage: Monopulse provides a 6–8 decibel superiority in signal-to-noise and interference ratio (SINR) depending on pulse duration, with corresponding reductions in bit error probability. This advantage is attributed to three distinct physical mechanisms: (1) spectral concentration in the passband of RC-filtering networks, (2) inherent differentiation matching natural RC-filter characteristics, and (3) reduced correlation loss during filter transduction—the Gaussian pulse loses 0–45% correlation with ideal form after RC-filtering, whereas monopulse preserves spectral fidelity.

Optimal Sampling Times: Closed-form expressions determine optimal detection sampling instances as functions of pulse width and filter time constant. For the Gaussian pulse, the optimal sampling time exhibits dependency on both the impulse duration σₛ (which varies from sub-nanosecond to several nanoseconds per IEEE 802.15.4a) and the RC time constant τ. Analysis reveals four distinct operational regimes: initial energy accumulation phase, continued accumulation with decreasing rate, exponential decay following pulse passage, and the optimal sampling moment balancing signal energy accumulation against noise-induced exponential decay.

Comparative Performance Tables: Numerical solutions to the Fokker-Planck equations produce quantitative dependencies relating optimal sampling times, maximum signal-to-noise ratios, and minimum error probabilities to pulse width for both waveforms. A particularly interesting finding is the pronounced minimum in error probability at optimal RC filter time constants, reflecting the trade-off between low-frequency signal loss at short time constants and increased high-frequency noise transmission at longer time constants.

The derived analytical expressions and design recommendations directly support development of highly sensitive UWB receivers employing transimpedance amplifiers. These results justify selection of monopulse waveforms as the preferred signal shape for enhanced sensitivity and interference immunity in positioning and communication systems. The work establishes systematic design methodologies for optimizing receiver parameters—specifically RC time constants and detector sampling instant—based on known transmit pulse characteristics and operational bandwidth constraints. This analysis provides the theoretical foundation for improved hardware design and signal processing strategies in next-generation UWB systems operating under demanding sensitivity requirements and multipath propagation conditions characteristic of indoor positioning applications.

Aleksakina Ya.V., Voronkov G.S., Sultanov A.Kh., Kuznecov I.V. Comparative analysis of Gaussian and monocycle pulses in ultra-wideband systems: application of the Fokker-Planck equation // Radiotekhnika. 2026. V. 90. № 6. P. 76−89. DOI: https://doi.org/10.18127/j00338486-202606-08

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