Technical Reference

In-depth documentation of the physical models used in PULSE.

UWB Channel Modeling

The simulator implements the IEEE 802.15.3a channel model to simulate realistic Ultra-Wideband propagation. This approach provides a statistical representation of the channel impulse response (CIR) rather than a purely geometric ray-tracing one.

1. Total Path Loss Model

The signal attenuation $PL(f, d)$ in decibels is modeled as:

• $d$: Distance between tag and anchor.
• $n$: Path Loss Exponent (Environmental constant, $n \approx 2$ for LOS, $n > 3$ for NLOS).
• $\kappa$: Frequency decay factor.
• $X_\sigma$: Shadowing term (Log-Normal, $\sim \mathcal{N}(0, \sigma^2)$).

2. Multipath (Saleh-Valenzuela Model)

UWB signals arrive in "clusters" of rays due to reflections from the environment. The Channel Impulse Response (CIR) $h(t)$ is given by:

Where:

• Clusters ($l$): Groups of rays arriving from major reflectors.
• Rays ($k$): Individual multipath components within a cluster.
• $T_l, \tau_{k,l}$: Arrival times of clusters and rays.

Ranging Error Model

The theoretical distance measurement $d_{meas}$ is derived from the Time of Flight (ToF) with added stochastic errors:

Noise ($\varepsilon_{noise}$)

Random error bounded by the Cramér-Rao Lower Bound (CRLB), dependent on the Signal-to-Noise Ratio (SNR).

Bias ($b_{multipath}$)

systematic positive error caused when the direct path is attenuated or blocked (NLOS), leading the receiver to trigger on a later multipath component.

IEEE 802.15.4a Channel Parameters used in PULSE

Detailed parameters used in the simulator for different standard environments (from IEEE 802.15.4a).