Understanding wireless channels in complex mining environments is critical for designing optimized wireless systems operated in these environments. In this paper, we propose two physics-based, deterministic ultra-wideband (UWB) channel models for characterizing wireless channels in mining/tunnel environments — one in the time domain and the other in the frequency domain. For the time domain model, a general Channel Impulse Response (CIR) is derived and the result is expressed in the classic UWB tapped delay line model. The derived time domain channel model takes into account major propagation controlling factors including tunnel or entry dimensions, frequency, polarization, electrical properties of the four tunnel walls, and transmitter and receiver locations. For the frequency domain model, a complex channel transfer function is derived analytically. Based on the proposed physics-based deterministic channel models, channel parameters such as delay spread, multipath component number, and angular spread are analyzed. It is found that, despite the presence of heavy multipath, both channel delay spread and angular spread for tunnel environments are relatively smaller compared to that of typical indoor environments. The results and findings in this paper have application in the design and deployment of wireless systems in underground mining environments.^{†}

As mandated by the Mine Improvement and New Emergency Response Act (MINER Act) [

Characterization of wireless channels in underground mines has been extensively investigated for decades [

While it is mathematically useful, a statistical channel model does not reveal the important connection between the channel and the physical world. It is known that, in principle, with the knowledge of electromagnetic boundary conditions (e.g., location, shape, and electrical properties of all objects in the environment), field strength (and thus signal power) at any point can be determined by numerically solving Maxwell’s equations. As a result, a wireless channel, theoretically, should be treated as deterministic. A deterministic channel model is attractive as it provides physical insight into how the channel properties are affected by the physical environment. For example, a physics-based Ultra-wideband (UWB) channel model is proposed in [

Underground mining environments generally consist of mine entries and cross cuts that are similar to a road or subway tunnel. As a result, tunnel propagation theory has been applied to analyze radio propagation in mines [

For the modal method, tunnels are viewed as hollow dielectric waveguides, and analytical solutions of Maxwell’s wave equations are sought. It is found that while rigorous analytical solutions are available for circular tunnels [

Compared to existing literature [

_{1}(

_{0}_{1}(_{2}(

A general Wide Sense Stationary (WSS) UWB channel is often modeled as a tapped delay line [_{l}_{l}

In practice, the estimation of CIR

We consider a rectangular tunnel with its cross-sectional view depicted in _{0}_{0}_{t}_{m,n}_{0}_{,}_{0} becomes the point source itself and the ray path associated with the image _{0}_{,}_{0} becomes the well known line-of-sight (LOS) path. The path length _{m,n}_{m,n}

In _{⊥}_{,}_{||} are the Fresnel reflection coefficients for the perpendicular and parallel polarizations, respectively. Under grazing incidences, the Fresnel reflection coefficients can be approximated as [

_{⊥}_{,}_{||} and surface impedances Δ_{⊥}_{,}_{||} are given by:
_{a,b}_{a,b}/ε_{0} are the complex relative permitivities for the horizontal and vertical walls, normalized by the vacuum permitivity _{0}. _{a,b}

_{a,b}_{a,b}

It is apparent from _{m,n}

Mathematically, if the frequency

Assuming that the frequency is high and applying the Inverse Fast Fourier Transform (IFFT) to

In

Similarly, the corresponding time domain CIR for

With the derived CIR given in

Transmitter location: (_{0}_{0}_{0})

Receiver location: (

Source polarization

Dimensions of the tunnel (2

Electric properties of the tunnel walls (

It is interesting to note that upon fixing all the five factors above, CIRs for tunnel environments are deterministic and do not vary with time. NIOSH researchers have recently experimentally proven the time invariance of wireless channels for tunnel environments by showing that power measurement results taken on different dates in a train tunnel remained the same [

With the derived analytical CIR and channel transfer function, in this section, we introduce metrics for characterizing wireless channels.

To design an optimal communication system, multipath richness of the communication channel needs to be taken into consideration. The presence of a large number of multipath components often leads to multipath fading — an issue that has been combated in the wireless community for decades. On the other hand, advanced wireless techniques such as Multiple-Input Multiple-Output (MIMO) and Time Reversal (TR) [

It is generally challenging to determine the exact multipath components of a wireless channel unless the channel is extremely simple, as in the case for a two-ray model. Practically, advanced algorithms such as the CLEAN algorithm [

Theoretically, as shown in

As a special case, for

Another important metric for characterizing the multipath richness of wireless communication channels is the delay spread. Root Mean Square (RMS) delay spread is widely used to describe the time dispersion property of the channel and is closely related to the Inter Symbol Interference (ISI) of a communication system. A channel with a small RMS delay spread generally allows a wireless system to transmit signals faster without performance degradation caused by ISI. The corresponding metric in the frequency domain is the coherence bandwidth, which is the bandwidth over which the channel can be assumed flat.

With the derived analytical CIR, the RMS delay spread of the channel at a given distance can be readily computed as [

In addition to the multipath component number and the time delay, a more accurate CIR representation should also include channel directional properties, which are characterized by the direction of departure (DoD) and the direction of arrival (DoA) [

According to the original ray representation of the electrical field shown in

_{x,y}_{x,y}_{0}_{,}_{0} and the receiver Rx. It has been assumed in _{m}_{n}

Based on the modal method given in [

The received signal in the frequency domain can be obtained by multiplying the frequency spectrum of the transmitted pulse

Similar to the image orders

RF measurements were taken in a concrete tunnel shown in

Simulations were performed to analyze wireless channels in tunnel environments in both the time and the frequency domains. Measurement results taken in the concrete tunnel introduced in Section 4 will be used to validate the simulation results. Unless stated otherwise, parameters used in the simulations are listed in _{0}_{0}) and (

The contribution of each multipath component can be visualized through a heat map shown in _{m,n}_{0}_{,}_{0} denotes the amplitude of the LOS signal that always has the least attenuation caused by the channel. As a result, the center of the image plane is always red (maximum value). The intensities of each virtual signal source in _{0}_{,}_{0} for a better visualization effect.

It is found from

The RMS delay spreads computed based on the CIRs at different separation distances are shown in

One possible explanation for the smaller RMS delay spread in

For a deterministic model, each multipath component has a deterministic angular spread in both the

Two simulated channel transfer functions for typical short and long separation distances are shown in

It should be noted that UWB channel transfer functions for indoor environments can be measured through _{21} parameters by a Vector Network Analyzer (VNA). VNAs have been recently used to measure wireless channels for tunnel environments such as road tunnels [

_{p,q}_{1}_{,}_{1}) propagating in the tunnel. It appears from

Two physics-based, deterministic channel models for tunnel environments are investigated. The wideband CIR and channel transfer function are explicitly derived and the results are expressed with major controlling factors, such as tunnel dimensions, polarization, frequency, and electrical properties of tunnel walls included. The derived CIR is expressed in an analytical form similar to the classic tap delay line model widely accepted in the wireless communication field. The derived models are further validated by RF measurements in a concrete tunnel. Based on the derived deterministic channel models, the connection between environmental parameters such as tunnel dimensions and channel properties (RMS delay spread, multipath component number, and angular spread) are investigated. It is found that RMS delay spread for tunnel environments is highly related to the tunnel transversal dimensions. Specifically, RMS delay spread linearly increases with one of the transversal dimensions and is almost invariant to the change of the other transversal dimension. It is also found that, despite the large multipath component number, both RMS delay spread and angular spread for tunnel environments are generally smaller than typical indoor environments, making them suitable for wireless high-speed data transmission without performance degradation caused by ISI. Since underground mine entries show propagation characteristics similar to tunnels, the results in this paper enhance the understanding of radio channels in mining environments and have direct applications in mine safety and health. For example, knowing the wireless channels in the underground mining environments can help design and deploy optimized high speed wireless communication and tracking systems.

The authors would like to thank Mr. Timothy Plass for his help with collecting the measurement data. The authors also thank Dr. Joseph Waynert, Mr. Alan Mayton, and Mr. Joe Schall for reviewing the manuscript.

Disclaimer: The findings and conclusions in this paper are those of the authors and do not necessarily represent the views of NIOSH. Part of the results in this paper has been published in a conference proceeding in [

A general model for wireless data transmission.

Cross-sectional view of a rectangular tunnel.

A diagram to show that multipath components in a rectangular can be represented by corresponding rays oriented from image sources (_{m,n}

A picture of the concrete tunnel where propagation measurements were taken.

A heat map for visualizing the contribution of each multipath component (image) on the image plane. Each rectangular block (pixel) represents one image (_{m,n}

The maximum order of the image (ray) that needs to be included in the model varies with the separation distance.

Simulated CIRs in a tunnel environment at different transmitter-receiver separation distances.

Simulated RMS delay spreads at different transmitter-receiver separation d distances.

RMS delay spread varies with the dimensions of the tunnel and the polarization of the signal source.

Maximum spread angle varies with the separation distance.

An example of simulated channel transfer function

An example of simulated channel transfer function

A comparison between the simulated (based on the derived CIR) and measured signal power attenuation at 915MHz in the concrete tunnel.

A comparison between the simulated and measured power attenuation at 5.8 GHz in the concrete tunnel.

A list of the parameters used in the simulations.

Parameter | Value | Parameter | Value |
---|---|---|---|

2 | 1.83m | 2 | 2.35m |

_{0} | 0 | 0 | |

_{0} | 0.0457m | 0.0457m | |

| 8.9 |