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A temporal millimeter wave propagation model for tunnels is presented using ray frustum techniques and fast Fourier transform (FFT). To directly estimate or simulate effects of millimeter wave channel properties on the performance of communication services, time domain impulse responses of demodulated signals should be obtained, which needs rather large computation time. To mitigate the computational burden, ray frustum techniques are used to obtain frequency domain transfer function of millimeter wave propagation environment and FFT of equivalent low pass signals are used to retrieve demodulated waveforms. This approach is numerically efficient and helps to directly estimate impact of tunnel structures and surfaces roughness on the performance of millimeter wave communication services.

With the advent of widespread use of mobile communication services, the need for accurate wireless channel models for environments has increased [

In this paper, more direct, practical, and numerically efficient approach to characterize millimeter wave propagation channels of tunnels is proposed which gives time domain impulse responses of the demodulated baseband signals. Time domain propagation models have been given interest in the field of ultrawide band application, where impulse responses are obtained by inverse Fourier transform or convolution of time domain responses with very wide bandwidths [

Ray tracing techniques utilizing frustums can efficiently determine whether a ray hits obstacles and the scattering points on those obstacles [

Triangulated tunnel structures and ray frustums to find a ray path to RX.

Typical tunnel structure

Ray frustum and a ray path

Once the ray paths from the source position to the receiver position via scattering points are found, transfer function using geometrical optics field augmented by UTD solution can be obtained at each frequency.

The outgoing electric field from the transmitting antenna along the

Surface roughness should be taken into account in calculating

Then, the transfer function is

To retrieve time domain signal at the receiver, transfer functions at discrete frequencies should be evaluated and stored for reuse. The frequencies are fixed by the FFT of the source signal. The number of frequencies should be as small as possible to save simulation time and should be at least larger than that satisfying Nyquist sampling criterion.

Figure

Low pass equivalent signal spectrum of the transmitting antenna.

Source spectrum

Low pass equivalent signal

The number of samples of FFT to retrieve demodulated waveforms is determined by Nyquist sampling rate and the period of the signal. To simulate wireless propagation models, the period should at least be larger than maximum flight time of the wireless signals under consideration. If the period is chosen to be smaller than the flight time of the transmitted signal, intersymbol interferences or aliasings are observed. The number of sampling frequencies is determined by

The low pass equivalent signal

Time domain representation of the low pass equivalent of the received signal is

To verify the effectiveness of the formulation in Section

Dimension of a tunnel used to measure propagation loss.

Top view

Photograph of the test site

Cross section

Figure

Comparison of the power levels by measurement and simulation shows good agreement.

With the verified simulator, various parametric studies are performed which show the properties of the millimeter wave channel. Figure

Demodulated baseband signals of a curved tunnel obtained by the simulator.

Input signal

At point “A”

At point “B”

At point “C”

At point “D”

At point “E”

Figure

Received power levels in the second test tunnel.

Figure

Received power levels in the second test tunnel.

Positions of the transmitter and the receivers in the tunnel

At point “RX1”

At point “RX2”

At point “RX1”

At point “RX2”

Figure

Received power levels with the transmitter’s frequency changed.

Straight tunnel with roughness equal to zero

A tunnel with roughness equal to 2 cm

Figure

Flow chart to obtain time domain received signal.

The tunnel structure in Figure

Comparison of computation times for the tunnel structure with different level of discretization.

Number of mesh cells | Number of frustums | Block “A” | Block “B” |
Block “C” (1 point) |
---|---|---|---|---|

1,068 | 138,550 | 14.59 (sec) | 47.03 (sec) | 0.47 (sec) |

3,452 | 346,900 | 39.14 (sec) | 137.63 (sec) | 0.47 (sec) |

5,674 | 490,241 | 72.90 (sec) | 175.78 (sec) | 0.485 (sec) |

9,068 | 824,330 | 146.95 (sec) | 211.59 (sec) | 0.53 (sec) |

Although spatial division algorithms like kD-tree and octree are used, the computation times for the block “A” increase almost linearly with the number of mesh cells. This is because the bases of frustums are created from the mesh cells. For the block “B”, computation times needed to calculate received signals at 10,000 points are compared. The computation times increase logarithmically with mesh cells. For the block “C”, the computation times needed to obtain time domain received signal at one observation point remain almost the same. Although the total numbers of ray frustums change with mesh cells, the number of ray paths to the fixed receiver point remains almost the same. The frequency domain transfer function from the transmitter to the receiver is calculated at 512 frequencies. The FFT result of the transmitted signal is multiplied with the transfer function and IFFT is used to retrieve time domain received signal.

In this paper, properties of millimeter wave propagation in tunnels are investigated in terms of frequency domain path losses and time domain impulse responses which are demodulated signals at the output of the down-mixer. To efficiently simulate the time domain results, FFT and the concept of low pass equivalent signals are used. The impulse response shows directly the influences of scattering of waves from internal structures and surface roughness. From parametric studies using the simulator, multipath fading effects are shown to be mitigated in a tunnel with rough surface, although dominant signals strength decreases.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors are grateful to Dongha Kim and other members of Seoul Metropolitan Rapid Transit Corporation. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (no. NRF-2011-0014740).