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Based on realistic measurements in China, shadowing characteristics at the frequency of 2350 MHz were investigated in typical High-Speed Railway environments. After confirming that the measured shadowing satisfies wide-sense stationarity (assessed via the reverse arrangement test method), we quantify the shadowing correlation. Three types of correlation models are compared for the shadowing characterization, and the Normalized Mean Square Error is used to determine the best matching model: a single decaying exponential function. Decorrelation distances were found to be 11.9 m, 17.7 m, and 8.3 m in our three HSR scenarios, respectively. The results should be useful for the evaluation and verification of wireless communication in High-Speed Railway scenarios.

It is becoming increasingly apparent that providing broadband wireless communications to high-speed trains is a particularly important and challenging task. Passengers and railway operators are eager for higher data rates and more reliable wireless communications between the train and trackside networks, independent of their locations or speeds.

For the design and performance evaluation of wireless communication systems in High-Speed Railway (HSR) scenarios, it is of crucial importance to have accurate and realistic propagation channel models between the train and ground stations. Shadow fading is the large-scale fluctuation of the signal envelope due to large (with respect to a wavelength) objects obstructing the propagation paths between the transmitter and the receiver. The shadowing obstacle absorbs and/or blocks the transmitted signal and determines the relatively slow signal variations with respect to the nominal value given by path loss models. Hence the shadowing characterization results are usually used to adjust link budget path loss calculations for statistical coverage estimates in wireless network planning. An effect analogous to obstruction can also be observed in some channels with a line-of-sight (LOS) component, in which multiple reflections can induce relatively slow variation (in addition to the more rapid small-scale fading).

Previous work shows that the shadowing effect significantly affects handover behavior, intra- and inter-cell interference, and the diversity performance. For the HSR propagation environment, the shadowing effect is of primary importance for wireless network planning. To date, there has been increasing published literature on this research topic. Several shadowing models for open terrain settings have been proposed [

In this paper, we analyze the characteristics of the shadowing effect in typical HSR environments. After extracting the statistical properties of the shadowing effect, we employ a reverse arrangement test to verify the wide-sense stationarity (WSS) of shadowing records. Based on the verification of stationarity, we can (i) set any geographical point between the transmitter and receiver as the starting position for correlation estimation and (ii) extract the channel parameters from one measurement run rather than the ensemble averaging the samples from multiple measurements in homogeneous propagation environments. Then we compare three correlation models for the shadowing characterization, and the Normalized Mean Square Error (NMSE) is used to determine the best fitting model.

The rest of this paper is organized as follows. In Section

The radio environments of interest were probed with the well-accepted wideband channel sounder Propsound developed by Elektrobit. The transmitter uses a loadable rectangular chip sequence as the excitation signal. At the receiver, the channel impulse response (CIR) is obtained by a sliding correlator that correlates the received wave with a copy of the transmitter sequence. The measurement parameters are listed in Table

Channel measurement campaigns on HSR.

Item | Value |
---|---|

BT channel measurement [ | |

| |

Central frequency | 2350 MHz |

Snapshot rate | 984 Hz |

Bandwidth | 10 MHz |

Velocity | 240 km/h |

| 127 |

Power (OV) | 37 dBm |

| |

ZX channel measurement | |

| |

Central frequency | 2350 MHz |

Snapshot rate | 1986.5 Hz |

Bandwidth | 50 MHz |

Velocity | 200 km/h |

| 127 |

Power (TBV and ORC) | (30.8, 32.7) dBm |

Typical HSR terrains, the open viaduct (OV) and tree-blocked viaduct (TBV), which can incur the seasonal effects, and the open railway cutting (ORC) environments are considered in this paper. The viaduct is a long bridge-like concrete structure, built over the ground with height of approximately 10 m–20 m. The viaduct is one of the most common environments in HSR (occupying 80

In this paper, the OV experimental data was gathered from the measurement conducted on the Beijing-Tianjin (BT) HSR. The propagation environment was open and clear. It was composed of the viaduct and roadbed and covered with agricultural fields. No obstruction could be observed in the signal path. Technically, with no obstruction of the LOS component, the physical effect is not actually shadowing, but rather the large-scale variation of power due to multipath components whose effect can be analyzed analogously to the actual obstruction case. This measurement was performed in winter, 2011. For brevity, we do not include extensive details here; more detailed description can be found in [

The measurement data from the TBV and ORC environments are obtained from the measurement campaigns conducted on Zhengzhou-Xi’an (ZX) HSR in summer, 2012. The propagation sites are shown in Figures

Propagation condition of the TVB on ZX HSR.

Propagation condition of the ORC on ZX HSR.

In the TBV terrain, the transmitter and rail-track were separated by a distance of 92 m. The transmitter antenna was raised approximately 5 m high by a lift tower. This tower was located on the roof of a two-floor building with the height of 8 m which yielded the same height as the viaduct nearby. The transmitter (

To investigate the shadowing effect, the power attenuation, namely, path loss, needs to be extracted first. Commonly, the received power attenuation depends on the distance between the transmitter and the receiver. Here the received signal power at the time index

It is obvious that the standard deviation value of the open terrain is smaller than that in the tree-blocked terrain. This result is identical with the previous empirical studies which suggest that

When characterizing the shadowing effect, which is considered a random process, the properties of this phenomenon can be hypothetically characterized at any time instant by computing average values over the sample collection that describes the random process. In most previous research, the experimental shadowing data is simply assumed stationary.

If the experimental samples are stationary, two problems are solved. By invoking stationarity, (i) we can use the experimental data from one measurement run for the channel parametrization instead of ensemble averages (statistical averages) by taking all possible samples into account; (ii) we can set any geographical point between the transmitter and receiver as the starting position when simulating the correlated shadowing sequence or characterizing the correlation model.

In practice, measurement data are often collected under circumstances that do not permit an assumption of stationarity based on simple physical considerations. We use the reverse arrangement (RA) test for testing stationarity. This method does not require knowledge of the sampling distribution. The procedure is described in the Appendix.

By using this method, we divide the overall shadowing sample (Gaussian RVs in the dB scale) records into

Examination results for WSS shadowing characteristics. The solid blue lines denote the mean values of sequential mean square values. (a) Mean square values of subinterval shadowing samples from the OV environment. (b) Mean square values of subinterval shadowing samples from the ORC. (c) Mean square values of subinterval shadowing samples from the TBV.

From the equation (4.51)–(4.53) in [

Equations (

Comparisons of the simulated independent sequence and experimental result. The solid blue line denotes the simulated independent shadowing samples obeying the distribution of (

By using the result from our WSS verification, correlated shadowing results from one measurement run, having the same spatial intervals, can be used for ensemble averages. We denote all the gathered shadowing samples from overall snapshots by a measurement set

If observation samples are equally spaced

For the comparison, two additional correlation models are considered.

With the nonlinear least-squares estimation method, we can obtain the channel parameters with respect to (

Figure

Channel measurement campaigns on HSR.

Model 1: | Model 2: | |||
---|---|---|---|---|

Value | NMSE | Value | NMSE | |

OV | 11.9 | 0.25 | 8.2 | 0.37 |

TBV | 17.7 | 0.25 | 14.4 | 0.41 |

ORC | 8.3 | 0.40 | 6.6 | 0.47 |

| ||||

Model 3: | ||||

Value | Value | Value | NMSE | |

| ||||

OV | 0.86 | 13.2 | 5.0 | 0.27 |

TBV | 0.12 | 17.7 | 17.6 | 0.29 |

ORC | 0.99 | 8.36 | 8.36 | 0.42 |

Comparisons of three autocorrelation shadowing models against the raw data.

Figure

Correlation values against the transceiver separation.

That correlation in typical HSR scenarios is smaller than the correlation values in the cellular setting is worth emphasizing. In [

A statistical analysis of shadowing propagation data obtained from measurements carried out in typical HSR environments was performed at 2350 MHz. Based on the reverse arrangement test method, the stationarity of shadowing data was validated. By means of the stationary property, we can set any geographical point between the transmitter and receiver as the starting position when conducting the shadowing evaluations, and we can use the experimental data from one measurement run for the channel parameterizations instead of large (and expensive-to-obtain) ensemble averages (statistical averages).

In some prior work, an independent log-normal random process was used for the shadowing characterization, but because of the nature of real-world propagation, we showed that the shadowing samples are indeed correlated. Three types of autocorrelation models were compared for describing the correlated shadowing propagation mechanisms. According to our NMSE results, it was found that the single exponential model offers the best fit for the three HSR environments, OV, TBV, and ORC, yielding decorrelation distances of 11.9 m, 17.7 m, and 8.3 m, respectively. The result of this work is useful for the evaluation and verification of wireless communications in HSR scenarios, which can be directly used in wireless coverage prediction.

The WSS property can be verified by studying the variation in the series of correlated shadowing samples. Here we use the reverse arrangement test approach for the verification. This method does not require knowledge of the sampling distribution, and it involves the following: (a) computing the mean square values of samples in each subinterval; (b) performing the test of reverse arrangements. The main ideas are described in Validation Procedure [

Validation Procedure is as follows.

Consider a sequence of

Define

Count the total number of reverse arrangements

Calculate the acceptance region for the hypothesis. If the sequence of

Verify the stationarity hypothesis according to the acceptance region:

Now let it be hypothesized that the shadowing sample data are stationary. According to [

The authors declare no competing interests.

The research was supported in part by the NSFC projects under Grant no. 61371070, Beijing Nova Programme (Grant no. xx2016023), Beijing Natural Science Foundation (Grant no. 4142041), and the open research fund of National Mobile Communications Research Laboratory, Southeast University (no. 2014D05).