A good understanding of the fading characteristics in high speed railway environment is essential for the design of a high reliable railway wireless network. In this paper, measurements have been taken in both high speed viaduct and terrain cutting scenarios using track side base stations (BSs) of the railway wireless network in China. The measurement sites have been chosen with special care; thus the whole measured route can be characterized either by viaduct or terrain cutting. Kolmogorov-Smirnov (K-S) test has been first introduced in the statistical analysis to find out which is the most appropriate model for the small scale fading envelope. Though both Rice and Nakagami distributions provide a good fit to the first-order envelope data in both scenarios, only the Rice model generally fits the second-order statistics data accurately. For the viaduct scenario, higher Rice

As an international standard for railway communication and applications, GSM-R (GSM for Railway) has been adopted by China as a wireless communication platform to transfer security data of train control. With the rapid development of high speed railways in China, GSM-R networks have been widely deployed along the railway lines. Since GSM-R aims to transmit security data and information for train control, failure or obstruction of the wireless network will inevitably affect the normal running of the railway system. To provide a safe and reliable network, the design of a railway wireless network is of vital importance. In the meanwhile, appropriate wireless network design and optimization rely heavily on accurate prediction of radio wave propagation.

The propagation environment of the high speed railways is a lot different from the common public wireless network. As indicated in [

Besides, though Nakagami distribution has been widely accepted to be a very good fit to mobile radio channel characteristics [

This rest of the paper is organized as follows. A brief description of the measurement system and scenarios is given in Section

The narrowband measurements were done along the Zhengzhou-Xi’an high-speed railway of China with a special test system, which can collect signal level data from GSM-R track side BSs. During the measurements, the train was moving at a high speed of about 277–300 km per hour. The measurement system in the train periodically recorded the signal power value every 10 centimeters. Two typical viaduct and terrain cutting scenarios have been selected for analysis. And the measurements have been done twice in two different days to eliminate the effect of the measurement error. The following sections describe the measurement system and the measurement scenarios in greater detail.

The measurement system shown in Figure

Measurement parameters.

Parameter | Viaduct | Terrain cutting |
---|---|---|

Transmit power | 40 dBm | 40 dBm |

Transmit frequency | 932.4 MHz | 932.8 MHz |

Transmit antenna height | 23 m | 33 m |

Transmit antenna gain | 17 dB | 17 dB |

Receive antenna height | 3.5 m | 3.5 m |

Receive antenna gain | 0 dB | 0 dB |

Average train speed | 78.9 m/s | 82.0 m/s |

Measurement system.

The two chosen scenarios are shown in Figure

Measurement scenarios.

Viaduct scenario

Satellite image of measured viaduct

Terrain cutting scenario

Satellite image of measured terrain cutting

Various theoretical models have been presented to describe the small scale fading behavior of the mobile channel. In this section, both the envelope distribution and second-order statistics of the Rayleigh, Rice, and Nakagami fading models are discussed.

The Rayleigh probability density function (PDF) is given by [

And the maximum likelihood estimate of the parameter

The Rice PDF is expressed as

The parameter

The moments of the Rice distribution can be expressed as [

Since

From (

The Nakagami PDF of the envelope

The LCR of the signal envelope reveals information about how fast the received signal changes with time. It is defined as the average number of times the signal envelope crosses a certain threshold level in a positive-going direction per second. And the AFD is defined as the average time that the fading signal envelope remains below a certain threshold level [

For a fading signal, the LCR expressions for Rayleigh, Rice [

The AFD formulas for Rayleigh, Rice, and Nakagami models can be expressed as

To determine the small scale fading statistics of the received signal envelope, the effects of the path loss and shadowing have to be removed first. In order to extract the fading envelope, the received signal is normalized to its local mean value. So, for the received sample

For the first-order envelope, Kolmogorov-Smirnov (K-S) test is implemented to investigate the fitting performance of the predefined distributions for all the bins in both scenarios. It has been applied in [

The K-S statistic

Table

K-S testing results at 5% significance level.

First run | Second run | |||
---|---|---|---|---|

Viaduct | Terrain cutting | Viaduct | Terrain cutting | |

Rayleigh | 19.0% | 48.8% | 20.1% | 52.5% |

Rice | 74.7% | 85.2% | 74.7% | 93.8% |

Nakagami | 81.0% | 89.5% | 78.9% | 92.6% |

Sample empirical CDF of the small scale signal envelope and theoretical model fits for viaduct scenario. The Rice

Sample empirical CDF of the small scale signal envelope and theoretical model fits for terrain cutting scenario. The Rice

As the Rice model has a relatively strong physical significance, it has been selected to analyze the fading statistics in viaduct and terrain cutting scenarios. From the above test results, it can been seen that not all of the bins can be characterized as Rice distribution. Due to the randomness and complexity of the multipath signal components, signal envelope samples of some bins may show a complete different distribution. Thus, in order to obtain more accurate results, the estimated

Rice

Scenarios | Rice |
|||
---|---|---|---|---|

Minimum | Maximum | Mean | Standard deviation | |

Viaduct | 0 | 5.5600 | 2.3874 | 1.3314 |

Terrain cutting | 0 | 4.9200 | 1.3390 | 1.1329 |

The CDF of the obtained

CDF of the

Figure

Rice

All the obtained envelope data are first used to calculate the LCR and AFD values. After that, the measured envelope values are fitted to the theoretical distributions and then theoretical LCR and AFD values can be derived. For viaduct, the obtained Rice

The empirical and theoretical LCR results in viaduct and terrain cutting scenario for the first measurement are shown in Figure

Empirical LCR results in both scenarios for the first measurement, together with the theoretical results of Rayleigh, Rice, and Nakagami fading models.

Viaduct scenario

Terrain cutting scenario

The empirical and theoretical AFD results in viaduct and terrain cutting scenario for the first measurement are shown in Figure

Empirical AFD results in both scenarios for the first measurement, together with the theoretical results of Rayleigh, Rice, and Nakagami fading models.

Viaduct scenario

Terrain cutting scenario

This paper has presented empirical fading characteristic results in typical high speed railway viaduct and terrain cutting scenarios. Measurements were done by a special test system for GSM-R. The small scale fading envelope distribution has been fitted to theoretical Rayleigh, Rice, and Nakagami distributions. K-S test has been specially introduced as a goodness-of-fit test method to verify the suitability of a hypothesized distribution and the results show that both Rice and Nakagami distribution can describe the empirical data very well. Statistical analysis of the Rice

This work is supported in part by the Joint Funds of the Fundamental Research Funds for the Central Universities under Grant no. 2010JBZ008 and 2012YJS017, State Key Program of NSFC (Grant no. 60830001), the State Key Laboratory of Rail Traffic Control and Safety (Contract no. RCS2008ZZ006), (Contract no. RCS2008ZZ007), (Contract no. RCS2010 K008), Beijing Jiaotong University. At last but not least, the authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of this paper.