The validity of the maximum capacity criterion applied to realize highrank lineofsight (LoS) multipleinput multipleoutput (MIMO) channels is investigated for high speed railway scenarios. Performance is evaluated by ergodic capacity. Numerical results demonstrate that by simply adjusting antenna spacing according to the maximum capacity criterion, significant capacity gains are achievable. We find relatively low sensitivity of the system to displacements from the optimal point and angle in relatively short range. Thus, we present two proposals to reconfigure antenna arrays so as to maximize LoS MIMO capacity in the high speed railway scenarios
MIMO presents an attractive solution for meeting the requirements of next generation wireless communication system for the high speed railway. Since a high speed data rate is required for efficient voice and data transmission services in the future railways, and the bandwidth resources for the railway are limited, the capacity cannot be improved through increasing bandwidth. So MIMO is considered as an effective technique in longterm evolution for railway (LTER) to ensure the efficiency and reliability for data transmissions [
The development of MIMO systems over the past decade is based on the assumption of i.i.d Rayleigh fading [
The common characteristics of the above mentioned works are facts about the MIMO performance in a relatively short distance between transmitters and receivers, and meanwhile the low mobility of vehicles in scenarios. Thus, the performance of MIMO optimization design in high speed railways needs to be reassessed under a realistic high speed railway environment. In most scenarios of the high speed railway, the base stations are located less than 30 m away from the tracks, and most of the BS antenna heights are more than 30 meters, hence there are always a strong lineofsight (LoS) path between the transmitters and the receivers. Moreover, the channels exhibit a sparse multipath structure due to the lack of sufficient scatters in the railway environment [
In light of these facts, D2a scenario of WINNER II channel model is adopted, which is a realistic high speed railway transmission multipath propagation channel. The primary goal of the present paper is to verify the maximum capacity criterion in the high speed railway and then propose the methodologies for reconfigurable antenna arrays on maximizing the ergodic capacity of MIMO communication links through coverage area of the base station in viaduct scenarios.
The remainder of this paper is organized as follows. Section
According to the environment characteristics of high speed railways, D2a scenario is selected. D2a represents radio propagation in environments where MS is moving, possibly at very high speed, in a rural area. The link between the fixed network and the moving network (train) is typically an LoS type.
Figure
The simulation scenario.
In WINNER II D2a channel model, each channel realization is generated by summing contributions of eight clusters; each cluster is composed of twenty subpaths, which are associated with different delay, power, angleofarrival (AOA), and angleofdeparture (AOD) [
Single link in WINNER II channel model.
Delays are drawn randomly from the delay distribution defined in [
Normalize the delays by subtracting with minimum delay and sort the normalized delays to descending order as follows:
With exponential delay distribution the cluster powers are determined by
Assign the power of each ray within a cluster as
For the two strongest clusters, say
Subcluster information for intracluster delay spread clusters.
Subcluster  Mapping to rays  Power  Delay offset 

1  1, 2, 3, 4, 5, 6, 7, 8, 19, 20  10/20  0 ns 
2  9, 10, 11, 12, 17, 18  6/20  5 ns 
3  13, 14, 15, 16  4/20  10 ns 
The AOA for the
Ray offset angles within a cluster, given for 1°rms angle spread.
Ray number 
Basis vector of offset angles 

1, 2 

3, 4 

5, 6 

7, 8 

9, 10 

11, 12 

13, 14 

15, 16 

17, 18 

19, 20 

XPR is lognormal distributed. Draw XPR values as
For the clusters in D2a, say
Path loss model for the WINNER II D2a scenario has been developed based on results of measurements carried out within WINNER, and it is formed as
Using the simplified maximum capacity criterion in LoS MIMO systems, the problem of reduced capacity in a LoS scenario can be overcome [
To assess the performance of the stochastic channel in the presence of scatter, the notion of ergodic capacity must be employed. Note that the transmit power is equal to
It has been demonstrated that the capacity in LoS MIMO channel (ignoring any scatter components at this stage) is maximized, when the following criterion is fulfilled [
Positioning of the elements in a
The high speed railway scenarios have its distinctive characteristics, such as a relatively long distance between transmitters and receivers, the high speed of
We explore a
Ergodic capacity as a function of SNR for different antenna spacings (
It can be easily seen that the ULA with optimal antenna spacings shows superiority to other geometries over the entire SNR range. When the SNR reaches
The criterion for highrank LoS MIMO channels defines a number of MIMO architectures for systems with ULAs fixed at optimal locations. However, in high speed railway situations, there is a need for high capacity over an area, rather than to a fixed point. To examine the sensitivity of the performance of maximum capacity architectures in high speed railways, the capacity is now evaluated as a function of the displacement from the optimal point. The simulation is explored in the location range from
The variation of capacity with different displacements is shown in Figure
Ergodic capacity as a function of the displacement from the optimum point.
The sensitivity of the capacity performance for the optimum case is investigated by means of a narrow distance window, see Figure
Ergodic capacity as a function of the displacement from the optimum point.
There are some disadvantages for antenna array orientation in railway scenarios due to the fast moving of the train and the rapid change of the radio propagation environments. It is difficult to deal with this fast fading. On the other hand, it has some advantages that the route of the train is fixed and the path can be predicted. So, some special antenna types or programs can be chosen. It is clear that there is a dependence of the capacity to the azimuthal orientation of the two arrays (angles
The effect of ULA azimuthal orientation at MS ends on the capacity is shown in Figure
Ergodic capacity as a function of the angle deviation from the optimum angle (
Now theory and methods for exploiting the potential of reconfigurable RF frontends in high speed railway are not fully developed. The results of simulation offer a reference for reconfigurable antenna arrays on maximizing the capacity of MIMO wireless communication links in high speed railway scenarios. And there is measure data based on Propsound measurements, which is operated in viaduct scenarios [
According to [
Select four midpoints of the four linear regions as the optimal locations and use them to calculate optimal interelement spacings for the different reconfiguration antenna arrays involved in the four regions. The interelement spacings of ULA are adjusted for different regions, when the train travels through the coverage area of base stations.
The maximum capacity criterion defines a number of MIMO architectures for systems with antenna arrays fixed at optimal locations. However, there is a need for high capacity over an area, rather than to a fixed point. In the simulations, to examine the sensitivity of the performance of maximum capacity architectures under high speed railway scenarios, we can determine the advantage of the optimal antenna array basically stable in the small displacements range.
Select the edge point of base station coverage as the optimal location and obtain the optimal interelement spacing of the reconfigurable antenna array involved in all regions. The interelement spacing of ULA maintains invariable when the train travels through the linear coverage. This proposal maximizes the capacity of the coverage edge and minimizes the correlation of channel matrix in the coverage.
The corresponding parameters for optimum proposals are taken from Table
The parameters for optimum proposals.
RA  TA  CA  AA  

The region 
(0, 230)  (230, 320)  (320, 480)  (480, 500) 

385  225  100  14 

500  500  500  500 

22.23  12.96  5.76  0.81 

28.85  28.85  28.85  28.85 
In the maximum LoS MIMO capacity criterion, only LoS component of the channel response is considered. In railway scenarios, some degrees of scatterings are always present in the radio channel, and, hence, their effects must be accounted for the design of the MIMO system.
In Figure
Ergodic capacity as a function of
In this paper, we study the validity of the maximum capacity criterion in real high speed railway environment, which is applied to realize highrank LoS MIMO channels. D2a scenario of WINNER II channel model is adopted and it is a realistic high speed railway transmission multipath propagation channel. The ergodic capacity is used as the index to discuss the performance of reconfigurable antenna arrays. Numerical results demonstrate that significant capacity gains are achievable by simply adjusting antenna spacing according to the maximum capacity criterion. And we obtain relatively low sensitivity of the optimal antenna arrays to displacement from the optimal point and angle. So, we put forward two proposals for reconfigurable antenna arrays so as to maximize LoS MIMO capacity in the high speed railway scenarios. Then we find that the antenna array geometries obtained from the criterion are suboptimal, since the ergodic capacity decreases with the increment of
The authors would like to express their great thanks to the support from the National Natural Science Foundation of China under Grant 61222105, Beijing Municipal Natural Science Foundation under Grant 4112048, the Fundamental Research Funds for the Central Universities under Grant 2010JBZ008, Program for New Century Excellent Talents in University under Grant NCET090206, and the Key Project of State Key Laboratory under Grant RCS2011ZZ008.