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The LTE System Toolbox™ product provides a set of channel models for the test and verification of UE and eNodeB radio transmission and reception as defined in [1] and [2]. The following channel models are available in the LTE System Toolbox product.
Multipath fading propagation conditions
High speed train conditions
Moving propagation conditions
The multipath fading channel model specifies the following three delay profiles.
Extended Pedestrian A model (EPA)
Extended Vehicular A model (EVA)
Extended Typical Urban model (ETU)
These three delay profiles represent a low, medium, and high delay spread environment, respectively. The multipath delay profiles for these channels are shown in the following tables.
EPA Delay Profile
Excess tap delay (ns)  Relative power (dB) 

0  0.0 
30  –1.0 
70  –2.0 
90  –3.0 
110  –8.0 
190  –17.2 
410  –20.8 
EVA Delay Profile
Excess tap delay (ns)  Relative power (dB) 

0  0.0 
30  –1.5 
150  –1.4 
310  –3.6 
370  –0.6 
710  –9.1 
1090  –7.0 
1730  –12.0 
2510  –16.9 
ETU Delay Profile
Excess tap delay (ns)  Relative power (dB) 

0  –1.0 
50  –1.0 
120  –1.0 
200  0.0 
230  0.0 
500  0.0 
1600  –3.0 
2300  –5.0 
5000  –7.0 
All the taps in the preceding tables have a classical Doppler spectrum. In addition to multipath delay profile, a maximum Doppler frequency is specified for each multipath fading propagation condition, as shown in the following table.
Channel model  Maximum Doppler frequency 

EPA 5Hz  5 Hz 
EVA 5Hz  5 Hz 
EVA 70Hz  70 Hz 
ETU 70Hz  70 Hz 
ETU 300Hz  300 Hz 
In the case of MIMO environments, a set of correlation matrices is introduced to model the correlation between UE and eNodeB antennas. These correlation matrices are introduced in MIMO Channel Correlation Matrices.
The high speed train condition defines a nonfading propagation channel with single multipath component, the position of which is fixed in time. This single multipath represents the Doppler shift, which is caused due to a high speed train moving past a base station, as shown in the following figure.
The expression is the initial distance of the train from eNodeB, and is the minimum distance between eNodeB and the railway track. Both variables are measured in meters. The variable ν is the velocity of the train in meters per second. The Doppler shift due to a moving train is given in the following equation.
The variable is the Doppler shift and is the maximum Doppler frequency. The cosine of angle is given by the following equation.
For eNodeB testing, two high speed train scenarios are defined that use the parameters listed in the following table. The Doppler shift, , is calculated using the preceding equations and the parameters listed in the following table.
Parameter  Value  

Scenario 1  Scenario 3  
1,000 m  300 m  
50 m  2 m  
ν  350 km/hr  300 km/kr 
1,340 Hz  1,150 Hz 
Both of these scenarios result in Doppler shifts that apply to all frequency bands. The Doppler shift trajectory for scenario 1 is shown in the following figure.
The Doppler shift trajectory for scenario 3 is shown in the following figure.
For UE testing, the Doppler shift, , is calculated using the preceding equations and the parameters listed in the following table.
Parameter  Value 

300 m  
2 m  
ν  300 km/hr 
750 Hz 
These parameters result in the Doppler shift, applied to all frequency bands, shown in the following figure.
The moving propagation channel in LTE defines a channel condition where the location of multipath components changes. The time difference between the reference time and the first tap, Δτ, is given by the following equation.
The variable A represents the starting time in seconds and Δω represents angular rotation in radians per second.
The parameters for the moving propagation conditions are shown in the following table.
Parameter  Scenario 1  Scenario 2 

Channel model  ETU200  AWGN 
UE speed  120 km/hr  350 km/hr 
CP length  Normal  Normal 
A  10 μs  10 μs 
Δω  0.04 s^{–1}  0.13 s^{–1} 
Doppler shift only applies for generating fading samples for scenario 1. In scenario 2, a single nonfading multipath component with additive white gaussian noise (AWGN) is modeled. The location of this multipath component changes with time, according to the preceding equation.
An example of a moving channel with a single nonfading tap is shown in the following figure.
The LTEspecific parameters are scaled up in this plot.
In MIMO systems, there is correlation between transmit and receive antennas. This depends on a number of factors such as the separation between antenna and the carrier frequency. For maximum capacity, it is desirable to minimize the correlation between transmit and receive antennas.
There are different ways to model antenna correlation. One technique makes use of correlation matrices to describe the correlation between multiple antennas both at the transmitter and the receiver. These matrices are computed independently at both the transmitterreceiver and then combined by means of a Kronecker product in order to generate a channel spatial correlation matrix.
Three different correlation levels are defined in [1].
low or no correlation
medium correlation
high correlation
The parameters α and β are defined for each level of correlation as shown in the following table of correlation values.
Low correlation  Medium correlation  High correlation  

α  β  α  β  α  β 
0  0  0.3  0.9  0.9  0.9 
The independent correlation matrices at eNodeB and UE, R_{eNB} and R_{UE}, respectively, are shown for differents set of antennas (1, 2 and 4) in the following table.
Correlation  One antenna  Two antennas  Four antennas 

eNodeB 



UE 



The channel spatial correlation matrix, R_{spat}, is given by the following equation.
The symbol ⊗ represents the Kronecker product. The values of the channel spatial correlation matrix, R_{spat}, for different matrix sizes are defined in the following table.
Matrix size  R_{spat} values 

1×2 case 

2×2 case 

4×2 case 

4×4 case 

[1] 3GPP TS 36.101. "User Equipment (UE) Radio Transmission and Reception." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (EUTRA). URL: http://www.3gpp.org.
[2] 3GPP TS 36.104. "Base Station (BS) radio transmission and reception." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (EUTRA). URL: http://www.3gpp.org.
lteFadingChannel  lteHSTChannel  lteMovingChannel