Propagation Channel Models

1 PROPAGATION CHANNEL MODELS .......................................................................................................... 1

2 CHANNEL MODEL DESCRIPTION ............................................................................................................... 1

2.1 MULTIPATH FADING PROPAGATION CONDITIONS ......................................................................... 1

2.2 HIGH SPEED TRAIN CONDITION ........................................................................................................... 3

2.3 MOVING PROPAGATION CONDITION .................................................................................................. 7

2.4 MIMO CHANNEL CORRELATION MATRICES ..................................................................................... 8

3 EXAMPLES ....................................................................................................................................................... 10

3.1 EXAMPLE 1: LTE CHANNEL MODELS IN THE 3G EVOLUTION LAB LTE

TOOLBOX ............................................................................................................................................................... 10

3.1.1 Setup – Cell-wide settings ....................................................................................................................... 10

3.1.2 Subframe Resource Grid Generation ...................................................................................................... 11

3.1.3 Symbol and Indices Generation with Resource Grid Mapping .............................................................. 11

3.1.4 OFDM Modulation ................................................................................................................................. 11

3.1.5 Constructing the LTE fading channel ..................................................................................................... 11

3.1.6 Passing data through the fading channel ............................................................................................... 12

3.2 EXAMPLE 2: CHANNEL IMPULSE RESPONSE ................................................................................... 12

See also:

LteFadingChan, LteHSTChan, LteMovingChan.

1 Propagation Channel Models

The LTE Toolbox provides a set of channel models for the test and verification of UE and

eNodeB radio transmission and reception as defined in documents TS 36.101 and TS 36.104.

The following channel models are available in the LTE Toolbox:

Multipath fading propagation conditions

High speed train conditions

Moving propagation conditions

LTE Toolbox

Start page

2 Channel Model Description

The following section describes the LTE channel models.

2.1 Multipath Fading Propagation ConditionsThe multipath fading channel model specifies three different delay profiles which are

representative of low, medium and high delay spread environment. These are: Extended

Pedestrian A model (EPA), Extended Vehicular A model (EVA) and Extended Typical Urban

model (ETU). The multipath delay profiles for these channels are shown in Tables 1, 2 and 3.

Table 1 - Extended Pedestrian A model (EPA)

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

Table 2 - Extended Vehicular A model (EVA)

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

Table 3 - Extended Typical Urban model (ETU)

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

In addition to multipath delay profile a maximum Doppler frequency is specified for each

multipath fading propagation condition as shown as in Table 4. Note that all taps in Tables 1,

2 and 3 have a classical Doppler spectrum.

Table 4 - Channel model parameters

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 case of MIMO environments a set of correlation matrices is introduced to model the

correlation between UE and eNodeB antennas. These are introduced in Section 2.4.

2.2 High Speed Train ConditionThe high speed train condition defines a non fading 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 Figure 1.

Figure 1 - High Speed Train Condition

2sD is the initial distance of the train from eNodeB, and

minD is the minimum distance

between eNodeB and the railway track. Both values are in metres. v is the velocity of the

train in m/s. The Doppler shift due to a moving train is mathematically described as

tftf ds cos

where tf s is the Doppler shift and

df is the maximum Doppler frequency. The cosine of

angle t is given by:

22

min 2

2cos

vtDD

vtDt

s

s

, vDt s0 (1)

22

min 5.1

5.1cos

vtDD

vtDt

s

s

, vDtvD ss 2 (2)

)2( mod coscos vDtt s , vDt s2 (3)

For eNodeB testing two high speed train scenarios are defined which uses the parameters

listed in Table 5. The Doppler shift fs(t) is calculated using equations 1, 2 and 3 using the

parameters listed in the Table 5.

Ds/2

DmineN

odeB

Dmin

Railway track

UE travelling with speed v

Maximum Doppler Shift

Minimum Doppler Shift

Table 5 - Parameters for high speed train conditions for eNodeB testing

Parameter Value

Scenario 1 Scenario 3

sD 1000 m 300 m

minD50 m 2 m

v 350 km/h 300 km/h

df1340 Hz 1150 Hz

These scenarios result in Doppler shifts as shown in Figure 2 and Figure 3 and are applicable

to all frequency bands.

Figure 2 - Doppler shift trajectory for scenario 1

Figure 3 - Doppler shift trajectory for scenario 3

For UE testing the input parameters listed in Table are used to calculate the Doppler shift

using Equation 1, 2 and 3.

Table 6 - Parameters for high speed train condition for UE testing

Parameter Value

sD 300 m

minD2 m

v 300 km/h

df750 Hz

These parameters result in the Doppler shift shown in Figure 4 and is applied to all frequency

bands.

Figure 4 - Doppler shift trajectory for UE testing

2.3 Moving Propagation ConditionThe 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 ∆τ is:

)sin(2

tA

(4)

where A represents the starting time in seconds and ∆ω represents angular rotation in

radian/sec. Note that relative time between multipath components stays fixed.

The parameters for the moving propagation conditions are shown in Table 7. Doppler shift is

only applicable for generating fading samples for scenario 1.

Table 7 - Parameters for UL timing adjustment

Parameter Scenario 1 Scenario 2

Channel model ETU200 AWGN

UE speed 120 km/h 350 km/h

CP length Normal Normal

A 10 µs 10µs

∆w 0.04 s-1 0.13 s-1

In scenario 2 a single non fading multipath component with AWGN is modelled. The location

of this multipath component changes with time according to Equation 4.

An example of a moving channel with a single non-fading tap is shown in Figure 5. The LTE

specific parameters have been scaled up to produce this plot.

Figure 5 – Moving Propagation Condition with scaled parameters

2.4 MIMO Channel Correlation MatricesIn 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 minimise the correlation between transmit and receive

antennas.

There are different ways to model antenna correlation. One such 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

transmitter/receiver and are then combined by means of a Kronecker product in order to

generate a channel spatial correlation matrix.

Three different correlation levels are defined in the LTE specification TS 36.101: (i) low or no

correlation (ii) medium and (iii) high correlations. The parameter α and β are defined for each

level of correlation as Shown in Table 8.

Table 8 - Correlation Values

Low correlation Medium Correlation High Correlation

a b a b a b

0 0 0.3 0.9 0.9 0.9

The independent correlation matrices at UE and eNodeB (i.e. ReNB , RUE respectively) are

shown as in Table 9 and 10 for different set of antennas (i.e. 1, 2 and 4).

Table 9 - eNodeB Correlation Matrix

Correlation One

antenna

Two antennas Four antennas

eNode B

1eNBR

1

aa1

eNBR

1

1

1

1

*9

1*9

4*

91*

91*

94

94

91*

91

94

91

aaa

aaa

aaa

aaa

eNBR

Table 10 - UE Correlation Matrix

Correlation One antenna Two antennas Four antennas

UE 1UER

1

bb1

UER

1

1

1

1

*9

1*9

4*

91*

91*

94

94

91*

91

94

91

bbb

bbb

bbb

bbb

UER

The channel spatial correlation matrix (Rspar) is expressed as:

UEeNBspat RRR

where represent the Kronecker product. Table 11 defines the channel spatial correlation

matrix (Rspat).

Table 11 - Rspal correlation matrices

1x2 case

1

1*bb

UEspat RR

2x2 case

1

1

1

1

1

1

1

1

****

**

**

**

bababbaaaabbabab

bb

aa

UEeNBspat RRR

4x2 case

1

1

1

1

1

1

*

91

94*

91

91

94

94

91

91

94

91

**

**

*

bb

aaa

aaa

aaa

aaa

UEeNBspat RRR

4x4 case

1

1

1

1

1

1

1

1

*9

1*9

4*

91*

91*

94

94

91*

91

94

91

91

94*

91

91

94

94

91

91

94

91

**

**

*

bbb

bbb

bbb

bbb

aaa

aaa

aaa

aaa

UEeNBspat RRR

3 Examples

3.1 LTE Channel Models in the 3G Evolution Lab LTE ToolboxThis example is designed to aid understanding of the use of LTE channel model in a

simulation. In this example cell specific reference signals are generated and mapped onto a

resource grid. The resource grid undergoes OFDM modulation and is passed through a

fading channel.

3.1.1 Setup – Cell-wide settings

Cell-wide settings are specified in a structure. A number of the functions used in this example

require a subset of the settings specified below.

enb.NDLRB = 9; % No of DL-RB in total BW

enb.CyclicPrefix = 'Normal'; % CP length

enb.PHICHDuration = 'Normal'; % Normal PHICH duration

enb.CFI = 3; % 4 PDCCH symbols

enb.Ng = 'Sixth'; % HICH groups

enb.CellRefP = 1; % 1-antenna ports

enb.NCellID = 10; % Cell ID

enb.NSubframe = 0; % Subframe number 0

enb.DuplexMode = ‘FDD’; % Duplex mode

antennaPort = 0; % Antenna port 0

3.1.2 Subframe Resource Grid Generation

A resource grid can easily be created using toolbox function LteDLResourceGrid. This

creates an empty resource grid for one subframe.

subframe = LteDLResourceGrid(enb); % Create empty resource grid

3.1.3 Symbol and Indices Generation with Resource Grid Mapping

Cell-specific Reference symbols (CellRS) are generated and then mapped onto the Resource

Elements (RE's) of a resource grid using linear indices.

cellRSsymbols = LteCellRS(enb,antennaPort); % Cell reference

symbol

% generation

cellRSindices = LteCellRSIndices(enb,antennaPort,{'1based'});

% Indices generation

subframe(cellRSindices) = cellRSsymbols; %Resource grid mapping

3.1.4 OFDM Modulation

Perform OFDM modulation of the complex symbols in a ‘subframe’ according to cell wide

settings ‘enb’

[txWaveform,info] = LteOFDM(enb,subframe);

where ‘txWaveform’ are the transmitted OFDM modulated symbols and ‘info’ is a structure

contain details of the modulation process. The field info.SamplingRate provides the

sampling rate of the time domain waveform, and is given by

SR = 30.72MHz / 2048 * Nfft

where Nfft is the size of the OFDM IFFT.

3.1.5 Constructing the LTE fading channel

The following function generates an LTE multipath fading channel as specified in TS 36.101.

First the channel parameters are setup by creating a structure channel:

channel.Seed = 1; % Random number generator seed.

channel.NRxAnts = 1; % Number of receive antennas

channel.DelayProfile = 'EVA'; % Delay profile model (‘EPA’,’EVA’,’ETU’)

channel.DopplerFreq = 5; % Doppler frequency

channel.CarrierFreq = 2.6e9; % Carrier frequency

channel.MIMOCorrelation = 'Low';% Correlation between UE & eNodeB

channel.SamplingRate = info.SamplingRate; % Input sampling rate

channel.InitTime = 0; % Fading process time Offset

Note that the sampling rate within the channel model (channel.SamplingRate) must be set

to the value created by LteOFDM (info.SamplingRate).

3.1.6 Passing data through the fading channel

The ‘txWaveform’ is an array of LTE transmitted samples. Each row contains the waveform

samples for each of the transmit antennas. These waveforms are filtered with the delay

profiles as specified in the parameter structure channel using the following function:

rxWaveform = LteFadingChan(txWaveform, channel);

‘rxWaveform’ is the channel output signal matrix, where each row corresponds to the

waveform at each of the receive antennas ( since we have defined 1 receive antenna, the

number of rows of ‘rxWaveform’ matrix is one).

3.2 Channel Impulse ResponseThe following example demonstrates the use of LTE channel modelling toolbox in a

MathWorks Matlab® environment. This example shows how the impulse response of a 2x2

MIMO system can be achieved.

The input is a matrix of impulses where each impulse is separated by 300 samples. Each

column (where the column size represents the number of transmit antennas) in the matrix is

the input waveform to the channel model function and is therefore a series of impulses. This

series of impulses allows the changing impulse response of the channel to be viewed over

time. For clear visualisation the impulse spacing should be greater than maximum delay

spread of the channel).

The Input waveform is passed through the channel. Here the LTE Multipath fading channel

model is used. The output matrix has complex samples corresponding to each receive

antenna. This process is shown in Figure 6.

Figure 6 - Channel impulse response

The pre configuration of LTE multipath fading channel is done using a structure which could

be parameterise through a simple structure. The following Matlab code shows how to

parameterise the fading channel.

%Channel Parameterisation

channel.Seed = 1; % Channel seed

channel.NRxAnts = 2; % No of receive antennas

channel.DelayProfile = 'EVA'; % Delay profile

channel.DopplerFreq = 300; % Doppler frequency

channel.CarrierFreq = 2e9; % Carrier frequency

channel.MIMOCorrelation = 'Low';% MIMO Correlation

channel.SamplingRate = 1/10e-9; % Channel sampling rate

channel.InitTime = 0; % Initialise channel time

%The subsequent line of code creates two identical input streams

of data which are passed through two transmit antennas as in

Figure 6

nAntIn = 2; % Number of Transmit antennas

impulseSpacing = 300; % Greater than max ch delay spread

Transmit Antennas

Receiv

e Antennas

Antennas

Impulse

spacing

of 300 samples

… …

Time[s]

LTE Multipath Fading Channel

Input Impulse Stream

Impulses and corresponding response

Time[s]

1001... 100...

1001... 100...

T

x 1T

x 2

Output Stream Waveform

|H|

b

a

f … …

Transmit Antennas

lmn1o..p0r...

abcd... f0g...

Rx 1

Rx 2

noImpResponse = 150; % no of impulse responses to be calculated

nInputSamples = impulseSpacing * noImpResponse;

in = zeros(nInputSamples, nAntIn);

onesLocations = 1:impulseSpacing:nInputSamples;

in(onesLocations,1) = 1;

% Channel filtering

out = LteFadingChan(in, channel);

% Plotting receive waveform

for (antNo = 1: channel.NRxAnts)

figure

mesh(squeeze(abs(reshape(out(:,antNo),impulseSpacing,noImpRespon

se).')));

titleStr = ['Rx Antenna' num2str(antNo)];

title({'Channel Impulse Response for LTE fading

channel',titleStr});

ylabel('number of impulses');

xlabel('Impulse spacing [no of samples]');

zlabel('|H|');

end;

Figure 7 shows the channel impulse response at receive antenna 1.

Figure 7 – Channel impulse response

© Copyright 2009-2010 Steepest Ascent Ltd.

A Zadoff–Chu sequence is a complex-valued mathematical sequence which, when applied to radio signals, gives rise to an electromagnetic signal of constant amplitude, whereby cyclicly shifted versions of the sequence comprising the signal do not cross-correlate with each other when the signal is recovered at the receiver. A generated Zadoff–Chu sequence that has not been shifted is known as a "root sequence".

The sequence then exhibits the useful property that cyclic-shifted versions of itself remain orthogonal to one another, provided, that is, that each cyclic shift, when viewed within the time domain of the signal, is greater than the combined propagation delay and multi-path delay-spread of that signal between the transmitter and receiver.

The complex value at each position (n) of each root Zadoff–Chu sequence (u) given by

where

Zadoff–Chu sequence is known as a CAZAC sequence (constant amplitude zero autocorrelation waveform).

1.Properties of Zadoff-Chu sequences

1. They are periodic with period NZC if NZC is prime.

xu(n + NZC) = xu(n)

2. Given NZC is prime, Discrete Fourier Transform of Zadoff–Chu sequence is another Zadoff–Chu sequence conjugated, scaled and time scaled.

where is the multiplicative inverse of u

modulo NZC.

3. The autocorrelation of a prime length Zadoff–Chu sequence with a cyclically shifted version of itself also has zero auto-correlation. i.e. it is non-zero only at one instant which corresponds to the cyclic shift.

4. The cross correlation between two prime length Zadoff–Chu

sequences, i.e. different u, is constant

2.Usages

Zadoff–Chu sequences are used in the 3GPP LTE Long Term Evolution air interface in the definition of Primary Synchronization Signal (PSS) (so called primary synchronization channel), random access preamble (PRACH) , HARQ ACK/NACK responses (PUCCH) and sounding reference signals(SRS). The ZC sequences are used in LTE because they provide an advantage of having a lower Peak-to-Average-Power (PAPR) ratio as compared to Orthogonal Frequency Division Multiplexing (OFDM).

3.References

http://www.quintillion.co.jp/3GPP/Specs/

S. Beyme and C. Leung (2009). "Efficient computation of DFT of Zadoff-Chu sequences". Electron. Lett. 45 (9): 461–463. doi:10.1049/el.2009.3330.

Zadoff Chu (ZC) Sequences

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