This document describes the content of the two MATLAB® directories Correlation_Multiple_Cluster and Indoor. They contain MATLAB® scripts that enable their user to
• Derive the spatial correlation properties of a Uniform Linear Array (ULA) with omnidirectional antenna elements impinged by a variety of Power Azimuth Spectra (PAS), namely uniform, truncated Gaussian and truncated Laplacian, where the waves are gathered in a single or in multiple clusters. The relations applied to derive these properties are detailed in [1].
• Simulate an Indoor Multiple-Input Multiple-Output (MIMO) radio channel at link-level in compliance with the specifications of the IEEE 802.11 TGn Channel Model Special Committee [2].
Figure 1 summarises the interactions between the scripts of the two directories.
Figure 1: Interactions between the MATLAB® scripts (N stands for the half-domain definition)
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In the following sections, the packages will be described, their parameters will be listed and validation results will be presented to illustrate the working of the packages. Finally, the distribution terms of the packages will be stated at the end of the document. 2 Spatial correlation – Directory Correlation_Multiple_Cluster
The main script of this directory is geometry2correlation.m. Through a dialogue with the user, this script first collects all the information requested to fully characterise the scenario, namely the number of antenna elements of the ULAs at the Mobile Station (MS) and at the Base Station (BS), their spacings, the PAS types of the impinging waves, their Azimuth Spreads (AS), and their Angle of Departure (AoD)/Angle of Arrival (AoA). In a second phase, the spatial correlation properties are derived by the script correlation.m, assuming omnidirectional antenna elements. The first step of this phase is to normalise the PAS such that it can be regarded as a probability distribution, which means that
( )( )
( )
∫°∆
°−∆−
=180
180
1,min
,min
φ
φ
φφ dPAS (1)
where φ∆ stands for the half-domain definition of the PAS (domain assumed symmetric) and is a parameter fed to correlation.m. This normalisation step, performed in normalisation_*.m scripts, also serves to derive the standard deviation of the PAS regarded as a probability density function (pdf), based on the AS defined by the user. There is not necessarily an identity between them, as the AS is usually derived from measurements in the azimuth domain, where the azimuth belongs to [ ]φφ ∆∆− , with φ∆ worth at most 180°, whereas a pdf is typically defined over [ ]∞∞− , . In addition, the composite AoD/AoA and AS of a multimodal Laplacian PAS [3] can be derived with the help of stat_laplacian.m. Being normalised, the PAS is then integrated over its definition domain [ ]φφ ∆∆− , to derive the spatial correlation coefficients according to the relations established in [1]. The coefficients of the homogeneous products between real (imaginary) parts are derived in Rxx_*.m scripts, while the mixed products between real and imaginary parts are handled by Rxy_*.m scripts. Their outcome is combined to produce either complex field spatial correlation coefficients or real power ones, depending on the value of a calling variable of the correlation.m script. Finally, the correlation coefficients fill two matrices defined at the MS and at the BS, respectively and R . These spatial correlation matrices are combined through a Kronecker product as proposed in [4, 5]. The structure of the Kronecker product depends whether one wants to simulate a downlink transmission
MSR BS
MSBS RRR ⊗= (2)
or an uplink one
3
BSMS RRR ⊗= (3)
where represents the operator of the Kronecker product. ⊗ As a matter of illustration, Figure 2 shows bimodal PASs, where both clusters are constrained within [-60°, 60°] around their AOAs {-90°, 90°} and exhibit an AS of 30°. Note that the second cluster has half the peak power of the first one. The envelope correlation coefficient of two distant antennas impinged by these PASs is shown in Figure 3 as a function of the distance between the antennas. It exhibits oscillations which have also been reported in [3]. In this reference, it is claimed that the more different the mean AoA of the two clusters, the higher the spatial frequency of these oscillations. One can also notice the wider oscillations obtained with the truncated Laplacian PAS. They could be due to the stronger confinement of the Laplacian PAS.
-150 -100 -50 0 50 100 1500
0.2
0.4
0.6
0.8
1
1.2
1.4
Pow
er (L
inea
r)
φ [degree]
UniformTruncated GaussianTruncated Laplacian
Figure 2: Examples of 2-cluster PASs
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalised distance d/λ
Env
elop
e co
rrela
tion ρ
UniformTruncated GaussianTruncated Laplacian
Figure 3: Envelope correlation coefficient of the PASs shown in Figure 2
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3 Indoor MIMO WLAN radio channel – Directory Indoor
The Indoor directory of the package can be divided into two main parts: - A part that consists of scripts to compute a set of correlation matrices for ULAs; - A part that can be used to embed the generated MIMO channel into a broader, link-
level simulation. 3.1 Correlation matrix computation This part of the package consists of two scripts, which are made to derive the correlation matrices of ULAs for the six models of document [2]. This can be done in two different ways, interactive and automatic.
3.1.1 Interactive computation The script Geometry2TGnCorrelation.m initially prompts the user for the model to use (A-F) and the transmission direction (up- / downlink). In a second stage, for both BS and MS, the user is prompted for the number of antenna elements and their spacing in wavelengths. The outputs of this script are the correlation matrices at the transmitter RTx, at the receiver RRx, and their Kronecker product R. See Table 1 for an overview of all possible combinations.
3.1.2 Automatic computation The second script, SelfGeometry2TGnCorrelation.m, performs the same computations automatically for a pre-determined set of cases:
• The six A-F models, • Any ULA with 1, 2 or 4 antenna elements at either end, • Spacings of .5, 1 and 4 wavelengths at either end.
The outcome of this computation is 6*3*3*3*3 = 486 sets of 3 correlation matrices (RTx, RRx and R). 3.2 Link-level simulation The main script of this part of the Indoor package is example_MIMO.m. It shows how the scripts written to generate a MIMO radio channel can be embedded in a broader link-level simulation.
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Following the approach of Synopsys' COSSAP/CCSS (CoCentric System Studio) [6], the script distinguishes
• An initialisation phase, during which parameters are read and global variables are initialised,
• A processing phase, during which the actual simulation runs, • A post-processing phase, to exploit simulation results.
The basic idea behind the processing phase is to repeatedly generate a set of fading samples, using time-domain filtering, and to interpolate that set to derive the channel samples.
3.2.1 Initialisation phase At initialisation, the parameters of the set-up (PAS, AoD/AoA, AS, PDP, etc.) are initialised in IEEE_802_11_Cases.m. This is the script that ought to be updated, should the IEEE 802.11 TGn Channel Model Special Committee agree on new parameter set-ups for link-level simulations. For the time being, the script is compliant with [2]. Since all the geometric information required to derive the spatial correlation properties is available in the IEEE_802_11_Cases.m script, the computation of the spatial correlation matrices at Tx and Rx is performed from that script, by a call to the correlation.m script described in the previous section. Its outcome, two spatial correlation matrices, is combined in example_MIMO.m (with a call to init_MIMO_channel.m) by means of a Kronecker product into matrix . After that, a spatial correlation shaping matrix is derived from R by Cholesky or Square-Root Matrix decomposition [7], depending whether one is willing to deal with complex field correlation coefficients or real power ones. Whatever decomposition is selected, its argument should be positive definite. The MATLAB
R C
® implementation of the Cholesky decomposition tests by default the positive definition of its argument. As far as the Square-Root Matrix decomposition is concerned, such a test has been implemented in the code. Additionally, with a call to the init_Rice.m script, a Rice steering matrix is computed from the outer product of the steering vectors defined in Appendix B of [8], which writes as follows:
S
( )
( )[ ]
( )
( )[ ]
T
TxTxTx
TxTx
RxRxRx
RxRx
AoDndj
AoDdj
AoAndj
AoAdj
−
−
=
12
2
1
12
2
1
sinexp
sinexp.
sinexp
sinexp
λπ
λπ
λπ
λπ
MMS (4)
where λ is the wavelength, nTx and dTx represent respectively the number and the spacing of the antenna elements for the transmit ULA, nRx and dRx represent respectively the number and the spacing of the antenna elements for the receive ULA. AoARx and AoDTx represent the composite angles of the first tap, which are derived using stat_laplacian.m.
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This steering matrix is to be used further on to generate the LOS component of Models B and C, according to relation (5):
S
RiceiΗ
( )
++
−
+=
+=
CaS1K
1AoADoTtλvjπ2exp
1KKP
ΗΗ
iRx
0
i
ii
NLOSi
LOSi
cos (5)
where Ki and Pi are the Rice factor and the total power1 of the ith tap respectively, v0 stands for the environmental scatterer speed (defined as 1.2 km/h in [2]), a represents a vector of time-domain filtered Gaussian noise and DoT is the direction of travel. In the current implementation, DoT is hard-coded to 0. At the start of the simulation, a summary of the parameter setup of the simulation is printed to the screen. See Figure 4 for an example.
Figure 4: Example of display of simulation parameters at the start of a simulation The highlighted parameters are the ones that can be modified by the user of the package. Their names are:
• SimulationLengthInCoherenceTimes (initial value = 100) • FadingNumberOfIterations (initial value = 512) • SamplingRate_Hz (initial value = 125,000) • DownsamplingFactor (initial value = 48)
Below is an overview of how these parameters are used to calculate the other parameters shown (variable names, as they are used in the package, are in italic):
NumberOfIterations
samples fading of set a of Lengthlength Simulation
= (= 58 in Figure 4)
)(
_1*
__/
1
=
HzncylingFrequeFadingSampionserOfIteratFadingNumb
HzDfesherenceTimLengthInCoSimulation
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1 Pi represents the sum of the fixed LOS power and the variable NLOS power of the ith tap, the latter being defined by the model’s PDP. This leads to ( )( )ii K1.iPDPP += .
f_D_Hz mWavelength
msv0_
_= (with v0_ms set in [2])
Wavelength_m GHz) 5.25 or GHz 2.4 (either _
1HzquencyCarrierFre
=
FadingSampling- Frequency_Hz )4 Figure in 1,750(
____
)2( ==normDf
HzDf
(1) x represents the greatest integer less than or equal to x (e.g. 4.9 = 4). (2) f_D_norm is the normalised cut-off frequency, and can not be changed by the user, at the risk of simulation errors. This failure is due to the fact that the time-domain filters in init_fading_time.m are designed specifically for a given value of f_D_norm, and will not work correctly with values other than this specific one. The total number of interpolated samples (2,121,118 in Figure 4) is determined as NumberOfIterations * NumberOfSamplesPerIteration, where: NumberOfSamples-PerIteration
ngFactorOversampli*iteration per samples fading of Number=
3.2.2 Processing phase The philosophy of the process is to provide the main loop with a set of correlated fading samples in which the actual tap coefficients to be used during the simulation will be derived by simple linear interpolation. Its sequence is graphically represented in Figure 5. The main loop of example_MIMO.m is designed to process NumberOfIterations bursts of samples. Note that the size of a burst (i.e. the amount of channel samples in it) can slightly vary from one burst to the other, due to the interpolation process. The length of a burst can be expressed in coherence times, where the coherence time is defined as 1 / f_D_Hz. This SimulationLengthInCoherenceTimes is initially set to 100. A global variable keeps track of the running time instant, for book-keeping purposes. As is, the running time instant is incremented by FadingNumberOfIterations * FadingSamplingTime_s seconds at each iteration.
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Figure 5: example_MIMO.m loop structure
After having initialised the parameters of the set-up, especially the ones related to the fading properties, the main loop in example_MIMO.m is being started. In each iteration of the loop, the script init_fading_time.m is called to generate nPaths.nTx.nRx vectors of FadingNumberOfIterations fading samples, where nPaths is the number of taps of the PDP. To enable interpolation in the FadingMatrixTime, its last two columns are stored from one iteration to the next. The last column is required to derive the interpolated channel samples lying between the last fading sample generated by init_fading_time.m in the previous iteration, and the first new fading samples produced in the current iteration. The second to last column is stored for preventing interpolation failures (NaN - Not a Number value). Indeed, when the first interpolated position coincides with the first fading sample of FadingMatrixTime, numerical inaccuracies can lead to a situation where the interpolated position is erroneously interpreted as lying just before the fading sample (distance in the order of the machine’s numerical accuracy). The second to last column then serves as a back-up value, enabling a successful interpolation without really contributing to the interpolated outcome. The init_fading_time.m script contains two sets of hard-coded filter polynomial coefficients, one set for the bell-shape case, and one for the bell-shape + spike case. The frequency at which the spike occurs is determined by a hard-coded velocity v1 whose value is specified in [2]. These filters help to generate the fading samples by means of time-domain Gaussian filtering (see Figure 5). In the bell-shape case, only a
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single filter operation is needed to generate the FadingMatrix. In the bell-shape + spike case, the FadingMatrix generation is split into two separate filter operations. First, the FadingMatrix is calculated for the positions where the bell-shape part applies. After that, the same is done for the spike part. As a final step, these two matrices are integrated into a single FadingMatrix, which will be the output of init_fading_time.m. To prevent discontinuities here, the FilterStatesOut array contains the filter states at the end of an iteration, and will be used as an input to the next iteration. Due to the long transient of the filters, their states are initialised during the initialisation phase by generating 1,000 dummy fading coefficients so as to reach steady state. The Doppler spectrum in the bell-shape + spike case is shown in Figure 6 and the resulting impulse response of tap#3 of Model F is illustrated in Figure 7.
Figure 6: Doppler spectrum of the 3rd tap of Model F. It exhibits a spike at v1/λ Hz.
0 0.1 0.2 0.3 0.410-6
10-5
10-4
10-3
10-2
Time [s]
Tx#1 - Rx#1
| Σ H
| [dB
]
0 0.1 0.2 0.3 0.410-6
10-5
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10-2
Time [s]
Tx#1 - Rx#2
0 0.1 0.2 0.3 0.410-6
10-5
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Tx#2 - Rx#1
| Σ H
| [dB
]
0 0.1 0.2 0.3 0.410-6
10-5
10-4
10-3
10-2
Time [s]
Tx#2 - Rx#2
Figure 7: Narrowband impulse responses of a 2x2 set-up using Model F.
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An explicit seed of the random generator in init_fading_time.m can be used to enable the reproduction of simulations. This seed is initialised in the main script example_MIMO.m. If set to zero, a seed is derived from the clock. Using the fading traces from init_fading_time.m, Figure 8 shows the generation of channel samples for a certain tap k, transmitter Txi (with i = 1..N) and receiver Rxj (with j = 1..M) in example_MIMO.m.
Figure 8: Generation of FadingMatrixTime
The fading traces are gathered into a single matrix, FadingMatrixTime, which is correlated using the spatial correlation shaping matrix derived earlier. The lines of FadingMatrixTime, where each line correspond to a tap coefficient, are then scaled according to the PDP and the LOS component is added with the appropriate Rice factor, according to relation (3) of [2]. Since the LOS component is added after the PDP scaling, it introduces additional energy to the taps that have a LOS component as shown in Figure 9 for Model E. The first tap, whose NLOS power is initially set at -2.5 dB, raises above all other taps after the addition of a 6-dB strong LOS component.
C
5 10 15 20-30
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0
5
10Tx#1 - Rx#1
Pow
er [d
B]
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5
10Tx#1 - Rx#2
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10Tx#2 - Rx#1
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er [d
B]
Tap index5 10 15 20
-30
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-10
-5
0
5
10Tx#2 - Rx#2
Tap index
Figure 9: Example PDP plot for model E
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When model D or E is concerned, the effects of fluorescent lights on the channel are added to FadingMatrixTime, according to section 4.7.3 of [2]. Note that the small-scale fading is normalised so as to exhibit unit mean power. Once the normalised small-scale fading is set up, the large-scale fading is modelled, by weighting FadingMatrix with the path loss and the shadow fading defined in [2] as
( )dBngShadowFadidBPathLoss __1.10 +=
HH (8)
A summary of the complete processing phase is given in Figure 10. The values of Figure 4 are indicated as an example.
Figure 10: Processing phase overview
3.2.3 Post-processing phase As a matter of post-processing, the package contains the script plot_MIMO.m. It plots the nPaths.nTx.nRx impulse responses generated by example_MIMO.m, the nTx.nRx PDPs, the nTx.nRx cdfs of the taps, the nPaths spatial correlation functions and the nPaths.nTx.nRx Doppler spectra. Whenever possible (PDP, cdf, correlation, Doppler spectrum), the characteristics of the simulated MIMO channel are compared to a reference, either the Rayleigh distribution (cdf) or the desired curve (PDP, correlation, Doppler spectrum).
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Note that plot_MIMO.m uses a downsampled version of the CorrelatedFading matrix mentioned here above. The following pages present the impulse responses, the PDPs, the cdfs, the spatial correlation properties and the Doppler spectra of a 2x2 MIMO set-up working at 5.25 GHz carrier frequency ( f = 35/6 Hz), with one wavelength spacing at the transmitter and half a wavelength spacing at the receiver, in IEEE 802.11 TGn Models ‘B’ to ‘F’ sampled at 125 kHz with LOS conditions. 512 FadingNumberOfIterations, where each iteration has a length of 100 CoherenceTimes, have been generated. In order to reduce the set of output samples, a downsampling factor of 48 has been applied. Per block, one sample has been stored. Dashed red curves/markers correspond to the reference values, whereas the blue curves/markers are the outcomes of the simulation. Moreover, in the Doppler plot, the green curve represents the Welch periodogram [14, p. 256].
D
The match between reference curves and simulation results is satisfactory. Considering the LOS conditions, the achieved tap power distributions in Figures 16-20 fit the PDPs defined in IEEE_802_11_Cases.m. The addition of the LOS component causes the achieved PDP of Models B-D (Figures 16-18) to be shifted with respect to the reference one, up to the value of the K factor. For Models E and F, the first tap, which was weak, raises above all other taps due to the addition of the LOS component. In Figures 26-39, the spatial correlation coefficients of the simulated impulse responses match the coefficients computed during the initialisation phase. The spatial correlation tends to be significant for certain taps of the different models. This is partly due to the small spacing (half a wavelength) between the two receive antenna elements. Finally, the simulated Doppler spectra shown in Figures 40-54 reproduce the bell shape spectrum selected by IEEE 802.11 TGn Channel Model Special Committee. On these figures, the red vertical lines are drawn at Df± . The upper green line is set at the maximum of the Doppler spectrum, and the lower green line lies 10 dB below. Ideally, the Doppler spectrum should meet the crossing of the red and green lines. This would be the case, should the jitter be removed from the sampled spectra presented. The x-scale of the Doppler graphs differ in Model F, to enable to check the presence of the spike at normalised frequency 200/6 = 33.333. The 6-dB strong LOS component of Model E clearly appears in the Doppler spectra of tap #1 of Figure 43. However, the most explicit proof of its existence is the cdf of tap #1 in Figure 24, where the LOS component is clearly away from the Rayleigh reference (red curve). Similar conclusions can be drawn for Model F. On the other hand, the weaker 3-dB LOS component of Model D is not so visible. Its cdf almost merges with the cdfs of the Rayleigh distributed taps in Figure 23. However, it clearly emerges from the decaying Doppler spectrum in Figure 42.
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0 0.1 0.2 0.3 0.410-7
10-6
10-5
10-4
10-3
10-2
Time [s]
Tx#1 - Rx#1
|H| [
dB]
0 0.1 0.2 0.3 0.410-7
10-6
10-5
10-4
10-3
10-2
Time [s]
Tx#1 - Rx#2
0 0.1 0.2 0.3 0.410-8
10-6
10-4
10-2
Time [s]
Tx#2 - Rx#1
|H| [
dB]
0 0.1 0.2 0.3 0.410-7
10-6
10-5
10-4
10-3
10-2
Time [s]
Tx#2 - Rx#2
Figure 11: Impulse responses of IEEE 802.11 HTSG Channel Model Case B (9
taps)
0 0.1 0.2 0.3 0.410-8
10-6
10-4
10-2
Time [s]
Tx#1 - Rx#1
|H| [
dB]
0 0.1 0.2 0.3 0.410-8
10-6
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10-2
Time [s]
Tx#1 - Rx#2
0 0.1 0.2 0.3 0.410-8
10-6
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10-2
Time [s]
Tx#2 - Rx#1
|H| [
dB]
0 0.1 0.2 0.3 0.410-8
10-6
10-4
10-2
Time [s]
Tx#2 - Rx#2
Figure 12: Impulse responses of IEEE 802.11 HTSG Channel Model Case C (14
taps)
0 0.1 0.2 0.3 0.410-8
10-6
10-4
10-2
Time [s]
Tx#1 - Rx#1
|H| [
dB]
0 0.1 0.2 0.3 0.410-8
10-6
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10-2
Time [s]
Tx#1 - Rx#2
0 0.1 0.2 0.3 0.410-8
10-6
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Time [s]
Tx#2 - Rx#1
|H| [
dB]
0 0.1 0.2 0.3 0.410-7
10-6
10-5
10-4
10-3
10-2
Time [s]
Tx#2 - Rx#2
Figure 13: Impulse responses of IEEE
802.11 HTSG Channel Model Case D (18 taps)
0 0.1 0.2 0.3 0.410-8
10-6
10-4
10-2
Time [s]
Tx#1 - Rx#1
|H| [
dB]
0 0.1 0.2 0.3 0.410-8
10-6
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Time [s]
Tx#1 - Rx#2
0 0.1 0.2 0.3 0.410-8
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Time [s]
Tx#2 - Rx#1
|H| [
dB]
0 0.1 0.2 0.3 0.410-8
10-6
10-4
10-2
Time [s]
Tx#2 - Rx#2
Figure 14: Impulse responses of IEEE 802.11 HTSG Channel Model Case E (18
taps)
0 0.1 0.2 0.3 0.410-8
10-6
10-4
10-2
Time [s]
Tx#1 - Rx#1
|H| [
dB]
0 0.1 0.2 0.3 0.410-7
10-6
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10-4
10-3
10-2
Time [s]
Tx#1 - Rx#2
0 0.1 0.2 0.3 0.410-8
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Time [s]
Tx#2 - Rx#1
|H| [
dB]
0 0.1 0.2 0.3 0.410-7
10-6
10-5
10-4
10-3
10-2
Time [s]
Tx#2 - Rx#2
Figure 15: Impulse responses of IEEE 802.11 HTSG Channel Model Case F (18
taps)
14
2 4 6 8 10-30
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0Tx#1 - Rx#1
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er [d
B]
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er [d
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Tap index2 4 6 8 10
-30
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0Tx#2 - Rx#2
Tap index
Figure 16: PDPs of IEEE 802.11 HTSG Channel Model Case B (9 taps)
2 4 6 8 10 12 14-25
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0Tx#1 - Rx#1
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er [d
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er [d
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Tap index2 4 6 8 10 12 14
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0Tx#2 - Rx#2
Tap index
Figure 17: PDPs of IEEE 802.11 HTSG Channel Model Case C (14 taps)
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er [d
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er [d
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Tap index5 10 15 20
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0Tx#2 - Rx#2
Tap index
Figure 18: PDPs of IEEE 802.11 HTSG Channel Model Case D (18 taps)
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10Tx#1 - Rx#1
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er [d
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er [d
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Tap index5 10 15 20
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Tap index
Figure 19: PDPs of IEEE 802.11 HTSG Channel Model Case E (18 taps)
5 10 15 20-30
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er [d
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er [d
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Tap index5 10 15 20
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0
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10Tx#2 - Rx#2
Tap index
Figure 20: PDPs of IEEE 802.11 HTSG Channel Model Case F (18 taps)
15
-30 -20 -10 0 10 20-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#1 - Rx#1
log 10
CD
F
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0Tx#2 - Rx#1
log 10
CD
F
20 log10(h) [dB]-30 -20 -10 0 10 20
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#2 - Rx#2
20 log10(h) [dB]
Figure 21: cdfs of the taps of IEEE 802.11 HTSG Channel Model Case B (9 taps)
-30 -20 -10 0 10 20-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#1 - Rx#1
log 10
CD
F
-30 -20 -10 0 10 20-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#1 - Rx#2
-30 -20 -10 0 10 20-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#2 - Rx#1
log 10
CD
F
20 log10(h) [dB]-30 -20 -10 0 10 20
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#2 - Rx#2
20 log10(h) [dB]
Figure 22: cdfs of the taps of IEEE 802.11 HTSG Channel Model Case C (14 taps)
-30 -20 -10 0 10 20-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#1 - Rx#1
log 10
CD
F
-30 -20 -10 0 10 20-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#1 - Rx#2
-30 -20 -10 0 10 20-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#2 - Rx#1
log 10
CD
F
20 log10(h) [dB]-30 -20 -10 0 10 20
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#2 - Rx#2
20 log10(h) [dB]
Figure 23: cdfs of the taps of IEEE 802.11 HTSG Channel Model Case D (18 taps)
-30 -20 -10 0 10 20-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#1 - Rx#1
log 10
CD
F
-30 -20 -10 0 10 20-5
-4
-3
-2
-1
0Tx#1 - Rx#2
-30 -20 -10 0 10 20-5
-4
-3
-2
-1
0Tx#2 - Rx#1
log 10
CD
F
20 log10(h) [dB]-30 -20 -10 0 10 20
-5
-4
-3
-2
-1
0Tx#2 - Rx#2
20 log10(h) [dB]
Figure 24: cdfs of the taps of IEEE 802.11 HTSG Channel Model Case E (18 taps)
-30 -20 -10 0 10 20-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#1 - Rx#1
log 10
CD
F
-30 -20 -10 0 10 20-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0Tx#1 - Rx#2
-30 -20 -10 0 10 20-5
-4
-3
-2
-1
0Tx#2 - Rx#1
log 10
CD
F
20 log10(h) [dB]-30 -20 -10 0 10 20
-5
-4
-3
-2
-1
0Tx#2 - Rx#2
20 log10(h) [dB]
Figure 25: cdfs of the taps of IEEE 802.11 HTSG Channel Model Case F (18 taps)
16
0
2
4
0
2
40
0.5
1
⟨ h111 , hkl
1⟩C
orre
latio
n co
effic
ient
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
1 , hkl1⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40.2
0.4
0.6
0.8
1
⟨ h112 , hkl
2⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
2 , hkl2⟩
(k-1)*2 + l
0
2
4
0
2
40.2
0.4
0.6
0.8
1
⟨ h113 , hkl
3⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
3 , hkl3⟩
(k-1)*2 + l
0
2
4
0
2
40.2
0.4
0.6
0.8
1
⟨ h114 , hkl
4⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
4 , hkl4⟩
(k-1)*2 + l
0
2
4
0
2
40.2
0.4
0.6
0.8
1
⟨ h115 , hkl
5⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
5 , hkl5⟩
(k-1)*2 + l
0
2
4
0
2
40.2
0.4
0.6
0.8
1
⟨ h116 , hkl
6⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
6 , hkl6⟩
(k-1)*2 + l
Figure 26: Spatial correlation of the first six taps of IEEE 802.11 HTSG Channel Model
Case B (9 taps)
0
2
4
0
2
40
0.5
1
⟨ h111 , hkl
1⟩
Cor
rela
tion
coef
ficie
nt
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
1 , hkl1⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40
0.5
1
⟨ h112 , hkl
2⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
2 , hkl2⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h113 , hkl
3⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
3 , hkl3⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h114 , hkl
4⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
4 , hkl4⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h115 , hkl
5⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
5 , hkl5⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h116 , hkl
6⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
6 , hkl6⟩
(k-1)*2 + l
Figure 27: Spatial correlation of the first six taps of IEEE 802.11 HTSG Channel Model
Case C (14 taps)
0
2
4
0
2
40.2
0.4
0.6
0.8
1
⟨ h111 , hkl
1⟩
Cor
rela
tion
coef
ficie
nt
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
1 , hkl1⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40
0.5
1
⟨ h112 , hkl
2⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
2 , hkl2⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h113 , hkl
3⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
3 , hkl3⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h114 , hkl
4⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
4 , hkl4⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h115 , hkl
5⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
5 , hkl5⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h116 , hkl
6⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
6 , hkl6⟩
(k-1)*2 + l
Figure 28: Spatial correlation of the first six taps of IEEE 802.11 HTSG Channel Model
Case D (18 taps)
0
2
4
0
2
40.4
0.6
0.8
1
⟨ h111 , hkl
1⟩
Cor
rela
tion
coef
ficie
nt
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
1 , hkl1⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40
0.5
1
⟨ h112 , hkl
2⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
2 , hkl2⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h113 , hkl
3⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
3 , hkl3⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h114 , hkl
4⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
4 , hkl4⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h115 , hkl
5⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
5 , hkl5⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h116 , hkl
6⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
6 , hkl6⟩
(k-1)*2 + l
Figure 29: Spatial correlation of the first six taps of IEEE 802.11 HTSG Channel Model
Case E (18 taps)
0
2
4
0
2
40.4
0.6
0.8
1
⟨ h111 , hkl
1⟩
Cor
rela
tion
coef
ficie
nt
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
1 , hkl1⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40
0.5
1
⟨ h112 , hkl
2⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
2 , hkl2⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h113 , hkl
3⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
3 , hkl3⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h114 , hkl
4⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
4 , hkl4⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h115 , hkl
5⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
5 , hkl5⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h116 , hkl
6⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
6 , hkl6⟩
(k-1)*2 + l
Figure 30: Spatial correlation of the first six taps of IEEE 802.11 HTSG Channel Model
Case F (18 taps)
17
0
2
4
0
2
40.2
0.4
0.6
0.8
1
⟨ h117 , hkl
7⟩C
orre
latio
n co
effic
ient
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
7 , hkl7⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40.2
0.4
0.6
0.8
1
⟨ h118 , hkl
8⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
8 , hkl8⟩
(k-1)*2 + l
0
2
4
0
2
40.4
0.6
0.8
1
⟨ h119 , hkl
9⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
9 , hkl9⟩
(k-1)*2 + l
Figure 31: Spatial correlation of the last three taps of IEEE 802.11 HTSG Channel
Model Case B (9 taps)
0
2
4
0
2
40
0.5
1
⟨ h117 , hkl
7⟩
Cor
rela
tion
coef
ficie
nt
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
7 , hkl7⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40
0.5
1
⟨ h118 , hkl
8⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
8 , hkl8⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h119 , hkl
9⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
9 , hkl9⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1110, hkl
10⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
10, hkl10⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1111, hkl
11⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
11, hkl11⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1112, hkl
12⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
12, hkl12⟩
(k-1)*2 + l
Figure 32: Spatial correlation of the taps #7 to #12 of IEEE 802.11 HTSG Channel
Model Case C (14 taps)
0
2
4
0
2
40
0.5
1
⟨ h117 , hkl
7⟩
Cor
rela
tion
coef
ficie
nt
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
7 , hkl7⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40
0.5
1
⟨ h118 , hkl
8⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
8 , hkl8⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h119 , hkl
9⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
9 , hkl9⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1110, hkl
10⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
10, hkl10⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1111, hkl
11⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
11, hkl11⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1112, hkl
12⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
12, hkl12⟩
(k-1)*2 + l
Figure 33: Spatial correlation of the six middle taps of IEEE 802.11 HTSG Channel Model Case D (18 taps)
0
2
4
0
2
40
0.5
1
⟨ h117 , hkl
7⟩
Cor
rela
tion
coef
ficie
nt
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
7 , hkl7⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40
0.5
1
⟨ h118 , hkl
8⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
8 , hkl8⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h119 , hkl
9⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
9 , hkl9⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1110, hkl
10⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
10, hkl10⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1111, hkl
11⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
11, hkl11⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1112, hkl
12⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
12, hkl12⟩
(k-1)*2 + l
Figure 34: Spatial correlation of the six middle taps of IEEE 802.11 HTSG Channel Model Case E (18 taps)
0
2
4
0
2
40
0.5
1
⟨ h117 , hkl
7⟩
Cor
rela
tion
coef
ficie
nt
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
7 , hkl7⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40
0.5
1
⟨ h118 , hkl
8⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
8 , hkl8⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h119 , hkl
9⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
9 , hkl9⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1110, hkl
10⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
10, hkl10⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1111, hkl
11⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
11, hkl11⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1112, hkl
12⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
12, hkl12⟩
(k-1)*2 + l
Figure 35: Spatial correlation of the six middle taps of IEEE 802.11 HTSG Channel Model Case F (18 taps)
18
0
2
4
0
2
40
0.5
1
⟨ h1113, hkl
13⟩
Cor
rela
tion
coef
ficie
nt
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
13, hkl13⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40
0.5
1
⟨ h1114, hkl
14⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
14, hkl14⟩
(k-1)*2 + l
Figure 36: Spatial correlation of the last three taps of IEEE 802.11 HTSG Channel
Model Case C (14 taps)
0
2
4
0
2
40
0.5
1
⟨ h1113, hkl
13⟩
Cor
rela
tion
coef
ficie
nt
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
13, hkl13⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40
0.5
1
⟨ h1114, hkl
14⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
14, hkl14⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1115, hkl
15⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
15, hkl15⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1116, hkl
16⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
16, hkl16⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1117, hkl
17⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
17, hkl17⟩
(k-1)*2 + l
0
2
4
0
2
40.2
0.4
0.6
0.8
1
⟨ h1118, hkl
18⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
18, hkl18⟩
(k-1)*2 + l
Figure 37: Spatial correlation of the last six taps of IEEE 802.11 HTSG Channel Model
Case D (18 taps)
0
2
4
0
2
40
0.5
1
⟨ h1113, hkl
13⟩
Cor
rela
tion
coef
ficie
nt
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
13, hkl13⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40
0.5
1
⟨ h1114, hkl
14⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
14, hkl14⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1115, hkl
15⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
15, hkl15⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1116, hkl
16⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
16, hkl16⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1117, hkl
17⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
17, hkl17⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1118, hkl
18⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
18, hkl18⟩
(k-1)*2 + l
Figure 38: Spatial correlation of the last six taps of IEEE 802.11 HTSG Channel Model
Case E (18 taps)
0
2
4
0
2
40
0.5
1
⟨ h1113, hkl
13⟩
Cor
rela
tion
coef
ficie
nt
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
13, hkl13⟩
(k-1)*2 + l
Cor
rela
tion
coef
ficie
nt
0
2
4
0
2
40
0.5
1
⟨ h1114, hkl
14⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
14, hkl14⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1115, hkl
15⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
15, hkl15⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1116, hkl
16⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
16, hkl16⟩
(k-1)*2 + l
0
2
4
0
2
40
0.5
1
⟨ h1117, hkl
17⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
17, hkl17⟩
(k-1)*2 + l
0
2
4
0
2
40.2
0.4
0.6
0.8
1
⟨ h1118, hkl
18⟩
1 2 3 40
0.2
0.4
0.6
0.8
1⟨ h11
18, hkl18⟩
(k-1)*2 + l
Figure 39: Spatial correlation of the last six taps of IEEE 802.11 HTSG Channel Model
Case F (18 taps)
19
-2 0 2
10-5
Tap h111
-2 0 2
10-5
Tap h112
-2 0 2
10-5
Tap h113
-2 0 2
10-5
Tap h114
-2 0 2
10-5
Tap h115
-2 0 2
10-5
Tap h116
-2 0 2
10-5
Tap h121
-2 0 2
10-5
Tap h122
-2 0 2
10-5
Tap h123
-2 0 2
10-5
Tap h124
-2 0 2
10-5
Tap h125
-2 0 2
10-5
Tap h126
-2 0 2
10-5
Tap h211
-2 0 2
10-5
Tap h212
-2 0 2
10-5
Tap h213
-2 0 2
10-5
Tap h214
-2 0 2
10-5
Tap h215
-2 0 2
10-5
Tap h216
-2 0 2
10-5
Tap h221
-2 0 2
10-5
Tap h222
-2 0 2
10-5
Tap h223
-2 0 2
10-5
Tap h224
-2 0 2
10-5
Tap h225
-2 0 2
10-5
Tap h226
Figure 40: Doppler spectra of the first six taps of IEEE 802.11 HTSG Channel Model
Case B (9 taps)
-2 0 2
10-5
Tap h111
-2 0 2
10-5
Tap h112
-2 0 2
10-5
Tap h113
-2 0 2
10-5
Tap h114
-2 0 2
10-5
Tap h115
-2 0 2
10-5
Tap h116
-2 0 2
10-5
Tap h121
-2 0 2
10-5
Tap h122
-2 0 2
10-5
Tap h123
-2 0 2
10-5
Tap h124
-2 0 2
10-5
Tap h125
-2 0 2
10-5
Tap h126
-2 0 2
10-5
Tap h211
-2 0 2
10-5
Tap h212
-2 0 2
10-5
Tap h213
-2 0 2
10-5
Tap h214
-2 0 2
10-5
Tap h215
-2 0 2
10-5
Tap h216
-2 0 2
10-5
Tap h221
-2 0 2
10-5
Tap h222
-2 0 2
10-5
Tap h223
-2 0 2
10-5
Tap h224
-2 0 2
10-5
Tap h225
-2 0 2
10-5
Tap h226
Figure 41: Doppler spectra of the first six taps of IEEE 802.11 HTSG Channel Model
Case C (14 taps)
-2 0 2
10-5
Tap h111
-2 0 2
10-5
Tap h112
-2 0 2
10-5
Tap h113
-2 0 2
10-5
Tap h114
-2 0 2
10-5
Tap h115
-2 0 2
10-5
Tap h116
-2 0 2
10-5
Tap h121
-2 0 2
10-5
Tap h122
-2 0 2
10-5
Tap h123
-2 0 2
10-5
Tap h124
-2 0 2
10-5
Tap h125
-2 0 2
10-5
Tap h126
-2 0 2
10-5
Tap h211
-2 0 2
10-5
Tap h212
-2 0 2
10-5
Tap h213
-2 0 2
10-5
Tap h214
-2 0 2
10-5
Tap h215
-2 0 2
10-5
Tap h216
-2 0 2
10-5
Tap h221
-2 0 2
10-5
Tap h222
-2 0 2
10-5
Tap h223
-2 0 2
10-5
Tap h224
-2 0 2
10-5
Tap h225
-2 0 2
10-5
Tap h226
Figure 42: Doppler spectra of the first six taps of IEEE 802.11 HTSG Channel Model
Case D (18 taps)
-2 0 2
10-5
Tap h111
-2 0 2
10-5
Tap h112
-2 0 2
10-5
Tap h113
-2 0 2
10-5
Tap h114
-2 0 2
10-5
Tap h115
-2 0 2
10-5
Tap h116
-2 0 2
10-5
Tap h121
-2 0 2
10-5
Tap h122
-2 0 2
10-5
Tap h123
-2 0 2
10-5
Tap h124
-2 0 2
10-5
Tap h125
-2 0 2
10-5
Tap h126
-2 0 2
10-5
Tap h211
-2 0 2
10-5
Tap h212
-2 0 2
10-5
Tap h213
-2 0 2
10-5
Tap h214
-2 0 2
10-5
Tap h215
-2 0 2
10-5
Tap h216
-2 0 2
10-5
Tap h221
-2 0 2
10-5
Tap h222
-2 0 2
10-5
Tap h223
-2 0 2
10-5
Tap h224
-2 0 2
10-5
Tap h225
-2 0 2
10-5
Tap h226
Figure 43: Doppler spectra of the first six taps of IEEE 802.11 HTSG Channel Model
Case E (18 taps)
-40 -20 0 20 40
10-10
Tap h111
-40 -20 0 20 40
10-10
Tap h112
-40 -20 0 20 40
10-10
Tap h113
-40 -20 0 20 40
10-10
Tap h114
-40 -20 0 20 40
10-10
Tap h115
-40 -20 0 20 40
10-10
Tap h116
-40 -20 0 20 40
10-10
Tap h121
-40 -20 0 20 40
10-10
Tap h122
-40 -20 0 20 40
10-10
Tap h123
-40 -20 0 20 40
10-10
Tap h124
-40 -20 0 20 40
10-10
Tap h125
-40 -20 0 20 40
10-10
Tap h126
-40 -20 0 20 40
10-10
Tap h211
-40 -20 0 20 40
10-10
Tap h212
-40 -20 0 20 40
10-10
Tap h213
-40 -20 0 20 40
10-10
Tap h214
-40 -20 0 20 40
10-10
Tap h215
-40 -20 0 20 40
10-10
Tap h216
-40 -20 0 20 40
10-10
Tap h221
-40 -20 0 20 40
10-10
Tap h222
-40 -20 0 20 40
10-10
Tap h223
-40 -20 0 20 40
10-10
Tap h224
-40 -20 0 20 40
10-10
Tap h225
-40 -20 0 20 40
10-10
Tap h226
Figure 44: Doppler spectra of the first six taps of IEEE 802.11 HTSG Channel Model
Case F (18 taps)
20
-2 0 2
10-5
Tap h117
-2 0 2
10-5Tap h11
8
-2 0 2
10-5Tap h11
9
-2 0 2
10-5
Tap h127
-2 0 2
10-5Tap h12
8
-2 0 210-10
Tap h129
-2 0 2
10-5
Tap h217
-2 0 2
10-5
Tap h218
-2 0 210-10
Tap h219
-2 0 2
10-5
Tap h227
-2 0 2
10-5Tap h22
8
-2 0 2
10-5
Tap h229
Figure 45: Doppler spectra of the last three taps of IEEE 802.11 HTSG Channel
Model Case B (9 taps)
-2 0 2
10-5
Tap h117
-2 0 2
10-5
Tap h118
-2 0 2
10-5
Tap h119
-2 0 2
10-5
Tap h1110
-2 0 2
10-5
Tap h1111
-2 0 2
10-5
Tap h1112
-2 0 2
10-5
Tap h127
-2 0 2
10-5
Tap h128
-2 0 2
10-5
Tap h129
-2 0 2
10-5
Tap h1210
-2 0 2
10-5
Tap h1211
-2 0 2
10-5
Tap h1212
-2 0 2
10-5
Tap h217
-2 0 2
10-5
Tap h218
-2 0 2
10-5
Tap h219
-2 0 2
10-5
Tap h2110
-2 0 2
10-5
Tap h2111
-2 0 2
10-5
Tap h2112
-2 0 2
10-5
Tap h227
-2 0 2
10-5
Tap h228
-2 0 2
10-5
Tap h229
-2 0 2
10-5
Tap h2210
-2 0 2
10-5
Tap h2211
-2 0 2
10-5
Tap h2212
Figure 46: Doppler spectra of the taps #7 to #12 of IEEE 802.11 HTSG Channel
Model Case C (14 taps)
-2 0 2
10-5
Tap h117
-2 0 2
10-5
Tap h118
-2 0 2
10-5
Tap h119
-2 0 2
10-5
Tap h1110
-2 0 2
10-5
Tap h1111
-2 0 2
10-5
Tap h1112
-2 0 2
10-5
Tap h127
-2 0 2
10-5
Tap h128
-2 0 2
10-5
Tap h129
-2 0 2
10-5
Tap h1210
-2 0 2
10-5
Tap h1211
-2 0 2
10-5
Tap h1212
-2 0 2
10-5
Tap h217
-2 0 2
10-5
Tap h218
-2 0 2
10-5
Tap h219
-2 0 2
10-5
Tap h2110
-2 0 2
10-5
Tap h2111
-2 0 2
10-5
Tap h2112
-2 0 2
10-5
Tap h227
-2 0 2
10-5
Tap h228
-2 0 2
10-5
Tap h229
-2 0 2
10-5
Tap h2210
-2 0 2
10-5
Tap h2211
-2 0 2
10-5
Tap h2212
Figure 47: Doppler spectra of the six middle taps of IEEE 802.11 HTSG Channel Model Case D (18 taps)
-2 0 2
10-5
Tap h117
-2 0 2
10-5
Tap h118
-2 0 2
10-5
Tap h119
-2 0 2
10-5
Tap h1110
-2 0 2
10-5
Tap h1111
-2 0 2
10-5
Tap h1112
-2 0 2
10-5
Tap h127
-2 0 2
10-5
Tap h128
-2 0 2
10-5
Tap h129
-2 0 2
10-5
Tap h1210
-2 0 2
10-5
Tap h1211
-2 0 2
10-5
Tap h1212
-2 0 2
10-5
Tap h217
-2 0 2
10-5
Tap h218
-2 0 2
10-5
Tap h219
-2 0 2
10-5
Tap h2110
-2 0 2
10-5
Tap h2111
-2 0 2
10-5
Tap h2112
-2 0 2
10-5
Tap h227
-2 0 2
10-5
Tap h228
-2 0 2
10-5
Tap h229
-2 0 2
10-5
Tap h2210
-2 0 2
10-5
Tap h2211
-2 0 2
10-5
Tap h2212
Figure 48: Doppler spectra of the six middle taps of IEEE 802.11 HTSG Channel Model Case E (18 taps)
-40 -20 0 20 40
10-10
Tap h117
-40 -20 0 20 40
10-10
Tap h118
-40 -20 0 20 40
10-10
Tap h119
-40 -20 0 20 40
10-10
Tap h1110
-40 -20 0 20 40
10-10
Tap h1111
-40 -20 0 20 40
10-10
Tap h1112
-40 -20 0 20 40
10-10
Tap h127
-40 -20 0 20 40
10-10
Tap h128
-40 -20 0 20 40
10-10
Tap h129
-40 -20 0 20 40
10-10
Tap h1210
-40 -20 0 20 40
10-10
Tap h1211
-40 -20 0 20 40
10-10
Tap h1212
-40 -20 0 20 40
10-10
Tap h217
-40 -20 0 20 40
10-10
Tap h218
-40 -20 0 20 40
10-10
Tap h219
-40 -20 0 20 40
10-10
Tap h2110
-40 -20 0 20 40
10-10
Tap h2111
-40 -20 0 20 40
10-10
Tap h2112
-40 -20 0 20 40
10-10
Tap h227
-40 -20 0 20 40
10-10
Tap h228
-40 -20 0 20 40
10-10
Tap h229
-40 -20 0 20 40
10-10
Tap h2210
-40 -20 0 20 40
10-10
Tap h2211
-40 -20 0 20 40
10-10
Tap h2212
Figure 49: Doppler spectra of the six middle taps of IEEE 802.11 HTSG Channel Model Case F (18 taps)
21
-2 0 2
10-5Tap h11
13
-2 0 210-10
Tap h1114
-2 0 2
10-5Tap h12
13
-2 0 210-10
Tap h1214
-2 0 210-10
Tap h2113
-2 0 210-10
Tap h2114
-2 0 2
10-5Tap h22
13
-2 0 210-10
Tap h2214
Figure 50: Doppler spectra of the last two taps of IEEE 802.11 HTSG Channel Model
Case C (14 taps)
-2 0 2
10-5
Tap h1113
-2 0 2
10-5
Tap h1114
-2 0 2
10-5
Tap h1115
-2 0 210-10
Tap h1116
-2 0 2
10-10
Tap h1117
-2 0 2
10-10
Tap h1118
-2 0 2
10-5
Tap h1213
-2 0 2
10-5
Tap h1214
-2 0 2
10-5
Tap h1215
-2 0 210-10
Tap h1216
-2 0 2
10-10
Tap h1217
-2 0 2
10-10
Tap h1218
-2 0 2
10-5
Tap h2113
-2 0 2
10-5Tap h21
14
-2 0 2
10-5
Tap h2115
-2 0 210-10
Tap h2116
-2 0 210-10
Tap h2117
-2 0 2
10-10
Tap h2118
-2 0 2
10-5
Tap h2213
-2 0 2
10-5
Tap h2214
-2 0 2
10-5
Tap h2215
-2 0 210-10
Tap h2216
-2 0 2
10-10
Tap h2217
-2 0 2
10-10
Tap h2218
Figure 51: Doppler spectra of the last six taps of IEEE 802.11 HTSG Channel Model
Case D (18 taps)
-2 0 2
10-5
Tap h1113
-2 0 2
10-5Tap h11
14
-2 0 2
10-5Tap h11
15
-2 0 210-10
Tap h1116
-2 0 210-10
Tap h1117
-2 0 2
10-10
Tap h1118
-2 0 2
10-5
Tap h1213
-2 0 2
10-5
Tap h1214
-2 0 210-10
Tap h1215
-2 0 2
10-10
Tap h1216
-2 0 210-10
Tap h1217
-2 0 2
10-10
Tap h1218
-2 0 2
10-5
Tap h2113
-2 0 2
10-5Tap h21
14
-2 0 2
10-5
Tap h2115
-2 0 210-10
Tap h2116
-2 0 2
10-10
Tap h2117
-2 0 2
10-10
Tap h2118
-2 0 2
10-5
Tap h2213
-2 0 2
10-5
Tap h2214
-2 0 210-10
Tap h2215
-2 0 210-10
Tap h2216
-2 0 2
10-10
Tap h2217
-2 0 2
10-10
Tap h2218
Figure 52: Doppler spectra of the last six taps of IEEE 802.11 HTSG Channel Model
Case E (18 taps)
-40 -20 0 20 40
10-10
Tap h1113
-40 -20 0 20 40
10-10
Tap h1114
-40 -20 0 20 40
10-10
Tap h1115
-40 -20 0 20 40
10-10
Tap h1116
-40 -20 0 20 40
10-10
Tap h1117
-40 -20 0 20 40
10-10
Tap h1118
-40 -20 0 20 40
10-10
Tap h1213
-40 -20 0 20 40
10-10
Tap h1214
-40 -20 0 20 40
10-10
Tap h1215
-40 -20 0 20 40
10-10
Tap h1216
-40 -20 0 20 40
10-10
Tap h1217
-40 -20 0 20 40
10-10
Tap h1218
-40 -20 0 20 40
10-10
Tap h2113
-40 -20 0 20 40
10-10
Tap h2114
-40 -20 0 20 40
10-10
Tap h2115
-40 -20 0 20 40
10-10
Tap h2116
-40 -20 0 20 40
10-10
Tap h2117
-40 -20 0 20 40
10-10
Tap h2118
-40 -20 0 20 40
10-10
Tap h2213
-40 -20 0 20 40
10-10
Tap h2214
-40 -20 0 20 40
10-10
Tap h2215
-40 -20 0 20 40
10-10
Tap h2216
-40 -20 0 20 40
10-10
Tap h2217
-40 -20 0 20 40
10-10
Tap h2218
Figure 53: Doppler spectra of the last six taps of IEEE 802.11 HTSG Channel Model
Case F (18 taps)
22
4 Parameters
4.1 User-defined parameters Table 1 lists the parameters which can be changed by the user, to be found in the example_MIMO.m script. They describe the simulation scenario, either through their own value, or by reference to one of the six models proposed by the IEEE 802.11 TGn Channel Model Special Committee. Parameter name Usage Authorised value Connection Direction of connection, decides
whether the Kronecker product writes according to relation (2) or (3)
‘downlink’/’uplink’
Distance_Tx_Rx_m Distance between transmitter and receiver, in m. Used to compute the path loss, and to determine whether the simulation has LOS or NLOS conditions
Real
CarrierFrequency_Hz Carrier frequency, in Hz. Real PowerLineFrequency_Hz Power line frequency ‘50’ (Europe) or ‘60’
(US) NumberOfTxAntennas Number of antenna elements at
the transmitter Integer
Spacing_Tx Spacing of the regular geometry of the antenna elements at the transmitter, in wavelengths. Currently, ULA are assumed.
Real
NumberOfRxAntennas Number of antenna elements at the receiver
Integer
Spacing_Rx Spacing of the regular geometry of the antenna elements at the receiver, in wavelengths. Currently, ULA are assumed.
Real
IEEE_802_11_Case Case of the IEEE 802.11 TGn Channel Model to be simulated
‘A’ to ‘F’
CorrelationCoefficientType Nature of the correlation coefficients, either field complex or power real.
‘complex’/’real’
FadingNumberOfIterations Number of iterations of the vector of fading coefficients
Integer
SimulationLengthInCoherenceTimes Length of simulation in CoherenceTimes (1 / fD)
Integer
SamplingRate_Hz Sampling rate of the simulation, in Hz
Real
DownsamplingFactor Downsampling factor Integer RandomSeed Seed of the random generator. If
set to zero, a seed is generated internally from the clock.
Integer
Table 2: Global parameters, to be set in example_MIMO.m
23
4.2 Hard-coded parameters Beyond the definition of the simulation cases to be found in the initialisation section of the parameter file IEEE_802_11_Cases.m, a few other parameters are hard-coded in this file. They are listed in Table 2.
Parameter name Hard-coded value Half-domain definition ∆φ 180° Direction of movement 0 radians
Table 3: Hard-coded parameters in IEEE_802_11_Cases.m
In addition, there are also some hard-coded parameters which correspond to values proposed in [2]. These concern the values for v0 and v1 (for the calculation of the LOS component and the spike, respectively), as well as the parameters of the Gaussian variable and the tap modulation amplitude values used in the addition of the effects of fluorescent lights in models D and E. These are listed in Table 3.
Parameter name Hard-coded value Script Speed of moving scattering environment v0
1.2 km/h example_MIMO.m
Speed of car passing by v1
40 km/h example_MIMO.m
Mean of the Gaussian variable
0.0203 example_MIMO.m
Standard deviation of the Gaussian variable
0.0107 example_MIMO.m
Tap modulation amplitudes A0, A1, A2 in dB
0, -15, -20 add_fluorescent_effects.m
Table 4: Hard-coded spike parameters, corresponding to [2]
Finally, there are also two hard-coded parameters concerning the hard-coded filter from init_fading_time.m. These two parameters may NOT be changed by the user, or otherwise it will result in a mismatch between the assumptions of the filter design and the values set in example_MIMO.m, causing an unsuccessful execution of the simulation. The filter parameters can be found in Table 4.
Parameter name Hard-coded value Filter order 7 f_D_norm 1/300
Table 5: Hard-coded filter parameters
24
5 Distribution terms
The MATLAB® packages developed by AAU-CSys and customised by FUNDP-INFO inline with IEEE 802.11 TGN Channel Model Special Committee recommendations are free of use to any party having approved beforehand and on an individual basis the terms of the following agreement: 1. The receiving party agrees to acknowledge AAU-CSys' and FUNDP-INFO’s
parenthood on the MATLAB® packages by referencing in every publication it may produce in the future based on the use of these packages the JSAC paper [4] or any newer related publication.
2. The receiving party agrees to acknowledge cooperation with IST project IST-2000-
30148 I-METRA [13] in every publication it may produce in the future based on the use of these packages.
3. The receiving party agrees not to distribute the source code to third parties. 4. In order to ensure that any enhancement might benefit to the whole community using
the packages, the receiving party agrees to notify FUNDP-INFO of any change and/or improvement of the source code, and to document it.
As soon as the approval of a party on these terms will have been received, the MATLAB® packages will be sent to this party. 6 Conclusion
This document has described the content and the working of two MATLAB® packages, Correlation_Multiple_Cluster and Indoor, aimed at deriving the spatial correlation properties of a MIMO radio channel and at simulating it. These packages have been validated by checking their outcome against the IEEE 802.11 TGn Channel Model cases described in [2]. The parameters of the package have been listed. Finally, the terms of their distribution have been stated. 7 Revision history
Version Comment 3.1 January 2004 – Updated version, with clarifications on the addition on the
LOS component and descriptions of new features (explicit normalisation of the small-scale fading and initialisation of the filter states).
3.0 December 2003 – Conversion to time-domain Gaussian filtering 2.1 October 2003 – Updated version, including bug fixes and the addition of the
effects of fluorescent lights. 2.0 August 2003 - Updated version following changes in the description of the
Models (taps' properties identical to these of their cluster) and addition of a spike in the Doppler spectrum due to a moving car. Validation figures regenerated with new scenarios and addition of material related to the spike. Bibliographical references completed and resorted to fix duplicate numbering in version 1.0.
1.0 July 2003 – Initial version
25
26
8 References
[1] Schumacher L., Pedersen K. and Mogensen P., "From Antenna Spacings to Theoretical Capacities – Guidelines for Simulating Spatial Correlation in MIMO Systems", Proceedings of 13th IEEE International Symposium on Personal Indoor Mobile and Radio Communications, Lisbon, Portugal, September 2002. Available at http://www.info.fundp.ac.be/~lsc/Publications/2002/PIMRC/PIMRC02_p1172.pdf, last visited: July 18th, 2003.
[2] Erceg V. et al., IEEE 802.11 document 03/940r2 “TGn Channel Models”, January 2004. Available at ftp://ieee:[email protected]/11/03/11-03-0940-02-000n-tgn-channel-models.doc, last visited: January 20th, 2004.
[3] Buehrer M.R., "The Impact of Angular Energy Distribution on Spatial Correlation", Proceedings of 56th IEEE Vehicular Technology Conference VTC 2002 Fall, Vancouver (Canada), September 2002.
[4] Kermoal J.P., Schumacher L., Pedersen K. and Mogensen P., "A Stochastic MIMO Radio Channel Model with Experimental Validation", IEEE Journal on Selected Areas in Communications, vol. 20, n.6, August 2002, pp. 1211-1226.
[5] Pedersen K., Andersen J.B., Kermoal J.P. and Mogensen P., "A stochastic multiple-input-multiple-output radio channel model for evaluation of space-time coding algorithms", Proceedings of 52nd IEEE Vehicular Technology Conference VTC 2000 Fall, Boston (USA), September 2000, vol. 2, pp. 893-897.
[6] http://www.synopsys.com, last visited: July 31st, 2003 [7] Golub, G.H. and Van Loan, C.F., "Matrix Computation", The Johns Hopkins
University Press, 3rd edition, 1996. [8] MIMO Rapporteur, 3GPP document R1-02-0141 "MIMO conference call
summary", January 2002. [9] MIMO Rapporteur: 3GPP TSG R1-02-0181, "MIMO discussion summary",
January 2002. [10] Schumacher L., Kermoal J.P., Frederiksen F., Pedersen K.I., Algans A.,
Mogensen P., "MIMO Channel Characterisation", IST Project IST-1999-11729 METRA Deliverable D2, February 2001. Available at http://www.ist-metra.org/deliverables/AAU-WP2-D2-V1.1.pdf, last visited: August 14th, 2003.
[11] Heikkilä M.J., Majonen K., Fonollosa J.R., Gaspa R., Lagunas M.A., Lamarca M., Mestre X., Palomar D.P., Pérez-Neira A., Tiirola E., Ylitalo J., Dowds M., Lister D., "Review and Selection of Relevant Algorithms", IST Project IST-1999-11729 METRA Deliverable D3.2, June 2000. Available at http://www.ist-metra.org/deliverables/NMP-WP3-D3.2-V1.1.pdf, last visited: August 14th, 2003
[12] 3GPP TR 25.869, "Tx diversity solutions for multiple antennas", version 0.1.1 [13] http://www.ist-imetra.org, last visited: July 31st, 2003 [14] Kunt M., “Traitement numérique des signaux”, Kunt M., Presses Polytechniques
Romandes, 1984. [15] Lanzl C., IEEE 802.11 document 03/656r0 "Minutes of the High Throughput
Study Group Channel Model Special Committee Teleconference on 31 July 2003", August 2003. Available at ftp://ieee:[email protected]/11/03/11-03-0656-00-TGn-minutes-high-throughput-syudy-group-channel-model-special-committee-
teleconference-31-july-2003.doc, last visited: August 14th, 2003 [16] Li Q., Yu K., Ho M., Lung J., Cheung D. and Prettie C., IEEE 802.11 document
03/584r0 "On Tap Angular Spread and Kronecker Structure of WLAN Channel Models", July 2003. Available at ftp://ieee:[email protected]/11/03/11-03-0584-00-TGn-tap-as-kron-wlan-channel-model.ppt, last visited: August 14th, 2003
