EuCAP 2006 - European Conference on Antennas & Propagation

Session: Session 5A02P - MIMO Propagation Modelling (15b)
Type: Oral Propagation
Date: Friday, November 10, 2006
Time: 08:30 - 12:20
Room: Hermes
Chair: Karasawa & Bonek

Seq   Time   Title   Abs No
1   08:30   Low-Complexity Channel Emulation
Kaltenberger, F.1; Steinboeck, G.1; Humer, G.1; Zemen, T.2
1ARC Seibersdorf research, AUSTRIA;
2Forschungszentrum Telekommunkation Wien, AUSTRIA

The design and optimization of modern radio communication systems require realistic models of the radio propagation channel. Especially for the test of mobile radio hardware devices, real-time implementations of such channel models are required.

The COST 259 geometry based stochastic channel model (GSCM) assumes that the electromagnetic waves are scattered at objects randomly placed in the simulation environment and use ray tracing techniques to calculate the attenuation, delay, Doppler shift, direction of departure, direction of arrival, and polarization of every multipath component of the channel. Thus it gives a very realistic model of the radio channel.

However, the GSCM comes with a very high computational complexity, since for every propagation path, every time instance and every delay or frequency bin a complex exponential has to be evaluated. Especially on a real-time hardware channel emulator, like the ARC SmartSim, the number of paths P, that can be simulated, is limited by the available processing power.

To reduce the overall computational complexity, we derived a subspace representation of the time-variant transfer function of the channel. As basis functions we use multidimensional discrete prolate spheroidal sequences. We show, that the number of basis functions needed to represent the channel with a bias smaller than the machine precision is low compared to the number of simulated paths. Further, the subspace projection can be calculated approximately in O(1) operations. The overall complexity is thus reduced by one order of magnitude while at the same time, the number of paths is increased.

In this paper we also show how the subspace based method can be incorporated in a GSCM and implemented on the ARC SmartSim channel emulator. The hardware of the ARC SmartSim channel emulator is a modular architecture of a baseband signal processing unit, an analogue frontend and a high frequency frontend. The baseband signal processing unit is a parallel architecture of DSP boards, which basically consist of a Xilinx Virtex 2 FPGA (Field Programmable Gate Array) and a TI C6414 DSP (Digital Signal Processor). Both processors use fixed point arithmetic and thus have limited accuracy. The proposed subspace representation is able to exploit this fact allowing to trade efficiency for accuracy.

2   08:50   Estimated Capacities for a Multiple Input Multiple Output System Based on Outdoor to Indoor Measurements
Yepez, E.1; Falconer, D.1; Bultitude, R.2
1Carleton University, CANADA;
2Communications Research Centre, CANADA

In this paper we estimate the channel performance in terms of ergodic and outage rates based on measured channels in a university campus type of environment. The characteristics of the channels we measure are: (4x4) MIMO single user channels with non line of sight, outdoor to indoor and wideband for fixed wireless applications. These type of scenarios are of interest because they can be used to deploy high speed wireless internet applications.

The transmitter consists of a linear array of four antennas and it was fixed on the rooftop of a building. The receiver consists of a square-shaped four antenna array and it was placed indoors in each receive area. Additionally the receiver was moved to different locations within each receive area. In particular we consider channels that are fixed in time but vary in space, i.e.,channel variations occur when the receiver is positioned in different locations within each receive area.

The measured channels have variations in SNR from location to location in a given receive area that include effects of multipath propagation as well as obstruction shadowing. Additionally, there is SNR variation among different sub-bands in the measurement system bandwidth, eleven of which were identified as having independent variations. We study four receive areas (buildings) and normalize the average receive SNR to be the same for each receive area.

Our analysis is based on the eleven estimated independent sub-bands. We first study the spatial correlations of the channel elements and find that the measured channels can be considered uncorrelated. This can be explained by the NLOS property of the measured channels as well as the rich scattering. We then estimate the performance of the measured wideband channels in terms of ergodic and outage rates. We consider two cases: in the first case transmitter does not know the channel and receiver knows the channel; in the second case transmitter and receiver know the channel. In terms of ergodic rates we find that all receive areas have similar performance to the one achieved by (4x4) i.i.d Rayleigh channels. In terms of outage rates we find that there is a significant detriment for the first case; however for almost all the receive areas this is considerably improved (close to ergodic performance) for the second case.

The striking result of this analysis is that even though we have estimated that our measured channels have uncorrelated elements we still get that one of the outage rates is dramatically decreased with respect to (4 x 4) i.i.d. Rayleigh channels. This is actually explained by the variation of SNR in each of the locations where the receive unit was positioned, which causes a significant increase in the lower tail of the pdf of the channel capacity. We also observe that there is a further penalty in performance when shadowing is significant as it is shown for one of the receive areas.

3   09:10   Statistical Distribution of Eigenvalues in MIMO Channels
Taniguchi, T.; Sha, S.; Karasawa, Y.
The University of Electro-Communications, JAPAN

The performance of MIMO (multiple input multiple output) communication system such as capacity is strongly related to eigenvalues of MIMO correlation matrix. Consequently, in a time-variant MIMO channel, statistical distributions of eigenvalues have a significant importance. This paper overviews previous studies and presents some results about eigenvalue distribution in MIMO system under Rayleigh or Rician fading environment.

The propagation channel of a MIMO system with Nt and Nr transmitter and receiver antennas are represented by an Nr-by-Nt matrix H, with their (nr,nt) element means response between nt and nr-th elements. The joint distribution of R (=min{Nt,Nr}) eigenvalues of correlation matrix of H (it is know to be a Wishart matrix) is already derived, but if they are ordered, the marginal density functions have been derived only for the largest and the smallest eigenvalues in noncentral case, and only for the largest one in uncorrelated central case. Here, as a one of our results, we give the marginal density functions of all the ordered eigenvalues in closed form for independent and identically distributed (i.i.d.) noncentral case.

But marginal density functions generally have a complicated form or difficult to derive in some cases, hence their approximations easy to use in actual calculation is necessary. The infinite series expansion its truncation sometime requires long duration for sufficient precision, and the problem is not essentially solved. Here we present an approximation method based on space diversity theory of SIMO (single input multi output) system. Namely, the marginal density functions of all the eigenvalues in (Nt,Nr) MIMO system are approximated using gamma function, which represents the density function of signal to noise ration in array antennas. The mean of each eigenvalue required as a parameter is derived theoretically or through Monte Carlo method. Simulations are carried out, and the results of 3rd and 4th largest eigenvalues depicted in figures show the proposed method is effective for the approximation of all the eigenvalues.

4   09:30   Modeling Antenna Coupling and Correlation for Rapidly Fading MIMO Channels
Wallace, J.; Bikhazi, N.; Jensen, M.
Brigham Young University, UNITED STATES

In rich multipath environments, mobility limits channel state information (CSI) and effective capacity. Recent work [1] proves that transmit (TX) correlation guarantees capacity growth with additional antennas and suggests that for rapidly fading channels antennas should be placed arbitrarily close. We augment the MIMO modeling strategy in [1] to include the effects of electromagnetic antenna coupling. By constraining the radiated TX power, this new model reveals that capacity growth only comes from increased channel correlation, not antenna coupling. The new model also predicts that optimal antenna placement for rapid fading is not arbitrarily close, but on the order of 0.3 to 0.6 wavelengths.

We adopt the block-fading channel model in [1] with M transmitters and N receivers and block length T, or
X = (SNR/P)^(1/2) S H + W. (1)
The new scalar P is the average power radiated per unit time by the signal matrix S, allowing radiated power to be scaled. The covariance of the channel H is specified by separate directional models at TX and RX. Three pdfs for the multipath are considered: (1) full angular spread, (2) an L-path discrete model, and (3) a continuous von Mises cluster. The models show that capacity growth and optimal placement depend heavily on the multipath structure.

Conventional MIMO models that constrain the sum of the squared antenna currents do not properly constrain radiated power (P_rad), given by
P_rad = (1/T)E{Tr[SAS^H]}, (2)
where A is a coupling matrix and {.}^H is conjugate transpose. We consider two ways of constraining P_rad. The first approach follows [1] but scales S according to (2) to limit radiated power. Although suboptimal, this method allows direct comparison with previous results. The second approach is optimal and directly constrains system input power and P_rad.

Capacity growth and optimal antenna placement are assessed with effective gain (G_eff), indicating the factor by which TX power can be reduced for a constant capacity. Figure 1a plots G_eff as a function of M for a uniform linear array with a single cluster departing in the endfire direction, where increasing values of κ indicate a narrowing cluster. For very rich multipath (κ = 0), G_eff = 1, indicating no improvement with additional elements. For directional clusters, G_eff > 1 due to beamforming gain. This is in contrast to [1], where capacity growth occurs even for full angular spread.

Figure 1b plots G_eff for M = 2 with a single cluster in the broadside direction and κ = 10. The suboptimal (scaled P_tr) and optimal (P_in) solutions are different for wide spacings, but equivalent for close spacings. Clusters in the broadside and endfire (not plotted) directions lead to optimal antenna spacings of 0.6 and 0.3 wavelengths, respectively. Furthermore, when the direction of the multipath is unknown, the desirability of close spacings vanishes, and antennas should be placed far apart.

[1] S. A. Jafar and A. Goldsmith, "Multiple-antenna capacity in correlated Rayleigh fading with channel covariance information," IEEE Trans. Wireless Commun., vol. 4, pp. 990-997, May 2005.

5   09:50   Performance Analysis of Various MIMO Schemes by Using Measured MIMO Propagation Data in Residential Home Environment
Sakaguchi, K.; Tran, G.K.; Dao, N.D.; Araki, K.; Takada, J.
Tokyo Institute of Technology, JAPAN

MIMO-OFDM transmission system combining conventional Orthogonal Frequency Division Multiplexing (OFDM) with Multiple-Input Multiple-Output (MIMO) is the most promissing candidate for next generation wireless communication systems. By exploiting multiple antennas both at the transmitter (Tx) and the receiver (Rx), MIMO system can greatly increase the channel capacity at a given bandwidth and power.

When the Channel State Information (CSI) is available both at the Tx and Rx, singular value decomposition (SVD) based spatial multiplexing called SVD-MIMO is known to maximize the channel capacity. In the MIMO system without CSI feedback, simple spatial multiplexing is employed at the Tx, and there are several MIMO detection schemes at Rx, such as linear detection method of Minimum Mean Square Error (MMSE), and non-linear detection methods of Vertical Bell Labs Layered Space-Time (VBLAST) and QRM-MLD which is a low complexity version of Maximum Likelihood Detection (MLD) using QR decomposition and M-algorithm.

Most of the research in current literature focus on the system design aspects of the MIMO-OFDM system while the performance in real environments is seldom considered. Only few simulation or experiment based performance analysis can be found in the literature. Unrealistic simulation conditions or insufficient sample points in these literature are the main limitations in evaluating performance of the MIMO-OFDM system over large dynamic channel variations common in real environments.

In this paper, more than 50,000 spatial samples of MIMO channel were measured in a real residential home environment described in Image01. By using measured MIMO propagation data, throughput performance of MIMO-OFDM systems with various detection schemes, i.e. MMSE, VBLAST, QRM-MLD and SVD-MIMO were evaluated by computer simulation with conditions given in


Image01. Overview of measurement environment.

Table01. Simulation parameters.
System configurationSISO-OFDM, 4x4 MIMO-OFDM
OFDM configurationIEEE802.11a standard
Adaptive modulationMary QAM (Mary = 2, 4, 16, 64)
Total transmit power0 dBm
Noise power-92 dBm (NF = 7 dB)
Packet length60 bytes

The calculated throughput performance with respect to the distance from Tx is dipicted in Image02. From the image, the SVD-MIMO is found to provide the highest average throughput under the assumption of perfect CSI feedback especially at the longer distance from Tx. It was also found that the QRM-MLD can be considered the most preferable alternative detection scheme in the case where CSI is not available at the Tx. Furthermore, it was also found that the performance of MMSE degrades severely due to the existence of spatial correlation in the real home environment.

Image02. Average throughput performance.
6   10:40   On Distributed Scattering in Radio Channels and Its Contribution to MIMO Channel Capacity
Richter, A.; Salmi, J.; Koivunen, V.
Helsinki University of Technology, FINLAND

A well accepted geometric radio channel model approximates the radio channel impulse response by a superposition of a finite number of propagation paths. This approach is valid for generating a realisation of the radio channel, as long as the observed apertures in time, frequency and space are small. The necessary information for this channel model is a statistical model of the path parameters. The modelling accuracy can be controlled by the number of propagation paths used to generate the channel. These parameters can be derived from measurements of the channel. The parameter estimates are used to derive sufficient statistics for the radio channel propagation path parameters. For the parameter estimation algorithm, we need a channel model to describe the observations. It has to be a model, whose parameters can be estimated from the measurement data. Due to the observations uncertainty, usually determined by the measurement noise, calibration and modelling errors, the parameter estimation resolution and accuracy is limited. For a given model, the minimum achievable parameter variance can be determined using the Cramér- Rao-Lower bound. The chosen model is said to be too complex for the available amount of information if it turns out that the lower bound on the variance of one or several model parameters renders some of the parameter estimates meaningless. Consequently, we can not increase the number of propagation paths beyond this limit in order to enhance the accuracy of the radio channel model. It should be noted that several researchers have discovered this fact while analysing channel sounding measurements. It can be considered common knowledge that wideband radio channel measurements can be approximated using concentrated propagation paths with an accuracy of almost 100% down to only 30% or less, depending on the scenario. For this reason we propose to extend the data model by an additional component describing the distributed scattering (dense multipath component) of the radio channel. The model is parameterized by three parameters, a base delay, the coherence bandwidth or delay-spread, and the attenuation factor of the dense multipath component. We will also show in our paper that the distributed scattering contributes significantly to the capacity of the MIMO-wideband radio channel. In fact it can be oberved in channel sounding measurements that the distributed scattering is contributing typically more to the channel capacity than the concentrated propagation paths. This fact is easy to understand considering that the distributed scattering has usually a wide angular spread at the transmitter and the receiver. In the example below, the MIMO channel capacity estimated from a wideband channel measurement (120MHz BW,16 Tx and 16 Rx antennas) in a micro-cell environment is shown. The left hand side shows the MIMO channel capacity with optimum power control at the receiver and the right hand side the MIMO capacity without power control. At 37s the channel changes from NLOS to LOS (vertical line). One should note that keeping the total received power constant is feasible in MIMO wideband systems, if the system bandwidth is larger than the coherence bandwidth of the channel.

7   11:00   The Interdependence of Cluster Parameters in MIMO Channel Modeling
Czink, N.1; Bonek, E.1; Hentila, L.2; Kyosti, P.2; Nuutinen, J.-P.2; Ylitalo, Juha3
1Technische Universität Wien, AUSTRIA;
2Elektrobit Testing Ltd., FINLAND;
3University of Oulu, FINLAND


In order to find schemes that exploit the opportunities offered by the wireless MIMO channel, MIMO channel models that are detailed yet tractable are strongly needed. A promising approach involves cluster-based MIMO channel models. Multi-path clusters were defined as "propagation paths that show similar angles and delay", and were observed in measurements, e.g. by [1,2]. A promising approach of identifying, tracking, and parameterizing clusters is shown in [3]. The following parameters were evaluated for each cluster individually: power, power relative to the strongest cluster, number of coexisting clusters, number of paths within the cluster, mean delay, rms delay spread, mean azimuth of arrival (AoA), rms AoA spread, and mean azimuth of departure (AoD), rms AoD spread.

In this paper we discuss the interdependence of these cluster parameters, which is important to make a MIMO channel model consistent.


Starting point is a large number of clusters and their parameters obtained from indoor measurements using Elektrobit equipment (the full paper will provide details).

We use a kernel density estimator (KDE) to estimate the multivariate probability density function (pdf) of the cluster parameters. Note that this pdf will be 10-dimensional. By marginalizing this pdf to two selected domains of interest, we are able to identify the interdependence of these parameters.


This abstract presents two examples of two-dimensional estimated pdfs of different cluster parameters (the full paper will discuss more interdependences exhaustively).

Fig. 1 shows the dependence between the cluster delay spread and the AoA cluster spread. There is a strong cross-correlation of these parameters. Fig. 2 shows the correlation between the cluster relative power and the cluster delay spread. Evidently these parameters are correlated in a complex way.

We conclude that cluster-based channel models need to take the interdependence of cluster parameters into account in order to avoid model inconsistency. Our results are valuable to refine models like the IEEE 802.11 TGn, where interdependence of e.g. angle spread and delay spread had been introduced in an ad-hoc fashion.

Fig.1: Interdependence of cluster delay spread and AoA cluster spread

Fig.2: Interdependence of cluster relative power and cluster delay spread


[1] C.-C. Chong, C.-M. Tan, D. Laurenson, S. McLaughlin, M. Beach, and A. Nix, "A new statistical wideband spatio-temporal channel model for 5-GHz band WLAN systems," IEEE JSAC, vol. 21, pp. 139 - 150, Feb. 2003.

[2] K. Yu, Q. Li, D. Cheung, and C. Prettie, "On the tap and cluster angular spreads of indoor WLAN channels," IEEE VTC Spring 2004, Milano, Italy, May 17-19, 2004

[3] N. Czink, E. Bonek, L. Hentilä, J. Nuutinen, J. Ylitao, "Cluster-Based MIMO Channel Model Parameters Extracted from Indoor Time-Variant Measurements", submitted to IEEE GlobeCom 2006, San Francisco, USA

8   11:20   MIMO Channel Measurements & Analysis of a 2GHz Urban Cell Deployment
Beach, M.; Hunukumbure, M
University of Bristol, UNITED KINGDOM

Introduction: Air interface technologies employing Multiple-Input Multiple-Output (MIMO) signal processing techniques are now regarded as a key enabler in the design of future wireless access systems. However, much of the analysis reported in the literature on the performance benefits and optimisation of MIMO architectures, such as greatly enhanced spectrum efficiency and the application of channel feedback, is based on simplified antenna and propagation channel simulation models. This paper complements a previous MIMO measurement campaign conducted using realistic antenna elements embedded within practical handheld devices at 5GHz for indoor operation, with a rigorous measurement and analysis campaign for an outdoor deployment at 2GHz.

Equipment Customisation, Deployment and Trials:

A Medav RUSK channel sounder was customised for outdoor MIMO sounding at a centre frequency of 2GHz and a measurement bandwidth of 20MHz. A pair of dual slant polarised (45) UMTS sectorised panel antennas were installed with a horizontal spacing of approx. 3m on the roof of the Physics building at the University of Bristol providing 4-port MIMO transmission to the Central Bristol shopping and business districts. Pedestrian deployments of the 4-port MIMO receiving system was considered for the majority of the measurements, however dynamic channel measurements were also taken on the inner ring road and radial measurements aligned to the boresight of the transmitting antennas. The user was equipped with 3 sets of 4-element receiving antennas: 4 reference dipoles mounted on a cycle helmet, lap top equipped with 4 internally mounted PIFA antennas, and 4 slot antennas on a PDA form factor case. Each antenna set was used in turn to record 4 x 4 MIMO channel responses for both static (user stationary) and dynamic (user walking) for multiple locations. Some 116 walking measurements, each lasting approximately 6 seconds (covering >40 wavelengths at 2GHz), were recorded for each antenna type as well as 280 static deployments for different user orientations with respect to the basestation. All measurements were made during day-time, and recording parameters set such that Doppler induced channel variations can be recovered from the measured data.

Analysis of Results:

In addition to the classical channel parameters such as path loss, received SNR, delay spread and k-factor, data analysis specific to the operation of MIMO based techniques has been considered. For example, Narrowband H-matrices, eigen structure & determinant, correlation between signal ports Capacity & aggregated CCDF with normalisations (average path loss & fixed SNR). Correlation between capacity & H-matrix parameters. MIMO channel dynamics / Eigen Spectrum analysis Compare SISO, 2x2 & 4x4 configurations. The full paper will contain further details and specific examples drawn from this measurement campaign.


This work is currently supported under the UK Mobile VCE MIMO Elective programme by Nortel, BT Group plc, Fujitsu, Samsung and Toshiba. The authors are most grateful for both the financial and technical contributions from their sponsors. Thanks is also due to trials team, in particular Mark Oxley.

9   11:40   Parametric Characterization of Biazimuth and Delay Dispersion of Individual Path Components
Yin, X.1; Pedersen, T.1; Czink, N.2; Fleury, B. H.1
1Information And Signals Division, Department Of Communication Technology,Aalborg University,Denmark, DENMARK;
2Forschungszentrum Telekommunikation Wien (ftw.), Vienna, Austria, AUSTRIA

Due to the heterogeneity of the propagation environment, the received signal at the receiver (Rx) of a radio communication system is a superposition of a number of components. Each individual component, which we call "path component", is contributed by an electromagnetic wave propagating along a path from the transmitter (Tx) to the Rx. Along this path, the wave interacts with a certain number of objects referred to as scatterers. Due to the geometrical and electromagnetic properties of the scatterers, the individual path components may be dispersed in delay, direction of departure (DoD), direction of arrival (DoA), polarizations, as well as in Doppler frequency when the environment is time-variant.

In [1], a special form of the generalized von-Mises-Fisher distributions [2] is derived for characterizing the dispersion of individual path components in biazimuth (azimuth of departure (AoD) and azimuth of arrival (AoA)). This distribution maximizes the entropy under the constraint that the expectations and the correlation matrix of the two directions are fixed. Based on the SAGE algorithm, an estimation method is derived in [1] for the estimation of all parameters characterizing the biazimuth power spectrum of individual path components. Fig. 1 reports some preliminary results from an experimental investigation. Fig. 1 (a) depicts the (biazimuth) spectrum obtained from the measurement data using the Bartlett beamformer. Fig. 1 (b) shows the power spectrum estimated using the characterization proposed in [1]. It can be observed that the estimated path components shown in Fig. 1 (b) are significantly more concentrated than the corresponding components in the Bartlett spectrum shown in Fig. 1 (a). The blurring effect observed in Fig. 1 (a) is due to the limited resolution in azimuth of the used arrays.

Fig. 1. (a): Biazimuth Bartlett spectrum calculated from the received signal as is; (b): Contour lines of the estimated biazimuth power spectrum using the characterization proposed in [1].

In the full version of this paper, we propose an extension of the biazimuth von-Mises-Fisher distribution that is suitable for characterizing biazimuth and delay dispersion of individual path components. The analytical expression of the probability density function (pdf) of the distribution is presented. This pdf is utilized to characterize the biazimuth-delay power spectrum of each path component. Each path component is described by its nominal biazimuth and delay, spreads in biazimuth and delay, correlation coefficients between any two of the three elements as well as average power. In addition, the SAGE algorithm derived in [1] is extended to estimate the above parameters of individual path components. Experimental results obtained by applying the algorithm to measurement data are also reported.

[1] X. Yin, T. Pedersen, N. Czink, and B. H. Fleury, "Parametric characterization and estimation of bi-azimuth dispersion of multipath components," in Proc. of the Seventh IEEE International Workshop on Signal Processing Advances for Wireless Communications (SPAWC), Nice, France, 2006, invited.
[2] K. V. Mardia, "Statistics of directional data," Journal of the Royal Statistical Society. Series B (Methodological), vol. 37, pp. 349¨C393, 1975.

10   12:00   A Twin-Cluster MIMO Channel Model
Hofstetter, H.1; Molisch, A. F.2
1Eurecom Institute, FRANCE;


In recent years, Multiple-Input Multiple-Output (MIMO) techniques have become one of the most important research areas, are also currently being implemented in practical systems (IEEE 802.11n wireless LANs) and are envisioned for the long-term evolution of third-generation cellular systems (LTE). In order to develop and test those systems, good wireless propagation models are required. In particular, double-directional models, which describe the direction-of-arrival (DOA), direction-of-departure (DOD), and delays of the multipath components are important, because they allow a testing of different antenna configurations. This paper discusses a novel approach of a geometry based channel model that uses twin clusters of scatterers, and is parameterized using measurement evaluations. The concept of the model was derived within the COST 273 activity covering ideas and results of several working group members, and is used in the standardized COST 273 MIMO channel model.

Model Structure

In geometry-based stochastic channel models, it is assumed that each wave is reflected or diffracted at an interacting object (IO) and propagated towards the receiver. IOs are usually grouped into clusters, corresponding, e.g., to groups of buildings or objects in a room. In contrast to ray-tracing models the IOs are placed in accordance to stochastic distributions and not real world scenarios (maps). In single-bounce geometry-based models, it is assumed that there is only interaction with one IO for each wave. Such models are well suited for smart antenna systems with an antenna array only at one link end. Due to the geometrical placement of objects in space the relation between DoD, delay and DoA is given by a triangulation. Only two out of these three parameters can be chosen, the third one is derived from the geometry. To overcome this limitation, we introduce the concept of twin-clusters in COST 273. One cluster is split up into two represenations of itself: one that represents the cluster as seen by the BS and one as it is seen by the mobile terminal (MT) (Figure 1).
The two represenations are linked via a stochastic cluster link delay which is the same for all IOs inside a cluser. The cluster link delay ensures realistic path delays as, for example, derived from measurement campaigns, whereas the placement of the clusters is driven by the angular statistics of the cluster as observed from BS/MT respectively. Note that this approach is different from any multi-bounce model since the twin-cluster is only one cluster having a defined shape and placelement of IOs inside the cluster. It is placed twice on the map and both realizations look identical, like twins. Each ray propagated at the transmitter is bounced at each IO in the corresponding cluster and reradiated at the same IO of the twin cluster towards the receiver. In between the two representations of the cluster only the cluster link delay is added which is the same for all paths of a cluster.


We are proposing a new way of modeling multiple interactions of multipath components with IOs between transmitters and receivers which allow an independent adjustment of DOAs, DODs, and delays.

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