16 Introduction owledge d on realistic modeling of the cova ommn teeo the n the o the iance of the spatial channels Furthermore,in the Additionally,with the directional parameters,the propagation of the waves can be easily visualized when the actual (GBSM be obtained by spectral analysis of the measurement data. s,aoniedinowocd es,i.e.the spe ral-as d the C10)Podlander 01520)(1 andK(05)Tayem and Kwon ()T which o snot result in the onfor porameer c (19)(92).Ann In 1000's algorithms derived based on the parametric models of channel were appled to extracting the channel model parar s from the me urement be parameters of channels de ending on the generic model applied.These algorithm are also called super resolution methods,as they may achieve the o methodsTypic (2000)Zhang(2001),the eredexpectation-maximization(SAGE)algorithm Fe er and ero (104) (200201 0) and the variants of the SAGE algorithm by adopting models different from the widely used resolvable ecular path el Bengtsson and rsten(2000)Yin et al 2006a.1 algorithms these algo or ray-based channel (MIMO)simulations (Release )(2007).the WINNER I spatial channel model-enhanced (SCME) Models (IST-WINNER2.Tech.Rep. ced channel models REPORT ITU-R M.2135 Guidelines for considered as a ne arameters of the channel,such as the cl time-varian r.t ng results may not be aeigeahid usters. matic ering led alternative er Czink et al.(2005c)Czink et ders are refe n of various clustering am胸 Xiao et a ,(200 urr (200 ated16 Introduction There are also many practical concerns which require the knowledge of spatial characteristics of channel. For example, when the MIMO techniques are used in communication systems, the spatial diversity and/or multiplexing gains need to be evaluated based on realistic modeling of the covariance of the spatial channels. Furthermore, in the case where the beamforming technique is used in a base station, it is necessary to know the distribution of the energy in direction of arrival, e.g. how the energy is concentrated, what the spread of the energy in the dominant path is. Additionally, with the directional parameters, the propagation of the waves can be easily visualized when the actual constellation of the scatterers is presented for specific environments. The geometry-based channel modeling (GBSM) became flourishing in the last decade. One major reason is that the channel dispersion in the directional domains can be obtained by spectral analysis of the measurement data. The spatial-spectral analysis methods can be categorized into two classes, i.e. the spectral-based methods and the parametric-model-based methods. Theoretically, the conventional methods, such as periodogram Schuster (1898) and correlogram Chatfield (1989), belonging to the category of the spectral-based methods are not applicable in many cases due to the limit spatial aperture of the sensor array and the responses of the sensors. So the eigen-structure based methods have been widely adopted, which include the MUSIC algorithm and the variants thereof Kaveh and Barabell (1986), Stoica and Nehorai (1989), Rao (1990) Friedlander (1990), Krim et al. (1992), Jäntti (1992), Rao (1993), Krim and Proakis (1994), Asztély and Ottersten (1998), De Jong and Herben (1999),Wang et al. (2001), Salameh and Tayem (2006) and other subspace-based methods, such as the propagator method Marcos et al. (1994) Marcos et al. (1995) Tayem and Kwon (2005) Tayem and Kwon (2005), and ESPRIT (which does not result in a spectrum, but provides analytically the solutions for parameter estimates)Paulraj (1986), Jäntti (1992), Asztély and Ottersten (1998). In 1990’s, algorithms derived based on the parametric models of channel were applied to extracting the channel model parameters from the measurement data. The maximum likelihood estimator and the approximation of it with iterative estimate updating procedure can be used to estimate both the deterministic parameters and the statistical parameters of channels depending on the generic model applied. These algorithm are also called super resolution methods, as they may achieve higher resolution than the conventional spectral-based methods. Typical examples of these algorithms are the expectation-maximization (EM) algorithm Moon (1997) Frenkel and Feder (1999) Nielsen (2000) Zhang (2001), the space-alternating generalized expectation-maximization (SAGE) algorithm Fessler and Hero (1994) Fleury et al. (1999) Yin et al. (2006b) Taparugssanagorn et al. (2007) Yin et al. (2007), the Richter’s Maximum likelihood (RiMAX) algorithm Richter (2004) Richter (2005) Richter et al. (2000) Richter et al. (2003), and the variants of the SAGE algorithm by adopting models different from the widely used resolvable specular path model Bengtsson and Ottersten (2000) Yin et al. (2006a). These literature covered many aspects of the algorithms, including the impact of the antenna arrays used for data collection, the influence of the model mismatch between the usually applied resolvable specular-path model and the true scattering effect, also the analysis and comparison of these algorithms. These algorithms are applied to extract multi-dimensional parameters of channels from measurement data. The parameters include the direction of arrival, direction of departure, delay, Doppler frequency and polarization matrix of individual propagation paths. The estimates are used to construct the stochastic geometry-based or ray-based channel models, such as the well known 3GPP TR 25.996 models Spatial channel model for Multiple Input Multiple Output (MIMO) simulations (Release 7) (2007), the WINNER II spatial channel model-enhanced (SCME) WINNER II Channel Models (IST-WINNER2. Tech. Rep., 2007), the IMT-advanced channel models REPORT ITU-R M.2135 Guidelines for evaluation of radio interface technologies for IMT-Advanced (2007). In the spatial channel model, clustering of multiple paths is considered as a necessary step for generating the small-scale parameters of the channel, such as the cluster delay spread, cluster angular spread, and the time-variant behavior of the clusters. How to appropriately cluster the multiple propagation paths has been discussed in literature Czink et al. (2005a) Czink et al. (2005b). First visual-inspection-based clustering methods were proposed Czink et al. (2007c), which is impractical for a large amount of measurement data. Moreover, the clustering results may not be unique when the users have different opinion about the clusters. The automatic clustering methods were alternatively designed which require minimum interactions of users. These methods make use of the so-called multipath component distance measure, or environment characterization metric to group the paths into cluster Czink et al. (2005c) Czink et al. (2005b) Czink et al. (2006). Readers are referred to Czink (2007) for the detailed description of various clustering methods and their performance. The multipath clustering concept has also been extended to the modeling of time-variant channelsCzink et al. (2007a) Czink et al. (2007b) Xiao et al. (2007) Xiao and Burr (2008). The objective of introducing the time￾variant clusters is to reduce the computational complexity when generating spatial-correlated time-variant channel realizations or channel matrices. The parameters of the clusters, especially the centroid of clusters are tracked through