Modeling the MIMO Modeling the MIMO Propagation ChannelPropagation ChannelClaude OestgesMicrowave Laboratory, UniversitUniversit catholiquecatholique de de LouvainLouvain, BelgiumOutlineOutlinelMotivation and introductionlMIMO channel modeling Physical channel models Analytical (non physical) channel modelslA few challenges Use of multiple polarizations Antenna correlations vs. cross-channel correlations Validity of Kronecker structure and diagonal channels Key hole effectOestges, Joint NEWCOM-COST 273 Workshop, Bologna (Italy), January 19, 2005MotivationMotivation Why do we need channel models ? Prediction models for network planning Site-specific Antenna-dependent Excellent accuracy Standard models for system design and testing of signal processing algorithms Site- and antenna-independent Reduced accuracyOestges, Joint NEWCOM-COST 273 Workshop, Bologna (Italy), January 19, 2005Introduction to MIMOIntroduction to MIMOlMIMO = Multiple spaced or cross-polarized antennas at transmit (Tx) and receive (Rx) sides MIMO diversityMIMO diversity (Alamouti scheme, ST trellis codes) Improve quality (SNIR, BER) through redundancy Spatial multiplexingSpatial multiplexing (e.g. BLAST) Increase capacity/throughput (data rate) by opening parallel independent channelsOestges, Joint NEWCOM-COST 273 Workshop, Bologna (Italy), January 19, 2005Introduction to MIMOIntroduction to MIMO MIMO channels The channel is represented by a MR MT matrix H Need for modeling both individual individual matrix elements and relationshipsrelationships (correlations) between elementsMIMO channel HMTTxTxMRRxRxOestges, Joint NEWCOM-COST 273 Workshop, Bologna (Italy), January 19, 2005Introduction to MIMOIntroduction to MIMO Example for a 2 2 system/channel MIMO parameterization: correlationsOestges, Joint NEWCOM-COST 273 Workshop, Bologna (Italy), January 19, 2005MIMO channel modelsMIMO channel modelslPhysical channel models Ray-tracing Physical-statistical methods Geometry-based stochastic models (Double-)directional channel models (D)DCMlAnalytical (non physical) channel models Channel covariance matrix (full model) Simplified or specific modelsSite-specificOestges, Joint NEWCOM-COST 273 Workshop, Bologna (Italy), January 19, 2005Ray-tracing techniquesRay-tracing techniqueslModel features Buildings are represented by blocks with given material characteristics Path-loss, shadowing and multipaths are implicitly modelled together Geometrical optics: each mechanism is ray-modelled using Fresnel theory and Uniform Theory of Diffraction (UTD)antenna gain complex dyadic spreading and polarisationcoefficient factorOestges, Joint NEWCOM-COST 273 Workshop, Bologna (Italy), January 19, 2005Physical-statistical methods (I)Physical-statistical methods (I)lRay-tracing is highly site-specificlMore general model obtained by combiningA physical model, i.e. electromagnetic relationships between environmental and propagation variablesStatistical distributions of the environmental parameterslAdvantagesWide parameter rangeparameter range validity (frequency, etc.)Reduced computational cost thanks to pre-calculationpre-calculationHigh statistical accuracyOestges, Joint NEWCOM-COST 273 Workshop, Bologna (Italy), January 19, 2005Physical-statistical methods (II)Physical-statistical methods (II)The link between physical and environmental parameters is established by applying a ray-tracing tool in a canonical areaOestges, Joint NEWCOM-COST 273 Workshop, Bologna (Italy), January 19, 2005Geometry-based models (I)Geometry-based models (I)lOriginal approach Locate point scatterers according to a certain PDF (one- ring, two-ring, elliptical, Von Mises, etc.) Single scattering only (but can be extended) No range dependency (large-scale variations ?) No direct relationship with tap-delay line models Easy implementationOestges, Joint NEWCOM-COST 273 Workshop, Bologna (Italy), January 19, 2005Geometry-based models (II)Geometry-based models (II)lImproved approach (among others) Derive a geometricalgeometrical distribution of scatterers in order to match a given uni-polarized power-delay profile at a reference (maximal) range Scale Scale the scatterer distribution to any (smaller) range Integrate fixed and mobile channel dynamicsdynamics (appearance and disappearance of scatterers) Integrate dual-polarizationdual-polarization modeling (from ray-tracing results) Combine with directional antennaantenna patternsOestges, Joint NEWCOM-COST 273 Workshop, Bologna (Italy), January 19, 2005Geometrical interpretationGeometrical interpretation Local scattering ratioLocal scattering ratio = / + determined by Tx and Rx angle-spreadslocal scattererremote scattererextended scattererRxTxexclusion discOestges, Joint NEWCOM-COST 273 Workshop, Bologna (Italy), January 19, 2005Multi-polarized channelsMulti-polarized channelslFor dual-polarized channels The reflection coefficient is