Oestges

Modeling the MIMO Propagation Channel: 

Modeling the MIMO Propagation Channel Claude Oestges Microwave Laboratory, Université catholique de Louvain, Belgium

Outline: 

Outline Motivation and introduction MIMO channel modeling Physical channel models Analytical (non physical) channel models A few challenges Use of multiple polarizations Antenna correlations vs. cross-channel correlations Validity of Kronecker structure and diagonal channels Key hole effect

Motivation: 

Motivation 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 accuracy

Introduction to MIMO: 

Introduction to MIMO MIMO = Multiple spaced or cross-polarized antennas at transmit (Tx) and receive (Rx) sides MIMO diversity (Alamouti scheme, ST trellis codes) Improve quality (SNIR, BER) through redundancy Spatial multiplexing (e.g. BLAST) Increase capacity/throughput (data rate) by opening parallel independent channels

Introduction to MIMO: 

Introduction to MIMO MIMO channels The channel is represented by a MR  MT matrix H Need for modeling both individual matrix elements and relationships (correlations) between elements MIMO channel H MT Tx MR Rx

Introduction to MIMO: 

Introduction to MIMO Example for a 2  2 system/channel MIMO parameterization: correlations

MIMO channel models: 

MIMO channel models Physical channel models Ray-tracing Physical-statistical methods Geometry-based stochastic models (Double-)directional channel models (D)DCM Analytical (non physical) channel models Channel covariance matrix (full model) Simplified or specific models

Ray-tracing techniques: 

Ray-tracing techniques Model 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 polarisation coefficient factor

Physical-statistical methods (I): 

Physical-statistical methods (I) Ray-tracing is highly site-specific More general model obtained by combining A physical model, i.e. electromagnetic relationships between environmental and propagation variables Statistical distributions of the environmental parameters Advantages Wide parameter range validity (frequency, etc.) Reduced computational cost thanks to pre-calculation High statistical accuracy

Physical-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 area

Geometry-based models (I): 

Geometry-based models (I) Original 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 implementation

Geometry-based models (II): 

Geometry-based models (II) Improved approach (among others) Derive a geometrical distribution of scatterers in order to match a given uni-polarized power-delay profile at a reference (maximal) range Scale the scatterer distribution to any (smaller) range Integrate fixed and mobile channel dynamics (appearance and disappearance of scatterers) Integrate dual-polarization modeling (from ray-tracing results) Combine with directional antenna patterns

Geometrical interpretation: 

Geometrical interpretation Local scattering ratio =  / [ +  ] determined by Tx and Rx angle-spreads local scatterer remote scatterer  extended scatterer Rx Tx exclusion disc

Multi-polarized channels: 

Multi-polarized channels For dual-polarized channels The reflection coefficient is a matrix: ij is the reflection coefficient for incident wave polarized as the jth Tx antenna and reflected wave polarized as the ith Rx antenna  Scattering XPD (affecting scattered contribution only) Antennas are not ideal  Antenna XPD (affecting both LOS and scattered paths)

Scattering and antenna XPD: 

Scattering and antenna XPD Scattering XPD Antenna XPD V  Epol + a . EXpol

Double-directional (DD) models (I): 

Double-directional (DD) models (I) Directional models Originally, SIMO or MISO Example: COST 259 Radio environment (TU, etc.) Large-scale effects (dynamic behavior of clusters, shadowing, etc.) Mixed geometrical-stochastic approach Concept of far and local clusters Visibility regions Small-scale effects : fading (multipaths)

Double-directional (DD) models (II): 

Double-directional (DD) models (II) DD channel models Truly MIMO Related to physical propagation mechanisms Finite number of scatterers easy to implement Finite energy assumption is implicit Correlation between DoA, DoD and Doppler implicit

Double-directional (DD) models (III): 

Double-directional (DD) models (III) Example: COST 273 (modeling in progress) Based on COST 259, but extended to multiple antennas at the MS  DoA and DoD joint distributions, DoA and DoD related by means of a coupling matrix Parameterized model based on measurement data in different types of environments: large macrocells, small macrocells, microcells, picocells, tunnels, etc.

COST 273 model: 

COST 273 model Two components Adequate combining of a geometry-based model (DoAs and DoDs at each end, ~ COST 259) and a direction-coupling matrix Should be capable of representing uniquely-coupled modes (single and multiple –scattering with 1-to-1 coupling) and Kronecker-structured diffuse scattering modes Model parameters Number of non-zero entries in each row of the coupling matrix Ratio of most powerful “1” w.r.t. the other “1s”

MIMO channel models: 

MIMO channel models Physical channel models Ray-tracing Physical-statistical methods Geometry-based stochastic models (Double-)directional models Analytical (non physical) channel models Channel covariance matrix (full model) Simplified or specific models

MIMO channel covariance matrix: 

MIMO channel covariance matrix General model (Rayleigh) R is semi-positive definite Usual simplification: r1 = r2, t1 = t2 Correlations Antenna correlations (r and t) are well-known in MIMO studies (detrimental to capacity/performance) Cross-channel correlations (e.g.  s1 and s2 in 2  2 channels) are less used

Dual-polarized covariance matrix: 

Dual-polarized covariance matrix Channel matrix in dual-polarization schemes Hadamard product of the space-related matrix Hs (uni-polarized antennas) and the polarization-related matrix Hp (co-located antennas) For HV/HV scheme: Each correlation is the product of the usual space-related correlation (r, t, s1 or s2) and a polarization-related correlation (, , 1 or 2)

Ricean channels: 

Ricean channels Ricean fading Existence of a dominant component (often LOS) K-factor (K) = ratio of dominant (fixed, coherent) component to fading component Rayleigh channel is combined with Ricean matrix HRice General model Elements of HRice have unit power, but phase factors depending on array geometry and orientation

Kronecker model: 

Kronecker model Independence between DoAs and DoDs Example in 2  2 channels: s1 = r t and s2 = r* t For arbitrary array sizes: R = RR  RT Rx and Tx correlation matrices (easy physical interpretation) Validity Confirmed by some measurements (Yu et al., 2002) Questioned by recent measurement results (Oezcelik et al., 2003)

Virtual channel representation: 

Virtual channel representation Decomposition in the beamspace with predefined steering vectors 3 components Unitary steering matrices in the virtual domain ARx and ATx Power coupling matrix  ( is the element-wise square root) Angular resolution ~ number of virtual angles (cannot be chosen arbitrarily but are related to the actual antenna arrays)

Weichselberger model: 

Weichselberger model Joint correlation properties at Rx and Tx DoA and DoD relationship is preserved 3 components Spatial eigenbasis of Rx and Tx correlation matrices URx and UTx Power coupling matrix  ( is the element-wise square root) Structure of  strongly related to the radio environment If  is diagonal, each single DoD is linked to a single DoA If  is of rank one, the model reduces to the Kronecker model

Keyhole effect: 

Keyhole effect What is it ? Correlation matrices at both link ends have high rank Multipaths are forced to travel through a narrow keyhole, so the rank of the instantaneous channel matrix is low Keyhole effect occurs very seldom (apparently …) Gesbert model Both HT and HR have low correlation matrix ( i.i.d.) The channel is double-Rayleigh distributed

Channel model and mutual information (in Rayleigh fading): 

Channel model and mutual information (in Rayleigh fading) Exact closed-form of mutual information ? Upper-bound: inverse log2 and E Application to 2  2 schemes Cross-channel correlations sk play a symmetrical beneficial role on ergodic capacity (at least for 2 x M or M x 2 schemes) Generally not be true for outage capacity at low outage levels

Impact of cross-channel correlations (I): 

Impact of cross-channel correlations (I) For equal average energy, actual capacity is not always maximized by i.i.d. fading One-ring model Range-to-ring-radius ratio = 30 Broadside arrays dR = 0.38  dT = 30 dR SNR = 30 dB

Impact of cross-channel correlations (II): 

Impact of cross-channel correlations (II) Kronecker model will under-estimate capacity One-ring model Range-to-ring-radius ratio = 30 Broadside arrays dR = 0.38  dT = 30 dR SNR = 30 dB

Impact of cross-channel correlations (II): 

One-ring model Range-to-ring-radius ratio = 30 Broadside arrays dR = 0.38  dT = 30 dR SNR = 30 dB Impact of cross-channel correlations (II) Kronecker model will under-estimate capacity One-ring model (a.k.a. Jakes or Lee or Abdi et al. and used by Shiu et al.) has NO Kronecker structure

NEWCOM: analysis of diagonal channels (TU Wien – UCL): 

NEWCOM: analysis of diagonal channels (TU Wien – UCL) Let us consider M  M channels with All antenna correlations = 0 Maximum number of cross-channel correlations = 1 Example of 4  4 channel For these channels, the ergodic mutual information (capacity) is exactly linear in M

NEWCOM: analysis of diagonal channels (TU Wien – UCL): 

NEWCOM: analysis of diagonal channels (TU Wien – UCL) Propagation scenarios leading to M  M diagonal channels M DoDs coupling into M DoAs (1-to-1 coupling) All M steering/response vectors are orthogonal at each end Using a virtual channel representation, the coupling matrix is a sparse matrix with one entry in each row/column

Summary (I): 

Summary (I) MIMO channel models are essential for system design and simulation Physical models Independent of antenna configuration Fully physical models (ray-tracing, etc.) Prohibitive computation time Site-specific Parameterized models (e.g. DD models) Need to take into account different propagation methods For parameterized models, derivation from measured data might not be straightforward (parameter estimation methods, etc.)

Summary (II): 

Summary (II) Non physical models Directly obtained from measurements (including antennas) Manipulate with extra care (can lead to artifacts) Kronecker model is oversimplified (most geometry-based models have NO Kronecker structure) … is it important ? It depends on the considered metric … Diagonal channels: better than i.i.d. ?

Summary (III): 

Summary (III) Challenges Polarization modeling Experimental validation required Optimization of multi-polarized (larger than 2  2) systems Keyholes: where/when do they appear in real-world? Kronecker structure vs. real-world data? What makes a good analytical model of MIMO channels? It depends on the considered metric … What is an “ideal” MIMO channel ? Answers in the next presentation ?