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Topics in MIMO Channel Modeling
July 2003 Topics in MIMO Channel Modeling Keith Baldwin Mark Webster Steve Halford Intersil Baldwin/Webster, Intersil
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July 2003 Overview This presentation highlights several topics in MIMO channel modeling Topic 1: Saleh-Valenzuela PDP Generator Topic 2: Tap Azimuth Spectrum Topic 3: LOS antenna orientation Topic 4: Co-planar arrays Topic 5: Element azimuth gain Topic 6: Tx/Rx PAS independence The goal is not to force a change to the current modeling technique, but to broaden our understanding of channel modeling issues Additional complexity may make certain ideas unattractive Baldwin/Webster, Intersil
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End-to-End Channel Constituents
July 2003 End-to-End Channel Constituents Spatial environment (Topics 1 & 2) Tx and Rx antenna effects (Topics 3, 4, 5) h 1,1 h 1,3 TX Processing RX Processing r s h 3,1 h 3,3 Channel w/o Antennas Channel w/ Antennas Baldwin/Webster, Intersil
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Topic 1: Modification using Direct Saleh-Valenzuela MIMO
July 2003 Topic 1: Modification using Direct Saleh-Valenzuela MIMO Currently, 6 fixed channel models are specified See doc:IEEE r1 Derivatives of the Medbo models Patterned-off the Saleh-Valenzuela model A. Saleh and R. Valenzuela, “A Statistical Model for Indoor Multipath Propagation,” IEEE JSAC, Vol. SAC-5, No. 2, Feb. 1987, pp IEEE a used the Saleh-Valenzuela model directly See 02490r1P802-15_SG3a-Channel-Modeling-Subcommittee-Report-Final.doc This section presents the future possibility of using the Saleh-Valenzuela directly as a generalized front-end Baldwin/Webster, Intersil
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Current Method: Medbo-Derivative Model D Power Delay Profile
July 2003 Current Method: Medbo-Derivative Model D Power Delay Profile ~10 nsec Resolution -50 50 100 150 200 250 300 350 400 5 10 15 20 25 30 Delay in Nanoseconds Relative dB ~30 nsec Resolution ~50 nsec Resolution Baldwin/Webster, Intersil
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Direct Saleh-Valenzuela Method
July 2003 Direct Saleh-Valenzuela Method Simple Cluster Model Cluster Arrival Rate (Poisson) and Decay Rate Tap Arrival Rate (Poisson) and Decay Rate Binning in the Time Domain Specular Model… 3 clusters, Exponential TOAs, Trms = 47ns Down-sampled Coherently Combined 10 nsec Time Binning Power Delay Profile 100 GHz sample rate (0.010 nsec resolution) 100 MHz sample number (10 nsec resolution) Baldwin/Webster, Intersil
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Comparison of 2 Methods for Power Delay Profile Generation
July 2003 Comparison of 2 Methods for Power Delay Profile Generation Cluster Arrival Rate Cluster Decay Rate Tap Arrival Rate Tap Decay Rate Future Possibility Current Method Model Index Equivalent PDP Generators Saleh-Valenzuela PDP Generator Fixed Set of Medbo-Derivative PDP’s Identical Time-Bin Taps MIMO Channel Tap Generator MIMO Channel Tap Generator Antenna Characteristics Antenna Characteristics Channel Taps Channel Taps Baldwin/Webster, Intersil
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Why Use the Generalized Saleh-Valenzuela MIMO Model?
July 2003 Why Use the Generalized Saleh-Valenzuela MIMO Model? May generalize the model to a broader class of environments? Might allow reuse of the UWB model and MATLAB code for certain scenarios? Might allow direct comparisons between a UWB system and MIMO system Might allow greater channel randomization during packet error rate simulation? May provide statistical advantages since random specular values are generated and bin-aggregated? Baldwin/Webster, Intersil
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Topic 2: Tap Azimuth Spectrum
July 2003 Topic 2: Tap Azimuth Spectrum A MIMO channel is composed of clusters The clusters are composed of taps (time bins) The current model assigns a Power Azimuth Spectrum (PAS) to each tap Laplacian distribution with 5 degree spread See doc:IEEE r1 There has been some discussion on what the best tap angular spread should be This section suggests that if larger angular spreads are used for taps, it may be best to used a fixed number of discrete draws from the distribution to determine the tap correlations Baldwin/Webster, Intersil
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Time Bins Aggregate Paths of Nearly Equal Length
July 2003 Time Bins Aggregate Paths of Nearly Equal Length For example, a 30 nsec time bin resolution aggregates all multipath with path-differentials paths under 10 meters Coarse time bins aggregate large path differentials Scatterer Cluster Example Arrival Times v t RX TX Baldwin/Webster, Intersil
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Model D: 1st Cluster Laplacian July 2003 Tap Cluster Angular Angular
Spread 30 degrees Tap Angular Spread 5 degrees Laplacian Antenna Element Correlation For Tap -50 50 100 150 200 250 300 350 400 5 10 15 20 25 30 Delay in Nanoseconds Relative dB 10 nsec Bins: 3.3 meter Bins Model D Cluster 1 PDP 30 nsec Bins: 10 meters Bins 50 nsec Bins: 17 meters Bins Baldwin/Webster, Intersil
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Ray Tracing Example: Room-to-Room
July 2003 Ray Tracing Example: Room-to-Room From German00 Transmit Clusters Are Not Reciprocal to Receive Clusters Baldwin/Webster, Intersil
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Ray Tracing Example: Hall-to-Room
July 2003 Ray Tracing Example: Hall-to-Room From Browne02 Baldwin/Webster, Intersil
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Ray Tracing Example: With Single Room
July 2003 Ray Tracing Example: With Single Room From Trueman 03 Baldwin/Webster, Intersil
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Handling Larger Tap Angular Spreads
July 2003 Handling Larger Tap Angular Spreads Time bins aggregate multipath rays Some ray tracing examples suggest tap bins may have larger angular spreads Increasing the tap angular spread of the Laplacian may over-estimate the multipath richness Channel dimensionality is proportional to the number of independent multipath components Possible solution is to make a limited number of discrete draws from the distribution Larger Angular Spreads Decorrelate the antenna Elements Effectively an Infinite Sum Less element Decorrelation A Finite Sum Baldwin/Webster, Intersil
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Topic 3: LOS Antenna Orientation
July 2003 Topic 3: LOS Antenna Orientation Currently, antenna azimuth orientation is not important for the non-line of sight (NLOS) component Cluster angle of arrival (AOA) and cluster angle of departure (AOD) are assumed uniformly distributed from 0 to 2p See doc:IEEE r1 However, the line of sight (LOS) component is sensitive to orientation How should this be handled? Baldwin/Webster, Intersil
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July 2003 NLOS Component NLOS multipath components are randomly distributed around the Tx and Rx antennas Hence, antenna orientation is unimportant No Direct Path TX RX Baldwin/Webster, Intersil
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LOS: Two Examples Distinct LOS correlation behavior
July 2003 LOS: Two Examples Distinct LOS correlation behavior May be reflected in packet error behavior TX RX Example 1 TX RX Example 2 Baldwin/Webster, Intersil
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How Should LOS Antenna Orientation be Handled?
July 2003 How Should LOS Antenna Orientation be Handled? Should the antenna orientation be randomized from packet to packet? Uniformly 0 to 2p ? This may make the LOS correlation matrix more unmanageable during simulation Baldwin/Webster, Intersil
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Topic 4: Handling Co-Planar Antenna Geometries
July 2003 Topic 4: Handling Co-Planar Antenna Geometries Earlier discussions have focused on the use of an uniform linear array (ULA) All elements are co-linear All elements are uniformly spaced, D=2pd/l See doc:IEEE r1 This section shows the extension to elements arbitrarily located in the horizontal plane Form pairs of 2-element ULA’s Baldwin/Webster, Intersil
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Review of the Co-Linear Uniform Linear Array (ULA)
July 2003 Review of the Co-Linear Uniform Linear Array (ULA) θ Dr = D sinθ D = 2πd/λ TX RX S1 S2 Element Correlation – single wave s1 = βe-jωt, s2 = s1e-jDr , where b is the wave amplitude ρ12 = 1/β2 E{s2 s1*} = (1/β2 ) βe-jωtejDr βejωt = e-jDr = e-jDsinθ For plane waves from all directions, P(q) ρ12 = 0ƒ2π e-jDsinθ P(θ) dθ , where P(q) is the power azimuth spectrum Baldwin/Webster, Intersil
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Introducing the Co-Planar Array
July 2003 Introducing the Co-Planar Array 3 pairs 12 23 13 Each pair of elements fits into the same mathematical framework as for ULA pairs D = 2πd/λ θ Dr12 = D sinθ TX RX S1 S3 D = 2πd/λ S2 Dr23 = D cosθ Element Correlation 1 -> 2 ρ12 = 0ƒ2π e-jDsinθ P(θ) dθ (as before) Element Correlation 2 -> 3 Plane Wave s2 = βe-jωt, s3 = s1e-jDr23 ρ23 = 1/β2 E{s2 s1*} = (1/β2 ) βe-jωtejDr βejωt = e-jDr23 = e-jDcosθ Continuous PAS ρ23 = 0ƒ2π e-jDcosθ P(θ) dθ = ρ12 = 0ƒ2π e-jDsinθ P(θ) dθ Baldwin/Webster, Intersil
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Minor Modification of Correlation Equation for Co-planar Arrays
July 2003 Minor Modification of Correlation Equation for Co-planar Arrays Each pair of elements (k,l) defines a 2-element ULA with an Associated spacing, Dkl=2pdkl/l Associated angle, fkl , relative to azimuth, q (k,l) spacing (k,l) reference angle Baldwin/Webster, Intersil
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Topic 5: Antenna Element Gain
July 2003 Topic 5: Antenna Element Gain Real antennas elements often have directional gain This may be intentional as in the case of switched antenna pattern diversity, or unintentional as in the case of elements with significant mutual coupling. Each antenna element has a complex gain as a function of azimuth q: E(q) This section looks at an elementary model modification for handling azimuth gain Baldwin/Webster, Intersil
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Revisit the ULA with Omni-Directional Elements
July 2003 Revisit the ULA with Omni-Directional Elements θ Dr = D sinθ D = 2πd/λ TX RX S1 S2 Element Correlation – single wave s1 = βe-jωt, s2 = s1e-jDr , where b is the wave amplitude ρ12 = 1/β2 E{s2 s1*} = (1/β2 ) βe-jωtejDr βejωt = e-jDr = e-jDsinθ For waves from all directions, P(q) ρ12 = 0ƒ2π e-jDsinθ P(θ) dθ , where P(q) is the power azimuth spectrum Baldwin/Webster, Intersil
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Comments on ULA (co-linear) with Omni-Directional Elements
July 2003 Comments on ULA (co-linear) with Omni-Directional Elements Each antenna element has a complex gain, E = 1 The incident signal is expressed spatially by the Power Azimuth Spectrum (PAS) which is normalized, 0ƒ2π P(θ) dθ = 1. Consequently the autocorrelation elements of the correlation matrix are unit magnitude, ρ11 = ρ22 = 0ƒ2π e-j0 P(θ) dθ = 1. Baldwin/Webster, Intersil
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ULA with Directional Elements
July 2003 ULA with Directional Elements Direction-dependent complex gain added, E(q) In general, differs for each element D = 2πd/λ θ Dr = D sinθ TX RX S1 S2 single wave s1 = β e-jωt E1(θ), s2 = β e-jωt e-jDr E2(θ) where Ei(θ) = normalized voltage gain pattern of element i ρ21 = 1/β2 E{s2 s1*} = (1/β2 ) βe-jωtejDr βejωt E1(θ) E2(θ) = e-jDr E1(θ) E2(θ) = e-jDsinθ E1(θ) E2(θ) for waves from all directions ρ21 = 0ƒ2π e-jDsinθ P(θ) E1(θ) E2(θ) dθ E1(θ) E2(θ) Baldwin/Webster, Intersil
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Handling Antenna Element Gain
July 2003 Handling Antenna Element Gain An extra antenna-gain weighting was applied to the correlation equation Note, this assumes that The receive PAS is not influenced by the transmit antenna element gains The receiver perceived transmit antenna correlations are not influenced by the receive antenna gains This may be violated in some cases E.g., a highly directive pencil beam may reduce multipath, hence affecting the PAS Baldwin/Webster, Intersil
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Topic 6: Tx/Rx Decoupling
July 2003 Topic 6: Tx/Rx Decoupling MIMO channel modeling is greatly simplified when there is correlation decoupling between the transmitter and receiver antennas from the receiver’s perspective This is realized when Receive antenna element correlations dominated by the reflectors local to the receiver Transmit antenna element correlations (as observed by the receiver) are dominated by the reflectors local to the transmitter Some desired modeling features may violate this useful decomposition Antenna element gains Elevation dependences Polarization Baldwin/Webster, Intersil
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Decoupling the Tx/Rx Correlation
July 2003 Decoupling the Tx/Rx Correlation Let Sik* = signal from Tx ant i to Rx ant k With rikjl = E{ Sik* Sjl } = rij rkl , if independent Correlation between tx antenn i and j: rij Correlation between Rx antenna k and l: rkl h 1,1 h 1,3 TX Processing RX Processing r s h 3,1 h 3,3 Local Tx Scattering Dominates Tx Local Rx Scattering Dominates Rx Baldwin/Webster, Intersil
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Potential Violations Antenna element azimuth gain
July 2003 Potential Violations Antenna element azimuth gain High gains or deep nulls in some directions may impact the scattering observed by receiver/transmitter Antenna element elevation gain Example: Transmitter concentrating energy in elevation may impact the receivers observed PAS Antenna polarization Transmit polarization impacts received polarization Horizontal polarization (horizontal dipole) possess azimuth gain variations Horizontal Dipole Azimuth Response Baldwin/Webster, Intersil
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Tipped Antenna Element
July 2003 Tipped Antenna Element If a vertical antenna element over a ground plane is tipped to a slope, The azimuthal gain will vary with azimuth The elevation gain will vary with azimuth The polarization will change with azimuth Conventional Vertical Antenna Gain constant versus azimuth Polarization constant versus azimuth Tipped Vertical Antenna Gain varies versus azimuth Polarization varies versus azimuth Baldwin/Webster, Intersil
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July 2003 Generalized Response If independence is not possible, the situation becomes extremely complex Experimental data is needed to corroborate de-coupling assumptions Receive Antenna Correlation Not Independent of Transmit Antenna Receive Azimuth Elevation Polarization Vector of Tx Antenna Elements Azimuth, Elevation, Polarization Response Receive Antenna Elements Azimuth, Elevation, Polarization Reponse Baldwin/Webster, Intersil
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Polarization Transfer Function
July 2003 Polarization Transfer Function One simply way to decompose polarization is to break the Tx-to-Rx response up into four componentes: vert-vert, vert-horiz, horiz-vert, horiz-horiz See doc:IEEE r1 This decomposes the previous page’s expression into four components but angular dependences may remain: This complexity quickly grows Baldwin/Webster, Intersil
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July 2003 Conclusion Big-picture introductions were provided for several topics in MIMO channel modeling Topic 1: Saleh-Valenzuela PDP Generator Topic 2: Tap Azimuth Spectrum Topic 3: LOS antenna orientation Topic 4: Co-planar arrays Topic 5: Element azimuth gain Topic 6: Tx/Rx PAS independence It is hoped this has provided a deeper understanding of several issues Baldwin/Webster, Intersil
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