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Topics in MIMO Channel Modeling

Topics in MIMO Channel Modeling. Keith Baldwin Mark Webster Steve Halford Intersil. 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

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Topics in MIMO Channel Modeling

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  1. Topics in MIMO Channel Modeling Keith Baldwin Mark Webster Steve Halford Intersil Baldwin/Webster, Intersil

  2. 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

  3. 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 RX Processing TX Processing r s h 3,1 h 3,3 Channel w/o Antennas Channel w/ Antennas Baldwin/Webster, Intersil

  4. Topic 1: Modification using Direct Saleh-Valenzuela MIMO • Currently, 6 fixed channel models are specified • See doc:IEEE 11-03-161r1 • 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. 128-137 • IEEE 802.15.3a 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

  5. 30 25 20 15 Relative dB 10 5 0 -50 0 50 100 150 200 250 300 350 400 Delay in Nanoseconds Current Method: Medbo-Derivative Model D Power Delay Profile ~10 nsec Resolution ~30 nsec Resolution ~50 nsec Resolution Baldwin/Webster, Intersil

  6. 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

  7. Comparison of 2 Methods for Power Delay Profile Generation • Cluster Arrival Rate • Cluster Decay Rate • Tap Arrival Rate • Tap Decay Rate Future Possibility • Model Index Current Method 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

  8. 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

  9. 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 11-03-161r1 • 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

  10. 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

  11. 30 25 20 Relative dB 15 10 5 0 -50 0 50 100 150 200 250 300 350 400 Delay in Nanoseconds Model D: 1st Cluster Tap Angular Spread 5 degrees Cluster Angular Spread 30 degrees Laplacian Antenna Element Correlation For Tap 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

  12. Ray Tracing Example:Room-to-Room From German00 Transmit Clusters Are Not Reciprocal to Receive Clusters Baldwin/Webster, Intersil

  13. Ray Tracing Example:Hall-to-Room From Browne02 Baldwin/Webster, Intersil

  14. Ray Tracing Example:With Single Room From Trueman 03 Baldwin/Webster, Intersil

  15. 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

  16. 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 11-03-161r1 • However, the line of sight (LOS) component is sensitive to orientation • How should this be handled? Baldwin/Webster, Intersil

  17. 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

  18. TX TX RX LOS: Two Examples • Distinct LOS correlation behavior • May be reflected in packet error behavior Example 1 RX Example 2 Baldwin/Webster, Intersil

  19. 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

  20. 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 11-03-161r1 • This section shows the extension to elements arbitrarily located in the horizontal plane • Form pairs of 2-element ULA’s Baldwin/Webster, Intersil

  21. RX TX S1 D = 2πd/λ θ S2 Dr = D sinθ Review of the Co-Linear Uniform Linear Array (ULA) 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 = 0ƒ2πe-jDsinθ P(θ) dθ , where P(q) is the power azimuth spectrum Baldwin/Webster, Intersil

  22. RX TX S1 θ S2 S3 Dr12 = D sinθ Dr23 = D cosθ D = 2πd/λ 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 Element Correlation 1 -> 2 ρ12 = 0ƒ2πe-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 = 0ƒ2πe-jDcosθ P(θ) dθ = ρ12 = 0ƒ2πe-jDsinθ P(θ) dθ Baldwin/Webster, Intersil

  23. 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

  24. 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

  25. RX TX S1 D = 2πd/λ θ S2 Dr = D sinθ Revisit the ULA with Omni-Directional Elements 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 = 0ƒ2πe-jDsinθ P(θ) dθ , where P(q) is the power azimuth spectrum Baldwin/Webster, Intersil

  26. 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, 0ƒ2πP(θ) dθ = 1. • Consequently the autocorrelation elements of the correlation matrix are unit magnitude, ρ11 = ρ22 = 0ƒ2πe-j0 P(θ) dθ = 1. Baldwin/Webster, Intersil

  27. RX TX S1 θ S2 Dr = D sinθ E1(θ) E2(θ) ULA with Directional Elements • Direction-dependent complex gain added, E(q) • In general, differs for each element D = 2πd/λ 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 = 0ƒ2πe-jDsinθ P(θ) E1(θ) E2(θ) dθ Baldwin/Webster, Intersil

  28. 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

  29. 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

  30. Decoupling the Tx/Rx Correlation • Let Sik* = signal from Tx ant i to Rx ant k • With rikjl = E{ Sik* Sjl} = rijrkl , if independent • Correlation between tx antenn i and j: rij • Correlation between Rx antenna k and l: rkl h 1,1 h 1,3 RX Processing TX Processing r s h 3,1 h 3,3 Local Tx Scattering Dominates Tx Local Rx Scattering Dominates Rx Baldwin/Webster, Intersil

  31. 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

  32. 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

  33. 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

  34. 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 11-03-161r1 • This decomposes the previous page’s expression into four components but angular dependences may remain: • This complexity quickly grows Baldwin/Webster, Intersil

  35. 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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