1/93 Antenna Arrays with Parasitic Elements: a Technology for Compact MIMO Systems Dr. Constantinos B. Papadias Co-authors: O. Alrabadi & A. Kalis Broadband Wireless & Sensor Networks Group (B-WiSE) Athens Information Technology papadias@ait.edu.gr Talk given at the 2nd International Symposium on Applied Sciences in Biomedical and Communication Technologies Bratislava, Slovak Republic, Nov. 24-27, 2009
3/93 www.ait.edu.gr Classical MIMO i. High Cost due to Expensive RF components ii. High Spatial Correlation for Spacing less than λ/2 iii. Reduced Antenna Efficiency due to Strong Mutual Coupling iv. High Consumption of DC Power as Multiple IF/RF Front-ends are used Designing a Low Cost, High Performance Compact MIMO Transceiver Seems Contradictory Using Classical MIMO. No Capacity Gain (Over SISO) for D=λ/4 or less Î Motivation
6/93 Single antenna links: Shannon capacity “It is dangerous to put limits on wireless” Guglielmo Marconi, 1932 • The information-theoretic capacity of single-antenna links is limited by the link’s signal to noise ratio according to Shannon’s celebrated formula • Capacity grows logarithmically with the Tx power (i.e. to go from 1bps/Hz to 11 bps/Hz, the Tx power must be roughly increased by ~1000 times!) •Disclaimer: TX RX 2 log (1 SNR) [bps/Hz] C = + s k ( ) x k ( ) C. Shannon Bell Laboratories Technical Journal, 1950
7/93 Multiple antenna links • Keeping the game fair: total Tx power should remain the same • Questions: (1) What is the corresponding capacity? (2) How should we transmit from the different antennas? (3) How should the receiver operate? TX 1 RX 1 TX 2 RX 2 TX M RX N s k 1 ( ) s k 2 ( ) s k M ( ) x k 1 ( ) x k 2 ( ) x k N ( )
8/93 • We are primarily interested in the case where: – The transmitter only knows the channel statistics but not the channel realization H. This is sometimes referred to as ‘‘open-loop’’ operation – We also assume a coherent receiver that knows perfectly the MIMO channel H • The mutual information with equal power transmission from each antenna (a pragmatic popular approach), is ‘‘Open-loop’’ MIMO † 2 log det T o N n P C I M σ ⎧ ⎫ = + ⎨ ⎬ ⎩ ⎭ HH (see [Foschini ’96] [Foschini & Gans ’98][Telatar ’99] )
9/93 • The capacity can be written equivalently as: • This leads to the following equivalent representation of the MIMO channel in terms of independent component channels (often called ‘‘spatial modes’’): The Spatial Multiplexing Effect 2 2 2 1 1 SNR log 1 log 1 r r T o i i i i n P C M M λ λ σ = = ⎛ ⎞ ⎛ ⎞ = + = + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ∑ ∑ where are the eigenvalues of the channel matrix and is the rank of . 's i λ † HH r H r 1 ( ) s k ′ 1 λ + 1 ( ) x k ′ ( ) r s k ′ r λ + ( ) r n k ′ ( ) r x k ′ 1 ( ) n k ′
10/93 Rayleigh i.i.d. MIMO (open-loop) Outage Capacities SPECTRAL EFFICIENCY (bps/Hz) NUMBER OF UNCORRELATED ANTENNAS (M=N) 0 10 20 30 40 50 60 150 100 50 24dB 18 dB 12dB 6 dB 0 dB SPECTRAL EFFICIENCY vs. NUMBER ANTENNAS AT 1% OUTAGE 1×N Optimum Combining at 24 dB Predicted capacities
18/93 Space-time Block Coding Transmit Architecture ENCODER Space-Time Block Code / Mapping Input Data Stream TX 1 TX M { } %( ) b i { } ( ) b i { } 1 ( ) s k { } ( ) M s k … … • The original bit stream is first encoded • The encoded data are then mapped onto blocks of vector data that are then transmitted out of the antennas • In this fashion, encoding and spatial multiplexing are decoupled: encoding is a time-only operation, whereas the block code determines how the encoded data samples are mapped onto different antenna elements … … Encoded Input Stream (See [Tarokh et al. ’99])
19/93 • have double length but are used for 2 sub-streams, no redundancy • and are odd and even samples from the same user’s data An application to 2.5/3G voice: Space-Time Spreading • Based on Alamouti coding [Alamouti ’98] • Each user’s sub-streams are multiplexed as follows: 1 ( ) s i c 2 c 1 2 ( ) s i 2 2 ( ) s i ∗ c 1 1 ( ) s i c 1 2 ( ) s i ∗ c 2 1 ( ) s i c 2 1 1 2 ( ) ( ) s i s i ∗ − c c 1 1 2 2 ( ) ( ) s i s i ∗ + c c B2 B2 D D b i ( ) 1 ( ) s i c c 1 2 , ⇒ 2 ( ) s i [Hochwald, Marzetta, Papadias 2001]
25/93 IST Mobile Summit, Aveiro, Portugal, June 2003, EU-FP6 Project FITNESS HSDPA MIMO Video Transmission Prototype Demonstrating Multi-User Uplink Processing
27/93 MIMO in LTE (Rel. 8): an Overview • Transmission modes: – Downlink Single User Transmit Diversity – Downlink Spatial Multiplexing & Closed-Loop MIMO – Downlink Multi-User MIMO – Uplink Multi-User MIMO [3GA09]
30/93 IEEE Trans. on Information Theory, Special Issue on Space-Time Transmission, Reception, Coding and Signal Design, Vol. 49, No. 10, Oct. 2003. IEEE Journal on Selected Areas in Communications, Special Issue on MIMO, March 2003. IEEE Trans. on Signal Processing, Special Issue on Signal Processing for Communications, Vol.50, No. 10, Oct. 2002. EURASIP Journal on Applied Signal Processing, Special Issue on Space-Time Coding and Its Applications – Part I, Vol. 2002, No. 3, Mar. 2002. EURASIP Journal on Applied Signal Processing, Special Issue on Space-Time Coding and Its Applications – Part II, Vol. 2002, No. 5, May 2002. EURASIP Journal on Applied Signal Processing, Special Issue on MIMO Communications and Signal Processing, Vol. 2004, No. 5, May 2004. A. Tulino and S. Verdu, Random matrix theory and wireless communications, Foundations & Trends in Communications & Information Theory, Vol. 1, No. 1, 2004. A. Paulraj, R. Nabar and D. Gore, Introduction to Space-Time Wireless Communications, Cambridge University Press, Cambridge, UK, 2003. Alex Gershman, Editor, Space-Time Processing for MIMO Communications, Wiley 2005. T. Kaiser and A. Bourdoux, Editors, Smart Antennas – State of the Art, EURASIP Hindawi Book Series, 2004. H. Bolcskei, D. Gesbert, C. Papadias, A. J. Van der Veen, Editors, Space-Time Wireless Systems: From Array Processing to MIMO Communications, Cambridge University Press, 2006 Further Reading on MIMO
32/93 Yagi-Uda Antenna : Single Step Design Mainly designed and optimized using NEC2. Excitation can be an incident plane wave as in TV Rx or a voltage source. The Ladder Antenna Passive Directors Driven Dipole Passive Reflector S. Uda ‘’On the Wireless Beam of Short Electric Waves’’, Journal of the institute of Electrical Engineers of Japan’’, March 1926-July 1929
33/93 Harrington’s Reactively Controlled Array A Single Active Dipole Surrounded by Six Parasitic Dipoles Loaded with Reactances. Harrington Array Harrington, R. Reactively controlled directive arrays. IEEE Trans Antennas Propag 1978; 26(3): 390-395.
34/93 www.ait.edu.gr Switched Parasitic Arrays (SPA) After 1978 Dinger, R. Reactively steered adaptive array using microstrip patch elements at 4 GHz. IEEE Trans Antennas Propag 1984; 32(8): 848-856. Dinger, R. A planar version of a 4.0 GHz reactively steered adaptive array. IEEE Trans Antennas Propag 1986; 34(3): 427-431. Preston, S. L., Thiel, D. V., Smith, T. A., O’Keefe, S. G., Lu, J. W. Base-station tracking in mobile communications using a switched parasitic antenna array. IEEE Trans Antennas Propag 1998; 46(6): 841-844. Vaughan, R. Switched parasitic elements for antenna diversity. IEEE Trans Antennas Propag 1999; 47(2): 399-405.
35/93 Seven-Element ESPAR ESPAR is a modified version of the Harrington Array in the sense that monopoles rather than dipoles are used, and the variable reactive loads are integrated in the ground plane. Gyoda, K., Ohira, T. Design of electronically steerable pasive array radiator (ESPAR) antennas. Proc. IEEE Antennas Propag Soc Int Symp, 2000, 922-955.
36/93 www.ait.edu.gr Different Configurations T. Ohira and K. Gyoda, “Electronically Steerable Passive Array Radiator Antennas for Low-Cost Analog Adaptive Beamforming”, IEEE International Conference on Phased Array Systems and Technology, 2000. pp. 101 – 104 N-Element ESPAR
37/93 www.ait.edu.gr Monopoles and Dipoles 3D Pattern E-Plane By approximating the H-Plane to be omnidirectional, the array factor AF is easily found by the superposition of the currents induced on the dipoles/monopoles.
38/93 www.ait.edu.gr Analog Adaptive Beamforming: Only via ESPAR C. Sun, A. Hirata, T. Ohira, N. C. Karmakar, “Fast Beamforming of Electronically Steerable Parasitic Array Radiator Antennas: Theory and Experiment”, IEEE Transactions on Antennas ond Propagation, vol. 52, no. 7, July 2004, pp 1819-1832
39/93 www.ait.edu.gr Three Element ESPAR A 3-element ESPAR was mainly introduced for Pattern Diversity. Inter-element spacing of λ/4 and λ/20 was used The configuration is quite attractive for mobile terminal for mitigating the fading effect. T. Sawaya, K. Iigusa, M. Taromaru, and T. Ohira, “Reactance Diversity: Proof-of-Concept Experiments in an Indoor Multipath-Fading Environment with a 5-GHz Prototype Planar Espar Antenna”, Consumer Communications and Networking Conference, 5-8 Jan. 2004, pp. 678 – 680. M. Taromaru and T. Ohira, “Electronically Steerable Parasitic Array Radiator Antenna − Principle, Control Theory and its Applications −”, 28th General Assembly of International Union of Radio Science (URSI GA 2005).
41/93 Till Now Parasitic arrays have been used for 1. Designing fixed directive antennas 2. Reconfigurable arrays for i. Beam and Null Steering ii. Providing Reactance Diversity (Pattern or Angular Diversity) What about true MIMO (i.e. spatial multiplexing?) Can a compact parasitic array function as a MIMO terminal?
43/93 www.ait.edu.gr Classical MIMO i. High Cost due to Expensive RF components ii. High Spatial Correlation for Spacing less than λ/2 iii. Reduced Antenna Efficiency due to Strong Mutual Coupling iv. Interference Among the Parallel RF Chains v. High Consumption of DC Power as Multiple IF/RF Front-ends are used Designing a Low Cost, High Performance Compact MIMO Transceiver Seems Contradictory for Conventional MIMO. Compact Multi-Element Arrays C. Waldschmidt,, S. Schulteis, and W. Wiesbeck, “Complete RF System Model for Analysis of Compact MIMO Arrays”, IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 3, MAY 2004
44/93 www.ait.edu.gr Capacity Motivation The Capacity of a 2x2 system is greater than the ∞x1 C. B. Papadias, ``On the spectral efficiency of space-time spreading schemes for multiple antenna CDMA systems," Thirty-Third Asilomar Conference on Signals, Systems, and Computers, vol.1, 24-27 Oct. 1999.
45/93 www.ait.edu.gr Deploying Complex Decoupling Networks for Mitigating the Mutual Coupling Effect (Multi-port Conjugate Matching) Increased Complexity, Cost and Size Antenna BW Reduction Some Limited Solutions Narrowband Wideband J. Weber, C. Volmer, K. Blau, R. Stephan, and M. A. Hein, ``Miniaturized antenna arrays using decoupling networks with realistic elements," IEEE Trans. Microwave Theory Tech., vol.54, no.6, pp.2733-2740, June 2006.
46/93 www.ait.edu.gr Polarized Arrays Deploying Polarized Arrays Drawbacks: 1. Multiple Front-ends 2. Sub-channels Power Imbalance as the XPD is Environment and Handset Orientation Dependent. 3. Large Size e.g. Two Cross-Polarized Array Elements require an Area of λ2/4 . λ/2 λ/2
49/93 www.ait.edu.gr AF of 2-element λ/2 array (QPSK Signaling) C. Oestges and B. Clerckx,``MIMO Wireless Communication, From Real-World Propagation to Space-Time Code Design," pages 227-230, First Edition, 2007.
50/93 Till Now • In classic MIMO systems we map symbols on orthonormal functions in the antenna domain (on antenna elements). • We have considered mapping symbols directly on the wavevector domain. • This is a Beamspace-MIMO system. • We propose to use parasitic antennas to transmit different symbol pairs simultaneously towards different Angles of Departure at the transmitter, with a single active element.
53/93 www.ait.edu.gr Spatial Multiplexing (SM) via Beamforming (BF) ON-OFF Keying A. Kalis, A. G. Kanatas, M. Carras, A. G. Constantinides, ``On the performance of MIMO systems in the wavevector domain,“ IST Mobile & Wireless Communications Summit, 5-8 June 2006, Mykonos, Greece.
54/93 www.ait.edu.gr BPSK SM via BF E(Θ)=s 0 A(Θ) A. Kalis, A. G. Kanatas, C. Papadias, ``An ESPAR antenna for beamspace-MIMO systems using PSK modulation schemes," IEEE International Conference on Communications 2007, Glasgow, UK, June 24-28, 2007.
55/93 Tx 1 Tx 2 Tx 3 Rx 1 Rx 2 Rx 3 h 11 h 33 θ R,1 θ R,3 θ T,1 θ T,2 θ T,3 θ R,2 describe the coupling between the jth orthogonal basis radiation pattern of the Tx antenna with the ith orthogonal basis radiation pattern of the Rx antenna. { } ( , ) V H i j The Virtual Channel ˆ ˆ ˆ H R V T H H R R b T T R R b T bs bs V bs bs = + = + = + = + = + y Hx n A H A x n A A H A A x n A A H B x n y H x n % % % % % A. M. Sayeed, ``Deconstructing multiantenna fading channels," IEEE Trans. Signal Processing, vol. 50, pp. 2563-2579, Oct. 2002.
56/93 www.ait.edu.gr Troubles 1. Changing the driving point impedance when changing the loads. 2. The obtained pattern may not be a pure linear combination of the desired functions. 3. Can hardly be scaled to higher order modulation schemes.
57/93 www.ait.edu.gr Pattern Decomposition: A Novel Approach Example: BPSK Signaling O. N. Alrabadi, A. Kalis, C. Papadias and A. Kanatas, ``Spatial Multiplexing by decomposing the far-field of a compact ESPAR antenna," IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), 15-18 Sept 2008.
58/93 www.ait.edu.gr Circuit Relations of the 3-element ESPAR O. N. Alrabadi, A. Kalis, C. Papadias and A. Kanatas, ``Spatial Multiplexing by decomposing the far-field of a compact ESPAR antenna," IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), 15-18 Sept 2008.
59/93 www.ait.edu.gr Three-Element ESPAR Far-Field O. N. Alrabadi, C. B. Papadias, A. Kalis, N. Marchetti and R. Prasad ``MIMO Transmission and Reception Techniques Using Three-Element ESPAR Antennas," IEEE Communications Letters, Vol.13, Issue 4, April 2009 Page(s):236-238.
60/93 www.ait.edu.gr A Basis of Two Angular Functions AF O. N. Alrabadi, C. B. Papadias, A. Kalis, N. Marchetti and R. Prasad ``MIMO Transmission and Reception Techniques Using Three-Element ESPAR Antennas," IEEE Communications Letters, Vol.13, Issue 4, April 2009 Page(s):236-238.
62/93 www.ait.edu.gr All PSK Modulation Schemes cos(kdcos(Θ)) Î 1 As dÎ0 d=λ/16 and less ~0 Non-linear Mapping from the Reactance Space (X L ) to the Signal Space S O. N. Alrabadi, C. B. Papadias, A. Kalis and R. Prasad ``A Universal Encoding Scheme for MIMO Transmission Using a Single Active Element for PSK Modulation Schemes," IEEE Transactions on Wireless Communications.
65/93 www.ait.edu.gr Channel Model Parametric Channel Model J. Fuhl, A. F. Molisch and E. Bonek, ``Unified channel model for mobile radio systems with smart antennas," Ins. Elect. Eng. - Radar Sonar Navigation, vol. 145, pp. 32-4, Feb. 1998.
66/93 www.ait.edu.gr Channel Estimation O. N. Alrabadi, A. Kalis, C. Papadias and A. Kanatas, ``Spatial Multiplexing by decomposing the far-field of a compact ESPAR antenna," IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), 15-18 Sept 2008.
70/93 Performance Evaluation V. Barousis, A. G. Kanatas, A. Kalis, C. Papadias, ``A Limited Feedback Technique for Beamspace MIMO Systems with Single RF Front-end," IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)}, 15-18 Sept 2008.
71/93 www.ait.edu.gr Lack of Orthogonality Correlation may not be always zero among the basis when considering channels with narrow angular spread O. N. Alrabadi, C. B. Papadias, A. Kalis and R. Prasad ``A Universal Encoding Scheme for MIMO Transmission Using a Single Active Element for PSK Modulation Schemes," to appear at IEEE Transactions on Wireless Communications.
73/93 www.ait.edu.gr Spatial Multiplexing (SM) via Antenna Switching (AS) Motivation 1. Next generation wireless terminals (e.g. LTE and WIMAX) will use most probably a single antenna for uplink versus four antennas for downlink. Hence: There is no real MIMO for the uplink Transmission 2. We at AIT have some experience in designing an antenna switch system on the node level. Hence: A MIMO (SM or STBC) can be implemented using a switch antenna system during transmission whereas antenna selection diversity is used during reception. O. N. Alrabadi, C. B. Papadias, A. Kalis, N. Marchetti and R. Prasad ``Spatial Multiplexing via Antenna Switching," Accepted on 13 June 2009 at the IEEE Communications Letters.
74/93 www.ait.edu.gr Motivation, Cont. Energy Saving in WSN’s Motivation: Total Energy Saving is done by integrating a MIMO Transceiver for Transmitting on lower Power Level, Keeping the Same Data Rate and the Same Link Performance of SISO.
75/93 www.ait.edu.gr SM via AS, Cont. O. N. Alrabadi, C. B. Papadias, A. Kalis, N. Marchetti and R. Prasad ``Spatial Multiplexing via Antenna Switching," Accepted on 13 June 2009 at the IEEE Communications Letters.
81/93 www.ait.edu.gr Driving Impedance Variations C. Sun, A. Hirata, T. Ohira, N. C. Karmakar, “Fast Beamforming of Electronically Steerable Parasitic Array Radiator Antennas: Theory and Experiment”, IEEE Transactions on Antennas ond Propagation, vol. 52, no. 7, July 2004, pp 1819-1832 Port impedance varies according to loads used Increasing number of parasitic elements increases the resolution and directivity of the antenna but spread of port impedance values increases Frequency response and centre frequency depend on matching of port impedance to feed network One technique is to use dynamic (variable) matching instead of constant matching Addition of variable impedance to active element Matching performed based on value of imaginary part of port impedance to maintain efficiency
82/93 www.ait.edu.gr Design Considerations While varactor can give a large reactive range, their switching rate is slower than other switches like PIN Diodes M. D.~Migliore, D. Pinchera and F. Schettino, ``Improving Channel Capacity Using Adaptive MIMO Antennas," IEEE Transactions on Antennas and Propagation, vol.54,Nov 2006.
85/93 www.ait.edu.gr Devices Mobile Equipments: Cellular Phones, PDA’s, Laptops Access Points Motivation: The Capacity of a 2x2 system is greater than the ∞x1
86/93 www.ait.edu.gr Devices Wireless Sensor Nodes Motivation: Total Energy Saving is done by integrating a MIMO Transceiver for Transmitting on lower Power Level, Keeping the Same Data Rate of a SISO system. AIT’s SENSA
87/93 www.ait.edu.gr Ad-hoc Networks The performance of peer-to-peer communication links between 2 nodes equipped with 3-element ESPAR antennas is shown in the Figure beside. Etot (Θ,Φ)
88/93 www.ait.edu.gr Multi-User MIMO: Base-Station Capacity Enhancement Motivation: Number of Simultaneously Served Users is Upper-bounded by the Number of BS-Antennas Proposed Idea: Surround Each Active Antenna with two or three parasitic elements (PE), and external control circuit Requirement: Each Array (the single active and its PE) should be placed at sufficient distance from each other, so no mutual coupling among the arrays takes place. Proposed Topology: Collinear Topology Precoding Matrix (W): A block-diagonalizing matrix is proposed, so that the orthonormality of the basis is not destroyed.
89/93 www.ait.edu.gr Cognitive Radios (CR) By integrating Compact and Cheap Parasitic Arrays in the user’s handhelds, the spatially aware terminals can enhance the whole system capacity via 1. Interference reduction via null steering is controlled via cheap varactors. 2. Robust performance is done via space-time coding, and adaptive modulation. 3. Capacity attainment is done via spatial multiplexing and high M-array signaling. 4. Low-cost receiver diversity is done via angular diversity. 5. Beam-steering or beam-selection is implemented under poor MIMO channel conditions. 6. Hidden Terminal Problem is Solved by Scanning the Space Using a Directive Rotating Beam. Broadband ESPAR Arrays and Multi-band Parasitic Arrays are already Available.
93/93 [Alamouti ’98] S. M. Alamouti, “A Simple Transmit Diversity Technique for Wireless Communications", IEEE JSAC, vol. 16, Oct. 1998, pp. 1451-58. [Bolcskei et al. 06] H. Bolcskei, D. Gesbert, C. Papadias, A. J. Van der Veen, Editors, Space-Time Wireless Systems: From Array Processing to MIMO Communications, Cambridge University Press, 2006. [Foschini ’96] G.J. Foschini, "Layered space-time architecture for wireless communication in a fading environment when using multielement antennas," Bell Labs Tech. J., pp. 41-59, 1996. [Foschini & Gans ’98] G. J. Foschini and M. J. Gans, ‘‘On limits of wireless communications in a fading environment when using multiple antennas,’’ Wireless Personal Communications, vol. 6, pp. 311-335, 1998. [Hochwald et al. ’01] B. Hochwald, T. Marzetta and C. Papadias, ‘‘A transmitter diversity scheme for wideband CDMA systems based on Space-Time Spreading,’’ IEEE Journal on Selected Areas in Communications (J- SAC), special issue on wideband CDMA (II), vol. 19, No. 1, pp. 48-60, Jan. 2001. [Kuzminskiy et al. 05] A. Kuzminskiy, H. Karimi, D. Morgan. C. Papadias, D. Avidor and J. Ling, “Downlink Throughput Enhancement of IEEE 802.11a/g Using SDMA with a Multi- Antenna Access Point,” EURASIP Signal Processing, special issue on Advances in Signal Processing-assisted cross layer Designs, No. 86, Issue 2, pp. 1896-1910, Dec. 2005. [Li06] Kuo-Hui Li, (Intel Mobility Group), “IEEE 802.16e-2005 Air Interface Overview,” June 5, 2006, available on-line. [Papadias ’09] C. Papadias, “On the Spectral Efficiency of Space-Time Spreading Schemes for Multiple Antenna CDMA Systems,” 33rd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, Oct. 24-27, 1999. [Papadias & Foschini ’02] C. Papadias and G. Foschini, ``On the capacity of certain space-time coding schemes,’’ EURASIP Journal on Applied Signal Processing, special issue on Space-Time Coding and its Applications, pp. 447-458, vol. 5, May 2002. [Tarokh et al. ’99] V. Tarokh, H. Jafarkhani and A. R. Calderbank, ‘‘Space-time block codes from orthogonal designs,’’ IEEE Trans. on Information Theory, vol. 45, No. 5, pp. 1456 – 1467, July 1999. [Telatar ’99] E. Telatar, ‘‘Capacity of multi-antenna Gaussian channels,’’ European Transactions on Telecommunications, vol. 10, No. 6, pp. 585-595, Nov. / Dec. 1999. [3GA’09] 3G Americas, “MIMO Transmission Schemes for LTE & HSP Networks,” June 2009, available on-line. References