Abstract
A tutorial study is performed on thecapacity of multiple antenna wireless communication systems.Multiple antenna structures can be classified into single-inputmultiple-outputs (SIMO), multiple-inputs single-output (MISO), andmultiple-inputs multiple-outputs (MIMO) systems. Assuming that thechannel is known at receiver, capacity expressions are providedfor each structure, under the conditions of quasi-static flatfading. Also, information rate limits are provided in each casefor some suboptimal structures or detection techniques that may beused in practice. Using simulations for the case of flat Rayleighfading, capacities of optimal/suboptimal implementations arecontrasted for each multi-antenna structure. Discussions are madeon system design, regarding implementation complexity andpractical limitations on achieving these capacities. Inparticular, the problem of fading correlation and required antennaspacing, effect of fast channel fading, and lack of channelknowledge at receiver are discussed. Providing the results of themost recent researches considering the capacity of multi-antennasystems, as well as some new results, this paper can give a goodperspective for designing appropriate architectures in differentwireless communication applications.
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References
L.C. Godara, “Applications of Antenna Arrays to Mobile Communications, Part I: Performance Improvement, Feasibility, and System Considerations”, Proceedings of the IEEE, Vol. 85, No. 7, pp. 1031–1060, 1997.
L.C. Godara, “Applications of Antenna Arrays to Mobile Communications, Part II: Beam-Forming and Direction-of-Arrival Considerations”, Proceedings of the IEEE, Vol. 85, No. 8, pp. 1193–1245, 1997.
K. Pahlavan and A.H. Levesque, “Wireless Data Communications”, Proceedings of the IEEE, Vol. 82, No. 9, pp. 1398–1430, 1994.
B. Sklar, “Rayleigh Fading Channels in Mobile Digital Communication Systems; Part I: Characterization; Part II: Mitigation”, IEEE Communication Magazine, Vol. 35, No. 7, pp. 90–109, 1997.
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, No. 3, pp. 311–335, 1998.
BLAST: Bell Labs Layered Space-Time, Bell Labs projects, http://www.bell-labs.com/project/blast/
J.G. Proakis, Digital Communications, McGraw Hill, 2nd edn, 1989.
F.D. Neeser and J.L. Massey, “Proper Complex Random Proccesses with Applications to Information Theory”, IEEE Transactions on Information Theory, Vol. IT-39, No. 4, pp. 1293–1302, 1993.
T.L. Marzetta and B.M. Hochwald, “Capacity of a Mobile Multiple-Antenna Communication Link in Rayleigh Flat Fading”, IEEE Transactions on Information Theory, Vol. IT-45, No. 1, pp. 139–157, 1999.
C.E. Shannon, “Communication in the Presence of Noise”, Proceedings of the IRE, Vol. 37, No. 1, pp. 10–21, 1949. Reprinted as “classic paper” in Proceedings of the IEEE, Vol. 86, No. 2, pp. 447–457, 1998.
E. Telater, “Capacity of Multi-Antenna Gaussian Channel”, AT&T Bell Labs, Tech. Memo., June 1995.
E. Telatar, “Capacity of Multi-Antenna Gaussian Channels”, invited paper, European Transactions on Telecommunications, Vol. ETT-10, No. 6, pp. 585–595, 1999.
G. Caire and S. Shamai (Shitz), “On the Capacity of Some Channels with Channel State Information”, in IEEE Transactions on Information Theory, Vol. IT-45, No. 6, pp. 2007–2019, 1999.
G. Caire, G. Taricco and E. Biglieri, “Optimum Power Control over Fading Channels”, IEEE Transactions on Information Theory, Vol. IT-45, No. 5, pp. 1468–1489, 1999.
E. Biglieri, J. Proakis and S. Shamai (Shitz), “Fading Channels, Information-Theoretic and Communications Aspects”, invited paper, IEEE Transactions on Information Theory, Vol. IT-44, No. 6, pp. 2619–2692, 1998.
A. Lapidoth and P. Narayan, “Reliable Communication under Channel Uncertainty”, invited paper, IEEE Transactions on Information Theory, Vol. IT-44, No. 6, pp. 2148–2177, 1998.
G.G. Raleigh and V.K. Jones, “Multivariate Modulation and Coding for Wireless Communication”, IEEE Journal on Selected Areas in Communications, Vol. SAC-17, No. 5, pp. 851–866, 1999.
J.B. Anderson, “Array Gain and Capacity for Known Random Channels with Multiple Element Arrays at Both Ends”, IEEE Journal on Selected Areas in Communications, Vol. SAC-18, No. 11, pp. 2172–2178, 2000.
P. Balaban and J. Salz, “Optimum Diversity Combining and Equalization in Digital Data Transmission with Application to Cellular Mobile Radio-Part 1 and 2”, IEEE Transactions on Communications, Vol. COM-40, No. 5, pp. 885–907, 1992.
J.H. Winters, “On the Capacity of Radio Communication Systems with Diversity in a Rayleigh Fading Environment”, IEEE Journal on Selected Areas in Communications, Vol. SAC-5, No. 5, pp. 871–878, 1987.
D. Shiu, G.J. Foschini, M.J. Gans and J.M. Kahn, “Fading Correlation and Its Effect on the Capacity of Multi-Element Antenna Systems”, IEEE Transactions on Communications, Vol. COM-48, No. 3, pp. 502–513, 2000.
H. Viswanathan, “Capacity of Markov Channels with Receiver CSI and Delayed Feedback”, IEEE Transactions on Information Theory, Vol. IT-45, No. 2, pp. 761–771, 1999.
A. Goldsmith and P. Varaiya, “Capacity of Fading Channels with Channel Side Information”, IEEE Transactions on Information Theory, Vol. 43, No. 6, pp. 1986–1992, 1997.
G.G. Raleigh and J.M. Cioffi, “Spatio-Temporal Coding for Wireless Communication”, IEEE Transactions on Communications, Vol. COM-46, No. 3, pp. 357–366, 1998.
D. Brennan, “Linear Diversity Combining Techniques”, Proceedings of the IRE, Vol. 47, pp. 1075–1102, 1959.
W.C. Jakes, Microwave Mobile Communications, John Wiley & Sons, New York, 1974. Reprinted by IEEE Press, 1998.
M.V. Clark, L.J. Greenstein, W.K. Kennedy and M. Shafi, “MMSE Diversity Combining for Wide-Band Digital Cellular Radio,” IEEE Transactions on Communications, Vol. COM-40, No. 6, pp. 1128–1135, 1992.
J.H. Winters, J. Salz and R.D. Giltin, “The Impact of Antenna Diversity on the Capacity of Wireless Communication Systems”, IEEE Transactions on Communications, Vol. COM-42, Nos. 2–4, pp. 1740–1750, 1994.
G. Chyi, J.G. Proakis and C.M. Keller, “On the Symbol Error Probability of Maximum-Selection Diversity Reception Schemes over a Rayleigh Fading Channel”, IEEE Transactions on Communications, Vol.COM-37, No. 1, pp. 79–83, 1989.
A. Wittenben, “A New Bandwidth Efficient Transmit Antenna Modulation Diversity Scheme for Linear Digital Modulation”, in Proceedings of 1993 IEEE International Conference on Communications, ICC, May 1993, pp. 1630–1634.
N. Seshadri and J.H. Winters, “Two Signaling Schemes for Improving the Error Performance of FDD Transmission Systems Using Transitter Antenna Diversity”, in Proceedings of 43rd IEEE Vehicular Technology Conference, VTC, May 1993, pp. 508–511.
J.H. Winters, “The Diversity Gain of Transmit Diversity in Wireless Systems with Rayleigh Fading”, IEEE Transactions on Vehicular Technology, Vol. VT-47, No. 1, pp. 119–123, 1998.
S.M. Alamouti, “A Simple Transmit Diversity Technique for Wireless Communications”, IEEE Journal on Selected Areas in Communications, Vol. SAC-16, No. 8, pp. 1451–1458, 1998.
R.U. Nabar, D.A. Gore and A. Paulraj, “Optimal Selection and Use of Transmit Antennas in Wireless Systems”, in Proceedings of International Conference on Telecommunications, ICT, Acapulco, Mexico, U.S.A., May 2000.
D.A. Gore, R.U. Nabar and A. Paulraj, “Selecting an Optimal Set of Transmit Antennas for a Low Rank Matrix Channel”, in Proceedings of IEEE Conference on Acoustics, Speech, and Signal Processing, ICASSP, Istanbul, Turkey, June 2000, pp. 2785–2788.
S. Sandhu, R.U. Nabar, D.A. Gore and A. Paulraj, “Near-Optimal Selection of Transmit Antennas for a MIMO Channel Based on Shannon Capacity”, in Proceedings of 34th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, U.S.A., 2000, Vol. 1, pp. 567–571.
G.J. Foschini, “Layered Space-Time Architecture for Wireless Communication in a Fading Environment when Using Multi-Element Antennas”, Bell Labs Technical Journal, Vol. 1, No. 2, pp. 41–59, 1996.
T.L. Marzetta, “BLAST Training: Estimating Channel Characteristics for High Capacity Space-Time Wireless”, in Proceedings of 37th Annual Allenton Conference on Communication, Control, and Computing, Monticello, IL, Sept. 1999, pp. 958–966.
S.L. Ariyavisitakul, “Turbo Space-Time Processing to Improve Wireless Channel Capacity”, IEEE Transactions on Communications, Vol. COM-48, No. 8, pp. 1347–1359, 2000.
P.W. Wolniansky, G.J. Foschini, G.D. Golden and R.A. Valenzuela, “V-BLAST: An Architecture for Realizing Very High Data Rates over the Rich-Scattering Wireless Channel”, in Proceedings of ISSSE-98,Pisa, Italy, Sept. 1998.
G.D. Golden, G.J. Foschini, R.A. Valenzuela and P.W. Wolniansky, “Detection Algorithm and Initial Laboratory Results Using V-BLAST Space-Time Communication Architecture”, Electronic Letters, Vol. 35, No. 1, pp. 14–16, 1999.
G.J. Foschini, G.D. Golden, R.A. Valenzuela and P.W. Wolniansky, “Simplified Processing for High Spectral Efficiency Communication Employing Multi-Element Arrays”, IEEE Journal on Selected Areas in Communications, Vol. SAC-17, No. 11, pp. 1841–1852, 1999.
V. Tarokh, N. Seshadri and A.R. Calderbank, “Space-Time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction”, IEEE Transactions on Information Theory, Vol. IT-44, No. 2, pp. 744–765, 1998.
A. Naguib, V. Tarokh, N. Seshadri and A.R. Calderbank, “A Space-Time Coded Modem for High Data Rate Wireless Communication”, IEEE Journal on Selected Areas in Communications, Vol. SAC-16, No. 8, pp. 1459–1478, 1998.
V. Tarokh, A. Naguib, N. Seshadri and A.R. Calderbank, “Space-Time Codes for High Data Rate Wireless Communication: Performance Criteria in the Presence of Channel Estimation Errors, Mobility, and Multiple Paths”, IEEE Transactions on Communications, Vol. COM-47, No. 2, pp. 199–207, 1999.
V. Tarokh, A. Naguib, N. Seshadri and A.R. Calderbank, “Combined Array Processing and Space-Time Coding”, IEEE Transactions on Information Theory, Vol. IT-45, No. 4, pp. 1121–1128, 1999.
S. Kasturia, J. Aslanis and J.M. Cioffi, “Vector Coding for Partial Response Channels”, IEEE Transactions on Information Theory, Vol. IT-36, pp. 741–762, 1990.
V. Tarokh, H. Jafarkhani and A.R. Calderbank, “Space-Time Block Codes from Orthogonal Designs”, IEEE Transactions on Information Theory, Vol. IT-45, No. 5, pp. 1456–1467, 1999.
V. Tarokh, H. Jafarkhani and A.R. Calderbank, “Space-Time Block Coding for Wireless Communications: Performance Results”, IEEE Journal on Selected Areas in Communications, Vol. SAC-17, No. 3, pp. 451–460, 1999.
J. Salz and J.H. Winters, “Effect of Fading Correlation on Adaptive Arrays in Digital Mobile Radio”, IEEE Transactions on Vehicular Technology, Vol. VT-43, No. 4, pp. 1049–1057, 1994.
M.A. Khalighi, J.M. Brossier, G. Jourdain and K. Raoof, “Water Filling Capacity of Rayleigh MIMO Channels”, in Proceedings of PIMRC 2001, San Diego, CA, 30 Sept.–3 Oct. 2001, Vol. A, pp. 155–158.
M.A. Khalighi and G. Jourdain, “Increase in the Capacity of Transmit Diversity Systems by Optimal Power Allotment at Transmitter”, submitted to EURASIP Journal of Applied Signal Processing.
T. Rappaport, Wireless Communications, Englewood Cliffs, NJ, Prentice-Hall, 1996.
M.A. Khalighi, K. Raoof and G. Jourdain, “Capacity of Multi-Antenna Time-Dispersive Channels Subject to Fading”, in Proceedings of 18th GRETSI, Toulouse, France, 10–13 Sept. 2001, pp. 129–132.
N. Al-Dhahir, “FIR Channel-Shortening Equalizers for MIMO ISI Channels”, IEEE Transactions on Communications, Vol. 49, No. 2, pp. 213–218, 2001.
N. Al-Dhahir and A.H. Sayed, “The Finite-Length MIMO MMSE-DFE”, IEEE Transactions on Signal Processing, Vol. SP-48, No. 10, pp. 2921–2936, 2000.
N. Al-Dhahir, A.F. Naguib and A.R. Calderbank, “Finite-Length MIMO Decision Feedback Equalization for Space-Time Block-Coded Signals over Multipath-Fading Channels”, IEEE Transactions on Vehicular Technology, Vol. VT-50, No. 4, pp. 1176–1182, 2001.
H. Bölcskei, D. Gesbert and A.J. Paularj, “On the Capacity of OFDM-Based Multi-Antenna Systems”, in Proceedings of ICASSP 2000, Istanbul, Turkey, pp. 2569–2572, 2000.
H. Hashemi, “The Indoor Radio Propagation Channel”, Proceedings of the IEEE, Vol. 81, No. 7, pp. 943–968, 1993.
H. Suzuki, “A Statistical Model for Urban Multipath Propagation”, IEEE Transactions on Communications, Vol. COM-25, No. 7, pp. 673–680, 1977.
M.A. Khalighi, J.M. Brossier, G. Jourdain and K. Raoof, “On Capacity of Ricean MIMO Channels”, in Proceedings of PIMRC 2001, San Diego, CA, 30 Sept.–3 Oct. 2001, Vol. A, pp. 150–154.
P.F. Driessen and G.J. Foschini, “On the Capacity Formula for Multiple Input-Multiple Output Wireless Channels: A Geometric Interpretation”, IEEE Transactions on Communications, Vol.COM-47, No.2, pp. 173–176, 1999.
M. Dinis and J. Fernandes, “Life after Third-Generation Mobile Communications; Provision of Sufficient Transmission Capacity for Broadband Mobile Multimedia: A Step toward 4G”, IEEE Communication Magazine, Vol. 39, No. 8, pp. 46–54, 2001.
P.B. Rapajic and D. Popescu, “Information Capacity of a Random Signature Multiple-Input Multiple-Output Channel”, IEEE Transactions on Communications, Vol. COM-48, No. 8, pp. 1245–1248, 2000.
S. Shamai (Shitz) and A.D. Wyner, “Information-Theoretic Considerations for Symmetric, Cellular, Multiple-Access Fading Channels, Parts I and II”, IEEE Transactions on Information Theory, Vol. IT-43, No. 6, pp. 1877–1911, 1997.
A.D. Wyner, “Shannon-Theoretic Approach to a Gaussian Cellular Multiple-Access Channel”, IEEE Transactions on Information Theory, Vol. IT-40, No. 6, pp. 1713–1727, 1994.
A.J. Grant and P.D. Alexander, “Random Sequense Multisets for Synchrounous Code-Division Multiple-Access Channels”, IEEE Transactions on Information Theory, Vol. IT-44, No. 7, pp. 2832–2836, 1998.
S. Verdù and S. Shamai (Shitz), “Spectral Efficiency of CDMA with Random Spreading”, IEEE Transactions on Information Theory, Vol. IT-45, No. 2, pp. 622–640, 1999.
D.N.C. Tse and O. Zeitouni, “Linear Multiuser Receivers in Random Environments”, IEEE Transactions on Information Theory, Vol. IT-46, No. 1, pp. 171–188, 2000.
J. Evans and D.N.C. Tse, “Large System Performance of Linear Multiuser Receivers in Multipath Fading Channels”, IEEE Transactions on Information Theory, Vol. IT-46, No. 6, pp. 2059–2078, 2000.
P.S. Henry and B.S. Glance, “A New Approach to High-Capacity Digital Mobile Radio”, The Bell System Technical Journal, Vol. 60, No. 8, pp. 1891–1904, 1981.
W.C.Y. Lee, Mobile Cellular Telecommunications, McGraw Hill, 2nd edn, 1995.
F. Fujimoto and J.R. James, Mobile Antenna Systems Handbook, Artech House, 1994.
M.A. Khalighi, “Capacity of Communication Systems Using Multi-Element Array Antenna”, Internal Report No. 10/2000, LIS laboratory, Feb. 2000.
S. Catreux, “Multiple Input-Multiple Output Antenna Techniques in Cellular Systems”, Ph.D. Thesis, National Institute of Applied Sciences (INSA), Rennes, France, Mar. 2000.
W.C.Y. Lee, “Effects on Correlation between Two Mobile Radio Base-Station Antennas”, IEEE Transactions on Communications, Vol. COM-21, No. 11, pp. 1214–1224, 1973.
C.C. Martin, N.R. Sollenberger and J.H. Winters, “Field Test Results of Downlink Smart Antennas and Power Control for IS-136”, in Proceedings of IEEE 49th Vehicular Technology Conference (VTC), Houston, TX, May 16–20, 1999, Vol. 1, pp. 453–457.
P.B. Rapajic, “Information Capacity of the Space Time Division Multiple Access Mobile Communication System”, Wireless Personal Communications, Vol. 11, No. 1, pp. 131–159, 1999.
M. Zeng, A. Annamalai and V.K. Bhargava, “Recent Advances in Cellular Wireless Communications”, IEEE Communication Magazine, Vol. 37, No. 9, pp. 128–138, 1999.
T.M. Cover and J.A. Thomas, Elements of Information Theory, John Wiley & Sons, 1991.
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Khalighi, M.A., Raoof, K. & Jourdain, G. Capacity of Wireless Communication Systems Employing Antenna Arrays, a Tutorial Study. Wireless Personal Communications 23, 321–352 (2002). https://doi.org/10.1023/A:1021211513679
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DOI: https://doi.org/10.1023/A:1021211513679