Abstract
The facility of information exchange using wireless communication systems has affected many aspects of the modern lifestyle. In return for the growth of wireless applications, we have witnessed an ever growing demand for the high data rate wireless communication systems. However, the hostility of the wireless fading environment and channel variation makes the design of high rate communication system very challenging. To this end, multiple antenna systems have shown to be very effective in fading environment by providing significant performance improvements and achievable data rates in comparison to a single antenna systems. The performance gain achieved by multiple antenna system increases when the knowledge of the channel state information (CSI) at each end, either the receiver or transmitter, is increased. Although perfect CSI is desirable, practical systems are usually built on estimating the CSI at the receiver and possibly feeding back the CSI to the transmitter through a feedback link with a limited capacity.
While most of the research efforts has been focused on the outage probability minimization through an adaptive transmission scheme, the overall evaluation of the system throughput is not well addressed. However, the throughput is the actual performance measure for most of the practical applications, such as data transfer or video streaming.
In this work, we consider the problem of throughput maximization through a quantized feedback which is appropriate model for practical systems where the feedback link has limited capacity. We derive the optimal quantized rate control design for a general multiple transmit and multiple receive antenna system, and provide the mathematical framework to find such an optimal solution. Moreover, an adaptive gradient search algorithm has been proposed that can efficiently find the optimal solution.
It is shown that the proposed quantized rate control design considerably improves the throughput of a system for a given average power. Equivalently, for a targeted throughput, a huge saving in power can be obtained through quantized rate control. More importantly, only a few bits of feedback per block of transmission is needed to achieve most of the gain in the knowledge of CSI at the transmitter. Practicality of such a low rate feedback highly motivate the use of the proposed rate control strategy in order to maximize the system throughput.
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References
A. Goldsmith and P. Varaiya, “Capacity of fading channels with channel side information,” IEEE Transactions on Information Theory, 43(6): 1986–1992, Nov. 1997.
E. Biglieri, G. Caire, and G. Taricco, “Limiting performance of block-fading channels with multiple antennas,” IEEE Transactions on Information Theory, 47: 1273–1289, Sep 2001.
G. Caire, G. Taricco, and E. Biglieri, “Optimum power control over fading channels,” IEEE Transactions on Information Theory, 45(5): 1468–1489, Jul. 1999.
E. Telatar, “Capacity of multi-antenna Gaussian channels,” AT & T Bell Labs Internal Tech. Memo, June 1995.
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, 44(2): 744–765, Mar 1998.
G.J. Foschini and M.J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Communications, 6: 311, 1998.
G.J. Foschini and M.J. Gans, “Capacity when using multiple antennas at transmit and receive sites and rayleigh-faded matrix channel is unknown to the transmitter,” Advances in Wireless Communications, Eds. J.M. Holtzman and M. Zorzi, Kulwer Academic Publishers, 1998.
T.L. Marzetta and B.M. Hochwald, “Capacity of a mobile multiple-antenna communication link in Rayleigh flat fading,” IEEE Transactions on Information Theory, 45(1): 139–157, Jan 1999.
M.A. Khojastepour, X. Wang, and M. Madihian, “Optimal quantized power control in multiple antenna communication systems,” in Forty-third Annual Allerton Conference on Communication, Control, and Computing, Allerton House, Monticello, IL, September 28–30, 2005.
S. Bhashyam, A. Sabharwal, and B. Aazhang, “Feedback gain in multiple antenna systems,” IEEE Transactions on Communications, 50(5): 785–798, May 2002.
K.K. Mukkavilli, A. Sabharwal, E. Erkip, and B. Aazhang, “On beamforming with finite rate feedback in multiple-antenna systems,” IEEE Transactions on Information Theory, pp. 2562–2579, 2003.
D.J. Love and Jr. Heath, R.W., “Limited feedback unitary precoding for orthogonal space-time block codes,” IEEE Transacions on Signal Processing, 53: 64–73, 2005.
G. Caire and S. Shamai, “On the capacity of some channels with channel state information,” IEEE Trans, on Inform. Theory, 45: 1468–1489, 1998.
J. Hayes, “Adaptive feedback communications,” IEEE Transactions on Communications, 16: 29–34, 1968.
M.S. Alouini and A.J. Goldsmith, “Capacity of rayleigh fading channels under different adaptive transmission and diversity-combining techniques,” IEEE Journal on Selected Areas in Communications, Special Issue on Multi-Media Network Radios, 17: 837–850, 1999.
A.J. Goldsmith and S.-G. Chua, “Variable-rate variable-power mqam for fading channels,” IEEE Trans, on Communications, 45: 1218–1230, 1997.
A.J. Goldsmith and S.-G. Chua, “Adaptive coded modulation for fading channels,” IEEE Trans, on Communications, 46: 595–602, 1998.
C. Berrou, A. Glavieux, and P. Thitimasjshima, “Near shannon limit error correcting coding and decoding: Turbo-codes,” in IEEE Int. Conf. on Commu., Geneval, Switzerland, May 1993, pp. 1064–1070.
T. Richardson, M. Shokrollahi, and R. Urbanke, “Design of capacityapproaching irregular low-density parity-check codes,” IEEE Trans, on Info. Theory, 47(2): 619–637, Feb. 2001.
S. Vishwanath and A.J. Goldsmith, “Adaptive turbo-coded modulation for flat-fading channels,” IEEE Trans, on Communications, 51: 964–972, 2003.
N. Prasad, M.K. Varanasi, and M.A. Khojastepour, “Outage theorems for mimo fading channels,” in Forty-third annual Allerton conference on Communication, Control, and Computing, 2005.
R.K. Mallik, M.Z. Win, J.W. Shao, M.-S. Alouini, and A.J. Goldsmith, “ Channel capacity of adaptive transmission with maximal ratio combining in correlated rayleigh fading,” IEEE Transactions on Wireless Communications, 3: 1124–1133, 2004.
M.J. Hossain, P.K. Litthaladevuni, M.-S. Alouini, V.K. Bhargava, and A.J. Goldsmith, “Adaptive hierarchical modulation for simultaneous voice and multi-class data transmission over fading channels,” IEEE Transactions on Vehicular Technology (accepted for publication), 2005.
P. Sebastian, H. Sampath, and A. Paulraj, “Adaptive modulation for multiple antenna systems,” in Proceedings of Thirty-fourth Asilomar conference on signal, systems, and computers, 2000h.
S.A. Jafar, S. Vishwanath, and A.J. Goldsmith, “Throughput maximization with multiple codes and partial outages,” in Proceedings of Globecom Conference, San Antonio, Texas, USA, 2001.
J.C. Roh and B.D. Rao, “Adaptive modulation for multiple antenna channels,” in Proceedings of Thirty-six Asilomar conference on signal, systems, and computers, 2002.
C.-N. Chuah, D.N.C. Tse, J.M. Kahn, and R.A. Valenzuela, “Capacity scaling in mimo wireless systems under correlated fading,” IEEE Transactions on Information Theory, 48: 637–650, 2002.
V. Tarokh, H. Jafarkhani, and A.R. Calderbank, “Space-time block codes from orthogonal designs,” IEEE Transactions on Information Theory, 45: 1456–1467, 1999.
B. Hasibi and B.M. Hochwald, “High-rate codes that are linear in space and time,” IEEE Transactions on Information Theory, 48: 1804–1824, 2002.
L. Ozarow, S. Shamai, and A.D. Wyner, “Information theoretic considerations for cellular mobile radio,” IEEE Transactions on Vehicular Technology, 43: 359–378, May 1994.
R. McEliece and W. Stark, “Channels with block interference,” IEEE Transactions on Information Theory, 30(1): 44–53, Jan. 1984.
G. Caire, G. Taricco, and E. Biglieri, “Optimum power control over fading channels,” IEEE Transactions on Information Theory, 45(5): 1468–1489, 1999.
E. Jorswick, “Outage probability of multiple antenna systems: Optimal transmission and impact of correlation,” in Proc. of 13. Joint Conference on Coding and Communications, march 2004.
H. Boche and E. Jorswieck, “Outage probability of multiple antenna systems: Optimal transmission and impact of correlation,” in Proc. IZS, March 2004.
E. Jorswieck and H. Boche, “Optimal transmission strategy for multiple antenna systems with uninformed transmitter and correlation,” in Proc. Asilomar, 2003.
E. Jorswieck and H. Boche, “On the impact of correlation on the capacity in mimo systems without csi at the transmitter,” in Proceedings of CISS, 2003.
E. Jorswieck and H. Boche, “Behaviour of outage probability in miso systems with no channel state information at the transmitter,” in Proceedings of ITW, 2003.
H. Boche and E. Jorswieck, “Optimal power allocation for miso systems and complete characterization of the impact of correlation on the capacity,” in Proc. of ICASSP, 2003.
H. Boche and E. Jorswieck, “On schur-convexity of expectation of weighted sum of random variables with applications,” Journal of Inequalities in Pure and Applied Mathematics, 5: 46, 2004.
H. Boche and E. Jorswieck, “On the schur-concavity of the ergodic and outage capacity with respect to correlation in multi-antenna systems with no csi at the transmitter,” in Proceedings of Allerton, 2002.
G.J. Foschini,,” Bell Labs Technical Journal, 1: 41–59, 1996.
A. Sabharwal, E. Erkip, and B. Aazhang, “On channel state information in multiple antenna block fading channels,” in Proceedings ISITA, Hawaii, Nov 2000.
A. Narula, M.J. Lopez, M.D. Trott, and G.W. Wornell, “Efficient use of side information in multiple-antenna data transmission over fading channels,” IEEE Journal on Selected Areas of Communications, 16(8): 1423–1436, Oct 1998.
A. Narula, M.D. Trott, and G.W. Wornell, “Performance limits of coded diversity methods for transmitter antenna arrays,” IEEE Transactions on Information Theory, 45(7): 2418–2433, Nov 1999.
E. Visotsky and U. Madhow, “Space-time precoding with imperfect feedback,” in Proceedings ISIT 2000, Sorrento, Italy, June 2000.
S.A. Jafar and A. Goldsmith, “On optimally of beamforming for multiple antenna systems with imperfect feedback,” in Proceedings ISIT 2001, Washington DC, USA, June 2001.
K.K. Mukkavilli, A. Sabharwal, M. Orchard, and B. Aazhang, “Transmit diversity with channel feedback,” in Proceedings International Symposium on Telecommunications, Tehran, Iran, September 2001.
D.J. Love, R.W. Heath Jr., and T. Strohmer, “Grassmannian beamforming for multiple-input multiple-output wireless systems,” IEEE Transactions on Information Theory, 49: 2735–2747, 2003.
D.J. Love, R.W. Heath Jr., W. Santipach, and M.L. Honig, “What is the value of limited feedback for mimo channels?,” IEEE Communications Magazine, 42: 54–59, 2004.
B.M. Hochwald, T.L. Marzetta, and V. Tarokh, “Multi-antenna channelhardening and its implication for rate feedback and scheduling,” Submitted for publication to IEEE Transactions on Information Theory, 2003.
P. J. Smith and M Shafi, “On a gaussian approximation to the capatity of wireless mimo systems,” in Proceedings of International Conference on Communications, 2002.
Z. Wang and G.B. Giannakis, “Outage mutual information of space-time mimo systems,” in Proceedings of 40th Annual Allerton Conference on Communication, Control, and Computing, 2002.
S.P. Boyd and L. Vandenberghe, Convex optimization, New York: Cambridge, 2004.
J.C. Spall, Introduction to stochastic search and optimization: estimation, simulation, and control, Hoboken, NJ: Wiley-Interscience, 2003.
M. Raydan and B.F. Svaiter, “Relaxed steepest descent and cauchy-barzilai-borwein method,” Computational Optimization and Applications, 21: 155–167, 2002.
N. Andrei, “A new gradient descent method for unconstrained optimization,” Submitted for Publication to Journal of Mathematics of Computation, “ http://www.ici.ro/camo/neculai/newstep.pdf 02/22/2005”; also: ICI Technical Report, April 2004.
N. Andrei, “Relaxed gradient descent and a new gradient descent methods for unconstrained optimization,” Submitted for Publication to Journal of Mathematical Programming, “http://www. ici.ro/camo/neculai/newgrad.pdf 02/22/2005”; also: ICI Technical Report, August 2004.
S. Andardottir, “A review of simulation optimization techniques,” 1998.
P. Glasserman, Gradient estimation via perturbation analysis, Boston: Kluwer Academic Publishers, 1991.
M. Fu and J.-Q. Hu, Conditional Monte Carlo: Gradient Estimation and Optimization Applications, Boston: Kluwer Academic Press, 1997.
M. Fu, “Optimization via simulation: A review,” Annals of Operations Research, 53: 199–248, 1994.
H.J. Kushner and G. Yln, Stochastic approximation and recursive algorithms and applications, New York: Springer, 2003.
J. Nocedal and S. Wright, Numerical Optimization, Springer Verlag, 1999.
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Khojastepour, M.A., Wang, X., Madihian, M. (2007). Optimization of Wireless Multiple Antenna Communication System Throughput Via Quantized Rate Control. In: Agrawal, P., Fleming, P.J., Zhang, L., Andrews, D.M., Yin, G. (eds) Wireless Communications. The IMA Volumes in Mathematics and its Applications, vol 143. Springer, New York, NY. https://doi.org/10.1007/978-0-387-48945-2_6
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