A comparative analysis of transmit diversity and beamforming for linear and circular antenna arrays in a wireless communications system is presented. The objective is to examine the effect of random perturbations, angular power distributions on transmit diversity and beamforming system. The perturbations are modeled as additive random errors, following complex Gaussian multivariate distribution, to the antenna array steering vectors. Using outage probability, probability of error, and dynamic range of transmitter power as performance measures, we have shown significant effects of array perturbations on the two systems under spatially correlated Rayleigh fading channel. We also examine the effect of angular power distributions (uniform, truncated Gaussian, and truncated Laplacian), which corresponds to different propagation scenario, on the performance of the two systems. Results show that the central angle-of-arrival can have significant impact on system performance. And the transmit diversity system with truncated Laplacian distribution performs better as compared to other power distributions, and linear array is a preferable configuration for transmit diversity system. We conclude that array perturbations must not be neglected in the design of transmit diversity and beamforming systems.
1. Paulraj, A., R. Nabar, and D. Gore, Introduction to Space-time Wireless Communications, Cambridge University Press, 2003.
2. Winters, J. H., "The diversity gain of transmit diversity technique in wireless systems with Rayleigh fading," IEEE Trans. on Vehicular Tech., Vol. 47, No. 1, 119-132, Feb. 1998. doi:10.1109/25.661038
3. Friedlander, B. and S. Scherzer, "Beamforming versus transmit diversity in the downlink of cellular communication system," IEEE Trans. on Vehicular Tech., Vol. 53, No. 4, 1023-1034, Jul. 2004. doi:10.1109/TVT.2004.830980
4. Umrani, A. W. and V. K. Dubey, "Effect of angle of arrival on transmit diversity and beamforming systems under correlated fading," IEE Electronics Letters, Vol. 41, No. 6, Mar. 2005. doi:10.1049/el:20057830
5. Trees, H. L. V., "Optimum Array Processing, Part IV of Detection, Estimation and Modulation Theory," Wiley & Sons, Inc., 2002.
6. Lee, C.-C. and J. H. Lee, "Robust adaptive array beamforming under steering vector errors," IEEE Trans. Antennas & Propagations, Vol. 45, No. 1, 168-175, 1997. doi:10.1109/8.554254
8. Chong, C., C. Tan, D. Laurenson, S. McLaughlin, M. Beach, and A. Nix, "A new statistical wideband spatio-temporal channel model for 5 GHz band WLAN systems ," IEEE Selected Areas in Commun., Vol. 21, No. 2, 139-150, Feb. 2003. doi:10.1109/JSAC.2002.807347
9. Swindlehurst, A. L., M. A. Jensen, and B. D. Jeffs, "Modeling the statistical time and angle of arrival characteristics of an indoor multipath channel," IEEE Selected Areas in Commun., Vol. 18, No. 3, 347-359, Mar. 2000. doi:10.1109/49.840194
10. Christian, K., L. George, and J. B. Andersen, "Comparison of measured and predicted dispersion and direction of arrival for multipath in a small cell environment," IEEE Trans. Antennas & Propagations, Vol. 49, No. 9, 1254-1263, Sep. 2001. doi:10.1109/8.947016
11. Pedersen, K. I., P. E. Mogensen, and B. H. Fleury, "Power azimuth spectrum in outdoor environments," IEE Electronics Letters, Vol. 33, No. 18, 1583-1584, 1997. doi:10.1049/el:19971029
12. Salz, J. and J. H. Winters, "Effect of fading correlation on adaptive arrays in a digital mobile radio," IEEE Trans. on Vehicular Tech., Vol. 43, No. 4, 1049-1057, Nov. 1994. doi:10.1109/25.330168
13. Tsai, J.-A., M. Buehrer, and B. D.Woerner, "BER performance of a uniform circular array versus a uniform linear array in a mobile radio environment," IEEE Trans. on Wireless Commun., Vol. 3, No. 3, 695-700, May 2004. doi:10.1109/TWC.2004.826332
14. Umrani, A. W. and V. K. Dubey, "Corrections to BER performance of a uniform circular array versus a uniform linear array in a mobile radio environment ," IEEE Trans. on Wireless Commun., Vol. 5, No. 4, 732, 2006. doi:10.1109/TWC.2006.1618920
15. Tsai, J.-A., M. Buehrer, and B. D. Woerner, The impact of AOA energy distribution on spatial fading correlation of linear antenna arrays, Proc. IEEE Vehicular Tech. Conf. VTC'02, 939-937, 2002.
16. Tsai, J.-A., M. Buehrer, and B. D. Woerner, "Spatial fading correlation function of circular antenna arrays with Laplacian energy distribution," IEEE Commun. Letters, Vol. 6, No. 5, 178-180, May 2002. doi:10.1109/4234.1001656
17. Li, X. and Z. P. Nei, "Comments on spatial fading correlation of circular antenna arrays Laplacian energy distribution," IEEE Commun. Letters, Vol. 8, No. 5, 295, May 2004. doi:10.1109/LCOMM.2004.827375
18. Chen, Y., Z. Zhang, and V. K. Dubey, "Effect of antenna directivity on angular power distribution at mobile terminal in urban macro-cells: A geometric channel modeling approach," Wireless Personal Communications, Vol. 43, 389-409, 2007. doi:10.1007/s11277-006-9230-7
19. Allen, B., et al., "Performance comparison of spatial diversity array topologies in an OFDM based wireless LAN," IEEE Trans. Consumer Elect., Vol. 50, No. 2, 420-428, May 2004. doi:10.1109/TCE.2004.1309403
20. Johnson, N. L., S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, Vol. 1, Wiley & Sons, 1994.
21. Proakis, J. G., Digital Communications, McGraw Hill, 2001.
22. Rensburg, C.-V. and B. Friedlander, "Transmit diversity for arrays in correlated Rayleigh fading," IEEE Trans. on Vehicular Tech., Vol. 53, No. 6, 1726-1734, Nov. 2004. doi:10.1109/TVT.2004.836959
23. Anil, M. R. and L. J. Douglas, "Efficient quadratic detection in perturbed arrays via fourier transform techniques," IEEE Trans. on Signal Proces., Vol. 49, No. 7, 1269-1281, Jul. 2001.
24. Yu, J. and Y.-D. Yao, Evaluation of reverse link performance of a CDMA system with imperfect beamforming, IEEE Vehicular Tech. Conference VTC'04, 137-141, 2004.
25. Chen, Y., Z. Zhang, and T. Qin, "Geometrically based channel model for indoor radio propagation with directional antennas," Progress In Electromagnetic Research B, Vol. 20, 109-124, 2010. doi:10.2528/PIERB10022205
26. Chen, Y., Z. Zhang, L. Hu, and P. B. Rapajic, "Geometrical-based statistical model for radio propagation in rectangular office buildings," Progress In Electromagnetic Research B, Vol. 17, 187-212, 2009. doi:10.2528/PIERB09080603