IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 2, MARCH 2003 289 On Uplink CDMA Cell Capacity: Mutual Coupling and Scattering Effects on Beamforming Alexander M. Wyglinski, Student Member, IEEE, and Steven D. Blostein, Senior Member, IEEE Abstract—It has been shown that code-division multiple-access (CDMA) systems that employ digital beamforming and base-sta- tion antenna arrays have the potential to significantly increase capacity. Therefore, accurate performance prediction of such systems is important. We propose to take the electromagnetic behavior of the base-station antenna array into account, as well as its impact on wireless channel propagation. Specifically, the wide-band channel introduces scattering, while the mobile environment causes Doppler fading, which in turn degrades power controllability. We develop a more accurate performance analysis of antenna arrays, where the performance degradation in digital beamforming due to the combination of mutual coupling, scatter, and imperfect power control and its impact on uplink CDMA system capacity is quantified. In this analysis, a Rayleigh fading amplitude with varying angle-of-arrival spread is assumed, and maximum signal-to-noise ratio beamforming weights are used. These weights are further correlated with mutual coupling at the base-station array. Despite the degradation due to the combination of mutual coupling, scattering, and imperfect power control, significant capacity increases are possible. Index Terms—Antenna arrays, code-division multiple access (CDMA), mutual coupling, power control, scatter, smart antennas. I. INTRODUCTION O NE OF the significant challenges in enhancing the performance of next-generation communication systems involves making maximum use of limited spectrum while allowing for flexible multiple access. While code-division multiple access (CDMA) possesses a number of advantages for multiple access, its spectral efficiency is modest. Capacity analysis has been a subject of research for some time [1]. Recently, it has been proposed that greater frequency reuse can be achieved using multiple antenna arrays and digital beamforming at cellular base stations. In fact, this scenario has been analyzed previously, and significant uplink gains have been shown for both stream traffic capacity [2], [3] and Erlang capacity [4]. The objective of this paper is to investigate the performance of CDMA systems employing antenna arrays and digital beam- Manuscript received February 2, 2001; revised July 17, 2002. This paper was presented in part at the IEEE Vehicular Technology Conference (VTC-Fall 2000), Boston, MA, September 2000. This work was supported by the Cana- dian Institute for Telecommunications Research under the Networks of Centres of Excellence Program of the Government of Canada. A. M. Wyglinski was with the Department of Electrical and Computer En- gineering, Queen’s University, Kingston, K7L 3N6 ON, Canada. He is now with the Department of Electrical and Computer Engineering, McGill Univer- sity, Montréal, H3A 2A7 PQ, Canada (e-mail: alexw@tsp.ece.mcgill.ca). S. D. Blostein is with the Department of Electrical and Computer En- gineering, Queen’s University, Kingston, K7L 3N6 ON, Canada (e-mail: sdb@ee.queensu.ca). Digital Object Identifier 10.1109/TVT.2002.808797 forming under more realistic signal propagation assumptions. In particular, we develop a general method to analyze system per- formance taking into account mutual electromagnetic coupling of antenna array elements, scattering due to multipath propaga- tion, and the effect of imperfectly power-controlled cell traffic. Rather than treat each of these effects separately, we demon- strate their combined interaction and effects on multiaccess in- terference (MAI) reduction. Mutual coupling effects from an antenna array have been classically evaluated using an -port network representation [5]–[8], where -port circuit parameters form the elements of a mutual impedance matrix. For dipole antennas containing par- allel thin elements, analytically tractable expressions can be ob- tained. To take into account finite metal thicknesses and more accurate current distributions, numerical techniques can be em- ployed. Three methods for determining mutual impedances are employed and compared in this paper. Recently, mutual coupling analysis has been extended to beam-pattern synthesis [9]. A simplified mutual coupling analysis [10] has been applied to determining the sensitivity of coherent binary phase-shift keying transmission using beamforming in fading channels with scatter [11]–[13]. The mutual coupling analysis of [12] and [13], in particular their expression for the mutual impedance they obtained from [10], is restricted to parallel side-by-side antennas of equal length and odd multiples of half the wavelength. The impact of antenna spacing, angle spread, and spatial correlation on single-user bit error rate performance was assessed. The effects of scattering on plane wave propagation in an- tenna arrays may be conveniently quantified using a spatial dis- persion parameter known as angle spread and applied to de- termining second-order multichannel statistics [14]–[17]. How- ever, most of the techniques currently used for assessing the im- pact of scatter on CDMA system performance neglect the ef- fects of mutual coupling in the base-station antenna array. Ef- fects of scattering on signal amplitude and phase were consid- ered separately and in the absence of mutual coupling [14]. In [2], it was shown that the interelement antenna cross-correlation matrix due to the combined effects of scattering and multiac- cess interference can be approximated by white noise in certain propagation conditions. In [2], however, mutual coupling was ignored. Typically, imperfect CDMA power-control performance is analyzed by modeling the target signal-to-noise ratio as a log- normally distributed random variable [1], [18]. This is partly due to the presence of scattering and its effects on the power levels received at the base station, thus influencing the CDMA system capacity. This effect has not previously been investigated 0018-9545/03$17.00 © 2003 IEEE