Commentary on A. Habib and M. Rupp (2012), ``Antenna Selection in Polarized Multiple Input Multiple Output Transmissions with Mutual Coupling''

Abstract

Habib and Rupp [3] provided analytical results for mutual coupling between multiple dipole antennas with angular or spatial separation. However, the method of deriving mutual coupling from mutual impedance involved several inconsistencies on which depend the final results of multiple antenna system capacity presented in their paper. First, the expression of mutual impedance matrix (12) in [3] is adapted from [1] and contains the sum of two impedances, ZA + ZT , on the diagonal. This was a mistake in [1] which was later corrected in [2]. Second, the imaginary part of mutual impedance between skew dipoles shown in Fig. 3 [3] is incorrect and related statement in the text of Section 2.3 saying that “the imaginary part remains basically zero” is not true. The imaginary part of mutual impedance depends on the angle between dipoles and for the zero angle should coincide with the self-impedance, which is Z11 = 73.1+j 42.5 Ω for a half-wavelength dipole. This can be verified by references [4–7], the graphical representation of which results is shown in Fig. 1 illustrating the difference of imaginary part of mutual impedance from zero value. The equations formutual impedance (13)–(18) in [3] are based on [6,7], but have distance r dependent factor exp(jkr)/r replaced by the factor exp(jkx) / x with Fig. 1. Dependence of real and imaginary parts of mutual impedance on the angle between skew dipoles according to Richmond and Geary [5], Zhao, Li and Sun [6,7] and Han and Myung [4].