Statistical Modeling and Experimental Verification of Wideband MIMO Mobile-to-mobile Channels in Highway Environments Alenka G. Zaji´ c * , Gordon L. St¨ uber * , Thomas G. Pratt † , and Son Nguyen § * School of Electrical and Computer Engineering Georgia Institute of Technology, Atlanta, GA 30332 USA † Georgia Tech Research Institute, Atlanta, GA 30332 USA § Army Research Laboratory, Adelphi, MA 20783 USA Abstract— A three-dimensional reference model for wideband multiple-input multiple-output (MIMO) mobile-to-mobile (M-to- M) channels is reviewed. To validate the reference model, an experimental MIMO M-to-M channel-sounding campaign was conducted for M-to-M vehicular communication with vehicles travelling along expressways in a metropolitan area. The mea- sured data is processed and the channel statistics obtained from the reference model and from the empirical measurements are compared. The close agreement between the analytically and empirically obtained channel statistics confirms the utility of the proposed reference model. I. I NTRODUCTION Mobile-to-mobile (M-to-M) communications play an im- portant role in mobile ad-hoc wireless networks, intelligent transportation systems, and relay-based cellular networks. The statistical properties of M-to-M channels are quite different from conventional fixed-to-mobile cellular land mobile radio channels [1]. M-to-M communication systems are equipped with low elevation antennas and have both the transmitter (T x ) and receiver (R x ) in motion. Akki and Haber [1] proposed a two-dimensional (2-D) reference model for single-input single- output (SISO) M-to-M Rayleigh fading channels. Channel sounding measurements for narrow-band and wide-band SISO M-to-M channels have been reported in [2], [3], respectively. The reference model for narrow-band multiple-input multiple- output (MIMO) M-to-M channels has been proposed in [4], based on 2-D radio propagation. All previously reported models are two-dimensional and accurate only for certain environments, e.g., rural areas. For urban environments, the tree-dimensional (3-D) models are more appropriate. Hence, we have recently proposed the 3-D reference models for narrowband and wideband MIMO M-to-M multipath fading channels [5], [6]. We have also derived the first- and second- order statistics for the proposed models [6], [7] along with simulation models [8]. 0 Prepared through collaborative participation in the Collaborative Technology Alliance for Communications & Networks sponsored by the U.S. Army Research Laboratory under Cooperative Agreement DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. This paper verifies our 3-D wideband MIMO M-to-M reference model in [6] by using MIMO M-to-M channel measurements collected from vehicles travelling along the Interstate highways near the midtown Atlanta metropolitan area. First, we review our reference model. Then, we describe the measurement campaign and the data processing techniques used to process the measured data. Finally, we compare the space-Doppler power spectral density (sD-psd) and the power space-delay spectral density (psds) obtained from the reference model with those obtained from the measured data. The close agreement between the analytical and empirical curves confirms the utility of the proposed reference model. From the results we can observe that if the vehicles are driven in the rightmost or the leftmost lane and close to the large objects such as highway dividers or sound blockers on the edge of the highway, the single-bounced rays bear more energy than the double-bounced rays. On the other hand, if the vehicles are driven in the middle lanes of the highway or in the urban environment [9], the double-bounced rays are prevalent. The remainder of the paper is organized as follows. For ease of reference, Section II reviews our 3-D wideband MIMO M- to-M reference model. Section III describes the measurement campaign and the data processing techniques used to process the measured data. Section IV compares the analytical and em- pirical results for the sD-psd and the psds. Finally, Section V provides some concluding remarks. II. A 3-D THEORETICAL MODEL FOR WIDEBAND MIMO MOBILE- TO-MOBILE CHANNELS This section describes our 3-D theoretical model for wide- band MIMO M-to-M multipath fading channels proposed in [6]. We consider a wideband MIMO communication system with L t transmit and L r receive omnidirectional antenna elements. It is assumed that both the T x and R x are in motion and equipped with low elevation antennas. The radio propagation occurs in outdoor metropolitan environments that are characterized by 3-D non-isotropic scattering with either line-of-sight (LoS) or non-line-of-sight (NLoS) conditions between the T x and R x . The MIMO channel can be described by an L r × L t matrix H(t, τ )=[h ij (t, τ )] L r ×L t of the input delay-spread functions.