2D Mobile-to-Mobile Wireless Channel Model Prasad T. Samarasinghe, Tharaka A. Lamahewa, Thushara D. Abhayapala and Rodney A. Kennedy Applied Signal Processing Group, Research School of Information Sciences and Engineering, ANU College of Engineering and Computer Science, The Australian National University Canberra ACT 0200, Australia {prasad.samarasinghe,tharaka.lamahewa,thushara.abhayapala,rodney.kennedy}@anu.edu.au Abstract—A novel 2D Mobile-to-Mobile physical model is developed in this paper by considering the underlying physics of free space propagation. When compared to existing statistical channel models, the development and application of our new model is better in terms of complexity as it requires less parameters. In addition, the proposed new model is flexible in applying to any scattering environment whereas the design of the existing models could not easily be extended for any scattering environment. I. I NTRODUCTION Mobile-to-mobile (M2M) radio channels where both trans- mitter and receiver are in motion differ from conventional fixed-to-mobile radio channels where base station is fixed and it’s elevation is high. Mobile ad-hoc wireless networks and intelligent transport systems are the main examples of M2M systems. A detailed understanding of M2M radio channels is essential in order to enhance the performance of M2M chan- nels and to cope with the challenges faced by the development of future M2M radio transmission systems. Akki and Harber [1, 2] were the first to propose a M2M channel model which is a ray-tracing statistical channel model for single-input single-output (SISO) M2M Rayleigh fading radio channels under non-line of sight conditions. Simulation methods for SISO M2M channels have been proposed in [3– 5]. Also, P¨ atzold in [6] derived a two-dimensional (2D) ray-tracing model for multiple-input multiple-output (MIMO) M2M narrowband channels by considering a geometrical two-ring scattering model. St¨ uber in [7] proposed a similar 2D ray-tracing narrowband channel model for MIMO M2M channel based on ‘double-ring’ geometrical model. In [8], the narrowband channel model proposed in [9] was extended to a 2D wideband model. In [10] and [11], these two 2D M2M channels models were extended to 3D models by assuming scatterers are placed on cylinders. Combined two- ring model and elliptical-ring model is proposed in [12], where the received signal is constructed as a sum of the line-of-sight (LoS), single-bounced, and double-bounced rays with different energies. In [13], MIMO M2M ray channel model is discussed relating to T-junction environment. All the channel models discussed here are ray-tracing geometrical based channel models and one shortcoming of them is that they cannot be utilized to represent general scattering scenarios as, channel models are based on specific geometrical situations. Therefore in this paper, we propose a new M2M 2D wireless channel model, based on the underlying physics of free space wave propagation model this extends the fixed-to-mobile chan- nels proposed in [14, 15]. This model is a generalized model which can be applied to any scattering environment forming an ideal framework to build M2M communication systems. The paper is organized as follows. In section II, we present our new mobile-to-mobile channel model. By applying this to time correlation, we derive the general expression for SISO M2M temporal correlation in section III. Section III also covers the simulations we carried out for two example scattering distributions followed by conclusions in section IV. II. MOBILE- TO-MOBILE CHANNEL MODEL We consider a SISO mobile-to-mobile channel model where the mobile transmitter is located inside a scatterer free sphere of radius and the mobile receiver is located inside a scatterer free sphere of radius . It is assumed that scatterers are located outside the two scatter-free transmit and receive regions and are in the far-field of the receiver and transmitter regions. In this channel model ( ˆ , ˆ ) represents the effective random complex scattering gain function for a signal leaving the transmitter scatter-free region at a direction ˆ (relative to the transmitter region origin) and entering the receiver scatter- free region from a direction ˆ (relative to the receiver region origin). Suppose the transmitter is moving at constant velocity magnitude in the direction of unit vector ˆ and the receiver is moving at constant velocity magnitude in the direction of unit vector ˆ . Following the derivation of fixed-to-mobile channel model given in [14], the signal received at the mobile receiver at time can be written as ()= × ()( ˆ , ˆ ) − ˆ ⋅ ˆ ˆ ⋅ ˆ ˆ ˆ + (), (1) where is the n-sphere, () is the baseband transmitted signal, =2/ is the wave number with being the wavelength, () is the additive noise at the receiver, = √ −1 and ⋅ denotes the inner product between vectors and . The integration in (1) above is over the unit circles for a two dimensional multipath (or scattering) environment (n=1) or over the unit sphere for a three dimensional scattering environment (n=2). 978-1-4244-7907-8/10/$26.00 2010 IEEE