Wireless Communications Channel Modeling Based on Numerical Solutions of Maxwell Equations

The field strength level of received signal and its statistical distributions are important studies in the wireless communication and network planning. In this paper, we perform numerical solutions of Maxwell equations based on two fast methods of solutions of Method of Moment (MoM) equations, viz multi-level fast multipole method (FMM) [1] and the sparse matrix canonical grid method (SMCG) [1]. In the first problem, we solve a two-dimensional problem of urban area with distance of 1 kilometer at 900MHz for macrocell/microcell studies. The fast and slow fading effects are studied. The distance power gradient is studied. In the second problem, we solve a three-dimensional scattering problem of scattering by random rough surfaces for Ultrawideband (UWB) studies with bandwidth from 3GHz to 10GHz. The effects of pulse distortion and fast fading are studied. Results show that UWB has less fading compared with the narrow band pulse. In the last decade, the needs of wireless communication are expanded drastically. With the rapid growth of communications technology, cell sizes are getting smaller and the trend in development of wireless communication is the use of broader frequency band propagation (e.g. UWB propagation) and use of multiple-input and multiple-output systems. Therefore, site-specific propagation information is needed for the wireless communication network planning. The predication of field strength level and the statistical distribution of the scattered signal are the important studies in the signal propagation. Site-specific propagation channel modeling in wireless communications include heuristic statistical methods and approximate analytical methods. Approximate analytical methods include ray tracing [2]-[4] and the parabolic equation method (PEM) [5]-[6]. Exact solutions such as FDTD [7] have also been employed but have been limited to small size problems. In [8], a model based on the banded matrix iterative approach (BMIA) to the MoM is proposed to study the VHF propagation. In this paper, we employ the FMM method and the SMCG method to solve large-scale problem. In our analysis, we study the wave propagation with variable height of building with rough surface on rough terrain. The frequency of 900MHz is used. Propagation distance in the order of kilometers are concerned. The transmitter point source is located above the building. Figure 1 shows the Monte Carlo random generated profile of building on 1 km rough terrain. The received field is plotted on Figure 2. In the figure, we find that the distance power gradient is larger than that in free space. Both fast and slow fading are exhibited in the simulations. Next we study the UWB problem. Signal sources such as narrow band continuous wave (CW) signal and UWB signal are considered. Random rough surfaces are generated and 3D numerical solutions of Maxwell equations are 0-7803-8197-1/03/$17.00 (c)2003 IEEE -15 -10 -5 0 5 10 0 0.2 0.4 0.6 0.8 1 20log10(|Ey|/<|Ey|>) C D F of P (|E y |= ) C D F of P (|E y = <x ) f = 5.2 GHz CW Fig. 1