Wireless Communication

Chapter: Wireless Propagation Channels
Section: Channel Models, Indoor Propagation

Relevant Channel Parameters

Contributed by Peter E. Leuthold and Pascal Truffer

Several definitions exist for the scatter function of a multipath channel. Basically, these "parameters", "functions" and "profiles" describe the time and frequency dispersion of the channel. This contribution defines and discusses functions that defines delay spread and angle of arrival. For outdoor, vehicular channels, time dispersion is often a more useful parameter than angle of arrival, while for indoor systems with diversity, angle of arrival is more useful. Note however that if an antenna is in motion, there is a direct relation between angle of arrival and Doppler shift.

field delay-direction spread vector

A description of the dispersive radio channel can be based on the electric field delay-direction spread vector tex2html_wrap_inline903 defined in [4]. The vector tex2html_wrap_inline905 denotes the MT antenna location, and tex2html_wrap_inline907 and tex2html_wrap_inline909 are the delay and incidence direction variables, respectively, where tex2html_wrap_inline909 is determined by the azimuth tex2html_wrap_inline913 and the coelevation tex2html_wrap_inline915 in a spherical coordinate system.

The vector tex2html_wrap_inline903 can be decomposed into a sum of M components each originating from a hypothetical impinging wave:


The notation tex2html_wrap_inline919 means that the number of active paths or dominant waves varies with the location when the MT is moving along the trajectory. Under far field conditions the vector tex2html_wrap_inline903 has two components which correspond to the vertical and horizontal polarization.

Delay-Direction Spread Function

Considering simply one polarization component we define the scalar field delay-direction spread function tex2html_wrap_inline923 called FDDSF. The CIR follows by


where tex2html_wrap_inline925 is proportional to the field pattern of the MT antenna for the considered polarization.

We now assume that over a sufficiently small area A the wave incidence constellation, i.e. the number of active paths, relative delay, angle of arrival and amplitude, remains approximately constant. Consequently, the spatial variations of the FDDSF mainly result from the changes of the phase of the wave components.

Within the area A the wave incidence constellation is characterized by the local power delay-direction profile (PDDP)


which may be presented in the SCRM as the product


In this equation, tex2html_wrap_inline931 denotes the path loss for the distance tex2html_wrap_inline933 from the transmitter station to the area A and tex2html_wrap_inline937 is the local delay-direction scattering function (DDScF) in A. Since the components in (1) are regarded as independent we obtain with (4) the expression


that means each term is determined by the mean power tex2html_wrap_inline941 , the mean delay tex2html_wrap_inline897 , the mean incidence direction tex2html_wrap_inline899 and a local scattering function tex2html_wrap_inline937 which is considered to be identical for all components. Obviously, the variables M, tex2html_wrap_inline941 , tex2html_wrap_inline897 , and tex2html_wrap_inline899 are random variables.



Table 2: Description of the primary random variables M, tex2html_wrap_inline897 , tex2html_wrap_inline899 (delay spread tex2html_wrap_inline901 )

Their specification is given in Table 2 [2] with the exception of tex2html_wrap_inline941 which will be discussed later on.

Figure: Local PDDP generated with the SRCM

Figure 1 presents a realization of the local PDDP obtained with the SRCM. In this case as well as for the next Figures 2 to 6 the following parameters have been chosen: carrier frequency 5.2 GHz, MT velocity 1 m/s, delay spread tex2html_wrap_inline991 . Such a situation is typical for a small room environment.

Taking the expectation of the local DDScF over a class C of environments, i.e. a large room, yields the global DDScF


In accordance with the assumptions in Table 2 this function takes the form


where the global delay scattering function tex2html_wrap_inline995 (DScF) follows integrating tex2html_wrap_inline997 with respect to tex2html_wrap_inline909 . It is reasonable to choose the global DScF as an exponentially decaying function


that means the scattered power decreases with increasing delay. With regard to the channel simulation the global DDScF according to (7) and (8) can be considered as a target function which represents the expectation of Gaussian processes with the standard deviation tex2html_wrap_inline1001 and tex2html_wrap_inline1003 , respectively.

Figure: Global and local DScF

Figure 2 shows the successive approximation of the global DScF by the average of local DScFs.


Wireless Communication Peter E. Leuthold and Pascal Truffer, 1999