## Essay on Wireless Channel Models

Wireless Channel Models Various models have been used to represent the characteristics of wireless channels. Some models treat wireless channels in the same manner wired channels are under strict limitations to obtain high simplicity in the analysis. Other models have higher complexity to accommodate for actual conditions in wireless channels. The most common models used for wireless channels include the Additive White Gaussian Noise (AWGN) channel model, the Rayleigh channel model and the Rician channel model which are shown in figure 1.

Fig1: Wireless channel models: AWGN (top), Rayleigh (middle), Rician(bottom).AWGN Channel Model

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The AWGN channel model (or the Gaussian channel model) is the ideal model for wireless channels. In it is assumed that only the line of sight component of the signal exists and no other multipath component is present. Signals in the Gaussian channel model are affected only by additive white Gaussian noise (shown in figure 2) and by the propagation loss (L) which is defined as:L= (4?d/?)^2 (1)Where d is the distance and ? is the wavelength of the travelling waves. The Gaussian channel model can be used for direct line of sight communication but is oversimplified for multipath environments.

Fig2: Power spectral density of AWGN channels 

Rayleigh Channel Model

The Rayleigh channel model (or the Rayleigh faded model) is considered as the opposite extreme of the Gaussian channel model. It assumes that the line of sight component of the signal is completely blocked and that the received signal is the sum of several replicas of the original signal that reflected, diffracted and/or scattered which are called multipath components. Multipath components arrive at different tim…

…is considered as a pure Gaussian channel. When both line of sight signal and multipath signal components are present k takes the values between 4 dB and 12 dB.When the antennas are correlated at the transmitting or receiving side, due to close spacing between the antennas, the transmission coefficient matrix under Rician fading is further modified to become:H=v(k/(k+1)) H_LOS+v(1/(k+1)) ?R_r^(1/2) H?_MP R_t^(1/2) (6)Where Rr is the correlation matrix at the receiving side and Rt is the correlation matrix at the transmitting side. The correlation matrix R is defined by the uniform correlation matrix model to be:r_ij {¦(r,[email protected],i=j) ,|r|+?1 (7)Where r is correlated fading parameter between any two adjacent antennas. R can also be defined by the exponential correlation matrix model to be:r_ij {¦(r^(j-i),[email protected]_ij^*,i>j) ,|r|+?1 (8)

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