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Explain combined path loss and shadowing and outage probability under the effect of path loss and shadowing.

Ahmedabad University > Information and Communication Technology > Sem 5 > Wireless Communication

Marks: 20M

Year: August 2015

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Theory:

  • Combined path loss and shadowing

    Received signal power is usually varied because of path loss and shadowing effect. Here, pathloss is due to the transmission channel and power radiated by transmitter. In pathloss models, for a fixed distance between transmitter and receiver, path loss is same. We get varied path loss for some distance between transmitter and receiver as a result of blockage from objects between the two, scattering objects and changes in reflecting surfaces.

    Also, shadowing is caused by various obstacles between transmitter and receiver.

    Hence, we use statistical models to characterize the attenuation and the most general model used for this is log normal shadowing.

    Typically, models for path loss and shadowing are superimposed on each other in order to characterize the power falloff vs. distance along with the random attenuation occurred due to this path loss from shadowing. For this combined model, average path loss $\mu$$_{\psi}$$_{dB}$ is characterized by path loss model while shadow fading generates variations about this mean. $$ \frac{Pr}{Pt}(dB) = 10log10K - 10 \gamma log10 \frac{d}{d0} + \psi_{dB} $$

    Here, $\psi$$_{dB}$ = Gauss distributed random variable with zero mean and variance = $\sigma$$^2$$_{\psi}$$_{dB}$ - Outage probability: For wireless systems to be acceptable, received signal power should always be $\geq$ Pmin. Outage probability can be defined as: $$ p(P_{r}(d) \leq P_{min}) = 1 - Q \Bigg( \frac{P_{min} - (P_{t} + 10log_{10}K - 10 \gamma log_{10} (\frac{d}{d0}))}{\sigma _{\psi _{dB}}} \Bigg) $$

Here, Q function is the probability that a random variable x with zero mean and variance $\gt$ z. $ Q(x) = p(x > z) = \int_{z}^{\infty} \frac{1}{\sqrt{2\pi}} e^{- \frac{x^{2}}{2}} dy $ Q function and complementary error function can be converted each other with following equation. $ Q(z) = \frac{1}{2}er fc \bigg (\frac{z}{\sqrt{2}} \bigg ) $

Results

1. Combined Path Loss and Shadowing

Combines Path Loss and Shadowing


2. Outage Probability vs. Distance Outage Probability vs. Distance

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