outage probability

[logistic_guy]

In this problem we will explore the impact of different log-normal shadowing parameters on outage probability. Consider a cellular system where the received signal power is distributed according to a log-normal distribution with mean \(\displaystyle \mu_{\psi} \ \text{dBm}\) and standard deviation \(\displaystyle \sigma_{\psi} \ \text{dBm}\). Assume the received signal power must be above \(\displaystyle 10 \ \text{dBm}\) for acceptable performance.

(a) What is the outage probability when the log-normal distribution has \(\displaystyle \mu_{\psi} = 15 \ \text{dBm}\) and \(\displaystyle \sigma_{\psi} = 8 \ \text{dBm}\)?
(b) For \(\displaystyle \sigma_{\psi} = 4 \ \text{dBm}\), find the value of \(\displaystyle \mu_{\psi}\) required for the outage probability to be less than \(\displaystyle 1\%\) – a typical value for cellular systems.
(c) Repeat part (b) for \(\displaystyle \sigma_{\psi} = 12 \ \text{dBm}\).
(d) One proposed technique for reducing outage probability is to use macrodiversity, where a mobile unit’s signal is received by multiple base stations and then combined. This can only be done if multiple base stations are able to receive a given mobile’s signal, which is typically the case for \(\displaystyle \text{CDMA}\) systems. Explain why this might reduce outage probability.

 

[khansaheb]

In this problem we will explore the impact of different log-normal shadowing parameters on outage probability. Consider a cellular system where the received signal power is distributed according to a log-normal distribution with mean \(\displaystyle \mu_{\psi} \ \text{dBm}\) and standard deviation \(\displaystyle \sigma_{\psi} \ \text{dBm}\). Assume the received signal power must be above \(\displaystyle 10 \ \text{dBm}\) for acceptable performance.

(a) What is the outage probability when the log-normal distribution has \(\displaystyle \mu_{\psi} = 15 \ \text{dBm}\) and \(\displaystyle \sigma_{\psi} = 8 \ \text{dBm}\)?
(b) For \(\displaystyle \sigma_{\psi} = 4 \ \text{dBm}\), find the value of \(\displaystyle \mu_{\psi}\) required for the outage probability to be less than \(\displaystyle 1\%\) – a typical value for cellular systems.
(c) Repeat part (b) for \(\displaystyle \sigma_{\psi} = 12 \ \text{dBm}\).
(d) One proposed technique for reducing outage probability is to use macrodiversity, where a mobile unit’s signal is received by multiple base stations and then combined. This can only be done if multiple base stations are able to receive a given mobile’s signal, which is typically the case for \(\displaystyle \text{CDMA}\) systems. Explain why this might reduce outage probability.

show us your effort/s to solve this problem.