This problem shows how different propagation models can lead to very different SNRs $($and therefore different link performance$)$ for a given system design. Consider a linear cellular system using frequency division, as might operate along a highway or rural road. Each cell is allocated a certain band of frequencies, and these frequencies are reused in cells spaced a distance d away. Assume the system has square cells, $2$ km per side, and that all mobiles transmit at the same power P$.$

$$

 For the following propagation models, determine the minimum distance that the cells operating in the same frequency band must be spaced so that uplink SNR $($the ratio of the minimum received signal-to-interference power from mobiles to base station$)$ is greater than $20$ dB$.$

You can ignore all interferers except thosefrom the two nearest cells operating at the same frequency.$$

$($a$)$ Propagation from both signal and interference follow a free$-$space model.$$

$($b$)$ Propagation for both signal and interference follow the simplified path$-$loss model with d$0=100$m$,$ K $=1,$ and n $=3.$$$

$($c$)$ Propagation for the signal follows the simplified path$-$loss model with d$0=100$ m$,$ K $=1,$ andn $=2,$ while propagation of the interference follows the same model but with n $=4.$Base Station$/$Cell Center

 

2 Kms |1 12 Base Station/Cell Center d