Q$4)(10$ p $)$ Consider $7-$cell frequency reuse. Cell B$1$ is the desired cell and B$2$ is a cochannel cell as shown in the figure. Assume the following:

Co$-$channel interference is due to base B$2$ only.

Camer frequency, $f_e=2\mathrm{.}3GHz.$

Reference distance $d_0=0\mathrm{.}1km($assume free space propagation from the transmitter to $d_0).$

Assume omnidirectional antennas for both transmitter and receiver, where $G_{\text{b}\text{a}\text{s}\text{e}}=6$dBi and $G_{\text{m}\text{a}\text{b}\text{i}\text{l}\text{e}}=3$dBi.

Transmitter power, $P_t=10W($assume equal power for all base stations$).$

Path loss between the mobile and base B$1$ is given as

$PL(d)[dB]=PL(d_0)+10(3\mathrm{.}5)log(\frac{d}{d_0})+x_g,=0dB$

Path loss between the mobile and base B$2$ is given as

$PL(d)[dB]=PL(d_0)+10(4)log(\frac{d}{d_0})+x_{},=3dB$

Answer the following questions.

$($a$)$ For a mobile X located at the cell boundary of B$1($consider all the comer points$),$ find the minimum co$-$channel distance D to give a forward link C$/$I ratio of at least $18$ dB at least $98\%$ of the time. What is the minimum radius of the cell?

$($b$)$ If the system has an average call length of $3$ minutes with GOS$=0\mathrm{.}1\%,$ find the traffic capacity loss due to trunking for $180$ channels when going from omnidirectional antennas to $120$ sectored antennas. Assume that blocked call are cleared and the average per user call rate is $2$ calls per hour.

$\backslash$table$[[$Number of$,$Erlangs for GOS$=],[$Channels$,0\mathrm{.}01,0\mathrm{.}001],[30,20\mathrm{.}3,16\mathrm{.}65],[60,46\mathrm{.}9,40\mathrm{.}75],[120,102\mathrm{.}95,92\mathrm{.}95],[180,160\mathrm{.}4,147\mathrm{.}25]]$