Consider a hexagonal cellular geometry with cluster size $K=13$ in Figure $1.$ Assume shift parameters i and $j$

where $K1,2,3,$dots,$13$AAijKK$=13AA1,2,3,$dots,$13DA\frac{C}{\text{I}}$dBRAMHz$200kHzKK=13j.$

$(b)$ Find all the $co-$channel cells $of$ cell $A(i.e.,$ cell $1in$ each cluster$)in$ the first tier and label them with $Ain$

Figure $1.$

$(c)$ Show only one cluster labeled with cells using the notations above, $i.e.,1,2,3,$dots,$13,so$ that adjacent cells

are labeled with $no$ successive numbers $to$ reduce the adjacent channel interference.

$(d)$ Find the $co-$channel cell distance $D$ from the desired cell A for the first$-$tier $co-$channel cells only.

$(e)$ Also, find the value $of\frac{C}{\text{I}}indB,$ considering only the first$-$tier $co-$channel cells, and that the mobile station

$(MS)is$ located $at$ a distance equal $to$ the cell radius $R$ away from the desired base station $(BS)A.$ Note that

$we$ consider that all cells are center$-$excited.

$(f)If$ a mobile system $is$ launched using the above cellular pattern $in$ Figure $1$ with the system bandwidth $of50$

$MHz$ and the channel bandwidth $of200kHz,$ then find the total number $of$ channels per cell $in$ the system,

$as$ well $as$ the capacity $of$ the system $(in$ terms $of$ the number $of$ calls served simultaneously$)if$ the cluster

$(with$ size $K)is$ reused $5$ times $to$ cover a particular area.

Figure $1.$ A hexagonal cellular geometry with cluster size $K=13.j.$ Consider cells $in$ each cluster with size $K$ are denoted $as1,2,3,$dots,$13.$ And, the cell labeled with $A$

$is$ cell number $1in$ each cluster. Assume that $Ais$ the desired cell $of$ concern.

$(a)$ Find the values $of$ i and $jso$ that the aforementioned conditions for $K$ are satisfied, $i.e.,K=13$ and $j.$

$(b)$ Find all the $co-$channel cells $of$ cell $A(i.e.,$ cell $1in$ each cluster$)in$ the first tier and label them with $Ain$

Figure $1.$

$(c)$ Show only one cluster labeled with cells using the notations above, $i.e.,1,2,3,$dots,$13,so$ that adjacent cells

are labeled with $no$ successive numbers $to$ reduce the adjacent channel interference.

$(d)$ Find the $co-$channel cell distance $D$ from the desired cell A for the first$-$tier $co-$channel cells only.

$(e)$ Also, find the value $of\frac{C}{\text{I}}indB,$ considering only the first$-$tier $co-$channel cells, and that the mobile station

$(MS)is$ located $at$ a distance equal $to$ the cell radius $R$ away from the desired base station $(BS)A.$ Note that

$we$ consider that all cells are center$-$excited.

$(f)If$ a mobile system $is$ launched using the above cellular pattern $in$ Figure $1$ with the system bandwidth $of50$

$MHz$ and the channel bandwidth $of200kHz,$ then find the total number $of$ channels per cell $in$ the system,

$as$ well $as$ the capacity $of$ the system $(in$ terms $of$ the number $of$ calls served simultaneously$)if$ the cluster

$(with$ size $K)is$ reused $5$ times $to$ cover a particular area.

Figure $1.$ A hexagonal cellular geometry with cluster size $K=13.$