Q$9)(4$ Marks$)$ An X$-$band monostatic radar system is designed to operate at $10$ GHz using an antenna with a directive gain of $30$ dB $,$ a maximum output power of $40$ kW $,$ and a receiver power sensitivity $($i$.$e$.$ minimum detectable power$)$ of $1$ nW $.$ If this radar system is used to detect a missile with a scattering cross$-$section of $0\mathrm{.}5m^2,$ determine:

a$)$ The maximum detection range of this radar system: $[1\mathrm{.}5$ Marks$]$

b$)$ If the operating frequency is increased $16$ times, would the detection range increase or decrease and by what factor? $q,[0\mathrm{.}5$ Marks$]$

Explanation $($Steps to find the answers$)$: $(2$ Marks$)$