$($b$)$ An antenna is connected to an amplifier through a coaxial cable. The system operates at $300$

K $.$ The coaxial cable has an attenuation of $2$ dB $.$ The amplifier has a gain of $\backslash (15\backslash$mathrm$\{$~dB$\},\backslash$mathrm$\{$~s$\}\backslash )$ bandwidth of $100$ MHz $,$ and equivalent noise temperature of $150$ K $.$ Determine the noise figure of the coaxial cable $-$ amplifier cascade. To enhance detection capability, it is decided to install a preamplifier at the antenna terminal before the coaxial cable. The pre$-$amplifier has an equivalent noise temperature of $150$ K $,$ gain of $20$ dB $,$ and a bandwidth of $100$ MHz $.$ Determine the noise figure of the new system and verify whether signal detection will improve. $[8][$CO$03][$BTL $3]$