Q$4.$ a$)$ Define spectrum efficiency and explain its significance in mobile communications.

b$)$ Briefly explain how spectrum efficiency is measured in mobile networks and enumerate the factors influence it$.$

c$)$ What advancements are being explored to enhance spectrum efficiency in $5$G and beyond?

d$)$ In a digital communication system, the allocated frequency band for data transmission is $10$ MHz $.$ The system adopts a modulation scheme with a symbol rate of $1$Msymbols$/$s Each communication channel requires a bandwidth of $5$ kHz $.$ If the system design allows for the sharing of channels among multiple users, and one$-$fourth of the available channels are dedicated to control and synchronization, calculate the spectral efficiency of modulation. Assume the use of dense metropolitan area configurations with small cell sizes.