Consider a discrete memoryless source with an alphabet of four source symbols. $s(t)$ is a multi-level ( $-1,0,+1,+2$ ) signal representing a long sequence of random symbols from the above source which is generating $10^4$ symbols per second. Which of the following options is the correct value of equivalent Nyquist bandwidth of $s(t)$ ?

A wireless digital transmission scheme is using 16-QAM over an additive white Gaussian noise channel and a maximum-likelihood receiver. Consider the information bit rate from source to be $4 \times 10^6$ bits per second.

The minimum transmission bandwidth (in MHz) of the modulated signal necessary for optimum recovery of information at the receiver is $\_\_\_\_$ .

(rounded off to two decimal places)

A QPSK modulated signal from an additive white Gaussian noise (AWGN) channel is received with an $E_b / N_o=8.4 \mathrm{~dB}$ at the input of a coherent QPSK demodulator. A maximum-likelihood reception method is used in the demodulator.

Assume the complimentary error function

$$ \operatorname{erfc}(u) \cong\left[\frac{1}{(u \sqrt{\pi})}\right] \exp \left(-u^2\right) $$

Which is the nearest bit error rate (BER) at the output of the demodulator?

Let the relevant bandwidth $(B)$ of a digital communication system be 1 MHz and $k T=-174 \mathrm{dBm} / \mathrm{Hz}$, where $k$ is Boltzmann's constant and ' $T$ ' is equivalent noise temperature of the receiver. The power ( $S$ ) of signal received through an additive Gaussian channel is -80 dBm .

Which of the following options is/are TRUE about Shannon capacity ( $C$ ) of the channel?