Question

In this question we will determine the maximum achievable transmission rate in the downlink of a wireless communication network. Here are the specifications of interest:

- Base station (BS) transmit power. \(P_{t x}=200 \mathrm{~mW}\)

- Transmitter (BS) anterma gain: \(G_{C X}=7 d B\)

- Receiver (terminal) antenna gain: \(G_{\mathrm{rx}}=3 \mathrm{~dB}\)

- Quality requirement: \(\mathrm{SNR}>5 \mathrm{~dB}\)

- Carrier frequency: \(f=2 \mathrm{GHz}\)

- Receiver noise figure: \(F=3.98=6 \mathrm{~dB}\)

- Ambient temperature: \(T=290^{\circ} \mathrm{K}\)

- Boltzmann constant: \(k=1.38 \times 10^{-23}\) joule \({ }^{\circ} K\)

- Path loss: \(P L=\left(\frac{4 \pi}{\lambda}\right)^{2} d^{4}\)

- Maximum spectral efficiency according to Shannon's chamnel capacity theorem:

$$ \mu_{\max }=\log _{2}(1+S N R) \text { bits } / \sec / \mathrm{Hz} $$

Calculate the maximum achievable rate in bits/sec in the coverage area of the BS. \(\quad\) [Help: Noise power: \(P_{\mathrm{n}}=k T B F\) in linear scale.