Question

In a broadcasting communication system, the transmit power is 40 kW, the channel attenuation is 180 dB, and the white noise power PSD is 10×10−²¹ W/Hz. The message signal has a bandwidth of 10kHz.

a) Find the output SNR if the modulation is DSB.
NOTE 1: you do NOT need to know the power of the message to solve this problem. Why? Think about what you have and try to solve this problem by yourself before looking at TIP in the end of the HW.)
NOTE 2: you are given the PSD of the white noise. How can you get No from it?

Answer 1

To find the output SNR, one must first convert channel attenuation from dB to a linear scale, calculate noise power using PSD and bandwidth, and then use these values to determine the received power and finally divide it by the noise power to find the SNR.

Step-by-step explanation:

The question asks to find the output Signal-to-Noise Ratio (SNR) for a broadcasting communication system with a given transmit power, channel attenuation, white noise power Power Spectral Density (PSD), and message signal bandwidth, assuming Double Side Band (DSB) modulation. To answer this, we can use the relationship between the quantities given without needing the power of the message because DSB modulation allows us to infer the necessary information from the given variables.

First, we convert the channel attenuation from decibels (dB) to a linear scale by using the formula ∂ = 10^(attenuation in dB / 10). Then, given the white noise power PSD is 10×10−21 W/Hz, we can calculate the noise power (ℓo) by multiplying the PSD by the message signal's bandwidth. Finally, we divide the transmit power by the channel attenuation (now as a linear factor) to find the received power, and from there we calculate the SNR by dividing the received power by the noise power (ℓo).