Question

Problem 3 A receiver has a bandwidth of 1 MHz and a noise figure of 10 dB. The receiver sensitivity is -90 dBm. The Boltzmann constant is k=1.38x10-23 Joule/deg K, and the room temperature is 300 deg Kelvin. a) What is the ratio of the SNR at the input to the receiver (computed over the bandwidth of interest) to the SNR at the output of the receiver? b) What is the noise power at output of the receiver? c) Find the minimum SNR at which this receiver is designed to operate. d) The signal is subject to shadowing with standard deviation os = 10 dB. What should be the level of the received signals so that the system outage does not exceed 2%?

Answer 1

SNR is the Signal to Noise Ratio in receiver. Noise figure (NF) represents the degradation in SNR as the signal passes through a device. NF can be represented in the terms of noise factor (F), which is the ratio of SNR at the input of the receiver to the SNR at the output of the receiver.

1. i.e., $NF=10{log_{10}}^{F}$

Where F is the ratio of SNR at input to the SNR at output,

i.e., $F={SNR_{i}}/SNR_{o}$

Given NF=10 db

From above equations,

10 = 1010910
, Now the value of F is
1= log10
, $10^{1}=F$

Therefore, required ratio of SNR at input to the SNR at output is 10.

2. Noise power at output is given by,

B is the receiver bandwidth

k is boltzmann constant

Therefore, Noise power = 1.38 * 10-23 * 300 * 106 = 4.14 * 10-15 joule Hz

3. Minimum SNR required to operate is calculated by using the receiver sensitivity,

  Smin = (SNR)min * k * T * B * NF

(SNR)min=Smin / (k * T * B * NF) = (-90) / (1.38 * 10-23 * 300 * 106 * 10) = 65.2173 * 1014

4. SNR is also defined as the ratio of expected value to the standard deviation of the noise.

  $SNR=\mu /\sigma$

$\mu$ is the expected value (2% = 0.02) and $\sigma$ is the standard deviation of the noise (10db).

SNR = 0.02/10 = 0.002

We know that the level of received siganl is the sum of the SNR and the noise loss.