Noise and dB quiz#
Gaussian noise#
Exercise 111
Which is/are correct?
In Gaussian noise with a mean value of 0, the probability of the amplitudes 1 and 2 are the same.
In Gaussian noise with a mean value of 1, the probability of the amplitudes 1 and 2 are the same.
Gaussian noise has always an average value of 0.
In nature, many random processes occur with different underlying distributions. When multiple independent random processes are combined (summed together), the resulting distribution tends to approach a Gaussian distribution according to the central limit theorem. This is why many natural noise sources (like thermal noise) exhibit Gaussian characteristics.
Gaussian noise is helpful for modeling, e.g., in simulations.
Variance, i.e., the square of the standard deviation, defines the power of Gaussian noise.
Solution to Exercise 111
4, 5, 6
Decibels (dB)#
Exercise 112
Which is/are correct?
Multiplying in the linear (non-dB) scale corresponds to addition in dB scale.
Division in the linear (non-dB) scale corresponds to subtraction in dB scale.
Addition in the linear (non-dB) scale corresponds to exponentiation in dB scale, i.e., \(x+y \Rightarrow x^y [\mathrm{dB}]\).
When converting a power value to dB, we use the formula \(20 \log_{10}(x)\).
The voltage applied to an antenna is a power value.
When converting a non-power value to dB, we use the formula \(20 \log_{20}(x)\).
The decibel (dB) scale is useful for calculations where small variations in a parameter can result in very large numerical changes, such as in power measurements for antennas and communication systems.
Doubling the power of a signal increases its level by 3 dB.
Increasing the power of a signal by a factor of 10 increases its level by 10 dB.
dBmW is typically shortened as dBm.
Solution to Exercise 112
1, 2, 7, 8, 9, 10
Noise in frequency domain#
Exercise 113
Which is/are correct?
In GNU Radio, if we would plot Gaussian noise’s spectrum, then it would not look similar to its plot in the time domain, because a spectrum plots shows the energy distribution over many frequencies, which is typically shown in dB scale.
Gaussian noise in the time domain equals to Gaussian noise in the frequency domain.
Solution to Exercise 113
1, 2
Complex noise#
Exercise 114
Which is/are correct?
Complex noise consists of a real and imaginary part.
When we want to apply Gaussian noise to a complex signal, then it is applied to the real and imaginary part independently.
When complex Gaussian noise is added to a constellation diagram (like QPSK), we see a cloud of noise centered around the origin.
To generate complex noise with unit power, we divide by √2.
Solution to Exercise 114
1, 2, 4
Gaussian noise in a constellation diagram: Each symbol point gets its own cloud of noise. The noise is centered around each individual symbol point, creating a circular cloud of points around each ideal symbol location.
AWGN#
Exercise 115
Which is/are correct?
When we combine light of all colors, we get white light. Similarly, white noise contains all frequencies at equal intensity.
AWGN stands for asymptotic white Gaussian noise. It is called asymptotic, because it has two asymptotes on \(y=\pm\mu\).
If we want to model a noise which is additive and uniform over all frequencies, we can use AWGN.
Solution to Exercise 115
1, 3
SNR and SINR#
Exercise 116
Which is/are correct?
SNR = 1 dB means the signal and the noise power are the same.
SNR = -3 dB means that the signal is weaker than the noise.
SNR is the signal to noise ratio. If the signal is at 3 dBm and the noise at 1 dBm, SNR equals to 3 dBm.
SINR additionally integrates signal interference from all the other interfering signals compared to SNR which only integrates background noise, e.g., thermal noise in the receiver.
SNR has the unit dB.
SNR has the unit dBm.
Solution to Exercise 116
2, 4
SNR is unit-less. We rather say: SNR is expressed in dB.