# Digital Communications: Bit Error Rate (BER), C/N, Constellations

• Engineering
• ashah99
In summary, the problem statement is about finding the C/N ratio in relation to SNR (Eb/N0) without the given bandwidth or data rate. The solution involves using a QPSK modulation scheme and determining the decision threshold and RMS noise amplitude in order to decode the data. However, the discuss a drawback in using the given symbol with that pulse shape, as sharp transitions make it spectrally inefficient.
ashah99
Homework Statement
Please see a snippet of the problem below.
Relevant Equations
C/N = (Eb/N0) * (data rate/bandwidth)
Problem Statement:

I am not quite sure how to approach this problem and would appreciate the help. I how the C/N is closely related to the SNR (Eb/N0), but the question does not give the bandwidth or data rate for me to use the formula above. From the constellation diagram, my guess is this is QPSK modulation scheme, but even that is a guess. Can anyone help?

ashah99 said:
Homework Statement:: Please see a snippet of the problem below.
Relevant Equations:: C/N = (Eb/N0) * (data rate/bandwidth)

Problem Statement:

View attachment 291953
I am not quite sure how to approach this problem and would appreciate the help. I how the C/N is closely related to the SNR (Eb/N0), but the question does not give the bandwidth or data rate for me to use the formula above. From the constellation diagram, my guess is this is QPSK modulation scheme, but even that is a guess. Can anyone help?

tech99 said:
Unfortunately not, which is why I ask for help.

I could show you the entire problem if you would like, but it is irrelevant in my opinion. The other parts were to sketch the in-phase and quadrature phase voltage signals that would be sent to an IQ-modulator and to discuss a drawback in using the given symbol with that pulse shape (sharp transitions makes it spectrally inefficient is my answer).

tech99 said:

I think in essence we take the signal amplitude as 1 volt. As we have two quadrature carriers, half the power is in each, so each phase has 0.7 volt peak. Next we measure the distance between the nearest points on the constellation. This looks like 0.35 volt. So the decision threshold, where the detector decides 0 or 1, will be half that = 0.18 volt. Then we find the RMS noise amplitude, which is 1 Volt - 15dB = 0.18. So the detector is seeing a signal at the same amplitude as the RMS noise. In this situation it cannot decode data.
Sorry I am not too expert on these calculations and I might be slightly out in the explanation. There are several web sites talking about C/N and BER for different modulation schemes.

## 1. What is Bit Error Rate (BER) and why is it important in digital communications?

Bit Error Rate (BER) is a measure of the number of errors that occur in a digital communication system. It is calculated by comparing the number of bits received with the number of bits transmitted. BER is important because it provides an indication of the quality and reliability of the communication system. A lower BER indicates a better quality and more reliable system.

## 2. How is C/N (Carrier-to-Noise) ratio related to BER in digital communications?

C/N ratio is a measure of the strength of the signal compared to the level of background noise. It is directly related to BER in digital communications, as a higher C/N ratio results in a lower BER. This is because a stronger signal is less likely to be affected by noise, leading to fewer errors in the transmission.

## 3. What are constellations in digital communications and how do they affect BER?

Constellations in digital communications are graphical representations of the different signal points used to transmit data. They are typically plotted on a 2D grid, with each point representing a specific combination of amplitude and phase. The arrangement of these points can affect the BER, as a more densely packed constellation can lead to a higher likelihood of errors due to signal interference.

## 4. How does modulation scheme impact BER in digital communications?

Modulation scheme refers to the method used to encode data onto a carrier signal. Different modulation schemes have different levels of complexity and efficiency, which can impact the BER. For example, more complex modulation schemes may have a higher BER due to the increased likelihood of errors in the encoding process.

## 5. How can BER be improved in digital communications?

There are several ways to improve BER in digital communications, such as using error correction codes, increasing the C/N ratio, and using more efficient modulation schemes. Additionally, proper system design and regular maintenance can also help to reduce BER. It is also important to consider the trade-offs between BER and other factors, such as data rate and cost, when making design decisions for a digital communication system.

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