# How to draw constellation diagram of qpsk

Quadrature phase-shift keying is now the mainstream method used for modulation in cable modems, satellites, and numerous other wireless communication schemes. The signature constellation pattern of QPSK and related digital modulations schemes can be a bit baffling to novices. If a digital signal is used as the input to a conventional frequency modulator, the output will consist of a sine wave containing two distinct frequencies. Getting the original digital signal back requires a demodulation process that consists of passing the modulated signal through two filters, then translating the resulting signal back into logic levels.

This process of modulation is generally called frequency-shift keying, FSK. There is a method similar to FSK called phase-shift keying.

As you might suspect, FSK involves modulating the phase of the carrier rather than its frequency. The finite phase changes represent digital data. Using a digital signal to switch between two signals of equal frequency but opposing phase will generate a simple phase-modulated waveform.

Now consider multiplying the resulting phase-modulated waveform by a sine wave of equal frequency. This generates two component waveforms. One is a cosine waveform of double the received frequency. The other is a frequency-dependent term having an amplitude proportional to the cosine of the phase shift. Now, filtering out the doubled frequency term produces the original data used for modulating the transmission. The concept of quadrature phase shifting arises from the idea that there can be more than two states of phase shifting.

The carrier can experience numerous phase changes. Then multiplying the received signal by a sine wave of equal frequency will demodulate the phase shifts into voltage levels that are independent of frequency.

Thus in QPSK, the carrier undergoes four changes in phase. Each phase change can represent two binary bits of data. The point of this approach is that the carrier can transmit two bits of data instead of one, so the bandwidth of the transmission has effectively doubled.

The explanation and proof of QPSK concepts fall out of writing sine and cosine relationships in their exponential form Euler relationsthen recognizing trigonometric identities.

It is also superimposed on a dc offset of half the input amplitude. The accurate decoding of phase shifts present in all four quadrants requires that the input signal first is multiplied by both sine and cosine waveforms, then go through filtering to get rid of the 2x frequency, then go through data reconstruction. Photo courtesy of Maxim Integrated.

It turns out that it can be tough to synchronize a local oscillator with an input signal. If the phase of the local oscillator varies with that of the input signal, signals on the phasor diagram will be rotated from their expected position by an amount proportional to the phase difference.

If both the phase and frequency of the local oscillator are not fixed, the rotation on the phasor diagram is continuous.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts.

It only takes a minute to sign up. What is the intuitive way of understanding concept of constellations in digital communication? I know the Gram Schmidt Procedure, Orthonormal basis functions and how to find the constellation but just wish to know the physical significance of constellations.

What does this signify? Thanks a lot in advance. I'll summarise here. Consider what modulation is. We have some carrier, and then we modulate some parameter of that carrier to contain data. Consider first an unmodulated carrier. We will have in our receiver an RF mixer tuned to the carrier frequency.

The output of this mixer, receiving this unmodulated carrier, can be represented as:. The output of the mixer at any instant can be represented by a point on this plot, and since this is an unmodulated carrier at the mixer frequency, the point does not move.

### QPSK modulation and Demodulation

The blue vector most intuitively represents the signal. Its length corresponds to the amplitude of the signal. The angle of the vector represents the phase. We did not specify the phase or the amplitude of the unmodulated carrier we are receiving, so really any point on this plot represents an unmodulated carrier at the mixer frequency, except the very center, which represents receiving no signal at all. As we move away from the origin, the amplitude increases. As we rotate about the origin, the phase changes.

If we were receiving an AM signal, the point will move. We might be at any phase, because phase information is not relevant to AM, so the blue vector could be at any angle. But, the length of the vector will change with the amplitude. If we watch the point move over time, it will trace a line. If we measure the distance from the origin to the point over time, we recover the amplitude of the signal, which is our baseband signal. FM is similar, except the amplitude does not change, but the phase does.

Thus, the point will trace an arc around the origin. Measuring the rotation of this point recovers the signal. We do this just because it's more convenient to process and implement in hardware.

You can think of them as in phase and quadrature components, or sine and cosine components:.

A digital constellation represents the possible states in this graphical notation, and how each of those states corresponds to some bits. For example, take BPSK :.

There are far more than just two variants of QPSK. What they all have in common is this constellation:. The difference is in how the signal moves from state to state. Remember that this constellation just shows the state at the point at which the signal is sampled for each symbol.

Now, the simplest implementation would be to instantly change the phase for each symbol:. This would be simple to implement, and would be quite robust against timing errors between the transmitter and receiver, since if the receiver samples the symbol at a little bit the wrong time, it doesn't matter, because nothing is changing.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here.

Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I am unable to understand which values to use to generate the phase constellation diagram for my code?

What way in my code I can generate the correct phase constellation diagram? The QPSK symbol alphabet has four complex symbols. A set of random QPSK symbols can be created by generating an array of random integer numbers in To plot the constellation diagram, use the real part as x-values and the imaginary part as y-values in the plot command.

Additionally, use '. This could be the received signal in a communications system neglecting inter-symbol interference and other frequency-selective components.

Learn more. Asked 5 years, 1 month ago. Active 5 years, 1 month ago. Viewed 12k times. Programmer Programmer 6, 19 19 gold badges 56 56 silver badges bronze badges. Not sure what you're looking for.

Have you tried Signal Processing StackExchange? Can you give an example of a "phase constellation diagram"? I only know constellation diagrams which depict discrete-time data in the complex plane. Of which signal woul you like to create the constellation diagram?

It will be a circle. The constellation diagram is usually plotted of the transmit or received digital signal. Deve - Can you please then let me know what changes I need to do to plot my constellation diagram? Active Oldest Votes. Deve Deve 4, 2 2 gold badges 20 20 silver badges 26 26 bronze badges. Thanks a lot - I was finally able to implement the phase constellation plot for my code.

I have modified the code accordingly. Please comment on same. Without you answer and details listed I would have never been able to conceptualize the concept. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown.Documentation Help Center. A scatter plot or constellation diagram is used to visualize the constellation of a digitally modulated signal.

To produce a scatter plot from a signal, use the scatterplot function or use the comm. A scatter plot or constellation diagram can be useful when comparing system performance to a published standard, such as 3GPP or DVB.

You create the comm. ConstellationDiagram object with a default object or by defining name-value pairs. This example shows how to use constellation diagrams to view QPSK transmitted and received signals which are pulse shaped with a raised cosine filter.

Create a raised cosine transmit filter with samples per symbol, spsequal to Generate data symbols, apply QPSK modulation, and pass the modulated data through the raised cosine transmit filter.

You can display the constellation diagram of the transmitted signal using scatterplot. Since the signal is oversampled at the filter output, you need to decimate by the number of samples per symbol so that the scatter plot does not show the transition path between constellation points.

If the signal had a timing offset, you could provide that as an input parameter to display the signal constellation with the timing offset corrected. Alternately, you can use comm. ConstellationDiagramspecifying the number of samples per symbol, and if needed the timing offset. Also, using comm. ConstellationDiagram the reference constellation can be shown. Create a constellation diagram and set the SamplesPerSymbol property to the oversampling factor of the signal.

Specify the constellation diagram so that it only displays the last samples. To match the signal to its reference constellation, normalize the filter by setting its gain to the square root of the OutputSamplesPerSymbol property. This was previously specified as sps. The filter gain is nontunable so the object must be released prior to changing this value.

Display the constellation diagram of the normalized signal. The data points and reference constellation nearly overlap. To view the transmitted signal more clearly, hide the reference constellation by setting the ShowReferenceConstellation property to false.

You can also use scatterplot to view this noisy signal but there is no built in option to add the reference constellation using scatterplot. Constellation Visualization. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:.There exist other constellations that are more efficient in terms of energy required to achieve same error probability than the standard rectangular constellation.

But due to its simplicity in modulation and demodulation rectangular constellations are preferred. In any M-QAM constellation, in order to restrict the erroneous symbol decisions to single bit error, the adjacent symbols in the transmitter constellation should not differ more than one bit.

This is usually achieved by converting the input symbols to Gray coded symbols and then mapping it to the desired QAM constellation. But this intermediate step can be skipped altogether by using a Look-Up-Table LUT approach which properly translates the input symbol to appropriate position in the constellation.

### QAM Formats: 8-QAM, 16-QAM, 32-QAM, 64-QAM, 128-QAM, 256-QAM

We will exploit the inherent property of Karnaugh Maps to generate the gray coded QAM constellation. If you are familiar with Karnaugh Maps K-Maps used in digital electronics, it is easier for you to identify that the K-Maps are constructed based on Gray Codes. For a 4-ASK signal there are 4 amplitude levels. A 4 variable K-Map will look like the one shown below.

Construct an array with the numbers indicated in the square brackets as array indices. The array indices are the input to the QAM modulator and the corresponding array values are the QAM modulator output that are gray coded and mapped to constellation points.

So, care has to be taken when accessing the array values. Plot the in-phase and quadrature phase components QAM output and each point with the equivalent binary representation of the array index gives the QAM constellation where the adjacent symbols differ by only one bit.

The same approach can be used to construct rectangular constellation for QAM modulation for any values of M. Its easier to utilize Karnaugh Map baed gray code walks for generating the constellation for higher level QAMs. How negotiate both sites of a QAM based link the symbol mapping which is to be use? Is there any procedure standardized? LTE offers all possible combination of resource allocation that combines different time Domain, frequency Domain and the modulation schemes.

The question now is how can the receiver know exactly in which time slotat what frequency and in which modulation format the sender is sending the information.

Without knowing this information, the receiver cannot decode the captured signal. DCI carries all the necessary information for decoding the received data at the receiver. Not only in LTE, other wireless standards also has similar indicators.

## Constructing a rectangular constellation for 16-QAM

Yes, it is possible. If you have, please give me the link address. I am not sure whether you have checked this post on constellation construction using K-maps.

Why not 00,01,10,11? That is the basis of K-map. Last updated on June 17th, at pm 7 votes, average: 4.QPSK is a form of phase modulation technique, in which two information bits combined as one symbol are modulated at once, selecting one of the four possible carrier phase shift states.

The QPSK signal within a symbol duration is defined as. Therefore, the four possible initial signal phases are and radians. Equation 1 can be re-written as. The above expression indicates the use of two orthonormal basis functions: together with the inphase and quadrature signaling points:. Therefore, on a two dimensional co-ordinate system with the axes set to andthe QPSK signal is represented by four constellation points dictated by the vectors with.

In this implementation, a splitter separates the odd and even bits from the generated information bits. Each stream of odd bits quadrature arm and even bits in-phase arm are converted to NRZ format in a parallel manner.

After oversampling and pulse shaping, it is intuitively clear that the signal on the I-arm and Q-arm are BPSK signals with symbol duration. The signal on the in-phase arm is then multiplied by and the signal on the quadrature arm is multiplied by.

QPSK modulated signal is obtained by adding the signal from both in-phase and quadrature arms. Note: The oversampling rate for the simulation is chosen aswhere is the given carrier frequency and is the sampling frequency satisfying Nyquist sampling theorem with respect to the carrier frequency. This configuration gives integral number of carrier cycles for one symbol duration. In this implementation, the I-channel and Q-channel signals are individually demodulated in the same way as that of BPSK demodulation.

After demodulation, the I-channel bits and Q-channel sequences are combined into a single sequence. The complete waveform simulation for the aforementioned QPSK modulation and demodulation is given next.

The simulation involves, generating random message bits, modulating them using QPSK modulation, addition of AWGN channel noise corresponding to the given signal-to-noise ratio and demodulating the noisy signal using a coherent QPSK receiver.

The waveforms at the various stages of the modulator are shown in the Figure 4. The performance simulation for the QPSK transmitter-receiver combination was also coded in the code given above and the resulting bit-error rate performance curve will be same as that of conventional BPSK.

Provide your answer by showing calculations. Rayleigh channel used BER curves to show performance…plz i need it urgently…. So my solution for you is at first upsample of your NRZ data arbiary 4,8 or 16… and then taking convolution of upsampled data and root raised cosine filter will have give simply the output that you need.Instead of the conversion of digital bits into a series of digital stream, it converts them into bit pairs.

This decreases the data bit rate to half, which allows space for the other users. The QPSK Modulator uses a bit-splitter, two multipliers with local oscillator, a 2-bit serial to parallel converter, and a summer circuit.

Following is the block diagram for the same. The QPSK waveform for two-bits input is as follows, which shows the modulated result for different instances of binary inputs. The QPSK Demodulator uses two product demodulator circuits with local oscillator, two band pass filters, two integrator circuits, and a 2-bit parallel to serial converter.

Following is the diagram for the same. The two product detectors at the input of demodulator simultaneously demodulate the two BPSK signals. The pair of bits are recovered here from the original data.

These signals after processing, are passed to the parallel to serial converter. Quadrature Phase Shift Keying Advertisements. Previous Page. Next Page. Previous Page Print Page.

## thoughts on “How to draw constellation diagram of qpsk”