# modulation constellation

When we show the set of possible symbols for a givenmodulation scheme, we call it the “constellation”. Many modulation schemes can be defined by their constellation. To receive and decode BPSK we can use IQ sampling, like we learned about last chapter, and examine where the points end up on the IQ plot.

## What are constellation points in digital modulation?

Most digital modulation schemes involve a discrete number of symbols which are used to convey information. These symbols are mapped to a discrete set of magnitude and phase values on the I/Q plane, which are referred to as constellation points.

## What is a QAM constellation?

Quadrature Amplitude Modulation (QAM) Constellation What is a QAM Signal Quadrature Amplitude Modulation (QAM) uses many different phases known as states: 16, 32, 64, and 256. Each state is defined by a specific amplitude and phase. This means the generation and detection of symbols is more complex than a simple phase or amplitude device.

## What are the constellation diagram settings for DVB modulation?

The constellation diagram examples shown are based on 64 QAM modulation and use the following basic settings: maximum possible DVB data transmission rate of 6.92 Msps or 41.73 Mbit/s (64 QAM); Cosine roll-off filtering with roll-off factor r = 0.15 and PRBS (pseudo random binary sequence) data stream, no coding.

## What is a digital modulation scheme?

This is a digital modulation scheme, because the phase is changed in fixed steps instead of continuously as for analog modulation techniques. To get to the constellation diagram, we first switch to the analytic form of the waveform (see What is an Analytic Signal? for details), as follows.

## What is interference in a QAM signal?

Interferers are understood to be sinusoidal spurious signals occurring in the transmission frequency range and superimposed on the QAM signal at some point in the transmission path. After demodulation, the interferer is contained in the baseband form of low-frequency sinusoidal spurious signals.

## What causes phase jitter in QAM?

Phase Jitter or phase noise in the QAM signal is caused by transponders in the transmission path or by the I/Q modulator. It may be produced in carrier recovery, a possibility that is to be excluded here. In contrast to the phase error described above, phase jitter is a statistical quantity that affects the I and Q path equally. In the constellation diagram, phase jitter shows up by the signal states being shifted about their coordinate origin. Image below – Constellation Diagram — 64 QAM signal with Phase Jitter (PJRMS = 1.73°)

## What is QAM signal?

Each state is defined by a specific amplitude and phase. This means the generation and detection of symbols is more complex than a simple phase or amplitude device. Each time the number of states per symbol is increased the total data and bandwidth increases. The modulation schemes shown occupy the same bandwidth (after filtering), but have varying efficiencies (in theory at least).

## Is there always a combination of modulation errors that may be difficult to separate and identify?

In practice, there is always a combination of modulation errors that may be difficult to separate and identify, as such, it is recommended to evaluate the measured constellation diagrams using mathematical and statistically methods.

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## What is quadratic modulation?

Quadrature modulation methods are some combination of single-level or multilevel shift keying methods. Quadrature amplitude modulation (QAM) is most common; this technique is really a combination of N-level MASK with BPSK. At the receive side, this gives N 2 possible logic states that can be transmitted in a communications channel. The possible list of states can be visualized using a constellation diagram, which shows the list of possible states.

## What is QAM in 5G?

This modulation technique is used in 5G, where 64-QAM or 256-QAM is used in different frequency channels to provide multiple bit streams with a high data rate. Carrier aggregation provides another doubling of the data rate, ultimately reaching Gbps levels over the air.

## What is shift keying?

In this method, the transmitted signal is shifted between multiple phase levels and multiple amplitude levels , rather than having two different ASK signals that are out-of-phase.

## What is pulse code modulation?

Pulse code modulation methods use a stream of pulses rather than a sinusoidal carrier signal to transmit data. In these modulation schemes, the pulse stream is modulated by varying the pulse duration (pulse duration modulation, or PDM), phase between pulses (pulse phase modulation, or PPM), frequency (pulse frequency modulation, or PFM), or amplitude (pulse amplitude modulation, or PAM). Digital PAM is the method used today to transmit high data rates in Gbps channels over copper and fiber, and it may be the key to getting to 224 Gbps and higher data rates.

## What is modulation in communication?

Modulation refers to the technique of mixing two signals to transmit information. The two signals that are used in modulated communication are the carrier signal and the information signal. The only difference between analog and digital modulation is found in the information signals. In digital modulation, the information signal takes discrete levels, while in analog modulation, the information signal has no discretization and can take any level. The information signal is then used to modulate (vary) the phase, amplitude, and/or frequency of the carrier signal.

## What is the purpose of digital modulation in wireless systems?

Wireless and fiber systems use digital modulation formats to transmit at high data rates.

## What are the two types of modulation methods?

Modulation methods are divided into digital and analog formats.

## What is constellation diagram?

A constellation diagram is a diagram that shows how the information in a digital modulation scheme such as phase shift keying (PSK) is represented in a modulated carrier. This article is a bit of an experiment; instead of introducing the constellation diagram by simply presenting it, I’m going to try to have it emerge from the formulas of PSK modulation.

## What is QAM in modems?

In application such as cable or DSL modems for broadband internet, more elaborate constellations such as Quadrature Amplitude Modulation ( QAM) are used. In QAM, both the phase and the amplitude of the signal are adapted in order to be able to send more bits per symbol. An example is 16-QAM (4 bits per symbol), as shown in Figure 3. Cable modems typically use 64-QAM or 256-QAM, and, for DSL, constellations as large as 32768-QAM (15 bits per symbol) are used routinely.

## What is the waveform for MPSK?

by applying Euler’s formula. Because the waveform for MPSK is simply a cosine with a phase offset , the calculation of the analytic signal is the same as in the mentioned article on analytic signals.

## What is the formula for m = 0?

for m = 0, …, M ? 1. In this equation, A is the amplitude of the carrier, f c is the frequency of the carrier, and M is the number of phase offsets. This formula represents a carrier wave of which the phase is suddenly shifted for each new symbol (if that symbol is different from the previous one, of course). This is a digital modulation scheme, because the phase is changed in fixed steps instead of continuously as for analog modulation techniques.

## What is amplitude shift keying?

Amplitude Shift Keying (ASK) is the first digital modulation scheme we will discuss because amplitude modulation is the simplest to visualize of the three sinusoid properties. We literally modulate the amplitude of the carrier. Here is an example of 2-level ASK, called 2-ASK:

## How many bits per symbol?

In the above example each symbol represents one bit. How can we convey more than one bit per symbol? Let’s study the signals that travel down Ethernet cables, which is defined in an IEEE standard called IEEE 802.3 1000BASE-T. The common operating mode of ethernet uses a 4-level amplitude modulation (2 bits per symbol) with 8 ns symbols.

## How many cycles of the sinusoid are there in each symbol?

In real systems, the frequency of the carrier is usually much much higher than the rate the symbols are changing. In this example there are only three cycles of the sinusoid in each symbol, but in practice there may be thousands, depending on how high in the spectrum the signal is being transmitted.

## What does the IQ plot show?

The above IQ plot shows what we will transmit, or rather the set of symbols we will transmit from. It does not show the carrier, so you can think about it as representing the symbols at baseband. When we show the set of possible symbols for a given modulation scheme, we call it the “constellation”. Many modulation schemes can be defined by their constellation.

## What does the top plot of a signal show?

The top plot shows the discrete samples represented by red dots, i.e., our digital signal. The bottom plot shows what the resulting modulated signal looks like, which could be transmitted over the air. In real systems, the frequency of the carrier is usually much much higher than the rate the symbols are changing. In this example there are only three cycles of the sinusoid in each symbol, but in practice there may be thousands, depending on how high in the spectrum the signal is being transmitted.

## How to decode BPSK?

To receive and decode BPSK we can use IQ sampling, like we learned about last chapter, and examine where the points end up on the IQ plot. However, there will be a random phase rotation due to the wireless channel because the signal will have some random delay as it passes through the air between antennas. The random phase rotation can be reversed using various methods we will learn about later. Here is an example of a few different ways that BPSK signal might show up at the receiver (this does not include noise):

## How do we create this signal digitally?

How do we actually create this signal digitally, through code? All we have to do is create a vector with N samples per symbol, then multiply that vector by a sinusoid. This modulates the signal onto a carrier (the sinusoid acts as that carrier). The example below shows 2-ASK with 10 samples per symbol.

## What is digital modulation?

Most digital modulation schemes involve a discrete number of symbols which are used to convey information. These symbols are mapped to a discrete set of magnitude and phase values on the I/Q plane, which are referred to as constellation points.

## What is quadrature modulation?

Signals in quadrature are orthogonal and do not interfere with one another. Quadrature modulation takes advantage of this principal by combining two signals which are in quadrature for a combined output signal. The advantage of this is that the amplitude and phase of the combined output signal can be modulated independently or simultaneously, and can be accomplished digitally without adding unnecessarily complex RF hardware circuitry.

## Why is a constellation diagram important?

Constellation diagrams are an important tool in an engineer’s arsenal when determining whether or not a digitally modulated radio-frequency (RF) signal is behaving correctly, and troubleshooting the underlying issues when it is not. However, before delving into constellation diagrams and how they are used, it is important to understand the fundamentals behind digital modulation schemes and why they are used.