The phrase and the term “orthogonal” are widely used in engineering, but are also often misunderstood.

We can look at orthogonal signals in many ways: in the time domain, in the frequency domain, as a constellation, a representation widely used in a broad discipline called signal processing, and as an eye chart. Designers need to look at the relationship between the different signals in the signal space to see where the decoding thresholds should be (deciding which symbol is obtained), what is the distance between the symbolic representations, to assess the impact of noise to see any distortion in the channel, etc.

There are two useful tools for this: the constellation chart and the eye pattern. Both allow the designer to easily and efficiently monitor in real time the dynamic effects of noise, changes, tuning, filters (adaptive and others) and other intentional or unintentional changes in channel, circuit, hardware or algorithm. This makes both powerful and dramatic tools.

The constellation diagram

The constellation diagram is a two-dimensional graph with the x-axis representing the magnitude of the I signal and the y-axis representing the Q signal. It can be adjusted to a standard oscilloscope, which contributes to its convenience.

For a simple binary case, the corresponding signals fall on both sides of point 0 of the xy graph (Figure 1).

Figure 1: The constellation diagram is a two-dimensional xy graph that can be set to a standard oscilloscope and shows the quadrature relationship. (Image: MIT)

For a perfect 16-QAM system, the constellation model looks a little more complicated, of course (Figure 2):

Figure 2: The main diagram of the constellation easily shows details of more complex modulation schemes such as 16-stage QAM. (Image: MIT)

What happens to the constellation chart because real-world imperfections affect signals or there are time errors (oscillations and distortions) in the transmit or receive clocks? Perfectly spaced and spaced points on the chart begin to become “blurred” around their center point, and constellation points no longer consist of single points for each symbol. (Figure 3).

Figure 3: The “blurring” of the points in the constellation pattern shows the type and severity of channel noise, distortion, and other imperfections. (Image: Princeton University)

As noise, distortion, phase shift, and time errors increase, the points representing the symbols get closer and closer to each other, showing how the noise limit between them shrinks. (Figure 4).

Figure 4: The constellation diagram quickly shows how the noise margin decreases and the BER may increase as the channel or system becomes less ideal. (Image: Princeton University)

In fact, in extreme cases, the dot “cloud” of the symbol overlaps with its neighbors, which shows that it is no longer possible to determine the correct value without error. Blurring should not be symmetrical around the starting point, and this is often not the case. Changes in the relative distance of the magnitude signal cause the points to approach or move away along their I or Q axes, respectively. The displacement of the phase leads to the displacement (rotation) of the point to the other axis and the ideal square difference of 90⁰.

Although the constellation is a convenient qualitative instrument, it is also quantitative. By measuring the amount of movement left / right, up / down and rotational movement, much can be determined about the performance and damage to the channel and system. Because the constellation diagram has a starting point of 0.0 with information in both its x and y axes, as well as the angle of rotation, it provides a “polar” perspective on the signal situation – hence the name sometimes given. mentions rather than a constellation.

The next section will look at the eye diagram, which is often used in connection with the constellation.

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Additional references

Orthogonality

Orthogonal versus uncorrelated: problems

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What is “orthogonal”? (Part 3): signal constellations

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