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

Just as the time domain and the frequency domain are two legitimate ways of looking at a signal from different perspectives related to the Fourier transform, the constellation chart has an addition in a time domain called an eye chart or eye model. Like the constellation diagram, it reveals much about the state of the channel and signal space and is both qualitative and quantitative. However, unlike the constellation diagram, it is not limited to quadrature signals, although it is widely used for them, with one eye diagram for the I signal and one for the Q signal.

The eye chart is conceptually simple: it overlays all received and decoded signals starting from the same symbolic moment in time and shows transitions between symbol states. As more characters overlap, this reveals all possible trajectories of character transition. Can be used for binary signals as well as multi-level signals as an eye model for 16-QAM signal (Figure 1).

Figure 1: The eye chart is a summary in time domain of channel and signal performance created by overlaying all bits of data. (Image: Princeton University)

If the channel and decoding of the signal do not degrade or distort the signal, the eye will be quite wide open (if it was so perfect, the eye would not be blurred at all) (Figure 2).

Figure 2: The “open” eye corresponds to small, distinct points in the constellation diagram. (Image: Princeton University)

As noise, distortion, and intersymbol interference affect the canal, the eye becomes more closed (Figure 3)another point of view of constellation chart information.

Figure 3: Channel imperfections marked by blurred, blurred constellation points appear in the eye diagram as closing the eye in the vertical direction and flickering at the zero crossing points in the horizontal direction. (Image: Princeton University)

The eye chart can be used to qualitatively understand the nature of canal damage. Blurring at intersections indicates time problems, closing the eye reveals noise, distortion of the eye indicates bandwidth limitations, and more. Like the constellation chart, the eye model requires only a standard oscilloscope, and its horizontal (time) channel is synchronized with the system clock. Some oscilloscopes include a “mask” that is electronically superimposed on the range screen to indicate whether the eye model and this connection meet industry-defined performance and bit rate (BER) standards.

Both the constellation model and the eye chart can be used in real time to monitor the impact of changes in the channel, as well as the results of “fine-tuning” the channel and system using various adaptive filters or algorithms. Seeing the constellation point can expand, shrink and shift, or the eye can change shape and open / close while making these changes, like watching an MRI or X-ray image in real time.

Conclusion

Orthogonality is an important topic and problem of design in many engineering disciplines. Allows signals and forces to be divided into – or used as – independent components for analysis and construction. Understanding what it means in mathematically rigorous terms is important, as is understanding what it means in less rigorous scenarios.

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Additional references

Orthogonality

Orthogonal versus uncorrelated: problems

DesignFast Banner version: 791d2e94

What is “orthogonal”? (Part 4): eye diagrams

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