### Viewing a QAM Signal on a Constellation Diagram

A very common way to transmit wireless data is to use quadrature amplitude modulation (QAM). This method uses two amplitude modulated signals, combined into a single channel at the same carrier frequency to increase the symbol transmission rate. The two signals are out of phase with each other and are called the In-Phase (I) and Quadrature (Q) components of the transmission. At the transmitter end the two signals are combined and at the receiver end they are separated. A constellation diagram is a two-dimensional method of looking at the signal. Shown in Figure 1 is an example of a constellation diagram of a PHP cellular phone signal. On the upper left is the voltage vs. time trace of the in-phase signal and in the lower left the scope is showing the quadrature signal. The XY plot on the right side of the scope shows the ratio of I/Q. There are eight clearly defined states.

### Making Measurements

Though there are eight separate states in the XY plot of Figure 1, it is clear that the signal-to-noise ratio of this transmission is not ideal. A combination of white noise, phase noise, interference and distortion gives a width to each of the states. If a certain symbol receives too much noise, it could be closer to a different state in the constellation diagram and therefore be misinterpreted by the receiver. To capture the I and Q waveforms at the time when symbols are valid, it is mandatory that the symbol clock of the wireless transmission be used as the oscilloscope sampling clock. If a free-running sampling clock inside the oscilloscope is used, then the I and Q signals will be sampled at random times including transition times between states. A unique feature of Teledyne LeCroy oscilloscopes is the ability for the scope user to input an external sampling clock to replace the usual sampling clock of the instrument. #### Figure 1:

On the left are the voltage vs time traces of the I (upper) and Q (lower) signals. On the right is an XY plot of the same signals

Figure 2 shows the setup for the external clock. In this case the symbol clock has a threshold of zero volts (with an amplitude of at least 150 mv peak-to-peak). The external clock can also be ECL or TTL. #### Figure 2:

Setting up the external clock input for a 16 QAM signal. Note that the oscilloscope can be set to use ECL, TTL or 0V external clocks

Figure 3 shows the oscilloscope making a measurement on a 16 QAM signal using a cursor. Note that this waveform has much less noise/distortion than Figure 1, so the widths of the scattering in the XY plot are much smaller. #### Figure 3:

A cursor has been placed on the XY display. The particular data point is at a radius of 164 mV and an angle of -133.3 degrees. On the left side of the display the oscilloscope shows the point in time at which this data occurred

The engineer can place a cursor on a data point in the XY plot. The oscilloscope will then show the values of X/Y, X*Y, the radius and the angle of that point. On the left hand side the scope it will show the engineer the time point and the values of the I and Q waveforms that produced that particular point of the XY plot. For example, if there is a point of concern on the XY plot, the engineer can place a cursor on it and then zoom in to view the I and Q waveforms at that point in time. Conversely, the engineer can move a cursor along the I-vs.-Time and Q-vs.-Time waveforms and see where the cursor moves on the XY plot. This ability to have a cursor which tracks on both the XY plot and the signal vs. time traces is a unique feature of Teledyne LeCroy oscilloscopes. A wide variety of other measurements are available.

### Summary

A digital oscilloscope with an input for an external sampling clock can be a very useful tool for capturing and measuring wireless signals. The ability to view I and Q signals versus time while at the same time being able to view and measure the constellation display of the same signals can be very helpful. The scope used for the images in this paper was a Teledyne LeCroy Waverunner 640 Zi. For more information on this topic go to www.lecroy.com and read LAB Brief WM-303C “Constellation Displays – Analyze Quadrature Data Communications Signals Using X-Y Displays,” authored by Art Pini.