Sixteen unique 16-QAM symbols can each convey a unique 4-bit sequence.

In part 1 of this series, we discussed quadrature amplitude modulation (QAM), which results from summing amplitude-modulated cosine and sine waves of the same frequency. We also looked at the constellation diagram, which a test instrument such as an oscilloscope or vector signal analyzer can display in the modulation domain to help evaluate QAM systems. We illustrated the 16 unique symbols, each corresponding to a unique bit sequence, that a 16-QAM system can transmit.

How do we determine what bit sequence corresponds to each symbol?

For 16-QAM, we can guess that each of the 16 symbols will map to a four-bit binary sequence from 0000 to 1111 or 0 to 15 decimal. In general, for an n-QAM system (that is, a QAM system with n unique symbols), you can calculate the bits per symbol b as follows:

b = log₂n.

So for 16-QAM, b is four, as we surmised, and for 4096-QAM (4K QAM), the number of bits per symbol is

b = log₂(4,096) = 12.

For 16-QAM, how do we map our four-bit sequences to each symbol?

You can map these positions in various ways, as long as both the transmitter and receiver know the details. Figure 1 shows one rectangular mapping possibility.

Wait — the top row seems to start with a binary pattern, 0, 1, but then we have 3, 2, and the second row is 4, 5, but then 7, 6. Is there a pattern here?

I have made some adjustments to a binary sequence to implement Gray coding, which we looked at in an earlier article on testing PCIe gen 6 and about which we will have more to say shortly. For now, just note that a sequence of symbols represents a sequence of bits. Figure 2 shows a sequence of four 16-QAM symbols conveying 16 bits.

From a test and measurement perspective, what can we learn from the modulation-domain display?

Unlike the diagrams we’ve looked at so far, points on a real-world constellation diagram will not be nicely centered in their regions of validity. If we capture a nonrepeating 16-symbol sequence, it might look like Figure 3.

It looks like some of the symbols are migrating into their neighbor’s territory.

Right, that’s the reason to use Gray coding, which assures that adjacent four-bit sequences vary in only one bit position. Figure 4 provides examples, in which a signal that should occupy the 0001 position migrates one position to the right. In the top, binary-coded row, the dot is read as 0010, with both the third and fourth bit flipping, representing a two-bit error. In the bottom, Gray-coded row, the errant signal is read as 0011, a single-bit error, for which is easier and quicker to perform error detection and correction than for a two-bit error.

What else can we learn from the modulation-domain view?

If you look at Figure 3, what we really need is a way to quantify each dot’s deviation from its ideal position. The parameter we use to do that is error-vector magnitude (EVM). We’ll cover the details of EVM in the concluding part of this series.

Related EE World content

How to interpret a QAM display: part 1
Should I use a spectrum, signal, or vector network analyzer? part 3
What is PCIe gen 6 and how do I test it? Part 2
Types of waves in an oscilloscope
Testing Wi-Fi 6E performance
What you need to know about error analysis in PCIe 6.0 designs