# Find which signal was transferred in 32QAM

I've been assigned to solve a problem for 32QAM signals. The thing is, there are little to none sources in my native language to get any decent information on the topic.

The problem is (in its original form):

For 32QAM to determine which signal was transmitted using the minimum Euclidean distance between the symbols criteria, given that I and Q in the transmitted signal took values {+-1, +-3, +-5} and the received symbol sequence: [I, Q] = [1.5, -1], [-3.5, 4], [0.1, 0.1].

I assume, that [I, Q] can be replaced with [x, y] and the set of values is missing an A. If there are any misleading parts, I can specify them with my teacher, so you're welcome to ask.

It would be perfect if someone could explain the solution a bit for my further understanding or attach any sources to read.

• "and the set of values is missing an A" -- huh? I don't think anything's missing. – TimWescott Dec 15 '20 at 23:27
• The point $[-3.5,4]$ is a bit ambiguous because it is equal distance to both $[-3,3]$ and $[-3,5]$. – IanJ Dec 18 '20 at 22:04

Here's a sample 32QAM constellation. With the scaling you were given, there's dots at every possible combination of $$\lbrace -5 ... +5\rbrace$$ except for the four at $$(\pm 5, \pm 5)$$. "Minimum Euclidean distance" means that you find the dot that's closest to your actual received value and say that's the one -- i.e., if you receive $$(-2.5, 1.2)$$, then the nearest dot to that is $$(-3, 1)$$ and that's the one you decide on.
• I assume that's for 16QAM -- think it through. How many dots do you have when you cover all the possibilities of $\lbrace \pm 1, \pm 2 \rbrace$? – TimWescott Dec 16 '20 at 4:05