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I am simulating a QPSK modulation in GNU radio. Here is the flowgraph:

flowgraph.

The source is a binary stream coming from the Random Source block. There are 4 PSK Mod blocks configured identically (4 constellation points - a QPSK modulation, Grey coding and Differential encoding turned on, excess bandwidth set to 0,35). The modulators differ in the parameter samples/symbol (sps), which is set to 2, 4, 8, and 16. The constellation sinks are configured identically. What is expected to be shown on the constellation diagram is a plot with 4 constellation points that could be the tips of a square or 4 clusters of points that are concentrated around those 4 points as a certain amount of noise or imperfection of the system is added. Instead, we have the following:

Constellation diagram when sps is set to 16:

constellation diagram when sps is 16

Constellation diagrams for sps 2, 4 and 8 look the same but with less points on the sides of the rhombus and less points around tips of the rhombus that look like the extensions of the rhombus sides.

The question is why constellation diagrams look like this - why additional points are added and there are more and more of them as we increase the samples per symbol parameter so the diagram with sps 16 looks more like a rhombus than a 4 clusters of points? Why significant number of points appear around 4 tips of the rhombus looking like extensions of rhombus sides?

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What you are seeing is the transitions from one constellation point to another. In order to reduce the signal bandwidth, the baseband signal is low-pass filtered. This causes the transitions to not be instantaneous (i.e. the I and Q are not square waves), so they take some time. You are simply seeing those transitions. The low-pass filtering also causes the overshoot that you see at the constellation points.

Just to see, I tried putting this into R. This is not going to get quite the same result because I am not sure of the parameters GNURadio uses, but it illustrates Jim's point.

As you increase the samples per symbol, the number of "transition" samples increases, making the edges of the constellation clearer.

enter image description here

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  • $\begingroup$ Hi, Jim. Thank you for your message. The low pass filter you are mentioning is part of the PSK Mod blocks or the Constellation Sink blocks? $\endgroup$
    – Mirta Iva
    Oct 13, 2015 at 14:27
  • $\begingroup$ I don't know, I don't use Gnu Radio. The "Excess BW" parameter suggests that there is some kind of filtering, as well as the constellation itself, of course. $\endgroup$
    – Jim Clay
    Oct 13, 2015 at 16:12
  • $\begingroup$ @Peter - If transitions are instantaneous, constellation diagram would be 4 points, not a rhombus (your note: "making the edges of the constellation clearer" can suggest the contrary). $\endgroup$
    – Mirta Iva
    Oct 19, 2015 at 9:15
  • $\begingroup$ Excess BW parameter comes from raised-cosine filter used for pulse-shaping in the PSK Mod block. $\endgroup$
    – Mirta Iva
    Oct 19, 2015 at 9:28
  • $\begingroup$ @MirtaIva : Right, but you have to represent the "ideal" constellation with a real signal. In this case, the real signal is going to transition from one point of the constellation to the other. That's what I meant by "making the edges of the constellation clear" --- you are correct, though, the actual constellation is just the four points of the rhombus, not including the edges. $\endgroup$
    – Peter K. ♦
    Oct 19, 2015 at 12:09

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