# Methods for calculating signal quality metric

i'm sure this is a fairly large topic area, but I'm not quite sure where to start. I have a signal in which I can change several parameters, such as the frequency, gain, etc. The modulation is a differential BPSK, and my current metric for determining the signal quality is what percentage of my auto correlation (correlating the current bit signal with the previous bit) is above 0. If it's all above or below zero, a 100% signal quality. if it's half and half, then it's 0%, and then it's linear from there. Is there a better way of doing this? I'm wanting to be able to change my signal parameters in order to increase my signal quality, where a higher signal quality should be a higher reliability of receiving a message correctly.

I'm also looking at doing demodulation in the frequency domain, so then my calculations would probably need to change. Any input and references would be appreciated. Thanks!

• I'm not quite sure what you mean by " what percentage of my auto correlation is above 0" ? Do you mean $R_{xx}(0) > \sigma^2_{xx}/2$? – Peter K. May 12 '16 at 18:50
• The usual way to measure "signal quality" is by finding the bit error rate. Why do you want to use a different metric? What part of the system's behavior are you trying to evaluate? – MBaz May 12 '16 at 19:01
• @PeterK. I should have said i'm correlating with the previous bit's signal. I'll correct that in the post. – gerrgheiser May 12 '16 at 20:22
• @MBaz for this system, the data rate is fairly low, and the packet sizes are small, so in an ideal case there shouldn't be any bit errors. since i'm trying to measure this signal quality for different parameters, I'm wanting to only send a single message with each parameter set and get a signal quality from that. the system behavior i'm wanting to evaluate is something that should give me an idea if my Bit Error Rate will be low for future messages (assuming the channel doesn't change) – gerrgheiser May 12 '16 at 20:38
• One thing you may want to do is to look at the signal's eye diagram. Its usefulness is precisely that it tells you at a glance whether you'll get a good BER or not. – MBaz May 12 '16 at 21:07

For a discrete-time signal $y$, comparable to reference $r$, the SNDR would be: $$SNDR = \frac{E[r^2]}{E[(y-r)^2]}$$