# FSK real world application BER

I have designed a receiver for FSK reception in 434 MHz ISM band. For this I used USRP1 and GNU Radio. Now, I would like to measure performances of my receiver. For this purposes I did following:

1. I transmit over cable using signal generator a bunch of 10000 frames with pseudorandom data, with output power of signal generator as a parameter.
2. I have a sort of lookup table since the device is not able to measure absolute power, but rather relative to ADC full scale. So, the lookup table consisted of abosulte input power and gain as an input parameters while the output parameter is relative power. I obtained this lookup table with signal generator. The relative power is calculated by squaring magnitude of the complex baseband signal followed by averaging, which would basically lead to RMS value.
3. I measured relative noise power with antenna port terminated with 50 ohms. (Procedure same as above squaring and averaging)
4. Next, I combine data from 1), 2) and 3). I calculated SNR as relative signal power - relative noise power. For such calculated SNR, I plot PER and BER. BER is derived with: $$\text{BER} = 1 - \sqrt[n]{1-\text{PER}}$$

With this I get that my PER goes close to zero at around 20dB SNR value, which is too much in my opinion.

So, was my approach correct and are those values normal?

The relative power is calculated by squaring magnitude of the complex baseband signal followed by averaging, which would basically lead to RMS value.

To get an RMS value, you would need to then take the root of this result. That is, I understand your description as:

$$\frac{1}{n} \left( x_1^2 + x_2^2 + \cdots + x_n^2 \right)$$

but RMS is:

$$\sqrt{ \frac{1}{n} \left( x_1^2 + x_2^2 + \cdots + x_n^2 \right) }$$

If $x_1 \cdots x_n$ are the magnitudes of your samples, then the result of this expression is like an RMS voltage, and then of course power is proportional to the square of that, which would be equivalent to not taking the square in the first place. So you may have it right, but the wording is a bit ambiguous so I'd double-check it.

I calculated SNR as relative signal power - relative noise power.

After converting the powers to decibels, I hope.

Other than those things, which may not be problems anyway, your process sounds reasonable to me. Your results might be valid or there might be any number of things that went wrong.

So rather than guess, I'll suggest a way you might validate your empirical measurements: generate some AWGN in GNUradio, and make the same experiment in a purely simulated environment. If the results are pretty close to your real-world measurements, it's pretty likely they are correct. If not, you can investigate more.