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## Re: [Discuss-gnuradio] BER over air

 From: Mostafa Alizadeh Subject: Re: [Discuss-gnuradio] BER over air Date: Sun, 28 Dec 2014 18:24:04 +0330

Hi Martin,

Thank you for response. I don't want Eb/N0, because there is not bit stream but complex symbols.
As you said, there are two possible solutions:

1- If one uses a specific modulation, so by sending a long known bit sequence, the BER (bit error rate) can be found accordingly then the SNR can be obtained from the theoretical relationship between BER and SNR (here SNR is Eb/N0). I think this is not practical due to the fact that we use the analytic relationship while in practice we want to, for instance, prove that relationship is true.

2- Measuring SNR in analog is, in fact, a hard task. Because as you said it depends on both receiver hardware parameters (such as phase noise, frequency offset, timing offset, quantization, ... ) and channel characteristics (such as small and large scale fadings). This method also may need a sort of channel sounding to extract the channel response corresponding to the measurement environment.

The third way I could add here is: using a kind a calibration between Tx/Rx with sending a sine wave pilot. Suppose a sine wave (in base band) with frequency 'fm' is sent via a Tx with the power of 'A' dB. At Rx we take FFT of the signal which has a shape like this:

I assumed that the power level out of sine wave is about -10dBm, call it 'noise_floor', and the received power level of the sine is 0dBm, call it 'peak'. By using the following formula the SNR can be calculated:

SNR = peak - noise_floor - 10 log (N_fft/2).

N_fft is the number of fft points. Once the SNR value is calculated for 'A' dB Tx power, it seems reasonable to have different SNRs with changing just the Tx power.

I'm not sure whether this approach is accurate as we need or not!  Is it true? I want to know your recommendations.

Mostafa

On Sat, Dec 27, 2014 at 12:01 AM, Martin Braun wrote:
On 12/25/2014 11:06 AM, Mostafa Alizadeh wrote:
> I have a question regarding how it's possible to measure SNR @ an Rx
> with a USRP? In fact to obtain a graph of BER vs SNR I need to measure
> SNR !
>
> I didn't find anything specific to this question. However, I've heard
> it's possible to estimate an initial SNR in Rx by accounting noise
> figure of the USRP, then by changing the transmitter's power, different
> SNRs can be seen at Rx.
>
> Any idea please!?

Measuring exact SNR is a difficult science. What you can do quite easily
is to use the SNR estimator blocks. However, for accurate BER/SNR
curves, there's a catch-22 here because you're using the same noise to
estimate noise power that's affecting the signal (and hence, BER). So,
if you're writing a paper, don't forget to mention and explain this.

Also, when you say SNR, what *exactly* do you want? Is it Eb/N0?

If you want to figure out SNR by analog measurements (i.e. by measuring
the exact rx power and estimating the exact noise figure), that's a lot
of work. And your calibrations will be off if you open the window and
the temperature drops (depending on how accurate you need these values).

Also, when doing real measurements, you're including lots of other
effects (multipath, phase noise, quantization noise, frequency offset,
timing offset... most of these can be modeled as an additional noise
figure if they're static, but with some limited accuracy). Is that
really what you want?

If multipath is negligible you might be able to transmit a very long
known BPSK sequence and use the analytical functions for BER in AWGN to
estimate Eb/N0 (measure BER and solve for the Eb/N0). I'd need to have
another look at the math for our SNR estimators, but they probably do
something similar. This only works for *perfect time and frequency
synchronisation*!

M

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