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Re: [Discuss-gnuradio] BER over air

From: Marcus Müller
Subject: Re: [Discuss-gnuradio] BER over air
Date: Sun, 28 Dec 2014 17:41:25 +0100
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:31.0) Gecko/20100101 Thunderbird/31.2.0

Hi Mostafa,

On 12/28/2014 03:54 PM, Mostafa Alizadeh wrote:
Hi Martin, 

Thank you for response. I don't want Eb/N0, because there is not bit stream but complex symbols.
A symbol represents information you want to transmit. The unit for information is bit.

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: 

Inline image 1
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.
Assuming you're noise is a) purely additive, b) your channel is absolutely flat, and so is your noise (white), c) everything is linear (memoryless channel) and c) you're able to reliably measure the power of a infinitely narrow peak (which implies you can produce a infinitely narrow peak), this applies. As you can see in your picture, the peak is *not* infinitely narrow (obviously, the FFT has limited length, so frequency resolution can't be arbitrarily fine).
It's but a basic estimate. Giving you the rx power for a specific frequency and estimating noise power by averaging for a limited amount of time, you get something that, depending on how your system behaves, might or might not represent actual SNR well.

I have to stress this: SNR is *signal* to noise ratio. Signal is what your application defines to be signal!


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