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| From: | Marcus Müller |
| Subject: | Re: [Discuss-gnuradio] BER & SNR |
| Date: | Tue, 4 Jul 2017 12:48:37 +0200 |
| User-agent: | Mozilla/5.0 (X11; Linux x86_64; rv:45.0) Gecko/20100101 Thunderbird/45.8.0 |
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BER is an observation, a count, not an estimation – it only makes
sense to talk about a Bit Error Rate (BER) after a complete
physical layer receiver, i.e. at the bit level. You can estimate
the BER of a whole system if you know how it reacts to noise – but
that's typically not what you do. Instead, you just simulate with
various noise/distortion levels, measure for each of these and
write down the number of wrong bits. A good receiver will make
more of a noisy signal (lower BER) than a bad receiver for the
same modulation. So, BER depends on your receiver implementation. SNR, on the other hand, the Signal-to-noise-ratio, is not
something that depends on your implementation – it's really just
the ratio of Signal power to noise power. Since we're looking at a
noise reception, one can only write an estimator for these powers
– and thus, SNR is a measure relative to a mathematical model of
your reception, and not something that indicated demodulability.
It's very important to say where in the signal chain you
look at the SNR – is it directly at the antenna? After mixing to
baseband? After filtering to a channel bandwidth? It's equally
important to explicitly specify what you consider signal and what
you consider noise power – for example, one might say "OK, after
my timing recovery, I still have a bit of phase offset, but that's
OK, I just declare the difference between perfect constellation
point and actual recovered point "noise" and be done with it".
That's a very practical thing to look at – and, indeed, for the
decider, which has to convert complex numbers to bits, it just
looks like a random addition to the perfect signal, but that power
didn't come in as noise power – it's just an error we introduced
by not being able to perfectly synchronize. As another example, if you take any signal, and shift it in
frequency, then that doesn't change its power at all! So, a
reception with a terribly bad frequency offset still has the same
SNR as a perfectly synchronized one. UNLESS, that is, that you
declare the phase offset between recovered symbols and perfect
constellation points "noise". Now, depending on what you declare to be noise and what you
declare to be signal, you'd define different SNR estimators. I
constantly repeat this (I don't mind, someone has to): There's no single "right" SNR estimator. Everything depends on what you define to be noise and what you define to be signal. One man's noise is another man's signal. Coming back to your original question: > How Is it possible to get a good estimation of the BER without a costas loop?It's not an estimate. If you get BER of 0, then your receiver did
not make a single bit error, if you get BER=0.5, then every second
bit is wrong. So, that estimator is pretty much perfect. If you remove the phase synchronization (i.e. the costas loop) from your receiver, you make it a worse receiver. Then, your BER increases, if your receiver gets sufficiently bad. I hope that answers your question! If not, please don't hesitate to elaborate (in length!) Best regards, Marcus On 07/04/2017 11:49 AM, Rafik ZITOUNI
wrote:
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