Considering systems transmitting the signals from the analog sources, Shannon proposed to use, as a criterion of their performance (fidelity), the mean distance between the recovered and input signals, that is the mean square error (MSE).
This criterion is commonly used and has relatively easily measured analog - empirical MSE.
Nevertheless, MSE is not used in modern communications being replaced by several internally connected criterions: bit-rate and its closeness to the capacity of the channel, BER and by the power – bandwidth efficiency of transmission.
What is a reason?.- These criterions create a lot of tradeoffs which substantially complicate evaluation and comparison of real performance of different systems.
MSE seems to be much more convenient and adequate.
I would be pleased if somebody could give the examples of communication systems whose performance is assessed by MSE.
Could it be because in today's digital world, fidelity is taken for granted, and the user's perception of quality is now dominated by the user being bothered by breaks in transmission?
Let us confine a discussion by the most actual wireless communication systems (CS) for short range transmission of analog signals (their number grows more than exponentially: WSN, femtocells, robotics, RFID, Bluetooths,.intelligent towns,..).
Your question implicitly suggests that the basic criterion of their performance is "The main I get information reliably. How this is done - is not essential, if is not too expensive for me"?
I.e. assessment of real efficiency and quality (MSE) of transmission is not necessary. You agree?
Basically, yes. Continuity and reliability is now the #1 concern. Voice or music (hi-) fidelity quality is the #2 concern. Only if we get #1 right, can #2 then be given attention, or is automatically OK, and today is only interfered with by the well-known quantizing noise. (See e.g. http://en.wikipedia.org/wiki/Quantizing_noise). Today everything is analogue -> ADC -> digital transmission -> DAC -> analogue, so MSE can be calculated or measured accurately.
Thank you for the answer.
You wrote: "Today everything is analogue -> ADC -> digital transmission -> DAC -> analogue, so MSE can be calculated or modelled accurately".
What is worth accenting: calculation of MSE is possible only if we know prior probability distribution p(x) of the input signal and conditional distribution p(xˆ |x) of its estimates (values at the receiver output). The first one is usually assumed to be known, but derivation of the second one meets great mathematical difficulties. Namely: to calculate distribution p(xˆ |x), we should know conditional distributions of the signals at the output of the chain “ADC-> source coder -> channel coder -> modulator (keying)-> noisy channel -> demodulator - > channel decoder -> source decoder -> DAC”.
Even if high quality ADC is used and quantization errors can be neglected, calculation of MSE permitting to obtain the results useful for practice seems to be impossible (I don’t concern purely mathematical researches not aimed to applications).
I agree with the end of your sentence with small correction: not “modelled” but “measured”. Really, independently from do we know distributions or not, empirical MSE always can be measured as the averaged sum of a large number of values “input value minus its estimate formed by the receiver”^2.
Nevertheless, in none of applied works and documentation on communication systems which I looked through, MSE was not mentioned. May be I ’ve omitted the works which I search. Also, I have no answer - why MSE is not used in practice as clear, universal and informative measure of transmission quality? For this reason, I've decided to consult it in Research Gates.
If it would be so...
It is pity but BER is a problem. SNR at the channel output diminishes as 1/R^2 and at the greater distances, BER attains unacceptable values. This confines the range of reliable transmission.
Recently, BER is a single characteristic more the less directly concerning a quality of transmission. The bit rate is used as a characteristic of degree of the channel resources utilisation, not as a measure of the recovered signals accuracy.
Nevertheless, there exist rate-distortion theory which employs MSE of transmission but did I not see its applications in practice.
P.S. I'll add that measurement of BER is not easy task. It is enough to look at the ZigBee documentation and proposed there method of BER measurement. The same concerns the bit-rate and power-bandwidth efficiency of transmission.
It is also not completely clear - what is the capacity of the channel? Does it depend on the distance and changes of environment?
Dear Colltagues,
I've replaced a continuation of this part of discussion into the answers on my later question:
"Why MSE is not used as a measure of analog signals transmission quality?"
It can be found in RG under address https://www.researchgate.net/post/Why_MSE_is_not_used_as_a_measure_of_analog_signals_transmission_quality
With best regargs,
Anatoliy Platonov
Final comments, may be interesting:
1. Communication systems with feedback (FSC) can be designed for the given BER (more accurately, probability of the loss of information during sample transmission " word error rate" (WER) mu
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