04 сентября 2016г.
Signal power to noise power working relation on the measurement system receiver input without active masking noise influence.
While continuous signal transmitting in digital way receiving side mistakes sources are concentrating in modulated signal detector, i.e. mistakes appearance reason is coming from whole binary code one symbol false receiving due to the noise; and as for transmitting side – they are concentrating in continuous to digital process converter, i.e. there are three mistakes appearance reasons: continuous signal time sampling, continuous signal maximum values limitation and continuous signal quantization. Information transmission relative mistake effective value in the first approximation can be written in the following way [1]:
where δ1 is a relative mistake effective value caused by continuous signal time sampling;
δ2 is a relative mistake effective value caused by continuous signal maximum values limitation;
δ3 is a relative mistake effective value caused by continuous signal quantization;
δ4 is a digital signal reproduction relative mistake effective value caused by whole binary code one symbol false receiving due to the noise.
We can write the following equality for δ value: δ=5%.
There is a lot of formula (1) each part different variants selection according to written δ value. The variant of the first three parts squares sum is much bigger than the fourth part square is often used in practice but it is not economically profitable from signal source energy-consumption side. That is why let’s choose the variant of uniform information transmission relative mistake distribution between all parts of formula (1): di=0.5d while i=1,4, i.e. δ1=δ2=δ3=δ4=0.5δ=0.5*5%=2.5%=0.025. (2)
Digital signal reproduction relative mistake effective value caused by whole binary code one symbol false receiving due to the noise can be written in the following way [1]:
where H is a continuous signal maximum value to continuous signal effective value relation, i.e. peak-factor – in our case continuous signal is a sinusoid that’s why H=2;
Pfr is whole binary code one symbol false receiving probability;
N is a system canals quantity – in our case system is a vehicles speed measurement system “Iskra-1” with two canals that’s why N=2;
Let’s find Pfr value from formula (3) and then write it in the following way:
Allowed Pfr value and signal power to noise power maximum relation qmax2 value connection for amplitude modulation during no fluctuating signal incoherent receiving with small Pfr<=10-2 values can be written in the following way [2]:
But receiving place signal amplitude changing randomly in time in most of real cases. Such amplitude (and power) changes called fluctuations. The character of fluctuations make power probability density becomes closer to Rayleigh probability density. In this case qmax distribution is a Rayleigh distribution and it can be written in the following way [2]
Sources
1.
Маковеева М.М. Системы связи с подвижными объектами:
учебное пособие для вузов. М.: Радио и связь, 2006.
2.
Осинцев Д.А . Проектирование системы передачи данных телеметрических измерений. Методические указания к выполнению курсового проекта по курсу «Основы проектирования телекоммуникационных систем». Екатеринбург, 2016.
3.
Калмыков В.В. Радиотехнические системы передачи информации. M.: Радио и
связь, 1990.
