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Bit Error Rate given SNR Formula

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Bit Error Rate is defined as the ratio of the number of bit errors to the total number of bits transmitted over a communication channel. Check FAQs

BER opt = (\frac{1}{\sqrt{2 \cdot π}}) \cdot \frac{\exp (- \frac{{SNR opt}^{2}}{2})}{SNR opt}

BER_opt - Bit Error Rate?SNR_opt - Signal to Noise Ratio of Photodetector?π - Archimedes' constant?

Bit Error Rate given SNR Example

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Here is how the Bit Error Rate given SNR equation looks like with Values.

Here is how the Bit Error Rate given SNR equation looks like with Units.

Here is how the Bit Error Rate given SNR equation looks like.

2.6723 = (\frac{1}{\sqrt{2 \cdot 3.1416}}) \cdot \frac{\exp (- \frac{{0.151}^{2}}{2})}{0.151}

2.6723 = (\frac{1}{\sqrt{2 \cdot 3.1416}}) \cdot \frac{\exp (- \frac{{0.151}^{2}}{2})}{0.151}

2.6723 = (\frac{1}{\sqrt{2 \cdot 3.1416}}) \cdot \frac{\exp (- \frac{{0.151}^{2}}{2})}{0.151}

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Bit Error Rate given SNR Solution

Follow our step by step solution on how to calculate Bit Error Rate given SNR?

FIRST Step Consider the formula

BER opt = (\frac{1}{\sqrt{2 \cdot π}}) \cdot \frac{\exp (- \frac{{SNR opt}^{2}}{2})}{SNR opt}

Next Step Substitute values of Variables

∴

BER opt = (\frac{1}{\sqrt{2 \cdot π}}) \cdot \frac{\exp (- \frac{{0.151}^{2}}{2})}{0.151}

Next Step Substitute values of Constants

∴

BER opt = (\frac{1}{\sqrt{2 \cdot 3.1416}}) \cdot \frac{\exp (- \frac{{0.151}^{2}}{2})}{0.151}

Next Step Prepare to Evaluate

∴

BER opt = (\frac{1}{\sqrt{2 \cdot 3.1416}}) \cdot \frac{\exp (- \frac{{0.151}^{2}}{2})}{0.151}

Next Step Evaluate

∴

BER opt = 2.67229434579719

LAST Step Rounding Answer

∴

BER opt = 2.6723

Bit Error Rate given SNR Formula Elements

Variables

Constants

Functions

Bit Error Rate

Bit Error Rate is defined as the ratio of the number of bit errors to the total number of bits transmitted over a communication channel.

Symbol: BER_opt

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Bit Error Rate

Signal to Noise Ratio of Photodetector

Signal to Noise Ratio of Photodetector .

Symbol: SNR_opt

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Signal to Noise Ratio of Photodetector

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Transmission Measurements category

Go Optical Attenuation

α dB = \frac{10}{L 1 - L 2} \cdot \log 10 (\frac{V 2}{V 1})

Go Absorption Loss

α abs = \frac{C \cdot T ∞}{P opt \cdot t c}

Go Time Constant of Calorimeter

t c = \frac{t 2 - t 1}{\ln (T ∞ - T t1) - \ln (T ∞ - T t2)}

Go Scattering Loss

α sc = (\frac{4.343 \cdot 10^{5}}{l}) \cdot (\frac{V sc}{V opt})

How to Evaluate Bit Error Rate given SNR?

Bit Error Rate given SNR evaluator uses Bit Error Rate = (1/sqrt(2*pi))*(exp(-Signal to Noise Ratio of Photodetector^2/2))/Signal to Noise Ratio of Photodetector to evaluate the Bit Error Rate, Bit Error Rate given SNR is a key parameter that quantifies the performance of a digital communication system. It is defined as the ratio of the number of bit errors to the total number of bits transmitted, received, or processed over a communication channel. In other words, it is the number of received bits of a data stream over a communication channel that have been altered due to noise, interference, distortion, or bit synchronization errors. Bit Error Rate is denoted by BER_opt symbol.

How to evaluate Bit Error Rate given SNR using this online evaluator? To use this online evaluator for Bit Error Rate given SNR, enter Signal to Noise Ratio of Photodetector (SNR_opt) and hit the calculate button.

FAQs on Bit Error Rate given SNR

What is the formula to find Bit Error Rate given SNR?

The formula of Bit Error Rate given SNR is expressed as Bit Error Rate = (1/sqrt(2*pi))*(exp(-Signal to Noise Ratio of Photodetector^2/2))/Signal to Noise Ratio of Photodetector. Here is an example- 2.672294 = (1/sqrt(2*pi))*(exp(-0.151^2/2))/0.151.

How to calculate Bit Error Rate given SNR?

With Signal to Noise Ratio of Photodetector (SNR_opt) we can find Bit Error Rate given SNR using the formula - Bit Error Rate = (1/sqrt(2*pi))*(exp(-Signal to Noise Ratio of Photodetector^2/2))/Signal to Noise Ratio of Photodetector. This formula also uses Archimedes' constant and , Exponential Growth (exp), Square Root (sqrt) function(s).

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