Bit Error Rate given SNR Calculator

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✖Signal to Noise Ratio of Photodetector .ⓘ Signal to Noise Ratio of Photodetector [SNR_opt]

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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.ⓘ Bit Error Rate given SNR [BER_opt]

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Formula

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Bit Error Rate given SNR

Formula

`"BER"_{"opt"} = (1/sqrt(2*pi))*(exp(-"SNR"_{"opt"}^2/2))/"SNR"_{"opt"}`

Example

`"2.672294"=(1/sqrt(2*pi))*(exp(-("0.151")^2/2))/"0.151"`

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Bit Error Rate given SNR Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bit Error Rate = (1/sqrt(2*pi))*(exp(-Signal to Noise Ratio of Photodetector^2/2))/Signal to Noise Ratio of Photodetector
BER_opt = (1/sqrt(2*pi))*(exp(-SNR_opt^2/2))/SNR_opt
This formula uses 1 Constants, 2 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., 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., sqrt(Number)

Variables Used

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.
Signal to Noise Ratio of Photodetector - Signal to Noise Ratio of Photodetector .

STEP 1: Convert Input(s) to Base Unit

Signal to Noise Ratio of Photodetector: 0.151 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

BER_opt = (1/sqrt(2*pi))*(exp(-SNR_opt^2/2))/SNR_opt --> (1/sqrt(2*pi))*(exp(-0.151^2/2))/0.151

Evaluating ... ...

BER_opt = 2.67229434579719

STEP 3: Convert Result to Output's Unit

2.67229434579719 --> No Conversion Required

FINAL ANSWER

2.67229434579719 ≈ 2.672294 <-- Bit Error Rate

(Calculation completed in 00.004 seconds)

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Created by Vaidehi Singh

Prabhat Engineering College (P.E.C.), Uttar Pradesh

Vaidehi Singh has created this Calculator and 25+ more calculators!

Verified by Santhosh Yadav

Dayananda Sagar College Of Engineering (DSCE), Banglore

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Bit Error Rate given SNR Formula

Bit Error Rate = (1/sqrt(2*pi))*(exp(-Signal to Noise Ratio of Photodetector^2/2))/Signal to Noise Ratio of Photodetector
BER_opt = (1/sqrt(2*pi))*(exp(-SNR_opt^2/2))/SNR_opt

What is the significance of Bit Error Rate?

Bit Error Rate (BER) is a crucial parameter in digital communication systems. It quantifies the performance and reliability of a system by measuring the ratio of incorrectly transmitted bits to all transmitted bits over a given time period. A system with a high BER indicates more frequent errors, leading to poor performance and user experience, while a low BER represents a more reliable and efficient system. In BER testing, real sample data is transmitted over the appropriate protocol. The BER test shows the true real-world performance of the network, inclusive of the active components. The BER can be used to determine the quality of a signal and the relative success of packet delivery.

How to Calculate Bit Error Rate given SNR?

Bit Error Rate given SNR calculator uses Bit Error Rate = (1/sqrt(2*pi))*(exp(-Signal to Noise Ratio of Photodetector^2/2))/Signal to Noise Ratio of Photodetector to calculate 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 calculate Bit Error Rate given SNR using this online calculator? To use this online calculator for Bit Error Rate given SNR, enter Signal to Noise Ratio of Photodetector (SNR_opt) and hit the calculate button. Here is how the Bit Error Rate given SNR calculation can be explained with given input values -> 2.672294 = (1/sqrt(2*pi))*(exp(-0.151^2/2))/0.151.

FAQ

What is Bit Error Rate given SNR?

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 and is represented as BER_opt = (1/sqrt(2*pi))*(exp(-SNR_opt^2/2))/SNR_opt or Bit Error Rate = (1/sqrt(2*pi))*(exp(-Signal to Noise Ratio of Photodetector^2/2))/Signal to Noise Ratio of Photodetector. Signal to Noise Ratio of Photodetector .

How to calculate Bit Error Rate given SNR?

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 is calculated using Bit Error Rate = (1/sqrt(2*pi))*(exp(-Signal to Noise Ratio of Photodetector^2/2))/Signal to Noise Ratio of Photodetector. To calculate Bit Error Rate given SNR, you need Signal to Noise Ratio of Photodetector (SNR_opt). With our tool, you need to enter the respective value for Signal to Noise Ratio of Photodetector and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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