Probability Error of BPSK for Raised Cosine Filter Calculator

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Modulation Techniques

Modulation Parameters

✖Energy per Symbol is defined as the energy of each transmitted symbol of the modulated signal.ⓘ Energy per Symbol [ε_s]			+10% -10%
✖Noise density is defined as the power spectral density of noise or the noise power per unit of bandwidth.ⓘ Noise Density [N₀]			+10% -10%

✖The Probability Error of BPSK modulation occurs in distributed beamforming with phase errors.ⓘ Probability Error of BPSK for Raised Cosine Filter [e_BPSK]

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Formula

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Probability Error of BPSK for Raised Cosine Filter

Formula

`"e"_{"BPSK"} = (1/2)*erfc(sqrt("ε"_{"s"}/"N"_{"0"}))`

Example

`"0.499999"=(1/2)*erfc(sqrt("1.2e-11J"/"10"))`

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Probability Error of BPSK for Raised Cosine Filter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Probability Error of BPSK = (1/2)*erfc(sqrt(Energy per Symbol/Noise Density))
e_BPSK = (1/2)*erfc(sqrt(ε_s/N₀))
This formula uses 2 Functions, 3 Variables

Functions Used

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)
erfc - The error function is defined as the integral of the normal distribution from 0 to x scaled such that erf(±∞) = ±1. It is an entire function defined for real- and complex-valued numbers., erfc(Number)

Variables Used

Probability Error of BPSK - The Probability Error of BPSK modulation occurs in distributed beamforming with phase errors.
Energy per Symbol - (Measured in Joule) - Energy per Symbol is defined as the energy of each transmitted symbol of the modulated signal.
Noise Density - Noise density is defined as the power spectral density of noise or the noise power per unit of bandwidth.

STEP 1: Convert Input(s) to Base Unit

Energy per Symbol: 1.2E-11 Joule --> 1.2E-11 Joule No Conversion Required
Noise Density: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e_BPSK = (1/2)*erfc(sqrt(ε_s/N₀)) --> (1/2)*erfc(sqrt(1.2E-11/10))

Evaluating ... ...

e_BPSK = 0.499999381961277

STEP 3: Convert Result to Output's Unit

0.499999381961277 --> No Conversion Required

FINAL ANSWER

0.499999381961277 ≈ 0.499999 <-- Probability Error of BPSK

(Calculation completed in 00.004 seconds)

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< 14 Modulation Techniques Calculators

Bandwidth of Multilevel FSK

Go Bandwidth of Multilevel FSK = Bit Rate*(1+Rolloff Factor)+(2*Difference in Frequency*(Number of Level-1))

Bandwidth of Multilevel PSK

Go Bandwidth of Multilevel PSK = Bit Rate*((1+Rolloff Factor)/(log2(Number of Level)))

Probability Error of BPSK for Raised Cosine Filter

Go Probability Error of BPSK = (1/2)*erfc(sqrt(Energy per Symbol/Noise Density))

Bandwidth of FSK

Go Bandwidth of FSK = Bit Rate*(1+Rolloff Factor)+(2*Difference in Frequency)

Bandwidth of ASK given Bit Rate

Go Bandwidth of ASK = (1+Rolloff Factor)*(Bit Rate/Number of Bits)

Rolloff Factor

Go Rolloff Factor = ((Bandwidth of ASK*Number of Bits)/Bit Rate)-1

Bandwidth of Raised Cosine Filter

Go Bandwidth of Raised Cosine Filter = (1+Rolloff Factor)/(2*Signal Time Period)

Signal Time Period

Go Signal Time Period = (1+Rolloff Factor)/(2*Bandwidth of Raised Cosine Filter)

Probability Error of DPSK

Go Probability Error of DPSK = (1/2)*e^(-(Energy per Bit/Noise Density))

Bandwidth Efficiency in Digital Communication

Go Bandwidth Efficiency = Bit Rate/Signal Bandwidth

Symbol Time

Go Symbol Time = Bit Rate/Bits Conveyed Per Symbol

Baud Rate

Go Baud Rate = Bit Rate/Number of Bits

Sampling Theorem

Go Sampling Frequency = 2*Maximum Frequency

Sampling Period

Go Sampling Period = 1/Sampling Frequency

Probability Error of BPSK for Raised Cosine Filter Formula

Probability Error of BPSK = (1/2)*erfc(sqrt(Energy per Symbol/Noise Density))
e_BPSK = (1/2)*erfc(sqrt(ε_s/N₀))

Why BPSK is used?

It is used in OFDM and OFDMA to modulate the pilot subcarriers used for channel estimation and equalization. As we know different channels are used for specific data transmission in cellular systems. The channels used to transmit system related informations which are very essential are modulated using BPSK modulation.

How to Calculate Probability Error of BPSK for Raised Cosine Filter?

Probability Error of BPSK for Raised Cosine Filter calculator uses Probability Error of BPSK = (1/2)*erfc(sqrt(Energy per Symbol/Noise Density)) to calculate the Probability Error of BPSK, The Probability Error of BPSK for Raised Cosine Filter modulation occurs in distributed beamforming with phase errors. Generation of random BPSK modulated symbols are in +1′s and -1′s. Probability Error of BPSK is denoted by e_BPSK symbol.

How to calculate Probability Error of BPSK for Raised Cosine Filter using this online calculator? To use this online calculator for Probability Error of BPSK for Raised Cosine Filter, enter Energy per Symbol (ε_s) & Noise Density (N₀) and hit the calculate button. Here is how the Probability Error of BPSK for Raised Cosine Filter calculation can be explained with given input values -> 0.499999 = (1/2)*erfc(sqrt(1.2E-11/10)).

FAQ

What is Probability Error of BPSK for Raised Cosine Filter?

The Probability Error of BPSK for Raised Cosine Filter modulation occurs in distributed beamforming with phase errors. Generation of random BPSK modulated symbols are in +1′s and -1′s and is represented as e_BPSK = (1/2)*erfc(sqrt(ε_s/N₀)) or Probability Error of BPSK = (1/2)*erfc(sqrt(Energy per Symbol/Noise Density)). Energy per Symbol is defined as the energy of each transmitted symbol of the modulated signal & Noise density is defined as the power spectral density of noise or the noise power per unit of bandwidth.

How to calculate Probability Error of BPSK for Raised Cosine Filter?

The Probability Error of BPSK for Raised Cosine Filter modulation occurs in distributed beamforming with phase errors. Generation of random BPSK modulated symbols are in +1′s and -1′s is calculated using Probability Error of BPSK = (1/2)*erfc(sqrt(Energy per Symbol/Noise Density)). To calculate Probability Error of BPSK for Raised Cosine Filter, you need Energy per Symbol (ε_s) & Noise Density (N₀). With our tool, you need to enter the respective value for Energy per Symbol & Noise Density 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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