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Level Crossing Rate Formula

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Level Crossing Rate (LCR) refers to the statistical measure of how frequently a signal's envelope crosses a certain threshold level. Check FAQs

N R = (\sqrt{2 \cdot π}) \cdot F m \cdot ρ \cdot e^{- (ρ^{2})}

N_R - Level Crossing Rate?F_m - Maximum Doppler Shift?ρ - Normalized RMS Value?π - Archimedes' constant?

Level Crossing Rate Example

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Here is how the Level Crossing Rate equation looks like with Values.

Here is how the Level Crossing Rate equation looks like with Units.

Here is how the Level Crossing Rate equation looks like.

13.6741 = (\sqrt{2 \cdot 3.1416}) \cdot 0.0551 \cdot 0.1 \cdot e^{- ({0.1}^{2})}

13.6741 = (\sqrt{2 \cdot 3.1416}) \cdot 0.0551kHz \cdot 0.1 \cdot e^{- ({0.1}^{2})}

13.6741 = (\sqrt{2 \cdot 3.1416}) \cdot 0.0551 \cdot 0.1 \cdot e^{- ({0.1}^{2})}

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Level Crossing Rate Solution

Follow our step by step solution on how to calculate Level Crossing Rate?

FIRST Step Consider the formula

N R = (\sqrt{2 \cdot π}) \cdot F m \cdot ρ \cdot e^{- (ρ^{2})}

Next Step Substitute values of Variables

∴

N R = (\sqrt{2 \cdot π}) \cdot 0.0551kHz \cdot 0.1 \cdot e^{- ({0.1}^{2})}

Next Step Substitute values of Constants

∴

N R = (\sqrt{2 \cdot 3.1416}) \cdot 0.0551kHz \cdot 0.1 \cdot e^{- ({0.1}^{2})}

Next Step Convert Units

∴

N R = (\sqrt{2 \cdot 3.1416}) \cdot 55.1Hz \cdot 0.1 \cdot e^{- ({0.1}^{2})}

Next Step Prepare to Evaluate

∴

N R = (\sqrt{2 \cdot 3.1416}) \cdot 55.1 \cdot 0.1 \cdot e^{- ({0.1}^{2})}

Next Step Evaluate

∴

N R = 13.6740948551973

LAST Step Rounding Answer

∴

N R = 13.6741

Level Crossing Rate Formula Elements

Variables

Constants

Functions

Level Crossing Rate

Level Crossing Rate (LCR) refers to the statistical measure of how frequently a signal's envelope crosses a certain threshold level.

Symbol: N_R

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Level Crossing Rate

Maximum Doppler Shift

Maximum Doppler Shift or Max Doppler spread or, max Doppler frequency is refers to the maximum change in frequency a wireless signal due to the relative motion between the transmitter and receiver.

Symbol: F_m

Measurement: FrequencyUnit: kHz

Note: Value should be greater than 0.

Formulas to find Maximum Doppler Shift

Normalized RMS Value

Normalized RMS Value is a measure of the amplitude of a signal and is calculated by taking the square root of the average of the squared values of the signal over a specific time period.

Symbol: ρ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Normalized RMS Value

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

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)

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How to Evaluate Level Crossing Rate?

Level Crossing Rate evaluator uses Level Crossing Rate = (sqrt(2*pi))*Maximum Doppler Shift*Normalized RMS Value*e^(-(Normalized RMS Value^2)) to evaluate the Level Crossing Rate, The level crossing rate (LCR) formula is defined as the expected rate at which the Rayleigh fading envelope, normalized to the local rms signal level, crosses a specified level in a positive-going direction. Level Crossing Rate is denoted by N_R symbol.

How to evaluate Level Crossing Rate using this online evaluator? To use this online evaluator for Level Crossing Rate, enter Maximum Doppler Shift (F_m) & Normalized RMS Value (ρ) and hit the calculate button.

FAQs on Level Crossing Rate

What is the formula to find Level Crossing Rate?

The formula of Level Crossing Rate is expressed as Level Crossing Rate = (sqrt(2*pi))*Maximum Doppler Shift*Normalized RMS Value*e^(-(Normalized RMS Value^2)). Here is an example- 13.67409 = (sqrt(2*pi))*55.1*0.1*e^(-(0.1^2)).

How to calculate Level Crossing Rate?

With Maximum Doppler Shift (F_m) & Normalized RMS Value (ρ) we can find Level Crossing Rate using the formula - Level Crossing Rate = (sqrt(2*pi))*Maximum Doppler Shift*Normalized RMS Value*e^(-(Normalized RMS Value^2)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

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