Level Crossing Rate Calculator

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Frequency Reuse Concept

✖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.ⓘ Maximum Doppler Shift [F_m]			+10% -10%
✖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.ⓘ Normalized RMS Value [ρ]			+10% -10%

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

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Formula

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Level Crossing Rate

Formula

`"N"_{"R"} = (sqrt(2*pi))*"F"_{"m"}*"ρ"* e^(-("ρ"^2))`

Example

`"13.67409"=(sqrt(2*pi))*"0.0551kHz"*"0.1"* e^(-(("0.1")^2))`

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Download Mobile Radio Propogation Formulas PDF

Level Crossing Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

Level Crossing Rate = (sqrt(2*pi))*Maximum Doppler Shift*Normalized RMS Value* e^(-(Normalized RMS Value^2))
N_R = (sqrt(2*pi))*F_m*ρ* e^(-(ρ^2))
This formula uses 2 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

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)

Variables Used

Level Crossing Rate - Level Crossing Rate (LCR) refers to the statistical measure of how frequently a signal's envelope crosses a certain threshold level.
Maximum Doppler Shift - (Measured in Hertz) - 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.
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.

STEP 1: Convert Input(s) to Base Unit

Maximum Doppler Shift: 0.0551 Kilohertz --> 55.1 Hertz (Check conversion here)
Normalized RMS Value: 0.1 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_R = (sqrt(2*pi))*F_m*ρ* e^(-(ρ^2)) --> (sqrt(2*pi))*55.1*0.1* e^(-(0.1^2))

Evaluating ... ...

N_R = 13.6740948551973

STEP 3: Convert Result to Output's Unit

13.6740948551973 --> No Conversion Required

FINAL ANSWER

13.6740948551973 ≈ 13.67409 <-- Level Crossing Rate

(Calculation completed in 00.004 seconds)

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Created by Vidyashree V

BMS College of Engineering (BMSCE), Bangalore

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BMS College Of Engineering (BMSCE), Banglore

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< 16 Mobile Radio Propogation Calculators

Selective Retransmission

Go Selective Retransmission = (Number of Word Message Consist*Information Bits)/(Header Bits*Expected Number of Transmission+Number of Bits per Word*Expected One Transmission*Number of Word Message Consist)

Stop-and-Wait ARQ Technique

Go Stop-and-Wait ARQ Technique = (Number of Word Message Consist*Information Bits)/((Header Bits+Number of Bits per Word*Number of Word Message Consist)*Expected Number of Transmission)

Level Crossing Rate

Go Level Crossing Rate = (sqrt(2*pi))*Maximum Doppler Shift*Normalized RMS Value* e^(-(Normalized RMS Value^2))

Mobile Radio Distance

Go Transmitter Reciever Distance = (Path Loss Coefficient/Mobile Reciever Carrier Power)^(1/4)

Path Loss Coefficient

Go Path Loss Coefficient = Mobile Reciever Carrier Power/(Transmitter Reciever Distance^-4)

Mobile Reciever Carrier Power

Go Mobile Reciever Carrier Power = Path Loss Coefficient*Transmitter Reciever Distance^-4

Maximum Possible S by N Ratio

Go Maximum Possible S/N Ratio = Actual S/N Ratio at Output*Noise Figure of Amplifier

Noise Figure

Go Noise Figure of Amplifier = Maximum Possible S/N Ratio/Actual S/N Ratio at Output

Cumulative Distribution Function

Go Cumulative Distribution Function = Average Duration of Fade*Normalized LCR

Short Term Fading

Go Short Term Fading = Mobile Radio Signal*Long Term Fading

Mobile Radio Signal

Go Mobile Radio Signal = Long Term Fading*Multipath Fading

Multipath Fading

Go Multipath Fading = Mobile Radio Signal/Long Term Fading

Long Term Fading

Go Long Term Fading = Mobile Radio Signal/Multipath Fading

Serial to Parallel Modulation Time Period

Go Time Period = Symbol Duration/Block of N Serial Source

Block of N Serial Source

Go Block of N Serial Source = Symbol Duration/Time Period

Symbol Duration

Go Symbol Duration = Block of N Serial Source*Time Period

Level Crossing Rate Formula

Level Crossing Rate = (sqrt(2*pi))*Maximum Doppler Shift*Normalized RMS Value* e^(-(Normalized RMS Value^2))
N_R = (sqrt(2*pi))*F_m*ρ* e^(-(ρ^2))

What is the significance of level crossing rate and fading statistics?

The level crossing rate (LCR) and average fade duration of a Rayleigh fading signal are two important statistics which are useful for designing error control codes and diversity schemes to be used in mobile communication systems, since it becomes possible to relate the time rate of change of the received signal to the signal level and velocity of the mobile.

How to Calculate Level Crossing Rate?

Level Crossing Rate calculator uses Level Crossing Rate = (sqrt(2*pi))*Maximum Doppler Shift*Normalized RMS Value* e^(-(Normalized RMS Value^2)) to calculate 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 calculate Level Crossing Rate using this online calculator? To use this online calculator for Level Crossing Rate, enter Maximum Doppler Shift (F_m) & Normalized RMS Value (ρ) and hit the calculate button. Here is how the Level Crossing Rate calculation can be explained with given input values -> 13.67409 = (sqrt(2*pi))*55.1*0.1* e^(-(0.1^2)).

FAQ

What is 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 and is represented as N_R = (sqrt(2*pi))*F_m*ρ* e^(-(ρ^2)) or Level Crossing Rate = (sqrt(2*pi))*Maximum Doppler Shift*Normalized RMS Value* e^(-(Normalized RMS Value^2)). 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 & 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.

How to calculate 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 is calculated using Level Crossing Rate = (sqrt(2*pi))*Maximum Doppler Shift*Normalized RMS Value* e^(-(Normalized RMS Value^2)). To calculate Level Crossing Rate, you need Maximum Doppler Shift (F_m) & Normalized RMS Value (ρ). With our tool, you need to enter the respective value for Maximum Doppler Shift & Normalized RMS Value 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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