## Level Crossing Rate Solution

STEP 0: Pre-Calculation Summary
Formula Used
Level crossing rate = (sqrt(2*pi))*Maximum Doppler Shift*Specified envolope value normalized to rms* (e^(-(Specified envolope value normalized to rms^2)))
NR = (sqrt(2*pi))*fm*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 - Squre root function, sqrt(Number)
Variables Used
Level crossing rate - Level crossing rate the number of level crossings per second.
Maximum Doppler Shift - (Measured in Hertz) - Maximum Doppler Shift is the change observed in wavelength, or frequency when θ=0.
Specified envolope value normalized to rms - Specified envolope value normalized to rms is the value of the specified level R, normalized to the local rms amplitude of the lading envelope.
STEP 1: Convert Input(s) to Base Unit
Maximum Doppler Shift: 20 Kilohertz --> 20000 Hertz (Check conversion here)
Specified envolope value normalized to rms: 0.1 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
NR = (sqrt(2*pi))*fm*ρ* (e^(-(ρ^2))) --> (sqrt(2*pi))*20000*0.1* (e^(-(0.1^2)))
Evaluating ... ...
NR = 4963.37381313877
STEP 3: Convert Result to Output's Unit
4963.37381313877 --> No Conversion Required
4963.37381313877 <-- Level crossing rate
(Calculation completed in 00.000 seconds)
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## Credits

Created by Vidyashree V
BMS College of Engineering (BMSCE), Bangalore
Vidyashree V has created this Calculator and 25+ more calculators!
Verified by Rachita C
BMS College Of Engineering (BMSCE), Banglore
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## < 10+ Mobile radio propogation Calculators

Level Crossing Rate
Level crossing rate = (sqrt(2*pi))*Maximum Doppler Shift*Specified envolope value normalized to rms* (e^(-(Specified envolope value normalized to rms^2))) Go
Normalized LCR(nr)
Normalized LCR = Level Crossing Rate*sqrt(2*3.14)/(Beta*Velocity) Go
Maximum Doppler Shift
Maximum Doppler Shift = Velocity/(300000000/Carrier Frequency) Go
Coherence bandwidth for two random phases of two received signals
Coherence bandwidth random phase = 1/(4*3.14*Delta spread) Go
Coherence Bandwidth For Multipath Channel
Coherence Bandwidth = (1)/(50*RMS Delay Spread) Go
Delta spread = 1/(2*3.14*Coherence bandwidth) Go
Coherence Time
Coherence Time = 0.423/Maximum Doppler Shift Go

## Level Crossing Rate Formula

Level crossing rate = (sqrt(2*pi))*Maximum Doppler Shift*Specified envolope value normalized to rms* (e^(-(Specified envolope value normalized to rms^2)))
NR = (sqrt(2*pi))*fm*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*Specified envolope value normalized to rms* (e^(-(Specified envolope value normalized to rms^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 NR symbol.

How to calculate Level Crossing Rate using this online calculator? To use this online calculator for Level Crossing Rate, enter Maximum Doppler Shift (fm) & Specified envolope value normalized to rms (ρ) and hit the calculate button. Here is how the Level Crossing Rate calculation can be explained with given input values -> 4963.374 = (sqrt(2*pi))*20000*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 NR = (sqrt(2*pi))*fm*ρ* (e^(-(ρ^2))) or Level crossing rate = (sqrt(2*pi))*Maximum Doppler Shift*Specified envolope value normalized to rms* (e^(-(Specified envolope value normalized to rms^2))). Maximum Doppler Shift is the change observed in wavelength, or frequency when θ=0 & Specified envolope value normalized to rms is the value of the specified level R, normalized to the local rms amplitude of the lading envelope.
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*Specified envolope value normalized to rms* (e^(-(Specified envolope value normalized to rms^2))). To calculate Level Crossing Rate, you need Maximum Doppler Shift (fm) & Specified envolope value normalized to rms (ρ). With our tool, you need to enter the respective value for Maximum Doppler Shift & Specified envolope value normalized to rms 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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