Likelihood Ratio Receiver Calculator

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Radar Antennas Reception

Radar & Antenna Specifications

Special Purpose Radars

✖Probability Density Function of Signal and Noise describes the likelihood of signal having certain values or falling under certain ranges.ⓘ Probability Density Function of Signal and Noise [P_sn]			+10% -10%
✖Probability Density Function of Noise describes the likelihood of signal having certain values of noise or falling under certain ranges.ⓘ Probability Density Function of Noise [P_n]			+10% -10%

✖Likelihood Ratio Receiver is the measure of probability of occurrence of one event. In this case, noise or signal occurrence in receiver.ⓘ Likelihood Ratio Receiver [L_r]

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Formula

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Likelihood Ratio Receiver

Formula

`"L"_{"r"} = "P"_{"sn"}/"P"_{"n"}`

Example

`"2.845283"="0.754"/"0.265"`

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Likelihood Ratio Receiver Solution

STEP 0: Pre-Calculation Summary

Formula Used

Likelihood Ratio Receiver = Probability Density Function of Signal and Noise/Probability Density Function of Noise
L_r = P_sn/P_n
This formula uses 3 Variables

Variables Used

Likelihood Ratio Receiver - Likelihood Ratio Receiver is the measure of probability of occurrence of one event. In this case, noise or signal occurrence in receiver.
Probability Density Function of Signal and Noise - Probability Density Function of Signal and Noise describes the likelihood of signal having certain values or falling under certain ranges.
Probability Density Function of Noise - Probability Density Function of Noise describes the likelihood of signal having certain values of noise or falling under certain ranges.

STEP 1: Convert Input(s) to Base Unit

Probability Density Function of Signal and Noise: 0.754 --> No Conversion Required
Probability Density Function of Noise: 0.265 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_r = P_sn/P_n --> 0.754/0.265

Evaluating ... ...

L_r = 2.84528301886792

STEP 3: Convert Result to Output's Unit

2.84528301886792 --> No Conversion Required

FINAL ANSWER

2.84528301886792 ≈ 2.845283 <-- Likelihood Ratio Receiver

(Calculation completed in 00.004 seconds)

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Credits

Created by Santhosh Yadav

Dayananda Sagar College Of Engineering (DSCE), Banglore

Santhosh Yadav has created this Calculator and 50+ more calculators!

Verified by Ritwik Tripathi

Vellore Institute of Technology (VIT Vellore), Vellore

Ritwik Tripathi has verified this Calculator and 100+ more calculators!

< 14 Radar Antennas Reception Calculators

Omnidirectional SIR

Go Omnidirectional SIR = 1/(2*(Frequency Reuse Ratio-1)^(-Propagation Path Loss Exponent)+2*(Frequency Reuse Ratio)^(-Propagation Path Loss Exponent)+2*(Frequency Reuse Ratio+1)^(-Propagation Path Loss Exponent))

Dielectric Constant of Artificial Dielectric

Go Dielectric Constant of Artificial Dielectric = 1+(4*pi*Radius of Metallic Spheres^3)/(Spacing between Centers of Metallic Sphere^3)

Maximum Gain of Antenna given Antenna Diameter

Go Maximum Gain of Antenna = (Antenna Aperture Efficiency/43)*(Antenna Diameter/Dielectric Constant of Artificial Dielectric)^2

Metal-Plate Lens Refractive Index

Go Metal Plate Refractive Index = sqrt(1-(Incident Wave Wavelength/(2*Spacing between Centers of Metallic Sphere))^2)

Spacing between Centers of Metallic Sphere

Go Spacing between Centers of Metallic Sphere = Incident Wave Wavelength/(2*sqrt(1-Metal Plate Refractive Index^2))

Overall Noise Figure of Cascaded Networks

Go Overall Noise Figure = Noise Figure Network 1+(Noise Figure Network 2-1)/Gain of Network 1

Receiver Antenna Gain

Go Receiver Antenna Gain = (4*pi*Effective Area of Receiving Antenna)/Carrier Wavelength^2

Luneburg Lens Refractive Index

Go Luneburg Lens Refractive Index = sqrt(2-(Radial Distance/Radius of Luneburg Lens)^2)

Likelihood Ratio Receiver

Go Likelihood Ratio Receiver = Probability Density Function of Signal and Noise/Probability Density Function of Noise

Frequency Reuse Ratio

Go Frequency Reuse Ratio = (6*Signal to Co-channel Interference Ratio)^(1/Propagation Path Loss Exponent)

Directive Gain

Go Directive Gain = (4*pi)/(Beam Width in X-plane*Beam Width in Y-plane)

Signal to Co-channel Interference Ratio

Go Signal to Co-channel Interference Ratio = (1/6)*Frequency Reuse Ratio^Propagation Path Loss Exponent

Effective Aperture of Lossless Antenna

Go Effective Aperture of Lossless Antenna = Antenna Aperture Efficiency*Physical Area of an Antenna

Effective Noise Temperature

Go Effective Noise Temperature = (Overall Noise Figure-1)*Noise Temperature Network 1

Likelihood Ratio Receiver Formula

Likelihood Ratio Receiver = Probability Density Function of Signal and Noise/Probability Density Function of Noise
L_r = P_sn/P_n

How are decisions made using Likelihood Ratio?

The likelihood ratio serves as a decision metric in hypothesis testing. When comparing likelihoods under different hypotheses, it provides a measure of which hypothesis is more likely given the observed data. A likelihood ratio greater than 1 indicates that the hypothesis in the numerator is more likely, while a likelihood ratio less than 1 suggests that the hypothesis in the denominator is more likely.

How to Calculate Likelihood Ratio Receiver?

Likelihood Ratio Receiver calculator uses Likelihood Ratio Receiver = Probability Density Function of Signal and Noise/Probability Density Function of Noise to calculate the Likelihood Ratio Receiver, Likelihood Ratio Receiver is a type of receiver used in communication systems to make decisions about the transmitted message or signal. It is a theoretical receiver that aims to maximize the probability of correct decision-making in the presence of noise and other impairments. Likelihood Ratio Receiver is denoted by L_r symbol.

How to calculate Likelihood Ratio Receiver using this online calculator? To use this online calculator for Likelihood Ratio Receiver, enter Probability Density Function of Signal and Noise (P_sn) & Probability Density Function of Noise (P_n) and hit the calculate button. Here is how the Likelihood Ratio Receiver calculation can be explained with given input values -> 2.845283 = 0.754/0.265.

FAQ

What is Likelihood Ratio Receiver?

Likelihood Ratio Receiver is a type of receiver used in communication systems to make decisions about the transmitted message or signal. It is a theoretical receiver that aims to maximize the probability of correct decision-making in the presence of noise and other impairments and is represented as L_r = P_sn/P_n or Likelihood Ratio Receiver = Probability Density Function of Signal and Noise/Probability Density Function of Noise. Probability Density Function of Signal and Noise describes the likelihood of signal having certain values or falling under certain ranges & Probability Density Function of Noise describes the likelihood of signal having certain values of noise or falling under certain ranges.

How to calculate Likelihood Ratio Receiver?

Likelihood Ratio Receiver is a type of receiver used in communication systems to make decisions about the transmitted message or signal. It is a theoretical receiver that aims to maximize the probability of correct decision-making in the presence of noise and other impairments is calculated using Likelihood Ratio Receiver = Probability Density Function of Signal and Noise/Probability Density Function of Noise. To calculate Likelihood Ratio Receiver, you need Probability Density Function of Signal and Noise (P_sn) & Probability Density Function of Noise (P_n). With our tool, you need to enter the respective value for Probability Density Function of Signal and Noise & Probability Density Function of Noise 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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