RMS Delay Spread Calculator

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Frequency Reuse Concept

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✖Variance Mean Excess Delay is a statistical measure that quantifies the spread of a parameter of data points. It provides information about the values of the parameter are distributed around the mean.ⓘ Variance Mean Excess Delay [τ'']			+10% -10%
✖Mean Excess Delay refers to a metric used to quantify the time dispersion or spreading of signals in a wireless channel.ⓘ Mean Excess Delay [τ']			+10% -10%

✖RMS Delay Spread is a term used in wireless communication to describe the dispersion of multipath signals arriving at a receiver.ⓘ RMS Delay Spread [σ_t]

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Formula

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RMS Delay Spread

Formula

`"σ"_{"t"} = sqrt("τ''"-("τ'")^2)`

Example

`"0.286313s"=sqrt("0.084s"-("0.045s")^2)`

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RMS Delay Spread Solution

STEP 0: Pre-Calculation Summary

Formula Used

RMS Delay Spread = sqrt(Variance Mean Excess Delay-(Mean Excess Delay)^2)
σ_t = sqrt(τ''-(τ')^2)
This formula uses 1 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)

Variables Used

RMS Delay Spread - (Measured in Second) - RMS Delay Spread is a term used in wireless communication to describe the dispersion of multipath signals arriving at a receiver.
Variance Mean Excess Delay - (Measured in Second) - Variance Mean Excess Delay is a statistical measure that quantifies the spread of a parameter of data points. It provides information about the values of the parameter are distributed around the mean.
Mean Excess Delay - (Measured in Second) - Mean Excess Delay refers to a metric used to quantify the time dispersion or spreading of signals in a wireless channel.

STEP 1: Convert Input(s) to Base Unit

Variance Mean Excess Delay: 0.084 Second --> 0.084 Second No Conversion Required
Mean Excess Delay: 0.045 Second --> 0.045 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_t = sqrt(τ''-(τ')^2) --> sqrt(0.084-(0.045)^2)

Evaluating ... ...

σ_t = 0.286312766044408

STEP 3: Convert Result to Output's Unit

0.286312766044408 Second --> No Conversion Required

FINAL ANSWER

0.286312766044408 ≈ 0.286313 Second <-- RMS Delay Spread

(Calculation completed in 00.004 seconds)

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< 16 Frequency Reuse Concept Calculators

RMS Delay Spread

Go RMS Delay Spread = sqrt(Variance Mean Excess Delay-(Mean Excess Delay)^2)

Symbol Time Period

Go Symbol Time = (Forward Frame-(Time Slots+Reverse Frame))/44

Carrier Frequency using Maximum Doppler Shift

Go Carrier Frequency = (Maximum Doppler Shift*[c])/Velocity

Maximum Doppler Shift

Go Maximum Doppler Shift = (Velocity/[c])*Carrier Frequency

Reverse Frame

Go Reverse Frame = Forward Frame-(Time Slots+44*Symbol Time)

Time Slots

Go Time Slots = Forward Frame-(Reverse Frame+44*Symbol Time)

Forward Frame

Go Forward Frame = Time Slots+Reverse Frame+44*Symbol Time

Maximum Excess Delay

Go Maximum Excess Delay = Excess Delay Spread-First Arriving Signal

Channel Reuse Ratio

Go Co Channel Reuse Ratio = sqrt(3*Frequency Reuse Pattern)

M-Ary PAM

Go M-Ary PAM = 1-sqrt(1-M-Ary QAM)

Coherence Bandwidth for Random Phases of Two Received Signals

Go Coherence Bandwidth Random Phase = 1/(4*3.14*Delay Spread)

Coherence Bandwidth for Two Fading Amplitudes of Two Received Signals

Go Coherence Bandwidth Fading = 1/(2*3.14*Delay Spread)

Delay Spread

Go Delay Spread = 1/(2*3.14*Coherence Bandwidth Fading)

Coherence Bandwidth for Multipath Channel

Go Coherence Bandwidth = 1/(5*RMS Delay Spread)

Coherence Time

Go Coherence Time = 0.423/Maximum Doppler Shift

M-Ary QAM

Go M-Ary QAM = 1-(1-M-Ary PAM)^2

RMS Delay Spread Formula

RMS Delay Spread = sqrt(Variance Mean Excess Delay-(Mean Excess Delay)^2)
σ_t = sqrt(τ''-(τ')^2)

What are the different values of R.M.S delay speed in different environment?

In urban it is around 10-25 microseconds, Suburban area - 200-310 nanoseconds, Indoor - 10-50 nanoseconds.

Difference between doppler spread and doppler shift?

Doppler shift is the random changes in a channel introduced as a result of a mobile user's mobility. Doppler spread has the effect of shifting or spreading the frequency components of a signal. It is caused by time selective fading.

How to Calculate RMS Delay Spread?

RMS Delay Spread calculator uses RMS Delay Spread = sqrt(Variance Mean Excess Delay-(Mean Excess Delay)^2) to calculate the RMS Delay Spread, The RMS Delay Spread formula is defined as is a measure of the multipath profile of a mobile communications channel. It is generally defined as the difference between the time of arrival of the earliest component and the time of arrival of the latest multipath component. RMS Delay Spread is denoted by σ_t symbol.

How to calculate RMS Delay Spread using this online calculator? To use this online calculator for RMS Delay Spread, enter Variance Mean Excess Delay (τ'') & Mean Excess Delay (τ') and hit the calculate button. Here is how the RMS Delay Spread calculation can be explained with given input values -> 0.286313 = sqrt(0.084-(0.045)^2).

FAQ

What is RMS Delay Spread?

The RMS Delay Spread formula is defined as is a measure of the multipath profile of a mobile communications channel. It is generally defined as the difference between the time of arrival of the earliest component and the time of arrival of the latest multipath component and is represented as σ_t = sqrt(τ''-(τ')^2) or RMS Delay Spread = sqrt(Variance Mean Excess Delay-(Mean Excess Delay)^2). Variance Mean Excess Delay is a statistical measure that quantifies the spread of a parameter of data points. It provides information about the values of the parameter are distributed around the mean & Mean Excess Delay refers to a metric used to quantify the time dispersion or spreading of signals in a wireless channel.

How to calculate RMS Delay Spread?

The RMS Delay Spread formula is defined as is a measure of the multipath profile of a mobile communications channel. It is generally defined as the difference between the time of arrival of the earliest component and the time of arrival of the latest multipath component is calculated using RMS Delay Spread = sqrt(Variance Mean Excess Delay-(Mean Excess Delay)^2). To calculate RMS Delay Spread, you need Variance Mean Excess Delay (τ'') & Mean Excess Delay (τ'). With our tool, you need to enter the respective value for Variance Mean Excess Delay & Mean Excess Delay 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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