# Radar Equation Calculator

## Description

The Radar Equation Calculator app solves the basic radar equation for monostatic or bistatic radar systems. The radar equation relates target range, transmitted power, and received signal SNR. Using this app, you can:

Solve for maximum target range based on the transmit power of the radar and specified received SNR

Calculate required transmit power based on known target range and specified received SNR

Calculate the received SNR value based on known range and transmit power

## Open the Radar Equation Calculator App

MATLAB

^{®}Toolstrip: On the**Apps**tab, under**Signal Processing and Communications**, click the app icon.MATLAB command prompt: Enter

`radarEquationCalculator`

.

## Examples

### Maximum Detection Range of a Monostatic Radar

This example shows how to compute the maximum detection range of a 10 GHz, 1 kW, monostatic radar with a 40 dB antenna gain and a detection threshold of 10 dB.

From the **Calculation Type** drop-down list, choose
**Target Range** as the solution.

Choose **Configuration** as `monostatic`

.

Enter 40 dB for the antenna **Gain**.

Set the **Wavelength** to 3 cm.

Set the **SNR** detection threshold parameter to 10 dB.

Assuming the target is a large airplane, set the **Target Radar Cross
Section** value to 100 m^{2}.

Specify the **Peak Transmit Power** as 1 kW

Specify the **Pulse Width** as 2 µs.

Assume a total of 5 dB **System Losses**.

The maximum target detection range is 92 km.

### Maximum Detection Range of a Monostatic Radar Using Multiple Pulses

This example shows how to use multiple pulses to reduce the transmitted power while maintaining the same maximum target range.

Continue with the results from the previous example.

Click the arrows to the right of the **SNR** label.

The **Detection Specifications for SNR** menu opens.

Set **Probability of Detection** to 0.95.

Set **Probability of False Alarm** to
10^{–6}.

Set **Number of Pulses** to 4.

Reduce **Peak Transmit Power** to 0.75 kW.

Assume a nonfluctuating target model, and set the **Swerling Case
Number** to 0.

The maximum detection range is approximately the same as in the previous example, but the transmitted power is reduced by 25%.

### Maximum Detection Range of Bistatic Radar System

This example shows how to solve for the geometric mean range of a target for a bistatic radar system.

Specify the **Calculation Type** as ```
Target
Range
```

.

Specify the **Configuration** as
`bistatic`

.

Provide a **Transmitter Gain** and a **Receiver
Gain** parameter, instead of the single gain needed in the monostatic
case.

Alternatively, to achieve a particular probability of detection and probability of
false alarm, open the **Detection Specifications for SNR**
menu.

Enter values for **Probability of Detection** and
**Probability of False Alarm**, **Number of
Pulses**, and **Swerling Case Number**.

### Required Transmit Power for a Bistatic Radar

This example shows how to compute the required peak transmit power of a 10 GHz, bistatic X-band radar for a 80 km total bistatic range, and 10 dB received SNR.

The system has a 40 dB transmitter gain and a 20 dB receiver gain. The required receiver SNR is 10 dB.

From the **Calculation Type** drop-down list, choose
**Peak Transmit Power** as the solution type.

Choose **Configuration** as `bistatic`

.

From the system specifications, set **Transmitter Gain** to 40 dB
and **Receiver Gain** to 20 dB.

Set the **SNR** detection threshold to 10 dB and the
**Wavelength** to 0.3 m.

Assume the target is a fighter aircraft having a **Target Radar Cross
Section** value of 2 m^{2}.

Choose **Range from Transmitter** as 50 km, and **Range
from Receiver ** as 30 km.

Set the **Pulse Width** to 2 µs and the **System
Losses** to 0 dB.

The required Peak Transmit Power is about 0.5 kW.

### Receiver SNR for a Monostatic Radar

This example shows how to compute the received SNR for a monostatic radar with 1 kW peak transmit power with a target at a range of 2 km.

Assume a 2 GHz radar frequency and 20 dB antenna gain.

From the **Calculation Type** drop-down list, choose
**SNR** as the solution type and set the
**Configuration** as `monostatic`

.

Set the **Gain** to 20, the **Peak Transmit
Power** to 1 kW, and the **Target Range** to 2000 m.

Set the **Wavelength** to 15 cm.

Find the received SNR of a small boat having a **Target Radar Cross
Section** value of 0.5 m^{2}.

The **Pulse Width** is 1 µs and **System Losses**
are 0 dB.

### Related Examples

## Parameters

`Calculation Type`

— Type of calculation to perform

`Target Range`

(default) | `Peak Transmit Power`

| `SNR`

`Target Range`

– solves for maximum target range based on
transmit power of the radar and desired received SNR.

`Peak Transmit – Power`

computes power needed to transmit
based on known target range and desired received SNR.

`SNR`

– calculates the received SNR value based on known
range and transmit power.

`Wavelength`

— Wavelength of radar operating frequency

0.3 m (default) | `m`

| `cm`

| `mm`

Specify the wavelength of radar operating frequency in `m`

,
`cm`

, or `mm`

.

The wavelength is the ratio of the wave propagation speed to frequency. For electromagnetic waves, the speed of propagation is the speed of light.

Denoting the speed of light by *c* and the frequency (in hertz) of
the wave by *f*, the equation for wavelength is *λ* =
*c*/*f*.

`Pulse Width`

— Single pulse duration

1 µs (default) | `µs`

| `ms`

| `s`

Specify the single pulse duration in `µs`

,
`ms`

, or `s`

.

`System Losses`

— System loss in decibels (dB)

0 dB (default)

System Losses represents a general loss factor that comprises losses incurred in the system components and in the propagation to and from the target.

`Noise Temperature`

— System noise temperature in kelvins

290 K (default)

The system noise temperature is the product of the system temperature and the noise figure.

`Target Radar Cross Section`

— Radar cross section (RCS)

`1 m²`

(default) | `m²`

| `dBsm`

Specify the target radar cross section in `m²`

, or
`dBsm`

.

The target radar cross section is nonfluctuating.

`Configuration`

— Type of radar system

`Monostatic`

(default) | `Bistatic`

`Monostatic`

– Transmitter and receiver are co-located
(monostatic radar).

`Bistatic`

– Transmitter and receiver are not co-located
(bistatic radar).

`Gain`

— Transmitter and receiver gain in decibels (dB)

20 dB (default)

When the transmitter and receiver are co-located (monostatic radar), the transmit and receive gains are equal.

This parameter is enabled only if the **Configuration**
is set to `Monostatic`

.

`Peak Transmit Power`

— Transmitter peak power

1 kw (default) | `kW`

| `mW`

| `W`

| `dBW`

Specify the transmitter peak power in `kW`

,
`mW`

, `W`

, or
`dBW`

.

This parameter is enabled only if the **Calculation
Type** is set to `Target Range`

or
`SNR`

.

`SNR`

— Minimum output signal-to-noise ratio at the receiver in decibels

10 dB (default)

Specify an SNR value, or calculate an SNR value using Detection Specifications for SNR.

You can calculate the SNR required to achieve a particular probability of detection and probability of false alarm using Shnidman's equation. To calculate the SNR value:

Click the arrows to the right of the

**SNR**label to open the Detection Specifications for SNR menu.Enter values for Probability of Detection, Probability of False Alarm, Number of Pulses, and Swerling Case Number.

This parameter is enabled only if the **Calculation
Type** is set to `Target Range`

or ```
Peak
Transmit Power
```

.

`Probability of Detection`

— Detection probability used to estimate SNR

0.81029 (default)

Specify the detection probability used to estimate SNR using Shnidman's equation.

This parameter is enabled only when the **Calculation
Type** is set to `Peak Transmit Power`

or
`Target Range`

, and you select the **Detection
Specifications for SNR** button for the **SNR** parameter.

`Probability of False Alarm`

— False alarm probability used to estimate SNR

0.001 (default)

Specify the false-alarm probability used to estimate SNR using Shnidman's equation.

This parameter is enabled only when the **Calculation
Type** is set to `Peak Transmit Power`

or
`Target Range`

, and you select the **Detection
Specifications for SNR** button for the **SNR** parameter.

`Number of Pulses`

— Number of pulses used to estimate SNR

1 (default)

Specify a single pulse, or the number of pulses used for noncoherent integration in Shnidman's equation.

Use multiple pulses to reduce the transmitted power while maintaining the same maximum target range.

This parameter is enabled only when the **Calculation
Type** is set to `Peak Transmit Power`

or
`Target Range`

, and you select the **Detection
Specifications for SNR** button for the **SNR** parameter.

`Swerling Case Number`

— Swerling case number used to estimate SNR

`0`

(default) | `1`

| `2`

| `3`

| `4`

Specify the Swerling case number used to estimate SNR using Shnidman's equation:

– Nonfluctuating pulses.`0`

– Scan-to-scan decorrelation. Rayleigh/exponential PDF–A number of randomly distributed scatterers with no dominant scatterer.`1`

– Pulse-to-pulse decorrelation. Rayleigh/exponential PDF– A number of randomly distributed scatterers with no dominant scatterer.`2`

– Scan-to-scan decorrelation. Chi-square PDF with 4 degrees of freedom. A number of scatterers with one dominant.`3`

– Pulse-to-pulse decorrelation. Chi-square PDF with 4 degrees of freedom. A number of scatterers with one dominant.`4`

Swerling case numbers characterize the detection problem for fluctuating pulses in terms of:

A decorrelation model for the received pulses.

The distribution of scatterers affecting the probability density function (PDF) of the target radar cross section (RCS).

The Swerling case numbers consider all combinations of two decorrelation models (scan-to-scan; pulse-to-pulse) and two RCS PDFs (based on the presence or absence of a dominant scatterer).

**Calculation
Type** is set to `Peak Transmit Power`

or
`Target Range`

, and you select the **Detection
Specifications for SNR** button for the **SNR**
parameter.

`Target Range`

— Range to target

10 km (default) | `km`

| `m`

| `mi`

| `nmi`

Specify target range in `m`

, `km`

,
`mi`

, or `nmi`

.

This parameter is enabled only when the **Calculation
Type** is set to `Peak Transmit Power`

or
`SNR`

, and the **Configuration**
is set to `Monostatic`

.

`Transmitter Gain`

— Transmitter gain in decibels (dB)

20 dB (default)

When the transmitter and receiver are not co-located (bistatic radar), specify the transmitter gain separately from the receiver gain.

This parameter is enabled only if the **Configuration**
is set to `Bistatic`

.

`Range from Transmitter`

— Range from the transmitter to the target

10 km (default) | `km`

| `m`

| `mi`

| `nmi`

When the transmitter and receiver are not co-located (bistatic radar), specify the transmitter range separately from the receiver range.

You can specify range in `m`

,
`km`

, `mi`

, or
`nmi`

.

This parameter is enabled only when the **Calculation
Type** is set to `Peak Transmit Power`

or
`SNR`

, and the **Configuration**
is set to `Bistatic`

.

`Receiver Gain`

— Receiver gain in decibels (dB)

20 dB (default)

When the transmitter and receiver are not co-located (bistatic radar), specify the receiver gain separately from the transmitter gain.

This parameter is enabled only if the **Configuration**
is set to `Bistatic`

.

`Range from Receiver`

— Range from the target to the receiver

10 km (default) | `km`

| `m`

| `mi`

| `nmi`

When the transmitter and receiver are not co-located (bistatic radar), specify the receiver range separately from the transmitter range.

You can specify range in `m`

,
`km`

, `mi`

, or
`nmi`

.

This parameter is enabled only when the **Calculation
Type** is set to `Peak Transmit Power`

or
`SNR`

, and the **Configuration**
is set to `Bistatic`

.

## Version History

**Introduced in R2021a**

## See Also

### Apps

### Functions

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