# rdcoupling

Range Doppler coupling

## Syntax

• `dr = rdcoupling(fd,slope)` example
• `dr = rdcoupling(fd,slope,c)`

## Description

example

````dr = rdcoupling(fd,slope)` returns the range offset due to the Doppler shift in a linear frequency modulated signal. For example, the signal can be a linear FM pulse or an FMCW signal. `slope` is the slope of the linear frequency modulation.```
````dr = rdcoupling(fd,slope,c)` specifies the signal propagation speed.```

## Examples

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### Range of Target After Correcting for Doppler Shift

Calculate the true range of the target for an FMCW waveform that sweeps a band of 3 MHz in 2 ms. The dechirped target return has a beat frequency of 1 kHz. The processing of the target return also indicates a Doppler shift of 100 Hz.

```slope = 30e6/2e-3; fb = 1e3; fd = 100; r = beat2range(fb,slope) - rdcoupling(fd,slope);```

## Input Arguments

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### `fd` — Doppler shiftarray of real numbers

Doppler shift, specified as an array of real numbers.

Data Types: `double`

### `slope` — Slope of linear frequency modulationnonzero scalar

Slope of linear frequency modulation, specified as a nonzero scalar in hertz per second.

Data Types: `double`

### `c` — Signal propagation speedspeed of light (default) | positive scalar

Signal propagation speed, specified as a positive scalar in meters per second.

Data Types: `double`

## Output Arguments

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### `dr` — Range offset due to Doppler shiftreal scalar

Range offset due to Doppler shift, returned as an array of real numbers. The dimensions of `dr` match the dimensions of `fd`.

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### Range Offset

The range offset is the difference between the estimated range and the true range. The difference arises from coupling between the range and Doppler shift.

### Algorithms

The function computes `-c*fd/(2*slope)`.

## References

[1] Barton, David K. Radar System Analysis and Modeling. Boston: Artech House, 2005.

[2] Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005.