# Documentation

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## FMCW Range Estimation

The purpose of FMCW range estimation is to estimate the range of a target. For example, a radar for collision avoidance in an automobile needs to estimate the distance to the nearest obstacle. FMCW range estimation algorithms can vary in the details, but the typical high-level procedure is as follows:

1. Dechirp — Dechirp the received signal by mixing it with the transmitted signal. If you use the `dechirp` function, the transmitted signal is the reference signal.

2. Find beat frequency — From the dechirped signal, extract the beat frequency or pair of beat frequencies. If the FMCW signal has a sawtooth shape (up-sweep or down-sweep sawtooth shape), you extract one beat frequency. If the FMCW signal has a triangular sweep, you extract up-sweep and down-sweep beat frequencies.

Extracting beat frequencies can use a variety of algorithms. For example, you can use the following features to help you perform this step:

• `pwelch` or `periodogram`

• `psd`

• `findpeaks`

• `rootmusic`

• `phased.CFARDetector`

3. Compute range — Use the beat frequency or frequencies to compute the corresponding range value. The `beat2range` function can perform this computation.

While developing your algorithm, you might also perform these auxiliary tasks:

• Visualize targets in the range-Doppler domain, using the `phased.RangeDopplerResponse` System object™.

• Determine whether you need to compensate for range-Doppler coupling. Such coupling can occur if the target is moving relative to the radar. You can use the `rdcoupling` function to compute the range offset due to range-Doppler coupling. If the range offset is not negligible, common compensation techniques include:

• Subtracting the range offset from your initial range estimate

• Having the FMCW signal use a triangle sweep instead of an up sweep or down sweep

• Explore the relationships among your system’s range requirements and parameters of the FMCW waveform. You can use these functions:

• `range2time`

• `time2range`

• `range2bw`

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