# Doppler radar pulsed signal: Matlab analysis

|## Doppler Radar System Description

The Doppler radar performance makes an optimum use of the transmitted power and its weight is appropriate to be used in aircrafts. In addition, it’s crucial in military applications because it can detect objects that are moving fast and it’s able to eliminate the effect from the weather or other obstacles in the way. The Synthetic Aperture Radar (SAR), applied in astronomy, is based on this principle and it’s built with an antenna array.

A pulsed radar transmits a burst of pulses and it samples the received echo. Let’s assume we have the following radar system:

- Number of pulses in a burst: 32 pulses
- Number of resolution cells: 9
- PRI: 200 us
- Radar frequency: 17 GHz

The following diagram shows the pulse of the burst and the sampling times which correspond with the 9 resolution cells:

Therefore, the first 9 samples correspond with Pulse 1, the following 9 samples with Pulse 2 and so on, till we get a total of 288 samples.

## Doppler Processing

The Doppler processing consists in:

– For each resolution cell:

- Group the samples of all the pulses corresponding to that distance
- This group of samples will be affected by phase shifts due to the Doppler frequency: it will have a sinusoidal shape if there is a moving echo with a Doppler frequency
- Calculate the DFT of these samples. Each of these samples corresponds with a Doppler frequency and a speed, according to the following formulae:

- In this case:
- Sample #0 corresponds with speed 0
- Sample #1 corresponds with speed Av
- Sample #i corresponds with speed i·Av

- By inspecting the DFT:
- Sample #0 corresponds with a static clutter
- We are looking for mobile targets: we need to find the speeds different from zero, a peak over the background noise: we need to set a threshold empirically
- We can calculate the speeds corresponding to each target

- Repeat the process for each resolution cell

## Doppler Radar Echoes Graphic Analysis

The following image is a representation of the received echoes against their distance:

In this graph, we can observe the obstacles’ profile extracted from the 32 received echoes. The threshold level is not clear but we can place it in an amplitude of 1.5, approximately. The reason why this threshold is not entirely accurate is that there can be many echoes very close, but these echoes won’t necessary be from the target.

We can also estimate the resolution cells where the targets are: these are the cells 3, 6 and 8.

Analysing the FFT of the previous graph, we can obtain more information:

In this case, after measuring with the Matlab pointer, we can situate the threshold in a power amplitude of %, so the pulses that don’t pass the threshold won’t be counted as targets. From this graph, we can also deduce that there are 3 mobile targets in the speeds: 1.5, 2.2 y 2.8 m/s, respectively: the targets are moving at these speeds.

Note that we just analyse half of the frequency representation because in the frequency domain, there are replicas which contain the same information repeated.

## Conclusions and Considerations

From the previous graphs, we can conclude that we need to establish a trade-off between the detection probability and the false alarm probability. The Marcum curves provide the detection probability as a function of the radar coverage under noise and free of noise conditions.

In addition, from the frequency processing, we need to be careful with certain principles, such as the fact that if the Doppler frequency is an integer number of the frequency resolution in order to avoid the leakage effect.

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