What is the expected response of a Linear Frequency Modulated signal transmitted through 'Free Space' and 'Wideband Free Space' blocks?

https://www.mathworks.com/help/phased/ref/freespace.html#buiomyb-1 What is the expected frequency response when a linear frequency modulated pulse (chirp) is transmitted through a 'Free Space' or 'Wideband Free Space' block? The pulse in question will look something like the below spectrogram:

The 'Free Space' and 'Wideband Free Space' blocks have a carrier frequency associated with them that transform the above signal from baseband into a one-sided signal at the desired carrier frequency.

Why does the response have low edges as in the below image:

Answer 1

[MathWorks Support Team]

The input LFM signal in this example is from -75 MHz to 75 MHz.  The “Free Space” block is designed for a narrowband signal.  As the bandwidth of the input signal is 150 MHz and the carrier frequency is 10 GHz, the bandwidth is only 1.5% of the carrier frequency and is sufficiently small for the narrowband approximation to hold.  This means that this block is sufficient for these parameters.

Because this block is a narrowband model, it assumes the entire signal is attenuated equally.  The attenuation on the edges of the signal band is an artifact of the sampling rate; I was able to reproduce a flat response by increasing the sampling rate of the generated LFM signal.

For more information on the “Free Space” block, please refer to the following link:

https://www.mathworks.com/help/phased/ref/freespace.html

The other potential option for this model is the “Wideband Free Space” block.  For more information on the “Wideband Free Space” block, please refer to the link below:

https://www.mathworks.com/help/phased/ref/widebandfreespace.html

This block does not make the narrowband assumption and will display frequency dependent attenuation.  At a carrier frequency of 10 GHz, the two blocks will not display much difference in response.  The below image shows the frequency response of the LFM signal at a carrier frequency of 10 GHz with a sample rate of 512 MHz.

When the carrier frequency is changed to 300 MHz, the difference between the “Free Space” and “Wideband Free Space” blocks is more apparent:

The “Wideband Free Space” block can be used with the same inputs as the “Free Space” block.  It has an additional parameter, “Number of subbands”, to configure the number of subbands for processing.

The attenuation in the above response is given by the equation here:

https://www.mathworks.com/help/phased/ref/freespace.html#buiomyb-1