Should the transmitted signal be continuous in FMCW?

I am a novice in this field and working on respiration detection through near ultra-sound between $18 \textrm{kHz}$ and $20 \textrm{kHz}$.

In the referece article and other radar use articles, the generated signal was transmitted continuoulsy such as the picture below: My question is what if the interval would be allowed between the signals such as the picture below: I would like to know why the signla be tranmitted continuously and whether it is possible to be transmitted with intervals.

• What is the value of the signal where the gap exists? Note also that all signals that exist in reality are continuous -- it's impossible to create a discontinuous signal.
– MBaz
Sep 25 '17 at 13:41
• If there were gaps in the signal, then it wouldn't be an FMCW signal. "CW" in this context stands for continuous wave, or a sinusoid with constant envelope. Sep 25 '17 at 15:47
• Thank you for all the opinions. Pulsed signals might not useful and I have to check. Actually, pulsed signal seemed to have some information related to the respiration detection in the process of analysis (using x-correlation between intervaled transmitted and received signals rather than using continuous signals). I wanted to check whether it's the valid analysis. My team ignored doppler phase effect in this experimemt, though, interval inserted signal might not a valid way. Sep 26 '17 at 14:51

Let us say the sweep repetition interval is $T_s$, it is the part with frequency modulation. If interval $T_i = T_s/N$ for large N, then drawbacks are: loss of average power, decrease of maximum measurable unambiguous Doppler frequency and it might cause amplifiers to introduce unwanted transients in the signal. Therefore, there is no advantage of adding an interval.

However, if interval $T_i = N*T_s$ for large integer value of N, then it is no longer called an FMCW, rather it will be called LFM, linear FM modulated pulse signal. The processing of which is more complicated than that of FMCW.

The terminology is a bit confusing, so let me try and clarify. From your pictures, you seem to be looking at a chirp sequence radar. In such a signaling scheme, a sequence of linear FM signals (chirps) are transmitted. Each chirp in itself can be considered a "FMCW measurement", yielding a signal with a certain frequency (corresponding to the object distance and a Doppler-term) and phase. In order to resolve velocities of objects, the phase difference between the chirps in the sequence can be evaluated. I will not derive the whole thing here, you can read up on the basics yourself, e.g. here (module 1 is about FMCW, modules 2&3 explain the essence of the chirp sequence approach for velocity measurement).

Now to answer your question, yes you can have a "gap" between subsequent transmit chirps of a sequence. In fact, there probably should be, so as to have some time for the signal generator to "ramp down" before it can "ramp up" again. How much this gap should be depends on your application. The maximum unambiguous velocity you can measure is given by:

$v_{\mathrm{max}} = \frac{\mathrm{c}}{4f_0T_{\mathrm{p}}}$ ,

where $\mathrm{c}$ is the speed of light, $f_0$ the carrier frequency of your transmit signal, and $T_{\mathrm{p}}$ the chirp repetition rate (duration of chirp + what you define as the gap). The velocity resolution is then accordingly $v_{\mathrm{max}}$ divided by the number of chirps you transmit in a sequence.

Of course this is not an exhaustive answer, but hope it helps.

P.S. @Jason R: more precisely, I believe continuous refers to the transmit signal being of a duration much longer than the delay from object reflections so that transmission and reception happens at the same time (as opposed to pulsed radar where you essentially send a very short pulse and then "wait" for the reflections).