What kind of modulation is this?
Ok I did some signal forensics on the data capture and believe the modulation is a form of FSK.

The FSK modulation was +/- 20 KHz with a data rate of 38 KHz.  



UPDATE:  The OP discovery that this is "io-homecontrol" and the datasheet from ADI that he found has confirmed that this is indeed FSK with a deviation of 20KHz and 38.4 Kbps data rate.  Further this link gives more details on the modulation format: 

https://cansecwest.com/slides/2015/From_Baseband_to_bitstream_Andy_Davis.pdf

It looks like it may actually be Gaussian-FSK, with full-response signalling (BT=1), meaning the response for each bit is completed before the next bit starts. This can be easily implemented with a Gaussian filter (see Gaussian FIR filter with no multipliers?) followed by an NCO. In this case each data bit is represented as impulses followed by zeros for the full length of the filter and the output of the filter drives the frequency control word into the NCO (a digital VCO). (For partial-response signalling which requires a more complicated receiver and not what they are doing here, the zeros are shorter than the length of the filter, but that would also work).  Frequency deviation can be set with a multiplier gain constant between the filter output and NCO input. The choice to go with Gaussian FSK vs simple FSK is for better spectral containment in the transmitted waveform (and is the reason for the rounded transitions that we see).



I will include the plots in case anyone has further insight:

First a macro view in vicinity of the first burst, occurring around 0.93 seconds. To get this plot, I had removed a frequency offset corresponding to 0.2688 radians/sample after decimating by 10 samples, assuming the original sampling rate was 3 MHz, this corresponds to a 12.834KHz offset. 

This plot shows the unwrapped phase vs time (vertical axis is radians) and the corresponding magnitude vs time. I assume when the magnitude is low that we are viewing the noise, and the signal of interest is occurring only when the magnitude is higher.

  

Zooming in on the first part of the burst, the pulse starts at approx 0.9265 seconds, and at the start of the burst, the phase is "flat" for approximately 3 ms.  Corresponding to an unmodulated carrier, I believe, from comparing to the detail we see later.





After the 3 ms of the "flat phase" portion, there is a very long pattern of what appears to be 1 0 1 0 1 0 with a data rate of 37.5 KS/s.  The modulation is going between 0 and 180 degrees, but later we will see clear phase ramps making me suspect FSK instead of BPSK. (If it was MSK I would have expected to see evidence of 90 degree rotations, but the minimum rotation I found was 180 degrees).
Note at the very start of the pattern (assuming +180 =1 and -180 =0), we see 1 1 0 1 0 1 0 1... which then lasts with the 1 0 1 0 pattern for approx 90 ms before again inserting a "1 1" near the 1.02 second mark, and then continuing again as 0 1 0 1 0 1...  until the 1.414 second mark. (approx 0.4 seconds duration with a 1 0 1 0 pattern).  Note the "hump" in the overall trajectory; I believe that we are just seeing the wandering of the clock (either the radio or the sampling clock that took the data) given the long time durations involved.  







At 1.414 seconds the real data starts. (The first was probably a sync/acquisition pattern).  Looking first at a macro view we see a pattern that at this view appears to repeat 3 times before the burst ends.



Zooming in on the first region, we see consistent positive and negative phase sloped indicative of FSK. At the end of the data burst there is a long duration of 1's for 4 ms followed by the 101010 pattern again for about 14 ms. 





The next burst starting around 1.51 seconds, shortly after the first one again has the same starting pattern of an unmodulated carrier followed by the 101010 long modulation pattern.  (Although slightly different in that the start was 1 1 1 1 0 1 0 1 0 1 0 1 but the duration of the 1010 pattern before the data modulation was again 14 ms)