Since I rely on these forums to help me out, I'll post my experience and the solution that worked for me.
I had already been using the cm15a and TM751's. I had tried removing the TM751's when I upgraded to the cm15a from the cm11a, but the reception / range of the cm15a wasn't adequate.
I left the TM751's in place.
Then I got the OnAlert plugin to integrate the security devices I already had. The reception range of the cm15a was not adequate, even though my security console had no problems receiving the signals from the security sensors. I tried using an SR731 rf transceiver that I already had from another package deal. But it did not help.
I only had 1 out of 4 door sensors working with the cm15a, and it was the closest, through a few walls and about 20' away.
So I twisted the white antenna tube off of the cm15a, it was not glued, just came off with no problem, leaving the antenna wire visible.
I stripped about 1/4" of insulation from the end of the antenna wire and soldered on a 4 ft wire extension.
I got one of the wires from some phone line I had... 4-conductor solid copper phone line (in-wall type).
I ran the wire from the cm15a (which is plugged into an outlet behind a chair) about 1ft horizontally to the trim of a closet doorway, and then vertically along the edge of the door trim.
The wire is located where the trim meets the wall.
The next closest sensor then started working.
Then I stripped about 2 ft of the insulation from the end of the wire.
All sensors were then working.
I then added a longer length of bare wire to extend up and across the doorway along the edge of the trim.
Distance from antenna to farthest sensor is about 60 ft.