If you search through the older threads on the forums (here and elsewhere) you will find that a number of folks have been frustrated when trying to connect various single-ended sources to the DR-40.
It IS frustrating, but the engineers apparently designed the thing to be used with "professional" gear, and to work with balanced inputs only.
When I bought my DR-40 I was hoping to use it with my conrad-johnson stereo preamp to "rip" digital copies of my vinyl records. The C-J preamp has typical single-ended RCA outputs, and the recordings I made were unacceptably low in level.
Read through this thread:
https://www.tascamforums.com/threads/dr-40-recording-volume.6051/
If you connect a single-ended 1/4 inch plug to the input of the DR-40 it shorts the ring terminal to ground, bypassing the entire "cold" side of the differential input amplifier. You lose half of the gain, and recordings made that way will be reduced by -6dB.
If you connect a source that has plenty of gain, like a mixer console, you will be able to make a decent recording. But connecting a "consumer level" output (like a home stereo preamp, or, apparently, the receiver of the Alvoxcon wireless mic) won't work well.
I addition, you will lose the advantage of the noise reduction of the differential inputs.
If you look through the Reference Manual and the Owner's Manual for the DR-40 they indicate only that the input should be balanced TRS hot-cold-ground. There is no mention of any provision for connecting single-ended signals.
As I mentioned, some portable digital recorders ARE designed to work with single-ended inputs, but they have enough gain to work with consumer line level signals.
I think the designers of the DR-40 expected it to be used with pro-level signals.