THE RWS-434 RECEIVER REQUIRES A REGULATED 5 VDC POWER SUPPLY
THE TRANSMITTER WILL OPERATE FROM 3.0 TO 5.5 VOLTS DC
Since I am wanting this device to be fairly small in size, I thought I could use a small 9 volt battery with a 5 volt (7805) regulator. I was told that this was very inefficient so now I’m back to zero. But yes, I have thought of using 3 AAs or AAAs in series, but would this last very long? Is there anything smaller? I mean, look at a car remote starter/remote lock on a keychain. How can I get my device to be SMALL?
Three AAA cells will have more capacity than a 9v battery feeding a regulator, and three AA cells will have around 3 times the capacity of the AAA cells. As Leon said, you need to measure the current drain of the devices and select your power source based on that and the amount of time you need to have the device powered. The datasheet for the receiver and transmitter is available at the link you supplied. The receiver draws a maximum of 4.5 milliamps, so I think your batteries could last for a while: