That is correct: you will need a new receiver and transmitter. Many here recommend a FlySky radio system. Personally I like Spektrum just fine and the Dx2E radio with SR210 receiver are a good, low-cost option.
And any other system you get WILL be better than the Rx/ESC combo unit that came with the AMP.
Check out >
this post<, scroll down a bit and you'll see a photo of the electronics layout in my my AMP (now, technically a Circuit, but they are 99% the same so... whatever) with a Hobbywing Justock ESC and Spektrum SR310 receiver. The SR210 is two channel and the same physical size as the 310 (three channel). So the receiver is actually smaller than the stock AMP Rx/ESC combo unit.