# Why does QAM use two cycles instead of one per byte?

If you look at this image, you can see that you have 256 possible binary values by modulating the amplitude (the radius of the trigonometric circle) and the phase (the degrees) of the carrier. However, multiple diagrams like this one show that each value is actually two cycles long.

My question is why is there two cycles per value instead of one cycle? The constellation only goes to 360 degrees, so why is two cycles used? Wouldn't you be able to transfer data 2x faster if you used one cycle per value?

• It is common to see two (or more) samples per symbol due to pulse-shaping and managing frequency offsets between transmitter and receiver. With pulse shaping considerations alone, you will have some excess bandwidth, so one sample per symbol will not be sufficient. Common carrier tracking and timing recovery techniques (such as the Gardner Timing Error Detector) require 2 samples per symbol. – Dan Boschen Jul 2 '16 at 23:05

It doesn't matter how long you stay on one constellation point. The constellation diagram has NO ties to time whatsoever. The two base vectors $e_x, e_y$ (x-axis and y-axis) represent your real and imaginary part or "basic functions" your signal is made of. For example, if your signal consists of two functions (in this case, QAM, it consists of a real and an imaginary part including the amplitude)
$$e_x = A\cos(2\pi f_{carrier}t) \\ e_y = A\sin(2\pi f_{carrier}t) \\$$