Adjusting Transmission Power for QAM

If I transmit the 4-QAM symbol '1.00 + j1.00' but I then wanted to transmit it again at a quarter of the same transmit power. Do I simply divide '1.00 + j1.00' by 4 or do I need to do something different as I am dealing with power?

Thanks.

Answer 1

[Drew Davis]

If the amplitude of a symbol is Si then the power is proportional to the distance from the origin to the constellation point

power = |Si|^2 / 2

Therefore if you want a signal with quarter power

power / 4 = |Si_new|^2 / 2
|Si_new| = (power / 2)^0.5 = (|Si|^2 / 4)^0.5 = |Si| / 2

Thus the magnitude of the new signal should be half the magnitude of the old signal