Why the average signal power should be 1 When I read some books or papers related into signal modulation, for example, frequency-domain OFDM signal, it's always mentioned that the average power of signal is assumed to be 1.
Why does that assumption is taken? what's if that average signal power is more or less than one?
Assuming an average power of one for a signal, or for the noise, is a common assumption, mainly to simplify equations. It is assumed that for other powers, a scaling by the actual power can be done.
For instance, many denoising techniques set a threshold that is proportional to the noise power (the square root of it). In the theory, one often assumes (for computations) that $\sigma=1$, design an optimal $\lambda$ and set the actual threshold to $\lambda \sigma$.
The actual threshold is multiplied according to the estimated noise amplitude.