What is the unit-power information signal?

Question

I am learning signal processing for my subject and have some problems with the unit-power information signal. I refer to this paper: https://arxiv.org/pdf/1906.03949.pdf
In this paper, they formulate the received signal as: $y=h_{sd} sqrt{p}s+n$ with $h_{sd}$ is the channel, $p$ is the transmit power, $s$ is the unit-power information signal, and $n$ is the noise.
What is the unit-power information signal? As I understand, the unit-power signal is the signal that has the power of 1. However, how can I formulate it (e.g., using Matlab)? For example, with BPSK signal, the signal is formulated as:
$s_1(t) = A_c cos(2pi f_ct)$ and $s_0(t)=A_c cos(2pi f_ct + pi)$ for bit 1 and 0, respectively.
With a given transmit power $p$, how can I turn $s_1(t)$ and $s_0(t)$ into unit-power signal?
Is there any suggestion or reference?

Matt L. · Answer

The power of a deterministic signal $s(t)$ is given by
$$P_s=lim_{Ttoinfty}frac{1}{2T}int_{-T}^Ts^2(t)dttag{1}$$
A unit power signal is obtained by normalizing $s(t)$ by the root of its power:
$$hat{s}(t)=frac{s(t)}{sqrt{P_s}}tag{2}$$
In the case of $s(t)=Acos(2pi f_0t)$ you obtain from $(1)$
$$P_s=lim_{Ttoinfty}frac{1}{2T}int_{-T}^TA^2cos^2(2pi f_0t)dt=frac{A^2}{2}tag{3}$$
So the corresponding unit power signal is
$$hat{s}(t)=frac{sqrt{2}}{A}s(t)=sqrt{2}cos(2pi f_0t)tag{4}$$

What is the unit-power information signal?

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