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:

$s_1(t) = A_c \cos(2\pi f_ct)$ and $s_0(t)=A_c \cos(2\pi f_ct + \pi)$ 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?


1 Answer 1


The power of a deterministic signal $s(t)$ is given by


A unit power signal is obtained by normalizing $s(t)$ by the root of its power:


In the case of $s(t)=A\cos(2\pi f_0t)$ you obtain from $(1)$

$$P_s=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^TA^2\cos^2(2\pi f_0t)dt=\frac{A^2}{2}\tag{3}$$

So the corresponding unit power signal is

$$\hat{s}(t)=\frac{\sqrt{2}}{A}s(t)=\sqrt{2}\cos(2\pi f_0t)\tag{4}$$

  • $\begingroup$ Thanks Matt for the helpful answer. $\endgroup$
    – Fzzyy
    Commented Jul 25, 2020 at 2:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.