# pulse amplitude modulation

MPAM

In terms of the signal space representation, we set the quadrature component (encoded on \(\phi_2\) or \(\sin\)) to be 0.

\begin{equation}
s_i(t) = A_i g(t) \cos(2\pi f_c t)
\end{equation}

Where \(A_i = d(2i - 1 - M)\) where \(M\) is the signal constellation.

PAM is parametrized by \(d\) which is a function of signal energy, and the distance between two points on the signal constellation is \(2d\).

Average energy is given by

\begin{equation}
E = \frac{1}{M}\sum_{i =1}^{M}A_i^2
\end{equation}

Note that because the "sine" component is zero, the constellation diagram is a line.