BER calculation in DS-UWB system
Assume two discrete-time sequences: $x$ (length $L_\mathrm{x}$) and $y$ (length $L_\mathrm{y}$). Furthermore, $L_\mathrm{x} \geq L_\mathrm{y}$. To calculate the discrete-time (linear) convolution of $x$ and $y$, first pad $y$ with $L_\mathrm{x} - L_\mathrm{y}$ zeros, i.e.
$$
y'(n) =
  \begin{cases}
    y &amp; 0 \leq n &lt; L_\mathrm{y}\\
    0 &amp; L_\mathrm{y} &lt; n \leq L_\mathrm{x} - 1
  \end{cases}
$$
Then calculate the convolution of $y'$ and $x$ as described here, for example.