BER calculation in DS-UWB system I need to calculate BER (bit error rate) for a system using spreading spectrum DS over ultra wideband (UWB). Modulation is bpsk. The spreading sequence lengths are not equal for all users. Receiver is matched filter. I know the equations of DS-UWB transmission signal and template signal which I should use at receiver to extract the user's data. I know that I should use convolution between the received signal (transmitted + AWGN noise) and template signal. My problem is, how to calculate the result of that convolution? is it integration or multiplication?
thanks in advance
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.