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

  • $\begingroup$ It's not so clear what you're asking. Convolution is...convolution. It involves multiplicaton and integration. $\endgroup$ – Deve Jun 29 '13 at 10:45
  • $\begingroup$ @Deve thanks for response. Can you tell me some reference where I can find details how mathematically the convolution output is calculated for ds-uwb? $\endgroup$ – Mohammed Jul 1 '13 at 9:49
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    $\begingroup$ I'm afraid I can't. What makes the convolution in DS-UWB different from a conventional convolution? $\endgroup$ – Deve Jul 1 '13 at 11:50
  • $\begingroup$ @Deve Actually this is my problem, I don't know how to calculate convolution between two sequences with different lengths. $\endgroup$ – Mohammed Jul 1 '13 at 12:46

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. $$ y'(n) = \begin{cases} y & 0 \leq n < L_\mathrm{y}\\ 0 & L_\mathrm{y} < n \leq L_\mathrm{x} - 1 \end{cases} $$ Then calculate the convolution of $y'$ and $x$ as described here, for example.

  • $\begingroup$ The zero-padding is not required. It will just increase the amount of multiplications and since most of them will have one factor of zero, nothing is gained. $\endgroup$ – jan Aug 1 '13 at 9:55

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