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Additional resources for LabVIEW digital signal processing: and digital communications
As long as we can maintain that SNR, we can transmit data at a given rate and keep our probability of a bit error below our required threshold. Let us take a look at the following example, which illustrates the relationship between PM and SNR. 1: SNR versus Probability of Error For this example, we will use the signal shown in Figs. 8. 2. We want the system to have a maximum symbol error rate of 10−3. The first step will be to rearrange Eq. 4) to solve for the Q( ) function in terms of the symbol error probability.
48 from the table and now solve the following equation for EAV/N0. 552 3 N0 (c) Finally we have to normalize the given SNR per symbol to the symbol rate divided by bandwidth as in Eq. 5). To use Eq. 5) though, we must first know the bandwidth W. Again we can look at Ref. 2, the excess bandwidth, from Eq. (c) and insert Eq. (d) into Eq. 5) for W. 2 or approximately 20 dB. This exercise is mostly academic in that many digital communication texts contain plots of the required SNR per symbol (or per bit) versus probability of a bit error for some of the more common modulation schemes.
3. The other notable feature (or lack thereof) in this example is that the input size is not a power of 2. In this case, the complex FFT routine is actually implementing a complex discrete Fourier transform (DFT). If we want to ensure that an FFT is always performed, we will have to pad the data size up to the next power of 2 as shown in the improved VI in Fig. 3. Does it really matter whether the function performs an FFT or a DFT? From the discussion in , we can estimate that the computation of the DFT generally requires N 2 complex multiplications, where N is the number of points in the DFT.