6. Results¶

When the communication between the USRPs was established, the transmitted constellation below was obtained.

Figure 6.1 Transmitted Constellation

Using the reshape function in LabVIEW, the symbol rate of 62500 symbols/sec is multiplied by the number of samples per symbol, since the demodulator dunction assumes that this would be the sample rate of the input waveform. The received constellation is shown below. The $BER$ in this case is, evidently, 0.

Figure 6.2 Received Constellation without AWGN

The constellation on Figure 6.3 was obtained when adding AWGN, for a target $E_b/N_0$ (received $E_b/N_0$) of 5.The constellation will vary as the values of $E_b/N_0$ vary, making it either noisier, or making it resemble a noiseless channel.

Figure 6.3 Noisy Constellation

With AWGN, the $BER$ is calculated, then compared to the theoretical one, obtaining a $BER$ vs $E_b/N_0$ graph like the one depicted below in Figure 6.4. It can be seen that the simulated $BER$ follows, as expected, the same behavior as the theoretical $BER$, validating simulated results

Figure 6.4 BER vs Eb/No without coding

The $BER$ is also calculated for a the BCH code or a rate of (roughly) 1/2, and compared to the simulated $BER$ without coding. It can be observed from the graph below, that BCH greatly improves the $BER$. In this case, there is a gain of $3dB$ for a $BER=10^-5$

Figure 6.5 BER vs Eb/No with BCH coding