Results¶

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

Figure 2.2 Transmitted Constellation

Using an IQ sampling of 500k, obtaining a symbol rate of 62500 symbols/sec, without any noise, the received constellation is shown below. The $BER$ in this case is, evidently, 0.

Figure 2.2 Received Constellation without AWGN

The constellation on Figure 2.3 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 2.3 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 2.4. It can be seen that the simulated $BER$ follows, as expected, the same behavior as the theoretical $BER$.

Figure 2.4 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 2.4 BER vs Eb/No with BCH coding