-We will now have a look at the demodulation operation. Let us consider the demodulator also called the receiver. The input of the demodulator is the output of the communication channel. So we have a noisy and distorted signal as explained in episode 1. In this episode, we will only consider the impact of noise. So we will only consider the noisy signal. The first implemented function is the I-Q demodulator. At the input of this demodulator, we have a continuous noisy signal. At the output of this demodulator, we will get samples at the symbol period that will form a noisy constellation which we will detail. From the samples of this noisy constellation, we will make a decision on the transmitted symbols thanks to a symbol decision function. We are not interested in the transmitted symbols but rather in the transmitted bits. So we have to perform the reverse operation to the one done in the modulator, that is to say bits-symbols demapping. Let us illustrate this with the QPSK modulation. Here is the emission constellation. We recognize the four symbols that form the QPSK modulation. At the output of the I-Q demodulator, we do not have four points anymore but four point clouds. Each point corresponds to a noisy symbol. In order to make a decision regarding the transmitted symbols, we define decision zones for the symbols and thus for the bits. The first decision zone is the upper right corner. For each sample received in this zone, we decide that the transmitted symbol is the center of the red cloud in the upper right corner, corresponding to bits 11. Second decision zone, the upper left corner. For each received sample in this zone, we choose the symbol at the center of the red cloud, corresponding to bits 01. This way we define four decision zones with four associated symbols each time and, for each symbol, two bits. Let us have a look at the impact of noise on the received constellations. The noise level on the right-hand constellation is higher than the noise level on the left-hand constellation. Let us now look at the impact of noise on the symbol error rate or the bit error rate. For that purpose, we assume that we always transmit the same symbol corresponding to bits 11. The samples at the output of the I-Q demodulator are the red cloud. The decision zone for the symbol corresponding to bits 11 is the upper right corner. We note that errors will occur. These errors are defined in blue here. If we increase the noise, what will happen? The number of samples that fall outside the decision zone increases. The number of erroneous symbols, and thus the number of erroneous bits, will increase. The bit error rate will increase. Here is an important observation. In this constellation, there is a certain signal and noise levels. We multiply the signal and noise power by four. What do we notice? The number of samples falling outside the decision zone does not change. We can deduce that the error rate does not change and that the relevant parameter will not be the power of the signal or the power of noise alone. It will be the ratio between the signal power and the noise power. This ratio will be called SNR. The SNR is the ratio between P, the signal power, and Pb, the noise power. The noise power is defined in a B bandwidth. N0 is the noise power in a 1-Hz bandwidth. It is the spectral density of noise. During week 5, in the "Link budget" sequence, you will see how to determine this N0 value. The noise power in a B bandwidth thus equals the noise power in 1 Hz multiplied by the bandwidth in which this noise is calculated. We can deduce that the SNR equals P divided by N0 multiplied by B. In practice, what value will we choose for B? Rb, the bit rate, for example. If Rb = 55 Mbit/s, we will have B = 55 MHz. We note that P/N0Rb equals PTb/N0. But according to the definition of energy, PTb is the energy per bit that we note Eb. We can deduce that the SNR equals Eb/N0. This Eb/N0 parameter is essential. We will see it in the next sequence. To conclude this episode, we can say that decisions regarding symbols are made from the samples of a noisy constellation. For a given constellation, the bit error rate depends on the ratio between the signal power and the noise power.