-In this episode, we will see the last modulation class that we will study in this MOOC. PSK modulations, Phase-Shift Keying modulations. What is the difference with QAM modulations we previously studied? It is about the modulation constellation. In the case of the QAM modulation, symbols were distributed on a grid. In the case of the phase modulation, these symbols are distributed on a circle. Here is the I-Q modulator for this modulation. It is the first function, the bits-symbols mapping, that will be different compared to QAM modulations. The other functions, circled in blue, will be identical to those seen for the QAM modulation. Let us take an example, the eight phase-shift keying modulation, 8-PSK. So we have eight symbols. We have three bits per symbol. We note that the symbols will be equally distributed on a circle. This means that the angle between two adjacent symbols equals 2pi/8, thus pi/4. If we look at the symbol associated to bits 000, it is not on the I axis but phase shifted by pi/8. Let us take an example of bits-symbols mapping, the mapping corresponding to bits 000. We have seen that the angle of this symbol with respect to X-axis equals pi/8. We can deduce the values of symbols I and Q: cos(pi/8) and sin(pi/8). The adjacent symbol corresponding to bits 001 is phase shifted by pi/4 with respect to the first symbol. We can deduce the values of the symbols of the in-phase and in-quadrature channels: cos(pi/8 + pi/4) and sin(pi/8 + pi/4). Let us have a look at the signal spectrum and take the NRZ-type shaping as an example. We will have the same spectrum on channels I and Q with power mainly concentrated in a 2RsI bandwidth which also equals 2Rs. Like in the case of the QAM modulation, 2Rs equals 2Rb/m, Rb being the total bit rate and m the number of bits per symbol. After shaping, frequency transposition. We saw in the previous episodes that the bandwidth used does not change. To conclude, we can deduce that for a given bit rate the bandwidth used is divided by a m factor compared to the BPSK modulation, just like the QAM modulation. m being the number of bits per symbol. Let us get back to two modulations we have seen in previous episodes. First case, the BPSK modulation. We have seen that for this modulation, the constellation was made of two symbols, +1 and -1. These two symbols are on a circle. So it is a phase modulation, thus the name BPSK. These two points are also on a flattened grid. So it is also a QAM-type modulation. It is the 2-QAM modulation. Second specific case, the QPSK modulation. We see here the bi-dimensional constellation of this modulation, made of four symbols. These four symbols are on a circle and a grid at the same time. So it is a phase modulation, QPSK, but also a QAM modulation, the 4-QAM. To conclude on phase modulations, they are bi-dimensional modulations just like QAM modulations. The difference with the QAM modulation is that the symbols are on a circle. We also have a factor-m gain on the bandwidth used by the signal compared to the BPSK modulation.