-In this episode, we will have a look at the QPSK modulation, the Quadrature Phase Shift Keying modulation. We will see that this modulation allows us to gain a factor two regardingthe bandwidth used by the signal compared to the BPSK modulation from the previous episode. For the QPSK modulation, we use an I-Q modulator. This modulator has two inputs. A binary train on the "in-phase" channel and another one on the "in quadrature" channel. This modulator output is a modulated signal around the f0 carrier frequency. Note that this kind of modulator can only be used for carrier frequency modulations as we will explain later on. What is an I-Q modulator? Let us consider the in-phase channel. It has an input binary train, Bits I. The operations bits-symbols mapping and signal shaping are the same as those for the BPSK modulation. It is the same for the in-quadrature channel. After signal shaping, the two baseband signals enter a carrier frequency shift operation. Let us get back to the in-phase channel. This in-phase channel uses the same bits-symbols mapping and signal shaping than the BPSK modulation. We also get a constellation I, the BPSK constellation. We get the same on the in-quadrature channel. Notice that the bit rate on the in-quadrature channel is the same as the bit rate on the in-phase channel. If we look at the total bit rate, it equals the sum of the bit rates on the in-phase and in-quadrature channels. So it equals two times the bit rate on the in-phase channel and two times the bit rate on the in-quadrature channel. A modulation symbol S is made of two binary elements on the in-phase and in-quadrature channels. We deduce that the symbol rate equals the bit rate on the in-phase channel and equals the bit rate on the in-quadrature channel. That is to say half of the total bit rate. Back to the modulation symbol S. This symbol is made of 2 bits. This means that 4 symbols are possible. This is the reason why this modulation is called Quadrature Phase Shift Keying, QPSK, and also called 4-PSK. Let us look at the constellation of this modulation made of 4 points. We draw constellation I on X-axis and constellation Q on Y-axis. We get this constellation in the plane with, on X-axis, modulation I, and on Y-axis, modulation Q. This modulation is called "bidimensional modulation". Each symbol of the modulation is associated to 2 bits like shown on the slide. We call I(t) the output signal of shaping function . on the in-phase channel. If we consider the spectrum of this signal, in the case of a NRZ-type shaping, we get the following spectrum, the same as the one we had for the BPSK. Remember that the signal power was mainly concentrated in a bandwidth twice as large as the bit rate of this channel, thus 2RbI. But 2RbI, in the case of a QPSK modulation, equals the total bit rate. Let us look at the in-quadrature channel. Q(t) is the output signal of the shaping function. If we look at the spectrum of this signal, we get the same result as for the in-phase channel. This means, in the case of a NRZ-type shaping, that the signal power is mainly concentrated in a Rb-wide frequency band. To conclude, the bandwidths used on channels I and Q are identical. Let us have a look at the frequency shift operation. This operation uses I(t) and Q(t) as input signals. Remember that these I(t) and Q(t) baseband signals use the same bandwidth. We do not know how to superimpose them in baseband. But this superimposition is possible on carrier frequency. Here is how. For the in-phase channel, I(t), we will do the same as for the BPSK modulation. That is to say multiply the baseband signal by cos(2 x pi x f0 x t). For the in-quadrature channel, we multiply the Q(t) signal by -sin(2 x pi x f0 x t). That is to say a -pi/2 phase-shifted version of the signal used for the in-phase signal. The signal on carrier frequency is obtained by summing the two intermediate signals. Note that this frequency transposition allows channels I and Q to be separated upon reception, as we will see it in the "demodulation" part. Let us now have a look at the spectrum of the obtained signal. Let us consider a NRZ-type shaping. The signals on the I and Q channels are baseband signals, thus centered on 0 and spectrally identical. After the frequency transposition, we get a signal centered on the f0 frequency. Just like the BPSK modulation, the bandwidth used compared to the baseband signal has not changed. Let us compare it to the BPSK modulation for a NRZ-type shaping. We have seen in the case of the BPSK modulation that the signal power was mainly concentrated in a 2Rb-wide frequency bandwidth. We just saw in the case of the QPSK modulation that this frequency band equals Rb. So we can conclude that for a given bit rate, the bandwidth used is divided by two when we use a QPSK modulation. We will now conclude this episode. For a QPSK modulation, we have two baseband channels with a same bit rate. The carrier frequency transposition is done in a way to separate channels I and Q upon reception. The bandwidth used by the signal is divided by two compared to the BPSK modulation.