 Hello everyone, welcome to this session. I am Dr. Asha Tharangi and today we are going to learn quadrature phase shift keying that is QPSK modulation technique. At the end of this session you will be able to explain pi by 4 QPSK modulation technique, represent a given bit stream in pi by 4 QPSK form and state the difference between BPSK and QPSK. These are the contents we will be covering in this session. In the last session we discussed MRE signaling scheme. Now, before we discuss QPSK pause this video and recall what is the difference between BPSK and MRE PSK. Well, BPSK is binary modulation technique where only two phase angles are used to represent two symbols where each symbol is made up of single bit 1 or 0. Whereas MRE PSK is multi-level digital modulation technique where M different phase angles are used to represent M symbols where each symbol is made up of N bits such that M is equals to 2 raised to N. We know that in MRE phase shift keying that is MRE PSK M different phase angles are used to represent M symbols. This signal is represented by Si of t is equals to a cos 2 pi fct plus pi of i present for one symbol duration for i 1 to M and pi i is equal to 2 pi by M into i minus 1 plus constant for i equal to 1 to M. For example, when M is equal to 4 and constant equal to 0 then 4 phase shifts of signal are 0 pi by 2 pi and 3 pi by 2 and when M equal to 4 and constant is equals to pi by 4 then the four phase shifts are pi by 4, 3 pi by 4, 5 pi by 4 and 7 pi by 4. Both of these are 4 PSK signals which are different types of quadrature phase shift keying known as conventional QPSK and pi by 4 QPSK. Let us now see QPSK in detail. Quadrature phase shift keying that is QPSK is a type of MRE PSK. The odd numbered data bits from the input bit stream is known as in phase data and the even numbered data bits is known as quadrature phase data. In QPSK two successive bits are combined known as debits to form one symbol and therefore QPSK is represented using four symbols. Here each symbol is made up of one in-phase data bit and one quadrature phase data bit. As there are four symbols each symbol is represented by a signal such that the phase difference between two adjacent symbols is 90 degrees. Board rate of QPSK is equal to one half of the input bit rate. Now depending on the method of modulating the carrier by the in-phase data and the quadrature phase data and the type of carrier used QPSK are classified as conventional QPSK, offset QPSK and pi by 4 QPSK. Let us discuss pi by 4 QPSK in detail. Pi by 4 QPSK is obtained by adding additional pi by 4 phase shift in the phase of the carriers of the symbols that is constant is equals to pi by 4. There is no offset between in-phase and quadrature phase data bits and one pair of quadrature carrier is used for modulation. Table 1 shows the signal representation and their phase shifts for four symbols of pi by 4 QPSK. Let us now study pi by 4 QPSK modulator. Figure shows the block diagram of pi by 4 QPSK modulator. The input bit to be transmitted is converted to bipolar NRZ format. The signal is denoted by B of t and here bit 0 is represented by minus 1 volt and bit 1 is represented by plus 1 volt. The signal is then applied to serial to parallel converter to separate the even and odd numbered bit streams. Here B o of t is odd bit sequence and B e of t is the even bit sequence which are also called as in-phase signal and quadrature phase signal respectively. The in-phase signal or odd bit stream along with the carrier root of P s cos 2 pi f c t is applied to the balance modulator which produces the modulated output as shown. Also the quadrature signal or the even bit signal along with another carrier root of P s sin of 2 pi f c t is applied to another balance modulator which produces the modulated output as shown. Thus two carriers are used which are 90 degrees phase shifted to each other. They are also called as quadrature carriers. The two modulated outputs are then applied to an adder to generate the pi by 4 QPSK signal. Let us see this with an example. Consider the given input bit stream. Here red color bits indicate odd numbered bits and blue colored bits indicate even numbered bits of the input bit stream. The serial to parallel converter separates these even and odd bit stream signals as shown which act as two different modulating signals. The odd bit stream modulates the carrier root of P s cos 2 pi f c t to generate the modulated signal s o of t. And the even bit stream modulates the carrier root of P s sin of 2 pi f c t to generate the modulated signal s e of t. Thus it can be seen that s o of t and s e of t are actually BPSK signals. The symbol duration here is equal to 2 TB. These two BPSK signals are then added to generate the QPSK signal as shown. Thus we can see that when the sequence of the input bit stream is 1 0 the QPSK signal is the carrier phase shifted by pi by 4. When the sequence is 1 1 the QPSK signal is the carrier phase shifted by 7 pi by 4. When the sequence is 0 0 the QPSK signal is the carrier phase shifted by 3 pi by 4 and when the sequence is 0 1 the QPSK signal is the carrier phase shifted by 5 pi by 4. Thus four different phase angles are used to represent the QPSK signal. Let us see the phasor diagram of pi by 4 QPSK signal. QPSK signal is represented by the equation as shown. Cos 2 pi f c t and sin 2 pi f c t are the two quadrature carriers used for QPSK modulation. When the odd bit is 1 and even bit is 0 the QPSK signal s 1 of t for this symbol falls into the first quadrant as shown with the phase shift of pi by 4. The amplitude of QPSK is root of 2 ps. When the odd bit is 0 and the even bit is 0 the QPSK signal s 2 of t for this symbol falls into the second quadrant as shown with a phase shift of 3 pi by 4. When the odd bit is 0 and even bit is 1 the QPSK signal s 3 of t for this symbol falls into third quadrant as shown with the phase shift of minus 3 pi by 4 or 5 pi by 4. When the odd bit is 1 and even bit is 1 the QPSK signal s 4 of t for this symbol falls into the fourth quadrant as shown with the phase shift of minus pi by 4 or 7 pi by 4. Thus figure shows the complete phasor diagram of pi by 4 QPSK signal. Here maximum phase transition of plus or minus 3 pi by 4 is achieved. With this background now pause the video and plot the pi by 4 QPSK signal for the given input bit stream. Let us now derive the expression for bandwidth of QPSK signal. We know that bandwidth of BPSK signal is given by bandwidth is equals to 2 FB where FB is input bit rate and TB is equals to 1 by FB it is 1 bit duration. In QPSK 2 waveforms in phase signal B O of t and quadrature signal B E of t forms the base band signal which are used to get 2 BPSK signals. One symbol period for these signals is TS is equals to 2 TB. Thus bandwidth of QPSK signal is given by BW is equals to 2 upon TS which comes to be FB. Also we can see here that bandwidth of QPSK signal is half of the bandwidth of BPSK signal. Thus in this session we have seen what is pi by 4 QPSK signal, how it is generated and represented and what is the bandwidth of QPSK signal. These are the references used. Thank you.