Lecture psk qam, digital modulation
- 1. Phase Shift Keying ■ We shift the phase of the carrier signal to represent digital data. ■ How much shift is possible? 125
- 2. Binary Phase Shift Keying (BPSK) © Dr. Aimal Khan 126
- 3. Binary Phase Shift Keying (BPSK) ■ How much shift is possible? © Dr. Aimal Khan 127
- 4. Implementation of BPSK V V © Dr. Aimal Khan 128
- 5. BPSK 0 1 129
- 6. © Dr. Aimal Khan M-ary Phase Shift Keying ) 2 2cos( 2 M i tf T ES csi Mi Tt ,...,2,1 ,0 ■ There can be multiple levels, generally they are equal to 2 power of number of bits. ■ When multiple levels than we must map the bits to different levels ■ This can increase spectral efficiency ■ Cannot be implemented as BPSK given above, next slides explain how to implement ) 2 2cos( M i tfVS ci 130
- 7. © Dr. Aimal Khan M-ary PSK implementation ) 2 2cos( 2 M i tf T ES csi Mi Tt ,...,2,1 ,0 )2sin( 2 ) 2 sin()2cos( 2 ) 2 cos( )2sin() 2 sin()2cos() 2 cos( 2 )( tf TM i Etf TM i ES tf M i tf M i T ES cscsi ccsi )sin()sin()cos()cos()cos( 131
- 8. © Dr. Aimal Khan Conversion from M-levels (angle) to constellation points ) 2 2cos( 2 M i tf T ES csi Mi Tt ,...,2,1 ,0 )2sin( 2 ) 2 sin()2cos( 2 ) 2 cos( )2sin() 2 sin()2cos() 2 cos( 2 )( tf TM i Etf TM i ES tf M i tf M i T ES cscsi ccsi )sin()sin()cos()cos()cos( Inphase Component Quadrature Component 132
- 9. © Dr. Aimal Khan Mapper Pulse Shaping Multiplier M-ary ASK General Modulator Structure 000...00 000...01 . . . 111...11 Antenna MV V V . . . 2 1 133
- 10. © Dr. Aimal Khan Mapper Pulse Shaping M-ary PSK General Modulator Structure 000...00 000...01 . . . 111...11 Antenna XMXX VVV ..., 21 )2cos( 2 tf T c Pulse Shaping )2sin( 2 tf T c + - Inphase Quadrature X X QMQQ VVV ..., 21 134
- 11. © Dr. Aimal Khan Two Dimensional Symbol similar to a Point in Cartesian Coordinate System ),( QiXii VVV Mi ,...,2,1 135
- 12. © Dr. Aimal Khan Implementation of 4-PSK (QPSK) ■ Explained on the board 136
- 13. © Dr. Aimal Khan Mapper for M=4 QPSK 00 ) 12 cos( M E s ) 12 sin( M Es Inphase Quadrature i=1 sE 01 ) 22 cos( M Es ) 22 sin( M Es i=2 =0sE 0 2XV 2QV 1XV 1QV 137
- 14. © Dr. Aimal Khan 10 ) 32 cos( M Es ) 32 sin( M Es Inphase Quadrature i=3 =0 sE 11 ) 42 cos( M Es ) 42 sin( M Es i=4 =0sE Mapper for M=4 QPSK 3XV 4QV 3QV 138
- 15. 5.139 Constellation Diagrams ■ A constellation diagram helps us to define the amplitude and phase of a signal when we are using two carriers, one in quadrature of the other. ■ The X-axis represents the in-phase carrier and the Y- axis represents quadrature carrier.
- 16. Conversion from M-levels (angle) to constellation points Graphically M i2 ) 2 2cos( 2 M i tf T ES csi © Dr. Aimal Khan 140
- 17. M i2 ) 2 2cos( 2 M i tf T ES csi ) 2 cos( M i Es ) 2 sin( M i Es Conversion from M-levels (angle) to constellation points Graphically © Dr. Aimal Khan 141
- 18. M i2 ),( QiXii VVV Mi ,...,2,1 XiV QiV ) 2 2cos( 2 M i tf T ES csi Conversion from M-levels (angle) to constellation points Graphically © Dr. Aimal Khan 142
- 19. © Dr. Aimal Khan Relationship of Average Symbol Energy and Pulses Amplitudes ),( QiXii VVV Mi ,...,2,1 22 2 , QiXi isis VV VEE ■ From the previous constellation diagram it can be show that 143
- 20. QPSK Constellation Diagram Inphase axis Quadrature axis )0,(),( ),0(),( )0,(),( ),0(),( 444 333 222 111 sQX sQX sQX sQX EVVV EVVV EVVV EVVV 144
- 21. QPSK Constellation Diagram Inphase axis Quadrature axis )0,(),( ),0(),( )0,(),( ),0(),( 444 333 222 111 sQX sQX sQX sQX EVVV EVVV EVVV EVVV 00 01 10 11 145
- 22. Average Energy of a PSK symbol M i2 © Dr. Aimal Khan 146
- 23. © Dr. Aimal Khan Example of 8-PSK ■ Explained on the board 147
- 24. 8-PSK Constellation Diagram Inphase axis Quadrature axis ■ Further completed and explained on the board 148
- 25. Quadrature Amplitude Modulation (QAM)/ Amplitude Phase Shift Keying ■ We shift the phase of the carrier signal as well as the amplitude to represent digital data. ■ How many dimensions we have to modulate? ■ Thus it is the combination of ASK and PSK 149
- 26. Some Applications of QAM ■ 3G and 4G uses 16-QAM and 64-QAM ■ 64-QAM and 256-QAM are often used in digital cable television ■ 16-QAM and 64-QAM are currently used for DVB 150
- 27. M-ary QAM or M-QAM Mi Tt ,...,2,1 ,0 )2cos( icii tfVS Inphase axis Quadrature axis Example of non-square 4 QAM 151
- 29. © Dr. Aimal Khan Mapper Pulse Shaping M- QAM General Modulator Structure 000...00 000...01 . . . 111...11 Antenna XMXX VVV ..., 21 )2cos( 2 tf T c Pulse Shaping )2sin( 2 tf T c + - Inphase Quadrature X X QMQQ VVV ..., 21 153
- 30. Constellation Diagram for Square 4-QAM Inphase axis Quadrature axis d d 154
- 31. Mapper for Square 4-QAM Inphase axis Quadrature axis d d is mapped to is mapped to is mapped to is mapped to 155
- 32. Constellation Diagram for Square 8-QAM Inphase axis Quadrature axis 156
- 33. Constellation Diagram for Some 8-QAM Inphase axis Quadrature axis d d 157
- 34. Constellation Diagram for Square 16-QAM Inphase axis Quadrature axis 2d 2d 2d 2d 2d 2d 158
- 35. Constellation Diagram for Square 32-QAM Inphase axis Quadrature axis 2d 2d 2d 2d 2d 2d 2d 2d 2d2d 159
- 36. Constellation Diagram for Square 64-QAM Inphase axis Quadrature axis 2d 2d 2d 2d 2d 2d 2d 2d 2d2d 2d 2d 2d2d 160
- 37. How to calculate the average Symbol Energy of QAM? Inphase axis Quadrature axis 2d 2d 2d 2d 2d 2d 161
- 38. How to calculate the average Symbol Energy of QAM? Inphase axis Quadrature axis 2d 2d 2d 2d 2d 2d 22 , QiXi iis VV VE M i iss E M E 1 , 1 2 2 10 160 16 1 d dEs Example of 16 QAM with energy of each symbol on its top For Square 16-QAM ith symbol energy Average Symbol Energy 162
- 39. Finding d from Average Symbol Energy If the average symbol energy is given and we need to find d for any Square M-QAM from that average energy Calculate the average symbol energy in terms of d as given on the previous slides Equate d from the resulting solution e.g. For Square 16-QAM 2 2 10 160 16 1 d dEs 10 sE d 163
- 40. Natural Mapping Vs Gray Mapping ■ So far discussed that we can map them anywhere we desire, now ■ Natural Mapping: Just enumerates the symbols in binary form starting normally from the lowest value or phase ■ In Gray mapping: maximum 1 bit difference between Neighour symbols 000 001 010 011 100 101 110 111 000 001 010011 110 111 101 100 8-ASK in Natural Mapping 8-ASK in Gray Mapping 164
- 41. Inphase axis Quadrature axis 000 001 010 011 100 101 110 111 000 001010 011 110 111 101 100 Inphase axis Quadrature axis 8-PSK in Natural Mapping 8-PSK in Gray Mapping Natural Mapping Vs Gray Mapping 165
- 42. Natural Mapping for Square 16- QAM Inphase axis Quadrature axis 2d 2d 2d 2d 2d 2d 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 166
- 43. Gray Mapping for Square 16- QAM Inphase axis Quadrature axis 2d 2d 2d 2d 2d 2d 0000 0001 00100011 0100 0101 01100111 1000 1001 10101011 1100 1101 11101111 167
- 44. 168
- 46. © Dr. Aimal Khan Bandpass Demodulate Detector Pulse to Samples Receive Filter Sampler )2cos( 2 tf T c 170
- 47. © Dr. Aimal Khan Bandpass Demodulation/ASK Mapper Pulse Shaping LPF X X Channel Bandpass Modulator Bandpass Demodulator )2cos( 2 tf T c )2cos( 2 tf T c )2cos( 2 tf T c )2cos( 2 tf T c 171
- 48. )2cos( 2 )()( tf T tvts c T tv tr tf T tv T tv tf T tv tf T tvtr tftf T tv tf T tf T tvtr c c c cc cc )( )( ))22cos( )()( ))22cos(1( 2 12 )( ))22cos()0(cos( 2 12 )()( 2 )cos()cos( )cos()cos(thatknowwe )2cos()2cos( 2 )( )2cos( 2 )2cos( 2 )()( This Signal is at double the carrier frequency so will be filtered out by the low pass filter (LPF) )2cos( 2 )()( tf T tvtr c We assume no channel effects here for simplicity, therefore, transmitted signal s(t) is equal to the received signal r(t) © Dr. Aimal Khan 172
- 49. X+9p © Dr. Aimal Khan Bandpass Demodulation of PSK, QAM Mapper Pulse Shaping LPF X X Channel Inphase Bandpass Modulator )2cos( 2 tf T c )2cos( 2 )( tf T tv cX Pulse Shaping X Quadrature Bandpass Modulator )2sin( 2 tf T c )2sin( 2 )( tf T tv cQ + X Inphase Bandpass Demodulator )2cos( 2 tf T c X Quadrature Bandpass Demodulator )2sin( 2 tf T c LPF )2cos( 2 )( )( tf T tv tr cX )2sin( 2 )( tf T tv cQ )2cos( 2 )()( tf T tvts cX )2sin( 2 )( tf T tv cQ If noise is considered then we get and 173
- 50. T tv tr tf tv tftvtv T tr tf tv tf tv T tr tftftvtftftv T tr tf T tf T tvtf T tvtr X X c Q cXX X c Q c XX ccQccXX ccQcXX )( )( ) 2 )22sin( )(() 2 )22cos()( ( 2 )(2 )( ) 2 )22sin( )(() 2 )22cos(1 )(( 2 )( )2cos()2sin()()2cos()2cos()( 2 )( )2cos( 2 )2sin( 2 )()2cos( 2 )()( These Signals are at double the carrier frequency so will be filtered out by the low pass filter (LPF) We assume no channel effects here for simplicity, therefore, transmitted signal s(t) is equal to the received signal r(t) )2cos( 2 )()( tf T tvts cX )2sin( 2 )( tf T tv cQ )2cos( 2 )()( tf T tvtr cX )2sin( 2 )( tf T tv cQ Inphase Demodulation of PSK, QAM © Dr. Aimal Khan 174
- 51. T tv tr tf tv tvtftv T tr tf tv tf tv T tr tftftvtftftv T tr tf T tf T tvtf T tvtr Q Q c Q QcX Q c Q c XQ ccQccXQ ccQcXQ )( )( ) 2 )22cos( )(( 2 )( )´ 2 )22cos()( ( 2 )( ) 2 )22cos(1 )(() 2 0)22sin( )(( 2 )( )2sin()2sin()()2sin()2cos()( 2 )( )2sin( 2 )2sin( 2 )()2cos( 2 )()( These Signals are at double the carrier frequency so will be filtered out by the low pass filter (LPF) We assume no channel effects here for simplicity, therefore, transmitted signal s(t) is equal to the received signal r(t) )2cos( 2 )()( tf T tvts cX )2sin( 2 )( tf T tv cQ )2cos( 2 )()( tf T tvtr cX )2sin( 2 )( tf T tv cQ Quadrature Demodulation of PSK, QAM © Dr. Aimal Khan 175