Introduction to M-ary PSK, QAPSK and FSK

Keshav (2022]OP2591) Satyander Singh (2022]OP2600) Submitted To: Prof.Vinod Chandra Outline Abstract Introduction to M-ary PSK, QAPSK and FSK Comparison of M-Ary Modulation Schemes wrt Bandwidth Efficiency, Noise Performance and Implementation Complexity Summary References Modulation The process of varying one or more properties of a periodic waveform with a modulating signal that typically contains information to be transmitted. modulate mm um 3 Types of Modulation O Amplitude 이 s(t) = Acos(2πft+) M-ASK: Amplitude Shift Keying Frequency M-FSK: Frequency Shift Keying Phase M-PSK: Phase Shift Keying Amplitude + Phase 이 mll|lllw www M-QAM: Quadrature Amplitude Modulation Introduction What is M-Ary Modulation? In a M array modulation two or more bits are grouped together to form a symbol and an assigned signal is transmitted during the symbol period Ts by changing one of the parameter of the carrier (Amplitude, Frequency or Phase). Number of possible symbols given by M=2N. Then the symbol period is given by Ts = NTь. Ifphase of the carrier is modulated it is known as MPSK. 프 Pm = (2m +1) where m-0, 1, 2, ......., M-1 M If frequency is modulated it is known as MFSK. f = (k + 2m)fo where m=0, 1, 2, ......., M-1 Modulation of amplitude as well as phase is know as MQAPSK. Ο M-ary signaling scheme: In this signaling scheme 2 or more bits are grouped together to form a symbol. One of the M possible signals S₁(t),S2(t),S3(t),......SM(t) is transmitted during each symbol period of duration Ts. The number of possible signals = M = 2n, where n is an integer. 6 The symbol values of M for a given value of n: n M=2n Symbol 1 2 0,1 2 4 00, 01, 10, 11 3 8 000, 001, 010,011,... 4 16 0000, 0001, 0010,0011,.... 7 M-ary Phase Shift Keying(MPSK) In M-ary PSK, the carrier phase takes on one of the M possible values, namely 0 = 2* (i - 1)/M where i = 1, 2, 3, .....М. The modulated waveform can be expressed as S(t) = 2E T cos(2011) M OstsT, = 1,2. where E is energy per symbol = (log2 M) E T is symbol period = (log, M) Т. 8 The above equation in the Quadrature form is 2E S, (t) = cos 2E 1 2 cos (2nfot) i = 1,2,..... M 2Tt M sin (2ft) sin T [(2-1) By choosing orthogonal basis signals $ (t) = cos (2xft) 3 2 (t) = in (2ft) defined over the interval 0 ≤t STS 9 M-ary signal set can be expressed as Supsx (t) = { / 008 (i-1) (1)-ain [(i-15]02(1) } M-PSK cos (t)E i = 1, 2,....., М Since there are only two basis signals, the constellation of M-ary PSK is two dimensional. The M-ary message points are equally spaced on a circle of radius VE, centered at the origin. The constellation diagram of an 8-ary PSK signal set is shown in fig. 1 0 VE VE Fig: Constellation diagram of an M-ary PSK system(m=8) 1 1 M-PSK BPSK AQ QPSK 0' 8-PSK '011' 100, 000, OVOLO, 10, 11 Q 16-PSK Q '100' 101' EN 10' יחווי 1,0000. 12 10 Noise Immunity: Increasing M implies that the constellation is more densely packed, and hence the distance between the two points reduces, which leads to poor noise immunity. Bandwidth Efficiency: The first null bandwidth of M-ary PSK signals decrease as M increases while R is held constant. Therefore, as the value of M increases, the bandwidth efficiency also increases. 1 3 M-ary Frequency Shift Keying(MFSK) In M-ary FSK modulation the transmitted signals are defined by: 2E S(t) = COS where fe = ne/2Ts, for some fixed integer n. The M transmitted signals are of equal energy and equal duration, and the signal frequencies are separated by 1/2TsHertz, making the signals orthogonal to one another. 1 4 The channel bandwidth of a noncohorent MFSK is : RM B= 2log M This implies that the bandwidth efficiency of an M-ary FSK signal decreases with increasing M. Therefore, unlike M-PSK signals, M-FSK signals are bandwidth inefficient. However, Noise Immunity of M-FSK is better as compared to both M-PSK and M-QAPSK 15 M-ary Quadrature Amplitude Modulation (QAM) It's a Hybrid modulation As we allow the amplitude to also vary with the phase, a new modulation scheme called quadrature amplitude modulation (QAM) is obtained. The constellation diagram of 16-ary QAM consists of a square lattice of signal points. 1 6 Quadrature Amplitude Modulation Change both amplitude and phase s(t)=Acos(2Tπft+) Q ,0000,01001100"1000' Bits Symbols ,1000' s₁=3a+3ai ,0001,0101 ,1101"1001' '1001' s2=3a+ai a 3a $1100' 0ו1"ס1fו יווסויוורוי S3=a+3ai 0110..0190. .0101..011 '1101' S4=a+ai 16-QAM 64-QAM: 64 constellation points, each with 8 bits Noise Immunity and Bandwidth : Noise Immunity of M-QAM is superior to M-ary PSK. Bandwidth efficiency of M-QAM is identical to M-ary PSK. 1 8 Theory Details Comparison of dmin. 1. dmin decreases in case of MPSK and MQAPSK with increase of M. Hence, Noise Immunity also decreases. 2. Decrease in dmin is more rapid in MPSK as compared to that of MQAPSK. 3. dmin in MFSK increases with increase in M and hence the Noise Immunity for M-ary FSK increases as M increases. 4. MFSK is most immune to noise or symbol probability error. M=2 MPSK MFSK MQASK π min√4NE sin dmtn√2NE 6EN dmin M-1 4 2√E 2√E 2B 8 1.33/E 2.45/E 1.6/E 16 0.78 E 2.83E 1.26E 32 0.44/E 3.16/E 0.98E Table.1 Theory Details Comparison of Spectral Efficiency of Modulation Schemes M-PSK and QAPSK M-FSK h= Data rate 1 log, M [bits/sec/Hz BW 2 Data rate 2log, M h= [bits/sec/Hz BW M n (bps/Hz) M-2 M M-8 M-16 M-32 M-64 PSK 1/2 32 2 52 3 FSK 3/4 1/2 5/16 3/16 QAM 2 3 Table.2 From the above table we notice that in M ary PSK as the values of M increases the spectral efficiency also increases, a similar data is there in M ary QAPSK. In M ary FSK spectral efficiency is constant for M=2 and M=4 and after that it decreases continuously. MPSK Receiver and Transmitter M-ary PSK signal s(t) cos(2fo) TP 이 1 Senat to 2 b(t) parallel converter Digital 10 analog converter m(t) Sinusoidal signal source & phase modulator M-ary PSK signal Raise Input to power Correlator-1 Correlator-2 N-1 Bandpass fiter MM NT Analog to digital converter Parallel to serial converter Bit sequence b(t) Frequency divider by M cos(2xfo) s(t) sin(2f) TP M-ary PSK Transmitter block diagram sin(2nfot) M-ary PSK receiver 21 MFSK Transmitter and Receiver Bandpass fiterat Envelope detector 6 Input bit sequence b(t) b Serial to parallel converter b N-bit digital to analog converter s M-ary FSK signal Frequency modulator si Bandpass fiker at M-ary FSK Envelope detector Decision device selecting largest output N-bit analog 10 digital Parallel b b sorial Binary converter converter data signal sequence Clock at every T Bandpass fier at M-1 Envelope detector M-ary FSK transmitter Block diagram of M-ary FSK system 22 b MQAPSK Transmitter and Receiver Serial 이 paralel converter Digital to analog converter Digtal to analog VPc0s(2) AN Adder Clock at every T A converter VP, sin(2) Generation of QAPSK signal QASK signal Carrier recovery circuit A Raise Input to 4th power Analog dgital converter Analog to dgital converter PN-1 Parallel 이 serial converten Bt sequence bt) Bandpass feer 41% 084(2) Frequency divider by4 cos(2) sin(2) A QAPSK receiver block diagram 23 Implementation Complexity and Cost While assuming the complexity and cost same for transmitter of the three schemes we compared them only based on receiver complexity and cost. M Ary PSK In this scheme we require N square law device, 2 multiplier, 1 bandpass filter, 2 integrator, 1 analog to digital converter and 1 parallel to serial converter. M Ary FSK In this scheme for receiver we require M bandpass filter, M envelop detector, 1 decision device, 1 N bit analog to digital converter and 1 parallel to serial converter. M Ary QAPSK In this scheme we require 2 square law device, 2 multiplier, 1 bandpass filter, 2 integrator, 2 analog to digital converter and 1 parallel to serial converter. MODEL PRICES FOR COMPONENTS MUX/ Switch = Rs 10 Integrator= Rs 20 Multiplier= Rs 200 Bandpass filter=Rs 15 Implementation Complexity and Cost Decision device= Rs 20 Analog to digital converter= Rs 10 Parallel to Serial converter = Rs 5x N (where N is the no. ofbits per symbol) Envelop detector= Rs 15 M No. of Components Price (Rs) Ary M=4 M= M=1 M=3 M=6 M=4 M= M=1 M=3 M=6 8 6 2 4 8 6 2 4 PSK 9 10 11 12 13 475 680 885 109 129 0 5 FSK 11 19 35 67 131 170 290 520 100 196 이 이 QAPS 10 10 10 10 10 885 890 895 900 905 K Table.3 Thus, from above table we see that complexity of M-Ary PSK and FSK increases with increase in value of M whereas for QAPSK it remains same. Among PSK and FSK the latter shows rapid increase in complexity and hence becomes costly as M increase. Therefore, in terms of implementation QASK is best in terms of less complexity and cost. SUMMARY S.NO Parameter MPSK MFSK QAPSK Modulation Phase Frequency 2 Location of On circle On M signal axis Signal Points 3 Distance between signal points Error probability 5 Noise immunity least 6 Bandwidth required 7 Complexity 8 Cost 2NE Quadrature amplitude and Phase Signal points are placed symmetrically about origin E6 N -1 Highest Least Same as QAPSK Shows increase but less rapid than MFSK Increases with M but less rapid than MFSK Highest Highest among three Increases with M Increases with M Table.4 Less than MPSK but morethan MFSK for high value of М Better than MPSK Same as MPSK Remains almost same Least for high value of M . References Principle of Communication Systems by Taub and Schilling. Channel Capacity Calculations For M-ary N-dimensional Signal sets Philip Edward Mclllree, B.Eng. Communication Systems by S. Haykin. Modern Digital and Analog Communication Systems by B.P Lathi.