![8 – PSK Output Phase and Amplitude
Bandwidth
The Output of the Balanced Modulator
= (V Sinωat)(Sinωct)
Where V = ± 1.307 or ± 0.541
ωat = 2Πfat = 2Πfbt and ωct = 2Πfct
fa = Fundamental frequency = (fb/3)/2 = fb/6
= (V Sin 2Π(fb/6)t)(Sin2Πfct)
= V[1/2(Cos(fc-fb/6) - Cos(fc+fb/6))]
Here (fc + fb/6) – (fc - fb/6) = BW
Band Width = fb/6 + fb/6 = fb/3](https://image.slidesharecdn.com/unit3-marysignaling-200830191642/85/EC-8395-Communication-Engineering-Unit-3-m-ary-signaling-19-320.jpg)
![Output of balanced modulator can be expressed as
= Sinωat x Sinωct
=
where fa = (fb/3)/2 = fb/6
The output frequency spectrum range is from fc-fa to fc+fa
The minimum bandwidth or Nyquist bandwidth
B = (fc+fb/6)-(fc-fb/6)
B = fb/3
Bit rate at I or Q or C channel is = fb/3
The highest fundamental frequency fa = fb/2 (Generally)
= (fb/3)/2
= fb/6
]t)ff(2[Cos
2
1
]t)ff(2[Cos
2
1
acac ](https://image.slidesharecdn.com/unit3-marysignaling-200830191642/85/EC-8395-Communication-Engineering-Unit-3-m-ary-signaling-25-320.jpg)
![16 - QAM
• Here M = 16, 16 = 2N,then N=4
• The minimum bandwidth and baud rate = one fourth of the bit rate = fb/4
• The fundamental frequency fa = fb/2 , but fb = fb/4
• fa = (fb/4)/2 = fb/8
• Output of the balanced modulator = Sinωat x Sinωct
=
Where fa = fb/8
• The output frequency spectrum ranges are (fc-fb/8) to (fc+fb/8)
• Minimum bandwidth or Nyquist bandwidth is
B = (fc+fb/8) – (fc-fb/8)
= fb/4
]t)ff(2[Cos
2
1
]t)ff(2[Cos
2
1
acac ](https://image.slidesharecdn.com/unit3-marysignaling-200830191642/85/EC-8395-Communication-Engineering-Unit-3-m-ary-signaling-30-320.jpg)
EC 8395 - Communication Engineering - Unit 3 m - ary signaling
- 1. R.M.K. COLLEGE OF ENGINEERING AND TECHNOLOGY DEPARTMENT OF CSE EC 8395 COMMUNICATION ENGINEERING Dr.Kannan K Assistant Professor Department of ECE
- 2. Phase shift keying – BPSK, DPSK, QPSK – Principles of M- ary signaling M- ary PSK & QAM – Comparison, ISI – Pulse shaping – Duo binary encoding – Cosine filters – Eye pattern, equalizers UNIT III DIGITAL MODULATION AND TRANSMISSION
- 3. M – ary Signaling An M - ary transmission is a type of digital modulation where instead of transmitting one bit at a time, two or more bits are transmitted simultaneously The word binary represents two-bits. M simply represents a digit that corresponds to the number of conditions, levels, or combinations possible for a given number of binary variables. This is the type of digital modulation technique used for data transmission in which instead of one-bit, two or more bits called symbol or symbols are transmitted at a time. As a single signal is used for multiple bit transmission, the channel bandwidth is reduced.
- 4. M- ary Equation If a digital signal is given under four conditions, such as voltage levels, frequencies, phases and amplitude, then M = 4. The number of bits necessary to produce a given number of conditions is expressed mathematically as N = Log2M Where, N is the number of bits necessary. M is the number of conditions, levels, or combinations possible with N bits. The above equation can be re-arranged as 2N = M For example, with two bits, 22 = 4 conditions are possible.(00,01,10 & 11) In almost all applications, M = 2N and T = nTb, where n is an integer Each of the M signals is called a symbol
- 5. Bit rate ,Baud rate and Minimum Bandwidth With binary encoding, the bit rate and baud rate equal b = fb Here b – Baud rate(Symbol/Second) fb – bit rate(bits/Second With M – ary encoding, the relation between bit and baud rate is b = fb/N Here N – Number of bits encoded into each signaling element According to Nyquist rate in the sampling therem,the minimum theoretical bandwidth necessary to propagate a signal is called the minimum nyquist bandwidth or minimum Nyquist frequency fb = 2B where fb – bit rate(bps) B – Ideal Nyquist bandwidth Using M –ary encoding, the Nyquist formula is fb = 2B log2M Mlog f B 2 b N f B b
- 6. In general, (M-ary) multi-level modulation techniques are used in digital communications as the digital inputs with more than two modulation levels allowed on the transmitter’s input. Hence, these techniques are bandwidth efficient. There are many different M-ary modulation techniques. Some of these techniques, modulate one parameter of the carrier signal, such as amplitude, phase, and frequency. (i) M – ary ASK (ii) M – ary PSK (iii) M - ary FSK (iv) M - ary QAM Types of M- ary Techniques
- 7. M - ary PSK • M-ary Phase Shift Keying is a very efficient signaling scheme • The symbols are transmitted with different phase and frequency will remain same. • The number of possible signals are M = 2N, the duration of symbol is Ts = NTb , where Tb is bit duration. • In M - ary PSK, The PSK modulated signal can be written as
- 8. M- ary PSK Modulator • The modulator structure is straight forward and is given . From the data, Acm & Asm are obtained and fed into two balanced modulators. • The output of both modulators are added to form a MPSK modulated signal. Substituting value of phase in the above equation and expanding the cosine term, Sm (t) can be written as
- 9. M – ary PSK Modulator • The values of different phases for different values of M (M = 2N) are given below • For M = 4, phases are π/4, 3π/4, 5π/4 and 7π/4. • For M = 8, phases are π/8, 3π/8, 5π/8, 7π/8, 9π/8, 11π/8, 13π/8, 15π/8. • For M = 16, phases are π/16, 3π/16, 5π/16, 7π/16, 9π/16, 11π/16, 13π/16, 15π/16, 17π/16, 19π/16, 21π/16, 23π/16, 25π/16, 27π/16, 29π/16 31π/16. • For M = 32, phases are π/32, 3π/32, 5π/32, 7π/32, 9π/32, 11π/32, 13π/32, 15π/32, 17π/32, 19π/32, 21π/32, 23π/32, 25π/32, 27π/32, 29π/32 31π/32, 33π/32, 35π/32,37π/32, 39π/32, 41π/32, 43π/32, 45π/32, 47π/32, 49π/32, 51π/32, 53π/32, 55π/32,57π/32, 59π/32, 61π/32 63π/32.
- 10. • These phases are shown in Figure for M = 4, 8, 16. • The signal constellation of M-ary PSK is two dimensional and M message points are equally placed on the circle of radius √2Es and center at origin. The constellation diagram of MPSK using Gray coding for M = 4, 8, 16, 32 are given M = 8 M = 4
- 11. M = 16 M = 32
- 12. M - ary PSK Demodulator It is important in demodulation of the signal because the most likely errors caused by nois e involve the erroneous selection of an adjacent phase to the transmitted signal phase. In such a case, only a single bit error occurs in k-bit sequence. The general form of the optimum demodulator for detecting one of M signal in an AWGN channel is given. The low pass equivalent of transmitted signal is given by
- 13. The exponential factor under integral in the above equation is independent of the variable of integration, hence it can be taken outside the integral. The optimum demodulator can be implemented as a single matched filter or cross correlator receiver which computes the decision variable Um and decides in favor of maximum.
- 14. Equivalently the phase (θ) of the vector V is calculated by the phase detector and optimum demodulator decides in favor of the signal having the phase closest to the phase (θ).
- 15. 8 – PSK M = 8, WKT 2N = 8 , N = 3 3 bits forming a group and produces 8 different output phases I or Q determines the polarity of Signal logic 1 = +1 volts logic 0 = -1 Volts C or ̅C determines the Magnitude of the Signal logic 1 = 1.307 volts logic 0 = 0.541 volts Bandwidth Efficiency The bandwidth efficiency is defined as R/W where R is data rate and W is req uired bandwidth
- 16. 8 – PSK TRANSMITTER
- 17. 8 - PSK Constellation Diagram and Truth Table
- 18. 8 – PSK Phasor Diagram
- 19. 8 – PSK Output Phase and Amplitude Bandwidth The Output of the Balanced Modulator = (V Sinωat)(Sinωct) Where V = ± 1.307 or ± 0.541 ωat = 2Πfat = 2Πfbt and ωct = 2Πfct fa = Fundamental frequency = (fb/3)/2 = fb/6 = (V Sin 2Π(fb/6)t)(Sin2Πfct) = V[1/2(Cos(fc-fb/6) - Cos(fc+fb/6))] Here (fc + fb/6) – (fc - fb/6) = BW Band Width = fb/6 + fb/6 = fb/3
- 20. 8 – PSK Receiver
- 21. 16 - PSK • In this technique, M =16, i.e. 16 Different output phases • M=2N ; 16 = 2N ; N = 4(4 bits) • The minimum bandwidth and baud rate = 1/4th of bit rate i.e.. Fb/4 • With PSK, the angular separation between adjacent output phase is only 22.5o • 16-PSK can undergo only a 11.25o phase shift during transmission and still retain its integrity • Truth Table Constellation Diagram
- 22. 16 – PSK Modulator and Demodulator
- 23. QAM (QUADRATURE AMPLITUDE MODULATION • QAM is a popular Scheme for high rate, high bandwidth efficiency systems • QAM is a signal in which two carriers shifted in phase by 90 degrees (i.e. sine and cosine) are modulated and combined. As a result of their 90° phase difference they are in quadrature and this gives rise to the name. Often one signal is called the In-phase or “I” signal, and the other is the quadrature or “Q” signal • QAM = ASK + PSK • M - ary Quadrature Amplitude Modulation or M - QAM is a modulation where data bits select one of M combinations of amplitude and phase shifts that are applied to the carrier • The M possible waveforms may be described by M constellation points • The term M as in M-QAM indicates how many bits are transmitted per time interval or symbol for each unique amplitude/phase combination • The simplest form of QAM is 2-QAM, more commonly called QPSK or quadrature phase shift keying.
- 24. 8 - QAM • In this M = 8,ie 8 output amplitudes and phases are possible • M=2N ; 8 = 2N ; N = 3(Tribit).Three bits are grouped together • Only difference is the removal of inverters in the C channel of 8 PSK transmitter 8 – QAM TRANSMITTER
- 25. Output of balanced modulator can be expressed as = Sinωat x Sinωct = where fa = (fb/3)/2 = fb/6 The output frequency spectrum range is from fc-fa to fc+fa The minimum bandwidth or Nyquist bandwidth B = (fc+fb/6)-(fc-fb/6) B = fb/3 Bit rate at I or Q or C channel is = fb/3 The highest fundamental frequency fa = fb/2 (Generally) = (fb/3)/2 = fb/6 ]t)ff(2[Cos 2 1 ]t)ff(2[Cos 2 1 acac
- 26. 8 - QAM Truth Table
- 27. Phasor Diagram Constellation Diagram
- 28. 8 – QAM Output Phase and Amplitude
- 29. • I/Q bit decides polarity Logic 1 = +1 volts Logic 0 = -1 volts • C determines Magnitude Logic 1 = 1.307 Logic 0 = 0.541 8 - QAM RECEIVER
- 30. 16 - QAM • Here M = 16, 16 = 2N,then N=4 • The minimum bandwidth and baud rate = one fourth of the bit rate = fb/4 • The fundamental frequency fa = fb/2 , but fb = fb/4 • fa = (fb/4)/2 = fb/8 • Output of the balanced modulator = Sinωat x Sinωct = Where fa = fb/8 • The output frequency spectrum ranges are (fc-fb/8) to (fc+fb/8) • Minimum bandwidth or Nyquist bandwidth is B = (fc+fb/8) – (fc-fb/8) = fb/4 ]t)ff(2[Cos 2 1 ]t)ff(2[Cos 2 1 acac
- 31. 16 – QAM Transmitter
- 32. 16 – QAM Phasor and Constellation Diagram
- 33. 16 – QAM Truth Table
- 34. 16 – QAM Output Phase
- 35. COMPARISION OF DIGITAL MODULATION TECHNIQUES Digital Modulation Techniques Encoding Method Output Possibility Minimum or Nyquist Bandwidth Bit rate or Baud rate Bandwidth Efficiency ASK Single Bit 2 fb fb 1 FSK Single Bit 2 |fm-fs| + 2fb fb 1 BPSK Single Bit 2 fb fb 1 QPSK Two bit (Debits) 4 fb/2 fb/2 2 8-PSK Three bits (Tribits) 8 fb/3 fb/3 3 16-PSK Four bits (Quad bits) 16 fb/4 fb/4 4 8-QAM Three bits (Tribits) 8 fb/3 fb/3 3 16-QAM Four bits (Quad bits) 16 fb/4 fb/4 4
- 36. Practical Applications • BPSK: WLAN IEEE802.11b (1 Mbps) • QPSK: WLAN IEEE802.11b (2 Mbps, 5.5 Mbps, 11 Mbps) 3G WDMA DVB-T (with OFDM) • QAM: Telephone modem (16QAM) Downstream of Cable modem (64QAM, 256QAM) WLAN IEEE802.11a/g (16QAM for 24Mbps, 36Mbps; 64QAM for 38 Mbps and 54 Mbps) LTE Cellular Systems • FSK: Cordless telephone Paging system
- 37. THANK YOU