- 1. Topic : M-ary PSK & M-ary QAM By: Danish Amin
- 2. M-ary Encoding M-ary is a term derived from the word binary. M simply represents a digit that corresponds to the number of conditions, levels, or combinations possible for a given number of binary variables. For example, a digital signal with four possible conditions (voltage levels, frequencies, phases, and so on) is an M-ary system where M = 4. If there are eight possible conditions, M= 8 and so forth. The number of bits necessary to produce a given number of conditions is expressed mathematically as N = log2M where N = number of bits necessary M = number of conditions, levels, or combinations .
- 4. M-ary PSK
- 5. Constellation diagram of M-ary PSK
- 7. Working of 8-PSK Modulator 1. The incoming serial bit stream enters the bit splitter, where it is converted to a parallel, three channel output(the I or in-phase channel, the Q or in Quadrature channel, and the C or control channel). 2. The bit rate in each of the three channels is fb/3. 3. The bits in the I and C channels enter the I channel 2-to-4-level converter and the bits in the Q and C channels enter the Q channel 2-to-4-level converter. 4. Essentially, the 2-to-4-level converters are parallel-input digital-to-analog converter, (DACs). With two input bits, four output voltages are possible. 5. The I or Q bit determines the polarity of the output analog signal (logic 1=+V and logic 0 = -V), whereas the C or C’ bit determines the magnitude (logic 1= 1.307 V and logic 0 =0.541 V).
- 8. 6. Because the C and C’ bits can never be the same logic state, the outputs from the I and Q 2-to-4- level converters can never have the same magnitude, although they can have the same polarity. 7. The output of a 2-to-4-level converter is an M- ary, pulse amplitude- modulated (PAM) signal where M = 4. 8. It can be seen that the angular separation between any two adjacent phasors is 45°, half what it is with QPSK. 9. Therefore, an 8-PSK signal can undergo almost a ± 22.5°
- 12. 8-PSK Receiver
- 13. Quadrature Amplitude Modulation 1) Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information. It conveys two analog message signals, or two digital bit streams, by changing (modulating) the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or amplitude modulation (AM) analog modulation scheme. The two carrier waves of the same frequency are out of phase with each other by 90°, a condition known as orthogonality or quadrature. 2) The transmitted signal is created by adding the two carrier waves together. At the receiver, the two waves can be coherently separated (demodulated) because of their orthogonality property.
- 14. 3) Phase modulation (analog PM) and phase-shift keying (digital PSK) can be regarded as a special case of QAM, where the amplitude of the transmitted signal is a constant, but its phase varies. 4) This can also be extended to frequency modulation (FM) and frequency- shift keying (FSK), for these can be regarded as a special case of phase modulation. USES OF QAM 1) QAM is used extensively as a modulation scheme for digital telecommunication systems, such as in 802.11 Wi-Fi standards. Arbitrarily high spectral efficiencies can be achieved with QAM by setting a suitable constellation size, limited only by the noise level and linearity of the communications channel. 2) QAM is being used in optical fiber systems as bit rates increase; QAM16 and QAM64 can be optically emulated with a 3-path interferometer
- 15. QAM Modulator & Demodulator
- 16. M-ary QAM Definition: 1) In this modulation Technique the digital data is sent by varying both the envelope and phase(or frequency) of an RF carrier. 2) These modulation techniques map base band data into four or more possible RF carrier signals. Hence, these modulation techniques are called M-ary modulation. 3) The general form of an M-ary QAM signal can be defined as where Emin is the energy of the signal with the lowest amplitude and ai and bi are a pair of independent integers chosen according to the location of the particular signal point. In M-ary QAM energy per symbol and also distance between possible symbol states is not a constant.
- 17. 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. •The number of bits necessary to produce a given number of conditions is expressed mathematically as N = log2M where N = number of bits necessary M = number of conditions, levels, or combinations with possible N bits.
- 18. 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,…. …. …… ………. The symbol values of M for a given value of n:
- 19. Constellation diagram of M-ary QAM Fig: Signal Constellation of M-ary QAM for M=16
- 20. Fig: Signal Constellation of M-ary QAM for M=32
- 26. Power Efficiency and Bandwidth 1) Increasing M implies that the constellation is more densely packed, and hence the power efficiency (noise tolerance) is increased. Power efficiency of QAM is superior to M-ary PSK. 2) Bandwidth efficiency of QAM is identical to M-ary PSK. 3) The minimum bandwidth required for 8-QAM is fb / 3, the same as in 8-PSK.
- 27. 8-QAM transmitter The difference between the 8-QAM transmitter and the 8-PSK transmitter is the omission of the inverter between the C channel and Q product modulator.
- 29. Output phase & amplitude-verses- time relationship for 8-QAM
- 30. 8-QAM Receiver
- 31. 8-QAM Receiver • An 8-QAM receiver is almost identical to the 8-PSK receiver. • The differences are the PAM levels at the output of the product detectors and the binary signals at the output of the analog to digital converters. Because there are two transmit amplitudes possible with 8-QAM that are different from those achievable with 8-PSK,the four demodulated PAM levels in 8-QAM are different from those in 8-PSK. • Also with 8-QAM the binary output signals from the I-channel analog to digital converter are I and C bits, and the binary output signals from the Q channel analog-to-digital converter are the Q and C bits.
- 32. References • “Electronic Communications Systems” , fifth edition by Wayne Tomasi. • Jonqyin (Russell) Sun "Linear diversity analysis for QAM in Rician fading channels", IEEE WOCC 2014 • John G. Proakis, "Digital Communications, 3rd Edition • “Digital Communications” , Second Edition by Bernard Sklar
- 33. Thank You