EE 6331, Spring, 2009 Advanced Telecommunication                                                             Zhu Han Department of Electrical and Computer Engineering Class 13 Mar. 3rd, 2009

Outline Exam Review Geometric representation of modulation signals ADC/DAC PCM Geometric representation of modulation signals Linear modulation BPSK, DPSK; QPSK, offset QPSK, /4 QPSK Constant envelope modulation BFSK, MSK, GMSK Combined linear and constant envelope modulation MPSK QAM MFSK and OFDM ECE6331 Spring 2009

PAM, PWM, PPM, PCM ECE6331 Spring 2009

Quantization Scalar Quantizer Block Diagram Mid-tread Mid-rise ECE6331 Spring 2009

Equations ECE6331 Spring 2009

Quantization Noise ECE6331 Spring 2009

Example SNR for varying number of representation levels for sinusoidal modulation 1.8+6 X dB, example 3.1 Number of representation level L Number of Bits per Sample, R SNR (dB) 32 5 31.8 64 6 37.8 128 7 43.8 256 8 49.8 ECE6331 Spring 2009

Conditions for Optimality of Scalar Quantizers Let m(t) be a message signal drawn from a stationary process M(t) -A  m  A m1= -A mL+1=A mk  mk+1 for k=1,2,…., L The kth partition cell is defined as Jk: mk< m  mk+1 for k=1,2,…., L d(m,vk): distortion measure for using vk to represent values inside Jk. ECE6331 Spring 2009

Condition for Optimal Quantizer ECE6331 Spring 2009

Condition One ECE6331 Spring 2009

Condition Two ECE6331 Spring 2009

Vector Quantization image and voice compression, voice recognition statistical pattern recognition volume rendering ECE6331 Spring 2009

Numbers passed from ADC to computer to represent analogue voltage PCM 0000 1111 1110 1101 1100 1011 1010 1001 0001 0010 0011 0100 0101 0110 0111 Resolution= 1 part in 2n 0000 0110 0111 0011 1100 1001 1011 Numbers passed from ADC to computer to represent analogue voltage ECE6331 Spring 2009

Non-uniform Quantizer F: nonlinear compressing function F-1: nonlinear expanding function F and F-1: nonlinear compander y y ^ F Q F-1 x ^ x Example F: y=log(x) F-1: x=exp(x) We will study nonuniform quantization by PCM example next A law and  law ECE6331 Spring 2009

 Law/A Law ECE6331 Spring 2009

Geometric Representation of Modulation Signal Digital Modulation involves Choosing a particular signal waveform for transmission for a particular symbol or signal For M possible signals, the set of all signal waveforms are: For binary modulation, each bit is mapped to a signal from a set of signal set S that has two signals We can view the elements of S as points in vector space ECE6331 Spring 2009 16

Geometric Representation of Modulation Signal Vector space We can represented the elements of S as linear combination of basis signals. The number of basis signals are the dimension of the vector space. Basis signals are orthogonal to each-other. Each basis is normalized to have unit energy: ECE6331 Spring 2009 17

Example Two signal waveforms to be used for transmission The basis signal Q I Constellation Diagram Dimension = 1 ECE6331 Spring 2009 18

Constellation Diagram Properties of Modulation Scheme can be inferred from Constellation Diagram Bandwidth occupied by the modulation increases as the dimension of the modulated signal increases Bandwidth occupied by the modulation decreases as the signal points per dimension increases (getting more dense) Probability of bit error is proportional to the distance between the closest points in the constellation. Bit error decreases as the distance increases (sparse). Equation 6.62-6.64 ECE6331 Spring 2009 19

Concept of a constellation diagram ECE6331 Spring 2009

Example of samples of matched filter output for some bandpass modulation schemes ECE6331 Spring 2009

Linear Modulation Techniques Classify digital modulation techniques as: Linear The amplitude of the transmitted signal varies linearly with the modulating digital signal, m(t). They usually do not have constant envelope. More spectral efficient. Poor power efficiency Example: BPSK, QPSK. Non-linear ECE6331 Spring 2009 22

Binary Phase Shift Keying Use alternative sine wave phase to encode bits Phases are separated by 180 degrees. Simple to implement, inefficient use of bandwidth. Very robust, used extensively in satellite communication. Q State 1 State ECE6331 Spring 2009 23

BPSK Example 1 1 0 1 0 1 Data Carrier Carrier+ p BPSK waveform 24 1 1 0 1 0 1 Data Carrier Carrier+ p BPSK waveform ECE6331 Spring 2009 24

BPSK Virtue of pulse shaping equations 6.68-6.71 ECE6331 Spring 2009 25

BPSK Coherent demodulator 6.72 6.73 6.74 ECE6331 Spring 2009 26

Differential PSK encoding Differential BPSK 0 = same phase as last signal element 1 = 180º shift from last signal element ECE6331 Spring 2009 27

DPSK modulation and demodulation 6.75, 3dB loss EE 542/452 Spring 2008 EE 552/452 Spring 2007 28

Quadrature Phase Shift Keying Multilevel Modulation Technique: 2 bits per symbol More spectrally efficient, more complex receiver. Two times more bandwidth efficient than BPSK Q 11 State 01 State 00 State 10 State Phase of Carrier: p/4, 2p/4, 5p/4, 7p/4 ECE6331 Spring 2009 29

4 different waveforms cos+sin -cos+sin 11 01 00 10 cos-sin -cos-sin 30 ECE6331 Spring 2009 30

QPSK Example ECE6331 Spring 2009

QPSK Virtue of pulse shaping 6.80 ECE6331 Spring 2009 32

QPSK modulation ECE6331 Spring 2009 33

QPSK receiver ECE6331 Spring 2009 34

Differential Coherent DBPSK 3dB loss QPSK BER 6.79, the same as BPSK ECE6331 Spring 2009

Offset QPSK waveforms ECE6331 Spring 2009 36

Offset OQPSK QPSK can have 180 degree jump, amplitude fluctuation By offsetting the timing of the odd and even bits by one bit-period, or half a symbol-period, the in-phase and quadrature components will never change at the same time. 90 degree jump ECE6331 Spring 2009

Pi/4 QPSK signaling 135 degree Non-coherent detection 38 ECE6331 Spring 2009 38

Pi/4 QPSK transmitter 6.81-6.86 Example 6.9 ECE6331 Spring 2009 39

I. Differential detection of pi/4 QPSK Example 6.10 ECE6331 Spring 2009 40

II. IF Differential Detection ECE6331 Spring 2009 41

III. FM Discriminator detector ECE6331 Spring 2009 42

Constant Envelope Modulation Amplitude of the carrier is constant, regardless of the variation in the modulating signal Better immunity to fluctuations due to fading. Better random noise immunity Power efficient They occupy larger bandwidth ECE6331 Spring 2009 43

Frequency Shift Keying (FSK) The frequency of the carrier is changed according to the message state (high (1) or low (0)). One frequency encodes a 0 while another frequency encodes a 1 (a form of frequency modulation) Integral of m(x) is continues. Continues FSK ECE6331 Spring 2009 44

FSK Bandwidth Limiting factor: Physical capabilities of the carrier Not susceptible to noise as much as ASK Applications On voice-grade lines, used up to 1200bps Used for high-frequency (3 to 30 MHz) radio transmission used at higher frequencies on LANs that use coaxial cable ECE6331 Spring 2009

Multiple Frequency-Shift Keying (MFSK) More than two frequencies are used More bandwidth efficient but more susceptible to error f i = f c + (2i – 1 – M)f d f c = the carrier frequency f d = the difference frequency M = number of different signal elements = 2 L L = number of bits per signal element ECE6331 Spring 2009

FSK Coherent Detection ECE6331 Spring 2009 47

Noncoherent FSK ECE6331 Spring 2009 48

MSK modulation Equation 6.104, 6.105 ECE6331 Spring 2009 49

MSK reception ECE6331 Spring 2009 50

Minimum Shift Keying spectra 6.107 6.108 ECE6331 Spring 2009 51

GMSK spectral shaping ECE6331 Spring 2009 52

GMSK spectra shaping ECE6331 Spring 2009 53

Simple GMSK modulation and demodulation ECE6331 Spring 2009 EE 552/452 Spring 2007 54

Digital GMSK demodulator ECE6331 Spring 2009 55

8-PSK Signal Constellation Equation 6.113-6.120 ECE6331 Spring 2009 56

Pulse Shaped M-PSK ECE6331 Spring 2009 57

QAM – Quadrature Amplitude Modulation Modulation technique used in the cable/video networking world Instead of a single signal change representing only 1 bps – multiple bits can be represented buy a single signal change Combination of phase shifting and amplitude shifting (8 phases, 2 amplitudes) ECE6331 Spring 2009

QAM QAM As an example of QAM, 12 different phases are combined with two different amplitudes Since only 4 phase angles have 2 different amplitudes, there are a total of 16 combinations With 16 signal combinations, each baud equals 4 bits of information (2 ^ 4 = 16) Combine ASK and PSK such that each signal corresponds to multiple bits More phases than amplitudes Minimum bandwidth requirement same as ASK or PSK ECE6331 Spring 2009

16-QAM Signal Constellation ECE6331 Spring 2009 60

QAM vs. MFSK ECE6331 Spring 2009 61

Orthogonal frequency-division multiplexing Special form of Multi-Carrier Transmission. Multi-Carrier Modulation. Divide a high bit-rate digital stream into several low bit-rate schemes and transmit in parallel (using Sub-Carriers) ECE6331 Spring 2009

Comparison of Digital Modulation ECE6331 Spring 2009

Comparison of Digital Modulation ECE6331 Spring 2009

Spectral Efficiencies in practical radios GSM- Digital Cellular Data Rate = 270kb/s, bandwidth = 200kHz Bandwidth Efficiency = 270/200 =1.35bits/sec/Hz Modulation: Gaussian Minimum Shift Keying (FSK with orthogonal frequencies). “Gaussian” refers to filter response. IS-54 North American Digital Cellular Data Rate = 48kb/s, bandwidth = 30kHz Bandwidth Efficiency = 48/30 =1.6bits/sec/Hz Modulation: pi/4 DQPSK ECE6331 Spring 2009

Modulation Summary Phase Shift Keying is often used, as it provides a highly bandwidth efficient modulation scheme. QPSK, modulation is very robust, but requires some form of linear amplification. OQPSK and p/4-QPSK can be implemented, and reduce the envelope variations of the signal. High level M-ary schemes (such as 64-QAM) are very bandwidth efficient, but more susceptible to noise and require linear amplification. Constant envelope schemes (such as GMSK) can be employed since an efficient, non-linear amplifier can be used. Coherent reception provides better performance than differential, but requires a more complex receiver. ECE6331 Spring 2009