ECE 4331, Fall, 2009

1. ECE 4331, Fall, 2009 Zhu Han Department of Electrical and Computer Engineering Class 17 Oct. 22nd, 2009

2. Outline • Review • Line code: modulation but base band • Carrier systems: most digital systems, you can find a job now • ASK, OOK, MASK • FSK, MFSK • BPSK, DBPSK, MPSK • MQAM, MQPR • OQPSK, • Continuous phase modulation (CPM): MSK, GMSK

3. Receiver Structure • Matched filter: match source impulse and maximize SNR • grx to maximize the SNR at the sampling time/output • Equalizer: remove ISI • Timing • When to sample. Eye diagram • Decision • d(i) is 0 or 1 Noisena(t) gTx(t) gRx(t) d(i) ?

4. Matched Filter: optimal receive filter for maximized Matched filter example • Received SNR is maximized at time T0 example: Receive filter (mathed filter) transmit filter

5. Interpretation of Eye Diagram • 10 points in the final

6. Equalizer • When the channel is not ideal, or when signaling is not Nyquist, There is ISI at the receiver side. • In time domain, equalizer removes ISR. • In frequency domain, equalizer flat the overall responses. • In practice, we equalize the channel response using an equalizer

7. Different types of equalizers • Zero-forcing equalizers ignore the additive noise and may significantly amplify noise for channels with spectral nulls • Minimum-mean-square error (MMSE) equalizers minimize the mean-square error between the output of the equalizer and the transmitted symbol. They require knowledge of some auto and cross-correlation functions, which in practice can be estimated by transmitting a known signal over the channel • Adaptive equalizers are needed for channels that are time-varying • Decision-feedback equalizers (DFE’s) use tentative symbol decisions to eliminate ISI, nonlinear • Blind equalizersare needed when no preamble/training sequence is allowed, nonlinear • Turbo equalizers: iterative and nonlinear interleaving • Ultimately, the optimum equalizer is a maximum-likelihood sequence estimator, nonlinear

8. Error Rate Due to the Noise

9. Error Rate Due to the Noise Figure 4.5 Noise analysis of PCM system. (a) Probability density function of random variable Y at matched filter output when 0 is transmitted. (b) Probability density function of Y when 1 is transmitted.

14. ASK, OOK, MASK • The amplitude (or height) of the sine wave varies to transmit the ones and zeros • One amplitude encodes a 0 while another amplitude encodes a 1 (a form of amplitude modulation)

15. Binary amplitude shift keying, Bandwidth • d ≥ 0  related to the condition of the line B = (1+d) x S = (1+d) x N x 1/r

16. Implementation of binary ASK

17. OOK and MASK • OOK (On-OFF Key) • 0 silence. • Sensor networks: battery life, simple implementation • MASK: multiple amplitude levels

18. Pro, Con and Applications • Pro • Simple implementation • Con • Major disadvantage is that telephone lines are very susceptible to variations in transmission quality that can affect amplitude • Susceptible to sudden gain changes • Inefficient modulation technique for data • Applications • On voice-grade lines, used up to 1200 bps • Used to transmit digital data over optical fiber • Morse code • Laser transmitters

19. Example • We have an available bandwidth of 100 kHz which spans from 200 to 300 kHz. What are the carrier frequency and the bit rate if we modulated our data by using ASK with d = 1? • Solution • The middle of the bandwidth is located at 250 kHz. This means that our carrier frequency can be at fc = 250 kHz. We can use the formula for bandwidth to find the bit rate (with d = 1 and r = 1).

20. Frequency Shift Keying • One frequency encodes a 0 while another frequency encodes a 1 (a form of frequency modulation) • Represent each logical value with another frequency (like FM)

21. 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

22. Example • We have an available bandwidth of 100 kHz which spans from 200 to 300 kHz. What should be the carrier frequency and the bit rate if we modulated our data by using FSK with d = 1? • Solution • This problem is similar to Example 5.3, but we are modulating by using FSK. The midpoint of the band is at 250 kHz. We choose 2Δf to be 50 kHz; this means

23. 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

24. Phase Shift Keying • One phase change encodes a 0 while another phase change encodes a 1 (a form of phase modulation)

25. DBPSK, QPSK • Differential BPSK • 0 = same phase as last signal element • 1 = 180º shift from last signal element • Four Level: QPSK

26. QPSK Example

27. Bandwidth • Min. BW requirement: same as ASK! • Self clocking (most cases)

28. Concept of a constellation diagram

29. MPSK • Using multiple phase angles with each angle having more than one amplitude, multiple signals elements can be achieved • D = modulation rate, baud • R = data rate, bps • M = number of different signal elements = 2L • L = number of bits per signal element

30. 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)

31. 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

32. QAM and QPR • QAM is a combination of ASK and PSK • Two different signals sent simultaneously on the same carrier frequency • M=4, 16, 32, 64, 128, 256 • Quadrature Partial Response (QPR) • 3 levels (+1, 0, -1), so 9QPR, 49QPR

33. Offset quadrature phase-shift keying (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.

34. Continuous phase modulation (CPM) • CPM the carrier phase is modulated in a continuous manner • constant-envelope waveform • yields excellent power efficiency • high implementation complexity required for an optimal receiver • minimum shift keying (MSK) • Similarly to OQPSK, MSK is encoded with bits alternating between quarternary components, with the Q component delayed by half a bit period. However, instead of square pulses as OQPSK uses, MSK encodes each bit as a half sinusoid. This results in a constant-modulus signal, which reduces problems caused by non-linear distortion.

35. Gaussian minimum shift keying • GMSK is similar to MSK except it incorporates a premodulation Gaussian LPF • Achieves smooth phase transitions between signal states which can significantly reduce bandwidth requirements • There are no well-defined phase transitions to detect for bit synchronization at the receiving end. • With smoother phase transitions, there is an increased chance in intersymbol interference which increases the complexity of the receiver. • Used extensively in 2nd generation digital cellular and cordless telephone apps. such as GSM