EE521 Analog and Digital Communications James K. Beard, Ph. D. jkbeard@temple.edu Tuesday, March 1, 2005 http://astro.temple.edu/~jkbeard/ March 1, 2005 Week 7

Attendance March 1, 2005 Week 7

Essentials Text: Bernard Sklar, Digital Communications, Second Edition SystemView Office E&A 349 Tuesday afternoons 3:30 PM to 4:30 PM & before class MWF 10:30 AM to 11:30 AM Spring Break Next Week (March 8) Next quiz March 22 Final Exam Scheduled Tuesday, May 10, 6:00 PM to 8:00 PM Here in this classroom March 1, 2005 Week 7

Today’s Topics Take-Home Quiz Due Today SystemView Trial Version Installation Term Projects Coherent and non-coherent detection Discussion (as time permits) March 1, 2005 Week 7

Quiz Overview Practice Quiz was from text homework Quiz was similar Problem 1.1 page 51 Problem 2.2 page 101 Problem 3.1 page 162 Quiz was similar From homework problems Modifications to problem statement and parameters March 1, 2005 Week 7

Quiz timeline Quiz last week Follow-up quiz announced at end of class Open book Calculator No notes (will allow notes for next quiz & final) Follow-up quiz announced at end of class Take-home Will require SystemView to complete Will be deployed on Blackboard this week March 1, 2005 Week 7

The Curve March 1, 2005 Week 7

Scoring Template March 1, 2005 Week 7

Problem 1 Definitions Energy vs. power signals Section 1.2.4 pp 14-16 Energy signal – nonzero but finite energy Power signal – nonzero but finite power Definitions, equations (1.7) and (1.8) March 1, 2005 Week 7

Problem 1 Energy Spectra Section 1.4 pp 19, 20 Fourier transform of energy signal Energy spectrum March 1, 2005 Week 7

Problem 1 Power Spectra Section 1.4 pp. 19, 20 Autocorrelation of power signal Power spectrum March 1, 2005 Week 7

Identities Average power and autocorrelation function Power spectrum March 1, 2005 Week 7

Problem 1 Equations Part (a) Part (b) Part (c) Part (d) March 1, 2005 Week 7

Problem 1 Powers & Energies March 1, 2005 Week 7

Problem 1a Autocorrelation March 1, 2005 Week 7

Problem 1b Fourier Transform March 1, 2005 Week 7

Problem 1c Fourier Transform March 1, 2005 Week 7

Problem 1d Autocorrelation March 1, 2005 Week 7

Problem 1 Spectra March 1, 2005 Week 7

Problem 2, The Block Diagram Naturally sampled low pass analog waveform Local Oscillator LPF March 1, 2005 Week 7

Spectrum of Naturally Sampled Signal Shows Part I March 1, 2005 Week 7

Problem 2 Part II – The Figure BW BW – signal bandwidth W – maximum spectral spread W March 1, 2005 Week 7

Problem 2 Part 2 The signal x1(t) has a power spectrum Shifted left by k.fs The signal x2(t) Has a power spectrum that is one of the replicas shown in the previous slide Spectral distortion results from the slope of the natural sampling overall shape Error and distortion are determined by’ Aliasing into the passband from the other spectral replicas Residual high frequency terms from the LPF stopband Within these errors, x2(t) is a scaled replica of xs(t) Within this and the PAM quantization, xs(t) is a replica of the input signal March 1, 2005 Week 7

Problem 2 Part III (1 of 2) The minimum sample rate is 2.W The LPF Lower sample rates will allow splatter to alias into the signal band Signal will still be reproduced, with larger errors The LPF Passband extends to BW/2 Stopband begins at fs-W/2 March 1, 2005 Week 7

Problem 2 Part III (2 of 2) For a natural sampling duty cycle of d The minimum system sample rate for two samples is 2.fs/d Using a system sample rate that is a multiple of fs Provides the same sampling for every gate Allows accuracy of natural sampling with lower system sample rates The sample rate Determines the LPF transition band of fs-(W+BW)/2 Higher is better for filter cost/performance trade space The spectrum aliasing number k Should be significantly smaller than 1/d Avoid selecting spectrum near the null in natural sampling spectra March 1, 2005 Week 7

Question 3 – The Block Diagram Bandpass signal Local Oscillator LPF 2 March 1, 2005 Week 7

Problem 3 Part I The output signal xO(t) is the bandpass signal xB(t) shifted down in frequency by f0 For all-analog signals, the LPF Will supplement the last I.F. filter Can provide better performance than a bandpass filter For sampled signals, the LPF Provides anti-aliasing filtering – suppression of spectral images May allow decimation to sample rate near BW March 1, 2005 Week 7

Question 3, Part II Considerations are similar to those of Question 2 In Question 2, natural sampling generated an array of bandpass signals The complex rest of the circuit was a quadrature demodulator that selected one of the bandpass signals The duty cycle is not a part of Question 3 Minimum sample rate is 2.W LPF Bandpass to BW/2 Stopband begins at fs – W/2 March 1, 2005 Week 7

Problem 3 Part III Sample rates fs that alias f0 to ±fs/4 Nyquist criteria, including spectral spread Lowest sample rate is for a k of March 1, 2005 Week 7

Problem III Part IV Look at numerical values of LPF specs Bandpass to BW/2 Stopband begins at fs – W/2 Transition band is fs-(BW+W)/2 Shape factor is (2.fs-W)/BW LPF trade space is better for higher fs March 1, 2005 Week 7

Problem 3 Part V The sample rate at I.F. is 2.W For complex signals, the Nyquist rate is W Allowing for a shape factor for the LPF increases the sample rate above 2.W Decimation Minimum is a factor of 2 to produce a sample rate of W complex Aliasing considerations can drive a complex data rate higher than W Higher sample rates and simpler LPF will allow decimation of 3 or 4 to produce a complex sample rate near W Dual-stage digital LPF can provide a very high performance – a shape factor only slightly larger than 1 March 1, 2005 Week 7

SystemView I have a mini-CD-ROM with the trial version When you install During business hours When asked for “Regular” or “Professional” select “Professional” Call Maureen Chisholm at 678-218-4603 to get your activation code Other resources The student version will probably carry you another week The full version is available in E&A 604E – watch for two icons on the desktop and select the Professional version March 1, 2005 Week 7

Term Projects Interpret, plan, model Use SystemView Assignments deployed by email last week Your preferences and comments are encouraged Office hours Email March 1, 2005 Week 7

SystemView Assignment Objectives Generate test signal over speech band Determine fundamental simulation parameters SystemView sample rate Run end time Comm system sample rate Mimics Problem 3 Part V Successful completion is launch of your term project March 1, 2005 Week 7

Term Project Legend: From other sources Essential Information source Message symbols Optional Channel symbols X M I T Format Source encode Encrypt Channel encode Multi-plex Pulse modulate Bandpass modulate Freq-uency spread Multiple access Digital input Channel impulse response Bit stream Synch-ronization Digital baseband waveform Digital bandpass waveform Channel Digital output R C V Format Source decode Decrypt Channel decode Demul-tiplex Detect Demod-ulate & Sample Freq-uency despread Multiple access To other destinations Channel symbols Information sink Message symbols March 1, 2005 Week 7

System March 1, 2005 Week 7

Spectrum of Input Signal March 1, 2005 Week 7

Next Steps Sample at comm system sample rate Adjust SystemView sample rate Make it the comm system sample rate times a power of 2 This allows a power of 2 for both SystemView and comm system sampled data for the same run times Quantize to 16 bits Convert to bitstream Map characters to 2-bit symbols for QPSK or MSK March 1, 2005 Week 7

Sklar Chapter 4 Legend: From other sources Essential Information Message symbols Optional Channel symbols X M I T Format Source encode Encrypt Channel encode Multi-plex Pulse modulate Bandpass modulate Fre-quency spread Multiple access Digital input Channel impulse response Bit stream Synch-ronization Digital baseband waveform Digital bandpass waveform Channel Digital output R C V Format Source decode Decrypt Channel decode Demul-tiplex Detect Demod-ulate & Sample Freq-uency despread Multiple access To other destinations Channel symbols Information sink Message symbols March 1, 2005 Week 7

Detection Coherent Non-coherent BPSK MPSK FSK Differential PSK March 1, 2005 Week 7

Correlator Receiver The correlation functions fi(t) may be DECISION LOGIC The correlation functions fi(t) may be Signal replicas si(t) Orthogonal basis functions With the right decision logic – a maximum likelihood detector March 1, 2005 Week 7

Coherent Detection of BPSK The BPSK basis functions are Correlate with an orthogonal basis function March 1, 2005 Week 7

BPSK Demodulated Output Output is plus or minus the pulse amplitude, depending on the phase Coherence in this case lets us set the phase Φ to zero Not knowing Φ Causes a fundamental ambiguity Still allows us to detect bit changes March 1, 2005 Week 7

Coherent MPSK Detection M-ary PSK signals are The basis functions are March 1, 2005 Week 7

MPSK Demodulated Output Output is a complex number Magnitude is the pulse amplitude Phase is the modulation phase Not knowing the phase Causes a fundamental ambiguity Still allows us to detect phase changes March 1, 2005 Week 7

Coherent Detection of FSK FSK waveforms are We take the phase as zero, as before Basis functions are March 1, 2005 Week 7

Non-Coherent PSK Detection Differential PSK Unknown phase of signal is a random variable Phases of adjacent received pulses are compared Performance Coherent – measure one phase Non-coherent – measure two phases and subtract Non-coherent is inherently noisier by 3 dB March 1, 2005 Week 7

Non-Coherent FSK Use a filter bank Use I-Q demodulator Threshold the squared magnitudes March 1, 2005 Week 7

Example 4.1 pp. 187-188 Correlation is four-sample summation Waveform set is Correlation is by summation over k March 1, 2005 Week 7

Example 4.1 (Concluded) Correlator summation is What is z2? March 1, 2005 Week 7

Example 4.2 pp. 193-194 Phase as a function of propagation delay Phase changes by 360 degrees for each wavelength of change of path length Wavelength for 1 GHz is about 1 foot Conclusion Path length uncertainty of 3 inches will cause 90 degrees of phase uncertainty Coherent detection depends on real-time monitoring of received phase Phase-locked loops (PLLs) are needed to support coherent detection March 1, 2005 Week 7

Assignment Add quantization and the ADC to your term project Read Skar, sections 4.6, 4.7, 4.8, and 4.9 Look at symbol mapping for QPSK and MSK for your term project Back-up quiz grades will be given by email because next week is Spring Break March 1, 2005 Week 7