EE521 Analog and Digital Communications

EE521 Analog and Digital Communications James K. Beard, Ph. D. jkbeard@temple.edu Tuesday, March 29, 2005 http://astro.temple.edu/~jkbeard/ Week 13

Attendance Week 13

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 • Term Projects Due April 19 (Next Week) • Final Exam Scheduled • Tuesday, May 10, 6:00 PM to 8:00 PM • Here in this classroom Week 13

Today’s Topics • Term Project • Quiz • Main Quiz • Backup Quiz • Term Project • Discussion (as time permits) Week 13

Quiz Question 1 Parts I and II • Criteria for a signal to be a power/energy signal • Finite energy == energy signal • Finite power == power signal • Equations Week 13

Question 1 Part III: Power Spectrum of an Energy Signal • Energy spectrum is simply magnitude squared of Fourier transform of energy signal • Fourier transform of energy signal not defined • Use the Fourier transform of the autocorrelation function for the power spectrum Week 13

Question 2 Part I • This is a quadrature demodulator • The output x0(t) • Frequency shifted to baseband • Negative frequency image • Shifted to -2.f0 • Attenuated by LPF • Has a bandwidth of B/2 • LPF filter • Bandpass flat to B/2 • Stopband start by 2.f0 - B/2 • Leak-through from xB(t) may be considered too Week 13

Question 2 Part II (1 of 2) • Sample after the LPF • Nyquist sample rate is 2.B/2 or B • Waveform preservation to bandwidth W>B may be considered • Sample at I.F. • Sample rate equations Week 13

Question 2 Part II (2 of 2) • The L.O. at the sample times • Decimation opportunities • Output sample rate should be about B • Decimation by 2 may be possible Week 13

Question 3 • Antipodal pulses • Amplitude is 1 volt, duration is T seconds • Bandwidth is 1/T, noise PSD is N0 • BER is • What is Eb/N0? Week 13

Question 4 Part I (1 of 2) • Mean number of bit errors per unit time is • BER for four errors per hour at 1 MB/s Week 13

Question 4 Part I (2 of 2) • Using the base equation • The approximation given provides us with Week 13

Question 4 Part II • The SNR equation • Bandwidth of 1.2 MHz, bit rate 1 MBPS Week 13

Question 5 Part I • A linear block code has a generator matrix • Code words are found by left-multiplying by all 16 combinations of bits Week 13

Code Vectors Week 13

Question 5 Part II (1 of 2) • The code is systemic because the last four columns are an identity matrix • The parity array portion of the generator matrix is the first three columns Week 13

Question 5 Part II (2 of 2) • The parity check matrix augments the matrix P along the other index with an identity matrix Week 13

Question 5 Part III • The syndrome is S=r.HT • The received data vector r is {1,1,0,1,1,0,1} • The syndrome is {0,1,0} • Received data has a bit error • Corrected data vector is {1,0,0,1,1,0,1} • Decoded message is {1,1,0,1} Week 13

Question 5 Part IV • The minimum Hamming distance between codes • Hamming distance between codewords == Hamming weight of their sum • Hamming weight of a codeword == Hamming distance from the all-zeros codeword • Closed on subtraction means all differences are equal to one of the codewords • Thus, the smallest Hamming weight is the minimum Hamming distance • For our problem this is 3 Week 13

Question 5 Part V • Error-detecting and correcting capability • For a dmin of 3 • Correct 1 • Detect 2 Week 13

Question 6 ( 1 of 3) • Calculate the probability of message error for a (24,12) linear block code using 12-bit data sequences. Assume that the code corrects up to two bit errors per block and that the base BER is 10-3. Week 13

Question 6 (2 of 3) • Probability of a message error is the probability of 3 or more bit errors out of 24 • Binomial distribution • Incomplete beta function Week 13

Question 6 (3 of 3) • Probability of 3 errors is 1.98192E-06 • Probability of 3 or more errors is 1.99238E-06 • Differences is about 0.5% • Improvement in BER is a factor of 505 Week 13

Backup Quiz Question 1 Part I • See main quiz Question 2 • Equation for the output • LPF • Bandpass flat to B/2+Δf • Stopband start by 2.f0 - B/2-Δf • Leak-through from xB(t) may be considered too Week 13

Backup Quiz Question I Part II UNSAMPLED OUTPUT Week 13

From Inspection of Output • Use cursor readout in SystemView • Spectrum is down 30 dB at about 3700 Hz • Passband to 3700 Hz • Stopband starts by 16.5 kHz to attenuate image at 20 kHz • Operations • LPF to specifications • Sample at two times 3900 Hz Week 13

System Week 13

Critical Block Parameters LPF Parameters: Operator: Linear Sys Butterworth Lowpass IIR 4 Poles Fc = 6e+3 Hz Quant Bits = None Init Cndtn = 0 DSP Mode Disabled Max Rate = 100e+3 Hz Sampler Parameters: Operator: Sampler Interpolating Rate = 7.8e+3 Hz Aperture = 0 sec Aperture Jitter = 0 sec Max Rate = 7.8e+3 Hz Week 13

Spectrum of Sampled Output Week 13

Backup Quiz Question I Part III • Sample the 10,000 Hz signal. Use the lowest sample rate that preserves the signal. • See main quiz Question 2 Part II Week 13

Input Signal at 10,000 Hz Week 13

Sampled at 13,333 Hz WHOOPS Week 13

Sampled at 40,000 Hz Week 13

Parameters • Sample at 40,000 Hz • Frequency-shift down to baseband • 10,000 Hz frequency shift • Complex LO (digital quadrature demodulator) • Downsample to 8,000 Hz complex Week 13

Output Before Downsampling Week 13

Output Downsampled to 8 kHz Complex Without Filtering Week 13

Final System Block Diagram Week 13

Backup Quiz 2 Question 2 • See main Quiz 2 Question 5 • The received data vector r is {1,0,1,0,1,1,1} • The syndrome is {1,0,1} • Received data has a bit error • Corrected data vector is {1,0,1,0,0,1,1} • Decoded message is {0,0,1,1} • Other answers same as those of main quiz Week 13

EE521 Analog and Digital Communications