Modulation

1. Modulation Kevin BoldingElectrical EngineeringSeattle Pacific University

2. Digital Transmission of Analog Data Analog signal Sampling Convert to discrete samples (time domain) Quantizing Convert to discrete levels (amplitude) Digitaldata Optionally re-map to a different logical code (may expand) Coding Modulation Map to a physical code at desired frequency band Transmission Amplify and transmit

3. Sampling theorem: If sample rate >= 2x max frequency (f) And samples have infinite precision (analog)  Can reproduce signal exactly after filtering out frequencies >f Sampling Quantizing Coding Modulation Transmission Sampling 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 • Undersampling • If sample rate is < 2f then it is possible to map multiple waveforms to the data (aliasing) Pulse-Amplitude Modulation – PAM Samples have analog (infinite precision) values

4. PCM: Approximate analog samples with a discrete sample n bit sample  2n levels Sampling Quantizing Coding 7 8 10 13 13 12 10 7 2 1 1 1 2 5 7 8 Modulation Transmission 15 14 Pulse Code Modulation 13 12 11 10 9 8 7 6 5 4 3 2 1 0 • Errors • Not analog, so quantizing error is present • Each additional bit halves the quantizing error (in volts) • SNR is Power ratio (proportional to V2) • Each extra bit used increases SNR by factor of 4 (6 dB) • N bits  Signal/quantization error = 4n or 6n dB For n-bit quantization, the SNR =6.02(n) + 1.76 dB

5. Sampling Quantizing Coding Modulation Transmission Coding • Coding is the substitution of one digital code for another digital code • Incoming bit stream is assumed to be unencoded – raw bits (‘0’ means ‘0’ and ‘1’ means ‘1’) • Substitute code may alter or add to the bit stream in a way that can be inverted • Purposes of coding • Encryption • Redundancy to help with error detection and correction • Coding is addressed separately (later)

6. Sampling Quantizing Coding Modulation Transmission Modulation • Modulation: Alteration of one wave (carrier) to carry information provided by another (signal) • Amplitude Modulation • Frequency Modulation • Phase Modulation • If the Modulating signal is a digital signal, we have a wider variety of choices • Vary amplitude, phase, or frequency • ASK, PSK, FSK • Send more than one bit per symbol • Vary more than one aspect at the same time • QAM – varies both amplitude and phase • For digital data transmission, the Bit Error Rate is the measure of performance

7. Sampling Quantizing Coding Modulation Transmission Bit Error Rate • Digital signal quality is measured by the Bit Error Rate • Number of errors per bit transmitted, usually assuming uniform, non-correlated noise • For example, BER of 10-6 means an average of one error per million data bits transmitted

8. Sampling Quantizing Coding Modulation Transmission Bit Errors From Noise • If the SNR is too low, errors occur • If the noise causes the signal to cross the threshold, the bit will be read in error Errors from noise Threshold

9. Sampling Quantizing Coding Modulation Transmission Bit Errors from Bandwidth Limited ISI • If the bandwidth is too low so pulses spread out • Sequential pulses start to overlap and interfere with each other • Inter-symbol Interference (ISI) Pulse-spreading Threshold

10. Bit Errors from Delay ISI • Multiple paths (due to reflections) have different lengths • Each path has a different delay • Reflections overlap and spread out • Inter-symbol Interference (ISI) Image source: http://www.complextoreal.com/chapters/isi.pdf

11. Sampling Quantizing Coding Modulation Transmission Energy ratio E/N0 as a Measure of Quality of Signal • The “quality” of a modulated signal increases with: • Increased Signal-to-Noise ratio (S/N) • Increased Bandwidth-to-bitRateratio (B/R) • A combined metric can be formed by multiplying these • Eb/N0 : Energy per bit / Noise power density • Similar to SNR, but also accounts for the bandwidth used • Normally expressed in dB • Equal to SNR if transmitting 1bit/Hz • S/N * B/R = SB/NR = (S/R) / (N/B)S/R = signal power / bits / time = (signal power)(time)/bits = Energy per bit = E or EbN/B = Noise power / Bandwidth = Noise power density = N0

12. 0 1 0 1 1 1 0 1 0 0 0 1 0 1 +1 0 p, if s(t) = 1 -1 F(t)= 0, if s(t) = 0 BPSK Recovery (Coherent) X BPSK Data out LPF Recovered Carrier Binary Phase Shift Keying • Use PM techniques • Use phase angles (usually 0 and p) BPSK signal Carrier BPSK Signal x Carrier • Coherent Recovery (BPSK):In-phase carrier availableat receiver. • Incoherent Recovery (DPSK):Differential encoding allowsrecovery without carrier LPF of this recovers signal

13. BPSK uses two phase angles, 0 and p Two possibilities for symbol  One bit per symbol p 0 0,-1 0,1 BPSK 3p/4 p/4 1,1 1,-1 Sampling -1,-1 Quantizing -1,1 7p/4 5p/4 Coding QPSK Modulation Transmission QPSK • Noise causing phase change within +/- p/2 will not cause error • If we use more phase angles, we can send more data per symbol • Quadrature (or Quaternary) PSK • QPSK uses angles p/4, 3p/4, 5p/4, 7p/4 • Four possibilities for symbol  Two bits per symbol • Noise causing phase change within +/- p/4 will not cause error • Symbol error rate twice as high as BPSK, but sends twice as many bits/second  Efficiency tie?

14. Sampling QPSK Generation Q = Quadrature Phase Carrier (sine) X 3p/4 p/4 Quantizing I=1,Q=1 I=-1,Q=1 + Data QPSK Splitter p/2 Coding I = In Phase Carrier (cosine) X I=-1,Q=-1 I=-1,Q=1 Modulation 7p/4 5p/4 Transmission Generating QPSK • Generate two signals in quadrature to each other (p/2 out of phase) • Cosine and Sine work well • Horizontal axis is the I-axis, Vertical is the Q-axis • Represent bits: 0  -1, 1  +1 • Group consecutive bits together in pairs; first bit is value is I, second is Q • Multiply coordinates by the I and Q carriers and add

15. 3p/4 p/4 1 01 11 7p/4 5p/4 10 00 QPSK QPSK Waveform Larger phase offset  Earlier in time (waveform offset to the left) 11 01 00 11 10 Dotted line is reference for 11 (p/4).

16. Sampling Quantizing Coding Modulation Transmission Energy ratio and BER • Higher Eb/N0means more “resources” available to a signal • Resources = SNR and bandwidth • Real measure of quality is the BER • For a given modulation scheme, we can plot the BER vs. E/N0 • We want BER to be low • We expect BER to go down with increased Eb/N0 Worse Better

17. Generally known as Quadrature Amplitude Modulation (QAM) Shift both phase and amplitude to generate multiple constellation points Combines ASK and PSK Multi-phase, Multi-amplitude PSK p/4 3p/4 011 111 Bit assignment= High: x coordinate Mid : y coordinate Low : 0-inner; 1-outer 010 110 100 000 001 101 7p/4 5p/4 8QAM - 3 bits/baud

18. 8-QAM Waveform Bit assignment= High: x coordinate Mid : y coordinate Low : 0-inner; 1-outer p/4 3p/4 011 111 010 110 100 000 001 101 7p/4 5p/4 010 001 110 100 011 111 101 000

19. Impediments to High Data Rates • Standard signaling schemes achieve high data rates through • Complex Multi-bit Symbols • Needs High SNR • Suffers from slow and fast fading, interference • Wide Channels • Needs High BW • Suffers from frequency dependent fading (multipath) • High symbol rates • Needs high BW and SNR • Suffers from ISI (multipath)

20. Multi-Carrier Modulation • Divide the single-carrier channel (wide bandwidth) into N narrower channels • Split the data into N streams, each at 1/Nth the data rate • Send the N streams over N channels Power Frequency Power Frequency

21. Frequency Distortion and MCM FrequencyFading • Coherence bandwidth << channel width • A single channel exhibits frequency-dependent distortion in the presence of multipath frequency fading Power Power FrequencyFading Frequency Frequency • Coherence bandwidth > channel width • Each narrow channel is less subject to distortion • Difference channels experience different signal power, but this can be dealt with

22. ISI and MCM • High data rate requires short bit times • Multipath delay spread causes inter-symbol interference Single carrier – Short bit time Multi carrier – Long bit time Time Time • Each carrier has 1/Nth the data – 1/Nth the data rate • Pulses are N times longer • Tolerates a great deal more multipath delay spread

23. Multi-Carrier Modulation – The bad news • To separate each of the carriers, guard bands are required - this uses bandwidth and reduces efficiency • Radios that send/receive using multiple carriers require complex and expensive filters Power Frequency Power Frequency

24. 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -5 -4 -3 -2 -1 0 1 2 3 4 5 Orthogonal Carriers • Signals spread in bandwidth in a regular way, with peaks/zeros at multiples of the primary frequency (harmonics) Normalized Frequency 1 0.8 0.6 0.4 • We can choose carriers that line up with the zeros! 0.2 0 -0.2 -0.4 -5 -4 -3 -2 -1 0 1 2 3 4 5 Normalized Frequency • By choosing orthogonal carriers, the channel spacing is reduced and guard bands are un-needed • OFDM

25. Modulating Orthogonal Carriers A nice picture, but doesn’t this require ultra-complex radios? 1 Example: Spectrum Analyzer Fast Fourier Transform: • Maps time-domain signals to frequency bins. Essentially, gives power level of the signal in a frequency range. • Use FFT with bins equal to channels. Perfect for the receiver! 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -5 -4 -3 -2 -1 0 1 2 3 4 5 Normalized Frequency Example: Audio Equalizer Inverse Fast Fourier Transform: • Maps frequency bins to time-domain signals. • Use IFFT with bins equal to channels. Perfect for the transmitter!

26. The whole OFDM thing http://en.wikipedia.org/wiki/File:OFDM_transmitter_ideal.png http://en.wikipedia.org/wiki/File:OFDM_receiver_ideal.png