Coding No. 1  Seattle Pacific University Modulation Kevin Bolding Electrical Engineering Seattle Pacific University

Coding No. 2  Seattle Pacific University Digital Transmission of Analog Data Sampling Quantizing Coding Modulation Transmission Convert to discrete samples (time domain) Convert to discrete levels (amplitude) Optionally re-map to a different logical code (may expand) Map to a physical code at desired frequency band Amplify and transmit Analog signal Digital data

Coding No. 3  Seattle Pacific University Sampling Sampling theorem: If sample rate >= 2x max frequency (f) And samples have infinite precision (analog)  Can reproduce signal exactly after filtering out frequencies >f Pulse-Amplitude Modulation – PAM Samples have analog (infinite precision) values Undersampling If sample rate is < 2f then it is possible to map multiple waveforms to the data (aliasing) Sampling Quantizing Coding Modulation Transmission

Coding No. 4  Seattle Pacific University Pulse Code Modulation PCM: Approximate analog samples with a discrete sample n bit sample  2 n levels Errors Not analog, so quantizing error is present Each additional bit halves the quantizing error (in volts) SNR is Power ratio (proportional to V 2 ) Each extra bit used increases SNR by factor of 4 (6 dB) N bits  Signal/quantization error = 4 n or 6n dB Sampling Quantizing Coding Modulation Transmission For n-bit quantization, the SNR = 6.02(n) dB

Coding No. 5  Seattle Pacific University 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 Sampling Quantizing Coding Modulation Transmission Purposes of coding Encryption Redundancy to help with error detection and correction Coding is addressed separately (later)

Coding No. 6  Seattle Pacific University Modulation Modulation: Alteration of one wave (carrier) to carry information provided by another (signal) Amplitude Modulation Frequency Modulation Phase Modulation Sampling Quantizing Coding Modulation Transmission 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

Coding No. 7  Seattle Pacific University 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 means an average of one error per million data bits transmitted Sampling Quantizing Coding Modulation Transmission

Coding No. 8  Seattle Pacific University Bit Errors From Noise Sampling Quantizing Coding Modulation Transmission Threshold 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

Coding No. 9  Seattle Pacific University 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) Sampling Quantizing Coding Modulation Transmission Threshold Pulse-spreading

Coding No. 10  Seattle Pacific University 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:

Coding No. 11  Seattle Pacific University Energy ratio E/N 0 as a Measure of Quality of Signal E/N 0 : 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 Sampling Quantizing Coding Modulation Transmission The “quality” of a modulated signal increases with: Increased Signal-to-Noise ratio (S/N) Increased bitRate-to-Bandwidth ratio (B/R) A combined metric can be formed by multiplying these 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 E b N/B = Noise power / Bandwidth = Noise power density = N 0

Coding No. 12  Seattle Pacific University Energy ratio and BER Higher E/N 0 means 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/N 0 We want BER to be low We expect BER to go down with increased E/N 0 Worse Better Sampling Quantizing Coding Modulation Transmission

Coding No. 13  Seattle Pacific University Binary Phase Shift Keying Sampling Quantizing Coding Modulation Transmission Use PM techniques Use phase angles (usually 0 and  )  (t)= , if s(t) = 1 0, if s(t) = 0 X LPF BPSK Recovered Carrier Data out BPSK Recovery (Coherent) Coherent Recovery (BPSK): In-phase carrier available at receiver. Incoherent Recovery (DPSK): Differential encoding allows recovery without carrier

Coding No. 14  Seattle Pacific University QPSK BPSK uses two phase angles, 0 and  Two possibilities for symbol  One bit per symbol If we use more phase angles, we can send more data per symbol Quadrature (or Quaternary) PSK QPSK uses angles  Four possibilities for symbol  Two bits per symbol    BPSK     QPSK     Noise causing phase change within +/-  will not cause error Noise causing phase change within +/-  will not cause error Symbol error rate twice as high as BPSK, but sends twice as many bits/second  Efficiency tie? Sampling Quantizing Coding Modulation Transmission

Coding No. 15  Seattle Pacific University Generating QPSK Generate two signals in quadrature to each other (  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    I=-1,Q=1 I=-1,Q=-1 I=1,Q=1 I = In Phase Carrier (cosine) Q = Quadrature Phase Carrier (sine) X Data QPSK Generation Splitter X   + QPSK Sampling Quantizing Coding Modulation Transmission

Coding No. 16  Seattle Pacific University QPSK Waveform I=1,Q=1I=-1,Q=1I=-1,Q=-1I=1,Q=1I=1,Q=-1 Sampling Quantizing Coding Modulation Transmission

Coding No. 17  Seattle Pacific University Constant Envelope Modulation Signal is sent by modulating the phase or frequency of carrier BPSK, QPSK are the most common No signal is modulated on the amplitude Distortion of carrier amplitude does not affect the signal Can be linear or nonlinear in digital mobile systems Sampling Quantizing Coding Modulation Transmission

Coding No. 18  Seattle Pacific University QPSK Signal Transition Diagram Sampling Quantizing Coding Modulation Transmission Shows transitions possible from one state to the next In QPSK, all transitions are possible The diagonal transitions create a particularly abrupt change in phase Create large sidelobes outside of the primary band

Coding No. 19  Seattle Pacific University Offset QPSK Modular Circuit Sampling Quantizing Coding Modulation Transmission

Coding No. 20  Seattle Pacific University OQPSK Signal Space Sampling Quantizing Coding Modulation Transmission

Coding No. 21  Seattle Pacific University  /4 QPSK ~ X X +  /2  /4 ODD EVEN Every other symbol Sampling Quantizing Coding Modulation Transmission

Coding No. 22  Seattle Pacific University  /4-QPSK Signal Space Diagram (0, 1)A (0, 0)A (1, 1)A(1, 0)A (0, 0)B (0, 1)B (1, 1)B (1, 0)B Sampling Quantizing Coding Modulation Transmission