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 b /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 Bandwidth-to-bitRate 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 Binary Phase Shift Keying 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) +1 0 BPSK signal Carrier BPSK Signal x Carrier LPF of this recovers signal Coherent Recovery (BPSK): In-phase carrier available at receiver. Incoherent Recovery (DPSK): Differential encoding allows recovery without carrier

Coding No. 13  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. 14  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. 15  Seattle Pacific University QPSK Waveform Dotted line is reference for 11 (  ).     QPSK    Larger phase offset  Earlier in time (waveform offset to the left)

Coding No. 16  Seattle Pacific University Energy ratio and BER Higher E b /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 b /N 0 Worse Better Sampling Quantizing Coding Modulation Transmission

Coding No. 17  Seattle Pacific University Multi-phase, Multi-amplitude PSK Generally known as Quadrature Amplitude Modulation (QAM) Shift both phase and amplitude to generate multiple constellation points Combines ASK and PSK     8QAM - 3 bits/baud         Bit assignment= High: x coordinate Mid : y coordinate Low : 0-inner; 1-outer

Coding No. 18  Seattle Pacific University 8-QAM Waveform             Bit assignment= High: x coordinate Mid : y coordinate Low : 0-inner; 1-outer

Coding No. 19  Seattle Pacific University Impediments to High Data Rates Standard signaling schemes achieve high data rates through 1. Complex Multi-bit Symbols Needs High SNR Suffers from slow and fast fading, interference 2. Wide Channels Needs High BW Suffers from frequency dependent fading (multipath) 3. High symbol rates Needs high BW and SNR Suffers from ISI (multipath)

Coding No. 20  Seattle Pacific University 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 Frequency Power Frequency Power

Coding No. 21  Seattle Pacific University Frequency Distortion and MCM Frequency Power Frequency Power Frequency Fading Coherence bandwidth << channel width A single channel exhibits frequency-dependent distortion in the presence of multipath frequency fading Coherence bandwidth > channel width Each narrow channel is less subject to distortion Difference channels experience different signal power, but this can be dealt with

Coding No. 22  Seattle Pacific University ISI and MCM High data rate requires short bit times Multipath delay spread causes inter-symbol interference 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 Time Single carrier – Short bit time Time Multi carrier – Long bit time

Coding No. 23  Seattle Pacific University 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 Frequency Power Frequency Power

Coding No. 24  Seattle Pacific University Orthogonal Carriers Signals spread in bandwidth in a regular way, with peaks/zeros at multiples of the primary frequency (harmonics) Normalized Frequency We can choose carriers that line up with the zeros! By choosing orthogonal carriers, the channel spacing is reduced and guard bands are un- needed OFDM

Coding No. 25  Seattle Pacific University Modulating Orthogonal Carriers A nice picture, but doesn’t this require ultra-complex radios? 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! Inverse Fast Fourier Transform: Maps frequency bins to time-domain signals. Use IFFT with bins equal to channels. Perfect for the transmitter! Example: Spectrum Analyzer Example: Audio Equalizer

Coding No. 26  Seattle Pacific University The whole OFDM thing