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Bullock Engineering Research Copyright 2008
1
Digital vs. Analog Comms
A/D
5V analog = Digital 101
5V
Mod Demod
Digital 101 = 5V analog
5V
D/A
LO LO
Sampler
Analog + Noise
Digital
Mod Demod
LO LO
Analog System
Digital System
Perfect Reconstruction of the Digital Waveform Assuming No Bit Errors
Analog
PSK, FH, etc.
AM/FM etc
Bullock Engineering Research Copyright 2008
2
Digital Modulation
Bullock Engineering Research Copyright 2008
3
FSK and MSK Spectrums
Reduce Frequency Separation or Increase the Frequency Minimum Shift Key Rate - MSK
MSK
Bullock Engineering Research Copyright 2008
4
Continuous Phase - Phase Shift Keying CP-PSK
• Sinusoidal transitions from one phase state to another• No zero crossing, No AM• Remains at a phase state for a period of time• Used for packet radio and other burst type systems• Minimum Spectral Re-growth due to non-linearities
+45
-45
+135
-135
0,0
+90
-90
180 I Channel
Q Channel
Q
1
R
RR
R1,0
1,10,1
0
0
1
Bullock Engineering Research Copyright 2008
5
Spectral Re-growth
Output ofModulator
FilteredOutput SidelobesReduced
SpectralRe-growth(SidelobeRegeneration)
Bullock Engineering Research Copyright 2008
6
Practical Digital Waveform Impulse Response
MSKGaussian Filter
Ideal filter is the Sinx/x which is impossible to build These filters approx. this ideal filter
Sinx/x
Raised Cosine
Raised cosinesquared
Bullock Engineering Research Copyright 2008
7
Direct Sequence Spread Spectrum
SpreadSpectrumSpreader
Signal
SpreadSpectrum Signal
Jammer
Signal
Jammer
SpreadSpectrum
despreader
Jammer
Signal
SpreadSpectrumReceiver
Signal
Jammer
Fast PNCode
Fast PNCode
Filter
Bullock Engineering Research Copyright 2008
8
FH Spread Spectrum
Spread Spectrum JammerSignal
SpreadSpectrumSpreader
Signal
Jammer
SpreadSpectrum
despreader
SpreadSpectrumReceiver
PN HoppingSynthesizer
PNDehoppingSynthesizer
Jammer
Jammer
Filter
Spread Spectrum Signal
Spread Spectrum Signal
Spread Spectrum Signal
Bullock Engineering Research Copyright 2008
9
Multiple User Techniques
Code 1
Code 2
Code 3
System 1
System 2
System 3
time1 2 3 1 2 3
System 1 System 2 System 3
a. Time division multiple access
b. Code division multiple access.
.
FrequencySystem 1 System 2 System 3
c. Frequency division multiple access.
f2 f3f1
Bullock Engineering Research Copyright 2008
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Costas Loop
Signal 1
Signal 2
Bullock Engineering Research Copyright 2008
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OFDM Spectrum
0
0.2
0.4
0.6
0.8
1
1.2
-10 -5 0 5 10
Frequency
Ampl
itude Channel 2
Channel 3Channel 1
Bullock Engineering Research Copyright 2008
12
Chapter 3 The Receiver
PowerDivider
LO
IF BPFImageRejectFilter
T/RSwitch Limiter LNA IFAmp
AGC LO
LPF A/DConverter
ToDigitalProcessor
Transmitter
Superheterodyne
Bullock Engineering Research Copyright 2008
13
Phase Noise, Log-Log Scale
white noise fFlicker noise 1/fwhite FM 1/(f*f)
Flicker FM 1/(f*f*f)
Random walk FM 1/(f*f*f*f)dBc
10 kHz1 kHz100101
So(f)
Frequency
So(f) = power spectral density(radians2/Hz) dBc/Hz
1/(f*f*f*f) = close to carrier, difficult to measure, vibration, shock, temperature, environmental.
1/(f*f*f) =, observable in high quality oscillators, masked in low quality oscillators, not fully understood, physical resonance mechanism or actual parts in the oscillator.
1/(f*f) = common in passive-resonator like cesium and rubidium standards.
1/(f) = transistors, amplifiers, etc., noisy electronics, LNA helps.
f = produced like the 1/f noise, stages of amplification is mainly responsible, broadband noise.
Short term frequency/phase instability
Bullock Engineering Research Copyright 2008
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Group Delay
LinearReceiver
Constant Group Delay
Non-Linear
Receiver
ISI Dispersion
Non-Constant Group Delay
Bullock Engineering Research Copyright 2008
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Group Delay Compensator
Filter Response ______
Filter Group _______Delay
Constant Group Delay
Group Delay ______Compensator
Bullock Engineering Research Copyright 2008
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AliasingAliasing
Sample points in time
Waveform is sampled at the Nyquist rateEstimated FrequencyWaveform does not meet Nyquist criteriaAlias frequency produced by under-sampling the high frequency
tststststs
Bullock Engineering Research Copyright 2008
17
Control Theory Analysis and Root Locus Plot
Bullock Engineering Research Copyright 2008
18
AGC/PLL Comparison
Kd F(s) Threshold = 0 Kc Ko/S
a. AGC control system analysis block diagram.
b. PLL control system analysis block diagram.
+
-
Kd F(s) Threshold Integrator Ko+
-
V/dB 1/S dB/V
dB
dBmdBmDC offset
Kc
filter gain
phase
phase
phase error
V/phase filter no offset gain phase/V
VCO control curve
Amp control curve
Bullock Engineering Research Copyright 2008
19
Bode Plot for NegativeFeedback Systems
+20dB
0dB
Instability & oscillation criteria for negative feedback systems, 0dB Gain, -1800 phase shift
Gain
Phase
Frequency (log scale)
-1800
-2700
-10 dB
Gain Margin (-1800 phase shift) = 0dB – (-10dB) = 10 dB
-1000
Phase Margin(0dB gain) = -1000 – (-1800) = 800
Bullock Engineering Research Copyright 2008
20
Cascaded PN-code Matched Filters for Increased Process Gain and Margin
1 delay 1 delay 1 delay 1 delay
sum
1 -1 1 1Additional PN- Code(Or retrieve data direct)
444
44 4 4
4444
16
-4
Position of Pulse outputprovides data information
1 delay 1 delay 1 delay 1 delay
sum
1 -1 1 1PN- Code 111
11 1 1
4
-1
4 4
-4
1 1 1-1
1 1 1-1 -1-1 -1
1 1 1 1-1
Bullock Engineering Research Copyright 2008
21
Comparison between Absolute and Differential PPM
TOA Pulse 1Dead Time
TOA Pulse 2 TOA Pulse 3
Time Slots of PPM
Data output 011
Dead Time
Data output 000
Time Slots of PPM
. .
t0 t1 t2 t3 t4 t5 t6 t7
Dead Time
Absolute PPM
No Pulse detectedin Time Slots
No Data Output
Reference Pulse
Differential PPM
Reference Pulse
Dead Time
t0 t1
TOA Pulse 1
t2 t3 t4 t5 t6 t7 t0 t1
TOA Pulse 2
t2 t3 t4 t5 t6 t7
No Time Slots of PPMNo Dead Time
Received Pulse ok butNo time reference
No Data outputBut Provides reference
For next pulse
No Pulse detectedin Time Slots
No Data Output
Dead Time TOA Pulse 3
Time Slots of PPMData output 000
t0 t1 t2 t3
t0 t1 t2 t3t0 t1 t2 t3 t4 t5 t6 t7
Data Lost
Data Lost Data Lost
Bullock Engineering Research Copyright 2008
22
Coherent vs Differential Bit Errors
Coherent System
1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 1 0
Bit error
Differential System
1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1
Sent digital data
Sent digital data
Bit error
1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0
1 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1
Received digital data
Received digital dataTwo Received data errors
One Received data error
Bullock Engineering Research Copyright 2008
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Sliding Correlator
Bullock Engineering Research Copyright 2008
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Intersymbol Interference (ISI)• One received symbol interfering with adjacent received symbols• Caused by Dispersion
– Pulse stream/pulse consists of many frequencies – Fourier Series/Transform
– Frequencies propagate at different delays – non-constant group delay
Non-Linear
Receiver
ISIDispersion
Non-Constant Group Delay
ISI = -20log(Vh/Vl)
Vl = lowest Vpeak center of the eye.
Vh = highest Vpeak center of the eye.
Bullock Engineering Research Copyright 2008
25
CDF Equation For Gaussian Distribution
• Fx(x) = 1/2[1+erf(x/( ))], mean = 0• Fx(x) = 1/2[1+erf(-2/( ))]
– =1/2[1+erf(- )]– erf(-x) = -erf(x), -erf(1.414) = -.954– Fx(x) = 1/2[1- .954] = .023– Probability +/- 2 = 2*.023 =.0456– Probability inside curve = 1-.0456 = .954 = 95.4%.
2
22
Probability of Occurrence
Value x
Probability Density Function for Gaussian Distribution
x = - 2 x = +2
x = +1 x = -1 Fx(x) CDF
f
Cumulative Distribution Function for Gaussian Distribution
1 or 100%
.023
fx (x) for x = -2
fx (x) for x = -1
.15995.4%.
Bullock Engineering Research Copyright 2008
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Probability of Error Curves
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Eb/No (dB)
Pe
Coherent BPSKCoherent QPSKDPSKCoherent FSKNonCoherent FSK
Bullock Engineering Research Copyright 2008
27
Probability of Detection and False Alarms Curves
• Cumulative distribution function determines probabilities of one sided noise and S+N gaussian probability density functions
– CDF from the right – sum probabilities from the right.0 1.00E+00 0.00102259 #NAME? #NAME? 1 5 6.99 7.78
0.1 9.97E-01 1.34E-03 #NAME? #NAME? 1 5 6.99 7.780.2 9.89E-01 1.75E-03 #NAME? #NAME? 1 5 6.99 7.780.3 9.76E-01 2.28E-03 #NAME? #NAME? 1 5 6.99 7.780.4 9.57E-01 2.94E-03 #NAME? #NAME? 1 5 6.99 7.780.5 9.33E-01 3.78E-03 #NAME? #NAME? 1 5 6.99 7.780.6 9.06E-01 4.83E-03 #NAME? #NAME? 1 5 6.99 7.780.7 8.74E-01 6.14E-03 #NAME? #NAME? 1 5 6.99 7.780.8 8.38E-01 7.76E-03 #NAME? #NAME? 1 5 6.99 7.780.9 8.00E-01 9.76E-03 #NAME? #NAME? 1 5 6.99 7.78
1 7.59E-01 1.22E-02 #NAME? #NAME? 1 5 6.99 7.781.1 7.17E-01 1.52E-02 #NAME? #NAME? 1 5 6.99 7.781.2 6.73E-01 1.87E-02 #NAME? #NAME? 1 5 6.99 7.781.3 6.28E-01 2.30E-02 #NAME? #NAME? 1 5 6.99 7.781.4 5.83E-01 2.82E-02 #NAME? #NAME? 1 5 6.99 7.781.5 5.38E-01 3.43E-02 #NAME? #NAME? 1 5 6.99 7.781.6 4.94E-01 4.14E-02 #NAME? #NAME? 1 5 6.99 7.781.7 4.51E-01 4.98E-02 #NAME? #NAME? 1 5 6.99 7.78
0.00E+00
2.00E-01
4.00E-01
6.00E-01
8.00E-01
1.00E+00
1.20E+00
0
0.6
1.2
1.8
2.4 3
3.6
4.2
4.8
5.4 6
6.6
7.2
7.8
8.4 9
9.6
10.2
10.8
11.4 12
12.6
13.2
13.8
Energy
Pro
babi
lity
of O
ccur
ance
NoiseSignal + Noise
PdPfa Threshold
Bullock Engineering Research Copyright 2008
28
FEC Code GenerationBlock
Encoder
Figure 6.7.2.2a Block Codes (Hamming, Cyclic, RS Codes)
Figure 6.7.2.2b Rate 1/2 Convolutional Encoder
Information Input Bits
switch
Tapped Delay LineOutput Symbols Two times the
Input Rate
k Information Bits n bit code word n = Block Length
Maps k information bits into an n-symbol output block
XOR
XOR
•Convolutional code, rate ½, constraint length 7
Block Codes (Hamming, Cyclic, Reed Solomon Codes)
7-bit shift Register
1 2 3 4 5 6 7
Bullock Engineering Research Copyright 2008
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Example of Generating a Linear Systematic Block Code (7,4)
Generator Matrix Message Modulo-2(1000011) 1 (1000011)(0100110) 0(0010111) 1 (0010111)(0001101) 0
Systematic Code Word =(1010100)Identity MatrixMessages Codewords (7,4)(0000) (0000000)(0001) (0001101)(0010) (0010111)(0011) (0011010)(0100) (0100110)(0101) (0101011)(0110) (0110001)(0111) (0111100)(1000) (1000011)(1001) (1001110)(1010) (1010100)(1011) (1011001)(1100) (1100101)(1101) (1101000)(1110) (1110010)(1111) (1111111)
–4 bits of data–3 parity bits
Bullock Engineering Research Copyright 2008
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Error CorrectionError Vector H-T Coset, error vectorse6,e5,e4,e3,e2,e1,e0 * 0 1 1 0 e6 e6 1 0 0 0 0 0 0
1 1 0 e5 e5 0 0 1 0 0 0 0 01 1 1 = e4 e4 e4 0 0 1 0 0 0 01 0 1 e3 0 e3 0 0 0 1 0 0 01 0 0 e2 0 0 0 0 0 0 1 0 00 1 0 0 e1 0 0 0 0 0 0 1 00 0 1 0 0 e0 0 0 0 0 0 0 1
e5+e4+e3+e2 = 0e6+e5+e4+e1 = 0
e6+e4+e3+e0 = 10 0 1
3 equations, 7 unknowns (7-3=4), possible solutions = 24
Solve for a solution with the most zeros = all zeros except for e0 = 0000001 e6=e5=e4=e3=e2=e1=0 and e0 = 0000001 satisfies the three above equations with most zerosCorrect Code sent = 1010100
Vc = r+e = 1010101+ 0000001 = 1010100 Corrected bit in code word
Bullock Engineering Research Copyright 2008
31
Trellis Diagrams
Constant Mod hi = 1/4
Multi-h [1,2/4], [hi] = [1/4,2/4]
1st merge, need to make a decision2 possible paths
1st merge
Bullock Engineering Research Copyright 2008
32
Turbo CodesInformation Bits PAD
Interleaver
Encoder 1
Encoder 2
Mux Parallel/SerialPuncturing
+ Z-1 Z-1Z-1 Z-1
+
Turbo Encoder
Turbo Decoder
Turbo Encoded Output
Recursive Systematic Code Generator
Input
Decoder 1 Decoder 2Interleaver
De-Interleaver
De-InterleaverDe-MuxSerial/Parallel Insertion
Estimated Sequence
Turbo Encoded Input
PAD appends n – k tail bitsfor all zeros state, x0
Bullock Engineering Research Copyright 2008
33
Diffuse Reflection over a Glistening Surface
R
GlisteningSurface
hr
ht
Transmitter
Receiver
Reflected raysOff Glistening Surface
Bullock Engineering Research Copyright 2008
34
Antenna Diversity
Bullock Engineering Research Copyright 2008
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Quadrature GSO System
PD
PD
-+
PD
LO
PD
PD
-+
PD
LO
0
90
0
90
I
Q
wi
error i
error q
wq
int
int
I signal out
Q signal out
OMNI Antenna(Jammer only)
Directional Antenna(Signal + Jammer)
Jammer Only
Jammer Only
Bullock Engineering Research Copyright 2008
36
Wideband Adaptive Filter
LMS
Q-channel
WidebandSignal Only
High FreqWideband + NarrowbandSignal
DigitalFilter
DigitalFilter
LPF LPF LPF
LO
LPF
LPF
BPFBPFBPF
BPF
BPF
Synthesizer
-10 dB-10 dB
10 dB
10 dB
10 dB-10 dB
15 dB
30 dB30 dB
30 dB
10 dB
15 dB15 dB15 dB
-90o
I-channel
0o
4-portPD
10 dB
Update shared weights
ResidualNarrowbandSignal
NarrowbandSignal Estimate
Bullock Engineering Research Copyright 2008
37
GPS Landing Systems
D8PSK LPI/Anti-jam Data LinkSends GPS Corrections
Relative GPS for moving platforms (Aircraft Carriers)Kinematic Carrier Phase Tracking KCPT for CATIII landing systems
Bullock Engineering Research Copyright 2008
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MILCOM
Need to Provide a Military Communications Network
Bullock Engineering Research Copyright 2008
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Interferometer
Baseline
Antenna 1
Antenna 2
INTERFEROMETER
Phase 1
Phase 2
Measures the phase difference between two antennas
