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Motivation Technogenic vs thermal NDLs Adaptive NDLs
Adaptive Analog Nonlinear Algorithms and Circuitsfor Improving Signal Quality
in the Presence of Technogenic Interference
Alexei V Nikitin
Avatekh IncLawrence, KS 66044, USA
Ruslan L Davidchack
Department of MathematicsUniversity of LeicesterLeicester, LE1 7RH, UK
Tim J Sobering
Electronics Design LaboratoryKansas State University
Manhattan, KS 66506, USA
November 19, 2013
1/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
1 MotivationCommunications receivers resistant to technogenic interferenceNonlinear vs. linear: The rationale
2 Distributional di↵erences between thermal noise and technogenic signalsPractical example of increasing peakedness
3 Nonlinear Di↵erential Limiters (NDLs)2nd order NDL exampleExample of sub-circuit topologies
4 Adaptive NDLs (ANDLs)ANDLs at work
2/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Motivation
Communications receivers resistant to technogenic interference
RECEIVER
RF/analog
mixer/linearfilters
digital
ADC/DSP
man-madeinterference
IMPROVED RECEIVER
)
INCREASED CHANNEL CAPACITYin the presence of man-made interference
RF/analog
mixer/ANDLs
digital
ADC/DSP
−18 −12 −6 0 6 12 180
1
2
3
4
5
6
7 thermal SNR=20 dB
thermal SNR=10 dB
thermal SNR=0 dB
ANDL
linear
ANDL vs. linear: channel capacity
interference power in basebandrelative to thermal noise power (dB)
channelcapacity
(bps/
Hz)
Replacing certain analog filters in communications receiver by ANDLs provides resistance to man-made interference
ANDLs vs. linear: baseband SNR (14/15)
3/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Motivation
Nonlinear vs. linear: The rationale
Technogenic (man-made) signals are typically distinguishable from purelyrandom (e.g. thermal)
specifically, in terms of amplitude distributions/densities (non-Gaussian)
At any given frequency, linear filters a↵ect power of both noise and signalof interest proportionally, and cannot improve SNR in passbandNonlinear filters can reduce PSD of non-Gaussian interference in passbandwithout significantly a↵ecting signals of interest
increasing passband SNR and channel capacity
Linear filters are converted into Nonlinear Di↵erential Limiters (NDLs) byintroducing feedback-based nonlinearities into filter responses
NDLs/ANDLs are fully compatible with existing linear devices and systems
enhancements/low-cost alternatives to state-of-art interference mitigation methods
4/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Distributional di↵erences between thermal noise and technogenic signals
Amplitude vs. time
Amplitude density
integrator
di↵erentiator
bandpass
THERMAL
For Gaussian (e.g. thermal) signals, amplitude distributionremains Gaussian regardless of linear filtering
Amplitude vs. time
Amplitude density
integrator
di↵erentiator
bandpass
TECHNOGENIC
Amplitude distributions of non-Gaussian signalsare generally modifiable by linear filtering
5/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Distributional di↵erences between thermal noise and technogenic signalsMeasures of peakedness
Convenient measure of peakedness for z(t) = I (t) + iQ(t):
KdBG(z) = 10 lg
✓h|z|4i�|hzzi|2
2h|z|2i2
◆
angular brackets denote time averaging
based on definition of kurtosis for complex variables
“decibels relative to Gaussian” (dBG) – in relation to Gaussian distribution
KdBG vanishes for Gaussian distribution
KdBG < 0 for sub-Gaussian, KdBG > 0 for super-Gaussian
high peakedness ) frequent occurrence of outliers (impulsive)
6/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Distributional di↵erences between thermal noise and technogenic signalsPractical example of increasing peakedness
⇥
fTX = 2GHz
⇥lowpass
40MHz
I(t)
Q(t)
fRX = 2.065GHz
notch
65MHz
I(t)
Q(t)TX RX
I
I/Q signal traces
0 2 4 6 8 10 12
Q
time (µs)
am
plitu
de
−100 −50 0 50 100−225
−200
−175
−150
−125PSDs of I(t) + iQ(t)
PSD
(dBm/Hz)
frequency (MHz)−6 −4 −2 0 2 4 6
10−4
10−3
10−2
10−1
100
101
−0.5 dBG
10.9 dBG
I/Q amplitude densities
density
(σ−1)
amplitude (σ)
Green lines and text: before notch Blue lines and text: after notch
Notch filter reduces sub-Gaussian part of interference without a↵ecting signal of interestand/or PSD of mpulsive interference around baseband, enabling its e↵ective mitigation by NDLs
7/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Nonlinear Di↵erential Limiters (NDLs)
NDLs are designed for mitigation of impulsive interference(i.e. characterized by relatively high occurrence of outliers)
NDL
↵
z(t) ⇣(t)
B()
CSC
controlsignalcircuit
-controlledlowpass filterwith B=B()
input
z(t)
output
⇣(t)
↵
(t)
Block diagram of Nonlinear Di↵erential Limiter
Example of sub-circuit topologies (11/15)
Dynamic modification of filter bandwidth
based on magnitude of di↵erence signal
z(t)�⇣(t)“Bandwidth” B of NDL = bandwidth of
linear filter with same coe�cients
just convenient computational proxy
B is non-increasing function of |z�⇣|monotonically decreasing for |z�⇣|>↵
↵ is resolution parameter
Linear filter when ↵ ! 1
8/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Nonlinear Di↵erential Limiters (NDLs)
2nd order NDL example
⇣(t) = z(t) � ⌧ ⇣̇(t) � (⌧Q)2 ⇣̈(t) – second order linear lowpass filter
⌧ is time parameter, Q is quality factor
“bandwidth” is decreasing function of ⌧ , increasing function of Q
Constant-Q NDL:
⌧ (|z � ⇣|) = ⌧0 ⇥(
1 for |z � ⇣| ↵⇣|z�⇣|
↵
⌘�otherwise
� > 0
Canonical Di↵erential Limiter (CDL) for � = 1
Di↵erential over-Limiter (DoL) for � > 10 1 2 30
1
2
3
|z − ζ |/α
τ/τ0
CDL time parameter τ (|z−ζ |)
More on NDLs: US patent 8,489,666 (16 July 2013)
9/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Nonlinear Di↵erential Limiters (NDLs)
2nd order CDL: Nonlinear suppression of impulsive noise
“Disproportional” (nonlinear) suppression of impulsive noise by NDLs
2nd order linear
2nd order CDL
2nd order linear
2nd order CDL
Linear filter: Output noise is proportional to input noise NDL: Output is insensitive to impulsive noise
10/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Nonlinear Di↵erential Limiters (NDLs)
Example of sub-circuit topologies
OTA-based 2nd order CDL
�Vc+
�
+
�Vc+
+
��Vc+
+
�
�Vc+
�
+
x(t)�(t)
Vc
�C
C
�(t) = x(t) � ⌧ �̇(t) � (⌧Q)2 �̈(t)
Q =p� , ⌧ =
C
�Vc
Voltage-controlled 2nd order lowpass
g
m
+
�
+
g
m
+
�
+
g
m
+
�
+
KIb��
+ Vc
|z�⇣|
↵
Ib
Vc =1
K
⇥(
1 for |z � ⇣|↵
↵
|z�⇣| otherwise
0 1 2 3 4 50
0.2
0.4
0.6
0.8
1
1.2
|z − ζ | / α
Vc×
K
Control voltage Vc(|z − ζ |)
CDL control voltage circuit
Nonlinear Di↵erential Limiters (8/15)
11/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Adaptive NDLs (ANDLs)
An ANDL contains a sub-circuit (characterized by a gain parameter)that monitors a chosen measure of the signal+noise mixtureand provides a time-dependent resolution parameter ↵ = ↵(t)
to the main NDL circuitsuitable for improving quality of non-stationary signals under time-varyingnoise conditions
More on NDLs/ANDLs:
Nikitin AV: Method and apparatus for signal filtering and for improving properties of electronicdevices. WO 2013/151591 (10 October 2013)
This MILCOM’13 paper http://www.avatekh.com
12/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Adaptive NDLs (ANDLs)
ANDL example
3
ALLPASS
5 1
2
+
�ABS WMT
4
G
z(t)⇣(t)
↵(t)
G
gain
1 2nd order constant-Q DoL (� = 2) with ⌧0 = 12⇡f0
2 2nd order lowpass with ⌧ = ⌧0 (same Q)
3 Higher-order lowpass with ⌧ ⌧ ⌧0
4 WSMR circuit w/ 2nd order Bessel window (⌧b
=2⌧0/p3, Q=1/
p3)
5 Allpass with delay 2⌧0
13/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Adaptive NDLs (ANDLs)
ANDLs at work
⇥
Out-of-band transmitter
fTX
⇥A/D
A/D
linear
ANDL
baseband
Linear/ANDL receivers
fRX 6= fTX
I(t)
Q(t)
I(t)
Q(t)TX RX
“Native” RX signal
OOB
RED: 0 dB thermal SNR GREEN: 10 dB thermal SNR BLUE: 20 dB thermal SNR
Communications receivers resistant to man-made interference (3/15)
14/15
Motivation Technogenic vs thermal NDLs Adaptive NDLs
Adaptive NDLs (ANDLs)
ANDLs at work
⇥
Out-of-band transmitter
fTX
⇥A/D
A/D
linear
ANDL
baseband
Linear/ANDL receivers
fRX 6= fTX
I(t)
Q(t)
I(t)
Q(t)TX RX
“Native” RX signal
OOB
RX signal
w/o noise
S/N=−2.1dB S/N=9.4dB
frequency (MHz)
powerdensity
(dB)
PSDs in baseband
−3 −2 −1 0 1 2 3
−15
−10
−5
0
5
10 I
I/Q baseband traces (linear)
6 10 14 18 22 26
Q
am
plitu
de
S/N=−2.1 dB
I
I/Q baseband traces (ANDL)
6 10 14 18 22 26
Q
S/N=9.4 dBtime (µs)
am
plitu
de
LEFT: Interference PSD reduction in passband RIGHT: Baseband time domain I/Q traces
15/15
Appendix I Appendix II
Appendix I
Digital NDLs/ANDLs
NDLs/ANDLs are analog filterscombine bandwidth reduction with mitigation of interference
Also allow for near-real-time finite-di↵erence (digital) implementationsrelatively simple computationally inexpensive low memory requirements
Digital NDLs/ANDLs require high sampling ratesshould use multi-rate processing
widebandlowpass
analogNDL/ANDL
A/D
low-bit,high-speed A/D
digital NDL/ANDLwith downsampling
A/D
high-bit,low-speed A/D
(a)
(b)
Analog (a) and digital (b) NDL/ANDL deployments
16/15
Appendix I Appendix II
Appendix II
References to relevant work
Nikitin AV, Davidchack RL, Smith JEOut-of-band and adjacent-channel interference reduction by analog nonlinear filtersIn Proc. of the 3rd IMA Conference on Mathematics in Defence, Malvern, UK, 24 October 2013
Nikitin AVMethod and apparatus for signal filtering and for improving properties of electronic devices
WO 2013/151591 (10 October 2013)
Nikitin AVMethod and apparatus for signal filtering and for improving properties of electronic devices
US Patent 8,489,666 (July 16, 2013)
Nikitin AV, Epard M, Lancaster JB, Lutes RL, Shumaker EAImpulsive interference in communication channels and its mitigation by SPART and other nonlinear filtersEURASIP Journal on Advances in Signal Processing, 2012, 2012:79
Nikitin AVOn the interchannel interference in digital communication systems, its impulsive nature, and its mitigationEURASIP Journal on Advances in Signal Processing, 2011, 2011:137
Nikitin AVOn the impulsive nature of interchannel interference in digital communication systemsIn Proc. IEEE Radio and Wireless Symposium, Phoenix, AZ 2011:118-121
17/15