Adaptive Analog Nonlinear Algorithms and Circuits for

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

[email protected]

Ruslan L Davidchack

Department of MathematicsUniversity of LeicesterLeicester, LE1 7RH, UK

[email protected]

Tim J Sobering

Electronics Design LaboratoryKansas State University

Manhattan, KS 66506, USA

[email protected]

November 19, 2013

1/15

mailto:[email protected]




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

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

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


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


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


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

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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



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



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



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


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

http://www.avatekh.com



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



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



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

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Adaptive Analog Nonlinear Algorithms and Circuits for