Automatic Gain Control Response Delay and Acquisition in Direct-Sequence Packet

Radio Communications

Sure 2007Stephanie GramcDr. Noneaker

Research Motivation

Direct-sequence (DS) spread-spectrum modulation– Use of bandwidths much wider than minimum required for

simple point-to-point communication at the same data rate– Resistance to jamming– Resistance to detection– Sharing of channels among multiple users

Applications– Cellular code-division multiple-access networks– Tactical military radio networks– Wireless local area networks with high data rate

Research Purpose

Focus on acquisition of a DS packet– Timing uncertainty of arriving signal– Must achieve synchronization to demodulate data– Can be limiting factor in communication system

performance Model the delay caused by an AGC System’s

delay in responding to change in signal power

Analyze the effect of the AGC delay on acquisition performance

aM-1a3

a2a1

a0

Packet Transmission Format

Preamble sequence– Not modulated– Known a priori at receiver– Frequently changed for security– Let M = preamble length in chips– Preamble transmitted over time [0, MTc)– Values of +1, -1, j, or -j

Preamble Sequence Data

-1

0

1

0 1 2 3 4 5 6 7

s(t) Preamble Sequence

time (Tc chips)

s(t): Transmitted signal where

n(t): Additive White Gaussian Noise (AWGN) Channelwith spectral density of N0/2

r(t): Received signal

Communication System

1

0

( ) ( )c

M

i T c

i

s t a p T iT

1 if 0( )

0 otherwisec

cT

T Tp t

( ) ( ) ( )r t s t n t

t = kTs

s(t) r(t)

Chip-Matched

Filter

Sequence-Matched

Filter

n(t)

AGC Acquisition Algorithm

Preamble Matched Filter

IF Filter

Matched Filter

Input convolved with local copy of preamble

Example– M=7 and Sequence =

(+1, -1, -1, +1, -1, +1, +1)

– Preamble received at t=0– Peaks at t = 7(Tc ) = MTc

Output peaks when last chip of an incoming (matched) preamble sequence is received

Use an acquisition threshold to detect end of arriving preamble sequence

-2

0

2

4

6

8

0 2 4 6 8 10 12 14

Noise Free Matched Filter Output

Matched Filter (Alternate Representation)

Chip-Matched Filter:

– Convolve incoming signal with one chip of local preamble

Discrete time sequence matched filters– Sample chip-matched filter output at times t = kTc, k =0 to M-1

– Apply weight of ak to each output

– Produces a group of independent Gaussian random variable (sum represents matched filter output)

t = kTs Chip-

Matched Filter

Sequence-Matched

Filter

( ) ( ) ( )c cT c Th t p T t p t

Automatic Gain Control (AGC)

Gain is the increase in power of the received signal

AGC automatically adjusts the gain based on the strength of the input signal

Designed to keep average power constant into subsequent electronics

Weaker signals are amplified more: higher gain

Stronger signals are amplified less: lower gain

time

Gain levels for s(t) + n(t)

Idealized AGC Behavior

Gain levels for n(t)

0

2

4

6

8

10

12

-119 -79 -39 1 41 81

Automatic Gain Control Response Delay

Practical AGC has delayed response to signal-level change Effects input to matched filter effects acquisition algorithm Model response as linear with response delay tagc:

More Realistic AGC Behavior

tagctime

A0= Gain levels for n(t)

0

2

4

6

8

10

12

-120 -80 -40 0 40 80 120

A1= Steady state gain levels for s(t) + n(t)

0

1 00

1 AGC c

0 < t

( ) 0

t t < MT

AGCAGC

A

A AA t A t t ttA

Accounting for Channel Attenuation

Old approximation of idealized AGC system gain levels with

Develop gain approximations for AGC system with response delay

Adjust statistics to model linear delay in AGC system

1

0

1

1 0c

t < 0

( )

0 t < MT

( )

( ) ( )

s

c

s

c

t

NT

NP

T

Preamble Signal-to-noise Ratio

Noise power spectral density in received signal is:

Energy in received signal is:

SNR

0

2

N

2cE MPT

2

0

cMPTSNR

N

Mean of Matched Filter Output

AGC system with idealized instantaneous response

β is measure of IF filter bandwidth CA(i) measures characteristics of preamble sequence

Mean of Matched Filter Output

AGC system with response delay

agc

agc

0 i < 0

1| ( ) | 1 i < t

2

1[ ] 1

| ( ) | | ( ) | t i < M2

c As agc

i i sagcc A c A

agc agc s

agc

a

SNR i SNR SNRT C M i

M t M SNR M

SNR SNRE U jV M SNR Mt i SNR

T C M i T C M it i t i SNR M

t

t

1

1i = M

2

s

gc agc s

SNR SNR

M SNR M i SNR

i t i SNR M

Variance of Matched Filter Output

AGC system with idealized instantaneous response

2

2

[ ]

i < 02

( )1 i M

2 2 ( )

i i

c

s

c c

s s

VarU Var V

MT

M i T MiT

SNR M

Variance of Matched Filter Output

AGC system with response delay

2

2

2

2

2

2agc

2

[ ]

i < 02

( ) 33

2 3

( 2 ) 12 1 i < t

( ) ( )

( )

2 6

i i

c

s

c cagc agc

s s agc

c agc c

s

VarU Var V

MT

M i T MT SNR SNR SNR SNRt it

SNR t M M M SNR M

SNR SNR MSNR i

M SNR M M SNR M

M i T t MT

2

agc 1 2 1 ( )

t i M( ) 2 ( )

agc c

s s

SNR M i t MT

M SNR M M SNR M SNR M

Acquisition Algorithm

Let acquisition threshold = ηi

If Xi > ηi

– Declare hit– Enter verification mode to check if synchronization has

occurred If verified, enter data-detection mode If verification fails, return to acquisition mode

Let verification interval = Q– Amount of time required for receiver to determine if false

alarm occurred and return to acquisition mode

Probability of Not Acquiring a Packet

Probability of a miss– Acquisition fails because matched-filter output

does not exceed acquisition threshold when the end of the preamble is received

Probability of a false alarm– Acquisition fails because algorithm in in

verification mode when the end of the preamble is received and acquisition threshold is exceeded

P (not acquiring) = P (miss) + P (false alarm)

Simulate Matched Filter Output

Generate two independent Gaussian random variables with unit variance and zero mean: Ui and Vi

Scale Ui and Vi by standard deviation and mean expressions corresponding to current time in the simulation

Form test statistic: Xi =Ui2

+ Vi2

Simulation Times of Receiver System

i = 0 corresponds to time start of packet’s preamble is received

{Xi, i<0} correspond to time before packet’s arrival

{Xi, … Xtagc} correspond to time during reception of preamble effected by delay in AGC system

{Xtagc, … XM-1} correspond to time during reception of preamble with completely adjusted gain

XM corresponds to reception of full preamble sequence

Probability of Not Acquiring in AGC System with Idealized AGC Response

for M=26, Q=65

Probability

SNR (db)10

-6

10-5

0.0001

0.001

0.01

0.1

1

0 10 20 30 40 50 60

P(fa)P(miss)

0.001

0.01

0.1

1

0 10 20 30 40 50

t_agc = 0t_agc = 1t_agc = 3t_agc = 5

0.001

0.01

0.1

1

0 10 20 30 40 50

t_agc = 0t_agc = 1t_agc = 3t_agc = 5

Probability of Not Acquiring

Probability of Not Acquiring in AGC System with Response Delays

for M=26, Q=65

SNR (db)

Probability of Not Acquiring

Probability of Not Acquiring in AGC System with Response Delays

for M=100, Q=250

10-6

10-5

0.0001

0.001

0.01

0.1

1

0 10 20 30 40 50 60

t_agc = 0t_agc = 1t_agc = 5t_agc = 15t_agc = 25

SNR (db)

1

1.5

2

2.5

3

3.5

4

4.5

5

0 5 10 15 20 25 30

Simulation ResultsLinear Results

Percent of preamble effected by delay

Conclusions

Misses contribute to not acquiring for lower SNR values

False alarms contribute to not acquiring for higher SNR values

As the response delay time in the AGC system increases, probability of not acquiring increases

Increase Factor of Not Acquiring with AGC Delay Compared to Ideal AGC

Acknowledgments

Dr. Noneaker Javier Schlömann Dr. Xu Josh Lawrence Workshop Speakers

– Dr. Hubbard– Dr. Baum– Dr. Russell– Dr. Hubing

Questions

The Effect of Automatic Gain Control on Serial Matched-Filter Acquisition in Direct-Sequence Packet Radio Communications

Sure 2007Stephanie GramcDr. Noneaker

IF (Intermediate-frequency) Filter

IF filter rejects out of band noise power in received signal before inputting signal into AGC system

(1/3):– Ratio of signal power that is passed through the IF filter

– Ratio of the noise power passed through the IF filter

– Measure of the ratio of IF filter’s bandwidth to the bandwidth of

the DS signal

ns

n

s

Accounting for Signal Power

Power:

Energy:– Per chip:

– Per preamble:

2

1 1

0 0

2

( ) ( ) ( )

| ( ) | for 0

c c

M Mc

i T c i T cci i

c

Es t P a p t iT a p t iT

T

s t P t MT

22 2

( 1)| ( ) | c

c c

c

i Ts t dt PT E

iT

22 2| ( ) |

0

c

c c

MTE s t dt ME MPT

0.001

0.01

0.1

1

0 10 20 30 40 50 60

t_agc = 0t_agc = 1t_agc = 2t_agc = 3t_agc = 4t_agc = 5

SNR (db)

Probability of Not Acquiring

Probability of Not Acquiring in AGC System with Response Delays

for M=26, Q=65

Probability of Not Acquiring

Probability of Not Acquiring in AGC System with Response Delays

for M=100, Q=250

10-6

10-5

0.0001

0.001

0.01

0.1

1

0 10 20 30 40 50 60

t_agc = 0

t_agc = 1

t_agc = 5

t_agc = 10

t_agc = 15

t_agc = 20

t_agc = 25

SNR (db)