Transcript The Effect of Automatic Gain Control on Serial Matched

Automatic Gain Control Response
Delay and Acquisition in DirectSequence Packet Radio
Communications
Sure 2007
Stephanie Gramc
Dr. 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
Packet Transmission Format
Preamble Sequence
Data
s(t) Preamble Sequence
a0
1
a3
aM-1
0
a1
-1
0

1
Preamble sequence
–
–
–
–
–
–
a2
2
3
4
time (T chips)
c
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
5
6
7
Communication System
Preamble Matched Filter
n(t)
t = kTs
s(t)
IF
r(t) Filter
AGC
ChipMatched
Filter
SequenceMatched
Filter
Acquisition
Algorithm
M 1

s(t): Transmitted signal


1 if 0  T  Tc
s (t )   aipTc (T  iTc ) where pT (t )  
c
i 0
n(t): Additive White Gaussian Noise (AWGN) Channel
with spectral density of N0/2

r(t): Received signal
r (t )  s(t   )  n(t )
0 otherwise
Matched Filter
Noise Free Matched Filter Output

8

Input convolved with local
copy of preamble
Example
–
6
–
4
–

2
0

-2
0
2
4
6
8
10
12
14
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
ChipMatched
Filter
t = kTs
SequenceMatched
Filter
Matched Filter (Alternate Representation)

Chip-Matched Filter:
h(t )  pTc (Tc  t )  pTc (t )
–

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)
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
Idealized AGC Behavior
12
Gain levels for n(t)
10
8
6
4
Gain levels for s(t) + n(t)
2
0
-119
-79
-39
1
time
41
81
Automatic Gain Control Response Delay
12
10
More Realistic AGC Behavior
A0= Gain levels for n(t)
8
6
A1= Steady state gain
4
levels for s(t) + n(t)
2
0
-120
-80
-40
0
40
tagc



80
120
time
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:
0<t
 A0

 A0
A(t )   A0  At1AGC
t 0  t  tAGC

tAGC  t < MTc
 A1
Accounting for Channel Attenuation

Old approximation of idealized AGC system gain levels
with
1

( s  N 0 )


Tc
 (t )  

1
( s) ( P  

t<0
N
)
T
0
1
0  t < MTc
c

Develop gain approximations for AGC system with
response delay

Adjust statistics to model linear delay in AGC system
Preamble Signal-to-noise Ratio

Noise power spectral density in received signal is:
N0
2

Energy in received signal is:
E   MPTc
2

SNR
SNR 
 MPTc
2
N0
Mean of Matched Filter Output


 AGC system with
 idealized

response
0

 Tc | CA( M  i ) |
E[Ui  jVi ]  
  s (1  M  )

SNR

TcM


M

s
(1

)

SNR



instantaneous
i<0
1  i<M
i=M
β is measure of IF filter bandwidth
CA(i) measures characteristics of preamble sequence
Mean of Matched Filter Output

AGC system with response delay
0

i 
 1  SNR



 s
 M 2tagc 




1  SNR


E[Ui  jVi ]   tagc   s   M
 tagc  i 



1  SNR


 tagc   s   M


 tagc  i 
i<0
SNR
SNR

M
SNR   M

  Tc | CA( M  i ) |
 

SNR

SNR   M 
SNR
 i  1 
Tc | CA( M  i ) |  


2
 tagc  i   s  SNR   M

SNR


SNR   M   i  1 

SNR




2
 tagc  i   s  SNR   M 

1  i < tagc

 Tc | CA( M  i ) |

tagc  i < M
i=M
Variance of Matched Filter Output

AGC system with idealized instantaneous
response
VarUi  Var[Vi ]
 MTc
 2 s 


2

(
M

i
)
T
c 
MiTc




 2 s   2 s ( SNR   M )
2
i<0
1 i  M
Variance of Matched Filter Output

AGC system with response delay
VarUi  Var[Vi ]
 MTc
i<0
 2 s 

 ( M  i )Tc 2 
 3SNR 2
 SNR

MTc
SNR
SNR

t
agc

3




 itagc

2
 M

M
SNR


M
 2 s   3SNR stagc   M



 2
1
  SNR( SNR  2  M )  2SNR
1  i < tagc

 i 
   M ( SNR   M )

M
(
SNR


M
)

 
 ( M  i )Tc 2  tagcMTc 2  1  SNR  2 M 

1
(i  tagc) MTc 2
tagc  i  M






2

s

6

s

M
SNR


M

M
(
SNR


M
)
2

s
(
SNR


M
)






2
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
–

Probability of a false alarm
–

Acquisition fails because matched-filter output
does not exceed acquisition threshold when the
end of the preamble is received
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
1
0.1
0.01
Probability
P(fa)
P(miss)
0.001
0.0001
10
10
-5
-6
0
10
SNR 20
(db)
30
40
50
60
1
t_agc = 0
t_agc = 1
t_agc = 3
t_agc = 5
0.1
0.01
0.001
0
10
20
30
40
50
t_agc = 0
t_agc = 1
t_agc = 3
t_agc = 5
Probability of Not Acquiring in AGC
System with Response Delays
for M=26, Q=65
1
0.1
Probability of
Not Acquiring
0.01
0.001
0
10
20 SNR
(db)
30
40
50
Probability of Not Acquiring in AGC
System with Response Delays
for M=100, Q=250
1
0.1
t_agc = 0
t_agc = 1
t_agc = 5
t_agc = 15
t_agc = 25
0.01
Probability of
Not Acquiring
0.001
0.0001
10
10
-5
-6
0
10
20
30
SNR (db)
40
50
60
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
5
4.5
Simulation Results
Linear Results
4
3.5
3
2.5
2
1.5
1
0
5
10
15
20
25
Percent of preamble effected by delay
30
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 2007
Stephanie Gramc
Dr. Noneaker
IF (Intermediate-frequency) Filter


IF filter rejects out of band noise power in received signal before
inputting signal into AGC system

–

Ratio of signal power that is passed through the IF filter
n
–

s (1/3):
Ratio of the noise power passed through the IF filter
 Measure of the ratio of IF filter’s bandwidth to the bandwidth of
–
n

s
the DS signal
Accounting for Signal Power

Power:
M 1
Ec M 1
s(t )   P  aipTc(t  iTc)  
aipTc(t  iTc)

Tc i 0
i 0
2
| s(t ) |   2 P for 0  t  MTc

Energy:
–
Per chip:
(i  1)Tc

2
| s(t ) | dt   2 PTc   2 Ec
iTc
MTc
–
Per preamble: E 

0
2
| s(t ) | dt   2 MEc   2 MPTc
Probability of Not Acquiring in AGC
System with Response Delays
for M=26, Q=65
t_agc = 0
t_agc = 1
t_agc = 2
t_agc = 3 1
t_agc = 4
t_agc = 5
0.1
Probability of
Not Acquiring
0.01
0.001
0
10
20
30
SNR (db)
40
50
60
Probability of Not Acquiring in AGC
System with Response Delays
for M=100, Q=250
t_agc = 0
t_agc = 1
t_agc = 5
t_agc = 10
1
t_agc = 15
t_agc = 20
t_agc = 25
0.1
0.01
Probability of
Not Acquiring
0.001
0.0001
10
10
-5
-6
0
10
20
30
SNR (db)
40
50
60