Smart antennas and MAC
protocols in MANET
Lili Wei
2004-12-02
Contents
•
•
•
•
•
Smart antennas – basic concepts and algorithms
Background knowledge
System model
Optimum beamformer design
Adaptive beamforming algorithms
DOA estimation method
•
•
•
•
Schemes using directional antennas in MAC layer of
ad hoc network
Vaidya scheme1
Vaidya scheme2
Nasipuri scheme
Bagrodia scheme
Part I : Smart antennas
-- basic concepts and algorithms
Background Knowledge
Basic challenge in wireless communication:
---- finite spectrum or bandwidth
Multiple access schemes:
FDMA
TDMA
CDMA
SDMA
Spatial Division Multiple Access
---- Uses an array of antennas to provide control of space
by providing virtual channels in an angle domain
Directional Antennas
Sectorised antenna
Smart antenna
1) switched beam system
•Use a number of fixed beams
•Select one of several beams to
enhance receive signals
2) adaptive array system
•Be able to change its antenna pattern
dynamically;
System Model
Uniform Linear Array of M elements

x1 (t )  m(t )e j 2f ct


l d sin 

c
c
d
x2 (t )  m(t   )e j 2f c (t  )
xM (t )  m(t  (M  1) )e j 2f c (t ( M 1) )
System Model
Narrow Band array processing Assumption:
x1 (t )  m(t ) e
x2 (t )  x1 (t ) e
j 2f c t
 j 2 d sin
c
 j 2 ( M 1) d sin
xM (t )  x1 (t ) e
c
m(t )  m(t   )
1



d
 j 2
sin
e

c


  j 2 2 d sin

c

S  e





  j 2 ( M 1) d sin 
c
e



Array response vector
System Model
The Beam-former Structure
M
y (t )   wi* xi (t )
w1*
1
2
M
x1 (t )
x2 (t )
xM (t )
i 1
w1*
wM*
H
 w X (t )
y (t )
 w1 
w 
w  2 
 
 
 wM 
 x1 (t ) 
 x (t ) 
X (t )   2 




 x M (t ) 
A simple example
Design a beamformer with unit response at 600 and nulls at
00, -300, -750
Optimum Beamformer Design
Signal in AWGN and Interference
1
2
x1 (t )  i1 (t )  n1 (t )
x2 (t )  i2 (t )  n2 (t )
r (t )  X (t )  i(t )  n(t )
w1*
w1*
y (t )
X (t )  m(t )e j 2f ct S
H
y (t )  w r (t )
M
xM (t )  iM (t )  nM (t )
wM*

R  E r (t )r (t ) H
RI  N




H

 E  i(t )  n(t ) i(t )  n(t ) 



Optimum Beamformer Design
Under different criterions
Maximum SINR beamformer
wmax SINR 
RI1N S
H
S RI1N S
Mean-Square-Error optimum beamformer
1
wMMSE  PR S

P  E m(t )
2

Optimum Beamformer Design
Under different criterion
Minimum-Variance-Distortionless-Response beamformer
w MVDR 
R 1 S
H
S R 1 S
Maximum Likelihood optimal beamformer
w ML 
RI1N S
H
S RI1N S
Practical Issues
Issues
In practice, neither R nor RI+N is available to calculate
the optimal weights of the array;
In practice, direction of arrival (DOA) is also unknown.
Solution
Adaptive beamforming algorithms – the weights
are adjusted by some means using the available
information derived from the array output, array signal
and so on to make an estimation of the optimal weights;
DOA estimation methods
Adaptive Beamforming Algorithms
Block diagram of adaptive beamforming system
Adaptive Beamforming Algorithms
SMI Algorithm (Sample Matrix Inverse)
2. LMS Algorithm (Least Mean Square)
3. RLS Algorithm (Recursive Least Square)
4. CMA (Constant Modulus Algorithm)
1.
Adaptive Beamforming Algorithms
1. SMI Algorithm (Sample Matrix Inverse)
Estimate R using N samples:
1
ˆ
RN 
N
N
r r
i 1
i
r r
n 1 ˆ
Rˆ n 
Rn 1  n n
n
n
H
i
H
Use matrix inversion lemma:
Rˆ n
1
n  1  ˆ 1 Rˆ n 1 rn rn Rˆ n 1 ) 
 Rn 1 


H
n 
ˆ 1 r 
(
n

1
)

r
R
n
n 1
n

1
Then:
1
wn  Rˆ n S
H
1
1
Rˆ 0  cI
c0
k  1,2,....
Adaptive Beamforming Algorithms
2. LMS Algorithm (Least Mean Square)
According to orthogonality principle (data| error) of MMSE beamformer:
 
E r (t ) r (t ) H w  d * (t )
 0
Solution:
H
wn1  wn   rn (rn wn  d n* )  wn   rnen*
H
en  wn r n  d n
Need training bits and calculate the error between the received
signal after beamforming and desired signal;
• The step size u decides the convergence of LMS algorithm;
• Based on how to choose u, we have a set of LMS algorithm,
“unconstraint LMS”, “normalized LMS”, “constraint LMS”.
•
Adaptive Beamforming Algorithms
3. RLS Algorithm (Recursive Least Square)
Given n samples of received signal r(t), consider the optimization
problem—minimize the cumulative square error
n
min

k 0
nk
ek
2
0   1
Solution:
H
wn  wn1  Rˆ 1 (n)rn (rn wn1  d n* )
•
In some situation LMS algorithm will converge with very slow
speed, and this problem can be solved with RLS algorithm.
Adaptive Beamforming Algorithms
4. CMA (Constant Modulus Algorithm)
Assume the desired signal has a constant modulus, the existence of an
interference causes fluctuation in the amplitude of the array output.
Consider the optimization problem:
Solution:
2
2



1  H

2


min E  w r (t )  A  
2 
 


H
2
wn 1  wn   rn rn wn ( wn rn  A2 )
H
This is a blind online adaptation, i.e., don’t need training bits
• CMA is useful for eliminating correlated arrivals with different magnitude
and is effective for constant modulated envelope signals such as GMSK
and QPSK
•
DOA Estimation Method
MF Algorithm (Matched Filter)
2. MVDR Algorithm
3. MUSIC Algorithm (MUltiple SIgnal Classification)
1.
DOA Estimation Method
1.
MF Algorithm (Matched Filter)
The total output power of the conventional beamformer is:

P  E y(t )
•
•
•
•
•
•
2



2
H
H
 H

H
 E  w r (t )   w E r (t ) r (t ) w  w R w


The output power is maximized when w  S 0
The beam is scanned over the angular region say,(-900,900), in discrete
steps and calculate the output power as a function of AOA
The output power as a function of AOA is often termed as the spatial
spectrum
The DOA can be estimated by locating peaks in the spatial spectrum
This works well when there is only one signal present
But when there is more than one signal present, the array output power
contains contribution from the desired signal as well as the undesired
ones from other directions, hence has poor resolution
DOA Estimation Method
2. MVDR Algorithm
This technique form a beam in the desired look direction while taking into
consideration of forming nulls in the direction of interfering signals.

min E y(t )
Solution:
2
 min w
PMVDR ( ) 
H
H
Rw
subject to w S  1
1
H
S R 1 S
By computing and plotting pMVDR over the whole angle range, the DOA’s
can be estimated by locating the peaks in the spectrum
• MVDR algorithm provides a better resolution when compared to MF
algorithm
• MVDR algorithm requires the computation of a matrix inverse, which can
be expensive for large arrays
•
DOA Estimation Method
Comparison of resolution performance of MF and MVDR algorithms
Scenario: Two signals of equal power at SNR of 20dB arrive at a 6-element uniformly
spaced array at angles 90 and 100 degrees, respectively
DOA Estimation Method
3. MUSIC Algorithm (MUltiple SIgnal Classification)
MUSIC is a high resolution multiple signal classification technique based
on exploiting the eigenstructure of the input covariance matrix.
Step 1: Collect input samples and estimate the input covariance matrix
1
ˆ
R
N
N
r r
i 1
i
H
i
Step 2: Perform eigen decomposition
R̂V  V
  diag{1 , 2 ,, M }

V  q1 , q2 ,, qM

1  2    M
DOA Estimation Method
3. MUSIC Algorithm (MUltiple SIgnal Classification)
Step 3: Estimate the number of signals based on the fact :
The first K eigen vectors represent the signal subspace, while the last
M-K eigen vectors represent the noise subspace
• The last M-K eigen values are equal and equal to the noise variance
•
find the D smallest eigen values that almost equal to each other
Kˆ  M  D
Step 4: Compute the MUSIC spectrum
PMUSIC ( ) 
1
H
H
n n
S V V S

Vn  qK 1 , qK  2 ,, qM
find the K̂ largest peaks of Pmusic to obtain estimates of DOA

DOA Estimation Method
Comparison of resolution performance of MVDR and MUSIC
Scenario: Two signals of equal power at SNR of 20dB arrive at a 6-element uniformly
spaced array at angles 90 and 95 degrees, respectively
Summary of Part I
•
•
•
•
System model
Optimum beamformer design
Adaptive beamforming algorithms
1) SMI
2) LMS
3) RLS
4) CMA
DOA estimation method
1) MF
2) MVDR
3) MUSIC
Part II: Schemes using directional antennas
in MAC layer of ad hoc network
RTS/CTS mechanism in 802.11
A
B
C
RTS
D
RTS
CTS
DATA
CTS
DATA
ACK
ACK
E
RTS/CTS mechanism in 802.11
Nodes are assumed to transmit using omni-directional
antennas.
Both RTS and CTS packet contain the proposed duration of
data transmission
The area covered by the transmission range of both the
sender(node B) and the receiver (node C) is reserved during
the data transfer
This mechanism reduce collisions due to the hidden
terminal problem
However, it waste a large portion of network capacity.
Vaidya Scheme 1
Assumption:
Each node knows its exact location and the location of its
neighbors
Each node is equipped with directional antennas
If node X received RTS or CTS related to other nodes, then
node X will not transmit anything in that direction until that
other transfer is completed
That direction or antenna element would be said to be
“blocked”
While one directional at some node be blocked, other
directional at the same nodes may not be blocked, allowing
transmission using the unblocked antenna
Vaidya Scheme 1
A
B
C
D
E
DRTS
OCTS
OCTS
DRTS
OCTS
DATA
DATA
ACK
ACK
OCTS
Vaidya Scheme 1
Utilize a directional antenna for sending the RTS
(DRTS), whereas CTS are transmitted in all directions
(OCTS).
Data and ACK packets are sent directionally.
Any other node that hears the OCTS only blocks the
antenna on which the OCTS was received.
A possible scenario of collisions
A
B
C
D
DRTS
DRTS
OCTS
DATA
DRTS
ACK
OCTS
Vaidya Scheme 2
A node uses two types RTS packets: DRTS and ORTS
according to the following rules:
1) if none of the directional antennas at node X are blocked,
then node X will send ORTS;
2) otherwise, node X will send a DRTS provided that the
desired directional antenna is not blocked.
Vaidya Scheme 2
F
A
B
C
ORTS
ORTS
DRTS
D
OCTS
DATA
ACK
OCTS
Performance
5
10
15
20
25
4
9
14
19
24
3
8
13
18
23
2
7
12
17
22
1
6
11
16
21
Simulation mesh Topology (5X5)
Connections
802.11
Scheme1
Scheme2
1
21
157.50
146.73
165.89
2
22
89.90
85.31
81.30
3
23
22.00
91.39
105.03
4
24
89.29
82.30
82.83
5
25
157.94
153.30
163.37
Throughput
516.63
559.03
598.42
But what if we have no
location information ?
Nasipuri Scheme
Node A that wishes to send a data packet to B first sends
an omni-directional RTS packet
Node B receives RTS correctly and responds by
transmitting a CTS packet, again on all directions.
In the meanwhile, B can do DOA estimation from
receiving RTS packet
Similarly, node A estimates the direction of B while
receiving the CTS packet.
Then node A will proceed to transmit the data packets on
the antenna facing the direction of B.
Nasipuri Scheme
CTS
CTS
3
4
B
2
CTS
RTS
RTS
3
4
Data
A
2
RTS
1
RTS
1
CTS
Nasipuri Scheme
Bagrodia Scheme
Directional Virtual Carrier Sensing(DVCS)
Three primary capabilities are added to original 802.11 MAC
protocol for directional communication with DVCS:
1) caching the Angle of Arrival (AOA)
2) beam locking and unlocking
3) the use of Directional Network Allocation Vector (DNAV)
Bagrodia Scheme
1. AOA caching
Each node caches estimated AOAs from neighboring nodes
whenever it hears any signal, regardless of whether the
signal is sent to it or not
When node X has data to send, it searches its cache for
the AOA information, if the AOA is found, the node will
send a directional RTS, otherwise, the RTS is send omnidirectionally.
The node updates its AOA information each time it receives
a newer signal from the same neighbor.
It also invalidates the cache in case if it fails to get the CTS
after 4 directional RTS transmission.
Bagrodia Scheme
2. Beam locking and unlocking
(3)Data
(2)CTS
A
B
(4)ACK
(1)RTS
B
When a node gets an RTS, it locks its beam pattern
towards the source to transmit CTS
The source locks the beam pattern after it receives CTS .
The beam patterns at both sides are used for both
transmission and reception, and are unlocked after ACK is
completed.
Bagrodia Scheme
3. DNAV setting
DNAV is a directional version of NAV(used in the original
802.11 MAC), which reserves the channel for others only
in a range of directions.
Available directions for transmission
In the fig:
Three DNAVs are set up
towards 300, 750 and 3000 with
600 width.
Until the expiration of these
DNAVs, this mode cannot
transmit any signals with
direction between 0-1050 or
270-3300 , but is allowed to
transmit signals towards 1052700 and 330-3600
Bagrodia Scheme
A network situation where DVCS can improve the
network capacity with DNAVs
A
C
E
D
F
B
Bagrodia Scheme
Performance
Summary of Part II
Comparison of four schemes
RTS
CTS
Data
ACK
802.11
omni
omni
omni
omni
Vaidya 1
dir.
omni
dir.
dir.
Vaidya 2
dir./omni
omni
dir.
dir.
Nasipuri
omni
omni
dir.
dir.
Bagrodia
dir./omni
dir.
dir.
dir.
Conclusion
smart antenna is a technology for wireless systems that use
a set of antenna elements in an array. The signal from these
antenna elements are combined to form a movable beam
pattern that can be steered to a desired direction
smart antennas enable spatial reuse and they increase the
communication range because of the directivity of the
antennas
smart antennas can be beneficial for wireless ad hoc
networks to enhance the capacity of the network
To best utilize directional antennas, a suitable MAC protocol
must be designed
If the locations are unknown , DOA estimation may be
needed before sending directional signals
reference
J.C.Liberti, T.S.Rappaport, “Smart antennas for wireless
communications: IS-95 and third generation CDMA applications”
L.C.Godara, “Application of antenna arrays to mobile communicaitions,
part I: performance improvement, feasiblility, and system
considerations”
L.C.Godara, “Application of antenna arrays to mobile communications,
part II: beam-forming and direction-of-arrival considerations”
Y.b Ko, V.Shankarkumar and N.Vaidya, “Medium access control
protocols using directional antennas in ad hoc networks”
A.Nasipuri, S.Ye, J.You and R.Hiromoto, “A MAC protocol for mobile ad
hoc networks using directional antennas”
M.Takai, J.Martin, A.Ren and R.Bagrodia, “Directional virtual carrier
sensing for directional antennas in mobile ad hoc networks”
S.Bellofiore, J.Foutz, etc.. “Smart antenna system analysis, integration
and performance for mobile ad-hoc networks (MANETs)