Content
Codes
Håkon A. Hjortland
1
Department of Informatics
University of Oslo
Codes
Basics
My work
UWB meeting 2010-11-23
Håkon A. Hjortland (Univ. of Oslo)
Codes
Basics
Codes
UWB meeting 2010-11-23
1 / 17
Content
Håkon A. Hjortland (Univ. of Oslo)
Codes
Basics
Codes
UWB meeting 2010-11-23
2 / 17
Multiplex techniques
Multiplexing is used to allow several users to share the radio
medium:
CDMA (Code Division Multiple Access)
1
TDMA (Time Division Multiple Access)
Codes
Basics
My work
FDMA (Frequency Division Multiple Access)
Polarization
SDMA (Space-Division Multiple Access) - Cellular network,
directed antennas
MIMO (Multiple-Input and Multiple-Output)
ChDMA (Channel Division Multiple Access) - Impulse
response is the channel
Håkon A. Hjortland (Univ. of Oslo)
Codes
Basics
Codes
UWB meeting 2010-11-23
3 / 17
DSSS (Direct-Sequence Spread Spectrum)
Håkon A. Hjortland (Univ. of Oslo)
Codes
Basics
Codes
UWB meeting 2010-11-23
4 / 17
UWB meeting 2010-11-23
6 / 17
Misc
Multiply (XOR) the digital data with a higher-speed digital
“noise” signal before carrier wave modulation.
Spreads the energy over a wider bandwidth.
Receiver must listen for that particular “noise” to receive the
data.
Longer symbols give more processing gain.
Synchronous CDMA: Orthogonal channels. Requires rigid
synchronization (usable for base-to-mobile links).
Asynchronous CDMA: Different channels will interfere slightly
with each other, i.e. channels are not orthogonal. Requires
power control.
Håkon A. Hjortland (Univ. of Oslo)
Codes
UWB meeting 2010-11-23
5 / 17
Håkon A. Hjortland (Univ. of Oslo)
Codes
Codes
Basics
Codes
Basics
Properties
Code examples
m-sequence: Good periodic autocorrrelation.
Barker: Max ±1 out-of-phase autocorrelation. Single channel
only.
-1/1 (bipolar codes), -1/0/1 (ternary codes).
Orthogonality.
Ternary perfect-autocorrelation (seen in 802.15.4a):
Out-of-phase periodic autocorrelation is 0. Good for
synchronization purposes.
Out-of-phase correlation properties (synchronous /
asynchronous CDMA).
Walsh-Hadamard: Orthogonal. Not good out-of-phase
cross/auto-correlation properties.
Low cross-correlation.
Looking at periodic (cyclic) or aperiodic (partial)
auto/cross-correlation.
Gold: Good periodic auto/cross-correlation properties.
Kasami: Good periodic auto/cross-correlation properties.
“Selected random”: Pick and choose properties, use brute
force to get codes.
Håkon A. Hjortland (Univ. of Oslo)
Codes
My work
Codes
UWB meeting 2010-11-23
7 / 17
Content
1
Håkon A. Hjortland (Univ. of Oslo)
Codes
My work
Codes
UWB meeting 2010-11-23
8 / 17
“Selected random” codes
Codes
Basics
My work
Pick and choose properties, use brute force to get codes.
Håkon A. Hjortland (Univ. of Oslo)
Codes
My work
Codes
UWB meeting 2010-11-23
9 / 17
Håkon A. Hjortland (Univ. of Oslo)
Codes
My work
Codes
UWB meeting 2010-11-23
10 / 17
0
4
10
2
20
0
30
-2
40
-4
50
0
5
10
15
20
25
30
0
Figure:
Håkon A. Hjortland (Univ. of Oslo)
Codes
5
10
15
20
25
30
Figure:
UWB meeting 2010-11-23
11 / 17
Håkon A. Hjortland (Univ. of Oslo)
Codes
UWB meeting 2010-11-23
12 / 17
Codes
My work
Codes
My work
0
30
20
10
10
20
0
30
-10
40
-20
-30
50
0
10
20
30
40
50
60
0
10
20
Figure:
Håkon A. Hjortland (Univ. of Oslo)
Codes
My work
30
40
50
Figure:
Codes
UWB meeting 2010-11-23
13 / 17
Håkon A. Hjortland (Univ. of Oslo)
Codes
My work
Codes
UWB meeting 2010-11-23
14 / 17
600
30
20
500
10
400
0
300
-10
200
-20
100
-30
0
0
10
20
30
40
50
0
Figure:
Håkon A. Hjortland (Univ. of Oslo)
Codes
My work
Codes
UWB meeting 2010-11-23
15 / 17
Asynchronous CDMA (not orthogonal) => MAI => must
usually have power control.
This technique is for when different symbols are not sent at
the same time (that will only cause collision, not false
positives, though).
Example application: RFID.
Codes
10
15
20
25
30
Figure:
Near-perfect discrimination
Håkon A. Hjortland (Univ. of Oslo)
5
UWB meeting 2010-11-23
17 / 17
Håkon A. Hjortland (Univ. of Oslo)
Codes
UWB meeting 2010-11-23
16 / 17