Transcript STUDY OF DS-CDMA SYSTEM AND IMPLEMENTATION OF …

STUDY OF DS-CDMA SYSTEM AND
IMPLEMENTATION OF ADAPTIVE FILTERING
ALGORITHMS
By
Nikita Goel
Prerna Mayor
Sonal Ambwani
OBJECTIVES

Extensive Analysis of the Adaptive Algorithms in MATLAB
and LabVIEW and comparison of the Algorithms on various
points such as convergence, BER performance. The basic
signal model chosen is that of a multi-user DS-CDMA system.

Implementation of the Algorithms in C language.
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Design of a suitable GUI for the system.
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Interfacing the TI-DSP kit with the computer using the C
codes.
Understanding the Signal Model
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We are dealing with a DS-CDMA system with
multi-user communication.
(In a CDMA system, all the users transmit in the frequency spectrum
simultaneously and are coded using spread-spectrum techniques.)
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However, we are interested in the
communication of a single user of interest. The
other users become ‘Interferers’.
Key idea of the project: To develop online,
adaptive algorithms which are recursive in
nature to process real time data and work
towards the minimization of the MEAN-SQUARE
ERROR (MMSE) between the received signal
and the desired response.
BASIC BLOCK DIAGRAM
A
N
T
E
N
N
A
A
R
R
A
Y
Where,
Where,the
thereceived
receivedsignal
vectorrkrk(t)
(t) == xk
xk (t) + iik
k (t)
(t)++nnk
k (t)
(t)for
fori=1,2,…M.
k=1,2,…M.
M=
M=Number
Numberof
ofantenna
antennaarray
arrayelements
elementsininthe
thereceiver.
receiver.
Wk
Wk *= Adaptive tap weights ( called adaptive because the real-time received data
rk(t)
rk(t) is
is unknown
unknown or
or random
random in
in practical
practical cases
cases and
and aa stochastic
stochastic approach
approach is
is required
required
to estimate
to estimate
it )
it )
After arranging the M received signals rk(t) and the M tap
weights Wk * in the form of vectors R(t) and WH respectively,
the following mathematics is performed:
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Received Vector R(t)=X(t) + I(t) + N(t)
Weighted signal y(t) = WH R(t)
Error e(t) = y(t) – d(t) , where d(t) is the desired
response or the pilot signal which directly correlates
with the user of interest.
Mean Square Error= |e(t)|2
The weight vector W is derived such that it
minimizes the Mean-Square Error, |e(t)|2
Why Adaptive Algorithms?
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Fast and considerably reduce system overheads
as data can be processed online.
Process real-time and random data (Online).
Tend to the WMMSE in the mean-square sense
with probability 1.
Adapt easily to the communication system data.
Follow a general recursive pattern.
LMS ( Least Mean Squares)
Wn+1 = Wn –μ rn (rn Wn – dn*)
 Wlms
Wmmse (in the mean square sense)
Advantages:
 simplicity in implementation
 stable and robust performance against
different signal conditions
Disadvantage:
 Relatively slow Convergence ( but that can
be overcome by using normalised LMS)

H
CMA ( Constant Modulus Algorithm)

W
n+1
= Wn –μ( rn rn H Wn( | Wn H rn|2 – A2 ))
p(t)
Advantage:

Blind, Online scheme ( no pilot signal)
Tb
Disadvantages:
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Needs a constant modulus signal of interest
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Algorithm will not work for power-controlled CDMA
(wireless) system
RLS ( Recursive Least Squares)
Key Idea :
βn-k |e(k)|2 is to be minimized.
 Wn+1 = Wn –( R-1rn ( rn H Wn – dn* ))
 0<β<1 (usually close to 1).
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Advantages:
 Very Fast
Disadvantage:
 Increase in computational complexity
( something we realized while writing the C
programs and the LabVIEW codes)
EXPERIMENTAL DATA
Number of users (K) = 5
 Number of Array Elements (M) = 12
 Direction of Arrival for the user of interest
(the LOOK angle)=60o
 Direction of Arrival of the Interferers =
[-80o,-15o, 0o, 40o]
 Number of iterations or data points
considered (N)=1000
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EXPERIMENTAL RESULTS
Observe the peak at 60o ( the LOOK angle) and nulls at [-80o,-15o, 0o,40o]
the angles of arrivals of the interferers. The RLS curve converges fastest
and the best to the MMSE curve.
The above diagram depicts the adaptive algorithm at the receiver which essentially
deciphers which bit was transmitted by the user-of-interest.
The received vector r is passed through a linear filter characterized according to the
adaptive filtering technology used (LMS, RLS, CMA etc) .
The bit transmitted is decided by performing a hypothesis testing on
Sign(W T *r), i.e if Sign(W T *r), >0 then a +1 was transmitted, and if it is <0 then
-1 was transmitted.
The figure depicts the BER versus the user-of-interest SNR
Convergence: RLS converges best and fastest to the MMSE
GUI
The GUI has been implemented in
LabVIEW, because of the user-friendly
nature of the interface.
 We have also coded the algorithms in
LabVIEW, because of the novelty of the
idea.
contd..
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About LabVIEW
It is an out and out graphical programming
tool with an excellent and user-friendly
interface.
Terminology:
 A program in LabVIEW is called a VI
(Virtual Instrument).
 The graphical programming is done on the
Block-Diagram and the user interface is
called the Front Panel.

A Look at the GUI
…where the user can select the signals’ angles of arrivals and the operating SNR (in dB)
…where the Online Adaptive Algorithm can be chosen. On clicking on one of the
control buttons, thepower beam-pattern and the BER curves can be obtained.
BER plots from LabVIEW
A look at the TMS-320-C6211 DSP Board
The DSP Board Interfaced with the Code Composer Studio that executes the
C codes.
Results as seen after executing the LMS C code on the TI DSP
Weight Vector Wlms
Weight Vector Wlms
OBJECTIVES ACHIEVED
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The above described algorithms have been
implemented in MATLAB.
The codes have also been implemented in LabVIEW,
and the GUI has been developed in LabVIEW.
Stand-alone codes have been written in C.
Comparative analysis has been carried out by varying
the number of iterations N, changing the direction of
arrivals of the user of interest and the interferers.
Bit-Error-Rate performance for the three algorithms,
and the convergence issues have been compared.
Successfully Interfaced the TMS-320-C6211 DSP kit
with the C codes.
Additional Work Done
MATLAB analysis of some variants of LMS
like, sign-LMS, Constraint LMS, etc has
been done.
 Analysis of a Space Division Multiple
Access (SDMA) system in MATLAB,
LabVIEW and C.
 A simple Joint Space-Time Multiple Access
system has been considered.
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A preview of the Joint Space -Time
System
It is SDMA combined with the DS-CDMA
system, i.e. there is an Antenna Array at
the receiver which exploits the spatial
characteristics of the user of interest and
the interferers.
 We have not considered Multipath fading
and Rayleigh fading. We have an AWGN
channel, and AWGN channel fading is
taken into consideration.
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Joint ST : The 3-D space and time
plots
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The DS-CDMA signals have a 12 bit signature
sequence generated by a PN generator.
T=transmitted bit period for the user-of-interest and the
interferers
Ts =bit period of each signature bit (chip period)
Thus, T=12* Ts
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There are 12 antenna array elements at the
receiver.
We have plotted the power beam pattern with
respect to each signature bit, thus obtaining a
3-D plot.
3-D Power Beam Patterns for
Joint ST systems
LMS
CMA
RLS