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. 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. Implementation of the Algorithms in C language. Design of a suitable GUI for the system. Design of a suitable GUI for the system. Interfacing the TI-DSP kit with the computer using the C codes. Interfacing the TI-DSP kit with the computer using the C codes.

Understanding the Signal Model We are dealing with a DS-CDMA system with multi-user communication. 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.) However, we are interested in the communication of a single user of interest. The other users become ‘Interferers’. 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. 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 Where, the received vector r k (t) = x k (t) + i k (t) + n k (t) for i=1,2,…M. M= Number of antenna array elements in the receiver. W k *= Adaptive tap weights ( called adaptive because the real-time received data r k (t) is unknown or random in practical cases and a stochastic approach is required to estimate it ) ANTENNAARRAYANTENNAARRAY Where, the received signal rk (t) = xk (t) + ik (t) + nk (t) for k=1,2,…M. M= Number of antenna array elements in the receiver. Wk *= Adaptive tap weights ( called adaptive because the real-time received data rk(t) is unknown or random in practical cases and a stochastic approach is required to estimate it )

After arranging the M received signals r k (t) and the M tap weights W k * in the form of vectors R(t) and W H respectively, the following mathematics is performed: Received Vector R(t)=X(t) + I(t) + N(t) Received Vector R(t)=X(t) + I(t) + N(t) Weighted signal y(t) = W H R(t) Weighted signal y(t) = W H 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. 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 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? Fast and considerably reduce system overheads as data can be processed online. Fast and considerably reduce system overheads as data can be processed online. Process real-time and random data (Online). Process real-time and random data (Online). Tend to the W MMSE in the mean-square sense with probability 1. Tend to the W MMSE in the mean-square sense with probability 1. Adapt easily to the communication system data. Adapt easily to the communication system data. Follow a general recursive pattern. Follow a general recursive pattern.

LMS ( Least Mean Squares) W n+1 = W n –μ r n (r n H W n W n+1 = W n –μ r n (r n H W n – d n *) W lms W mmse (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)

CMA ( Constant Modulus Algorithm) W n+1 = W n –μ( r n r n H W n ( | W n H r n | 2 2 )) p(t) W n+1 = W n –μ( r n r n H W n ( | W n H r n | 2 – A 2 )) p(t)Advantage: Blind, Online scheme ( no pilot signal) Blind, Online scheme ( no pilot signal)TbDisadvantages: Needs a constant modulus signal of interest Needs a constant modulus signal of interest Algorithm will not work for power-controlled CDMA (wireless) system Algorithm will not work for power-controlled CDMA (wireless) system

RLS ( Recursive Least Squares) Key Idea : β n-k |e(k)| 2 is to be minimized. Key Idea : β n-k |e(k)| 2 is to be minimized. Wn+1 = Wn –( R -1 rn ( rn H Wn * )) Wn+1 = Wn –( R -1 rn ( rn H Wn – dn * )) 0<β<1 (usually close to 1). 0<β<1 (usually close to 1). Advantages: Very Fast Very Fast Disadvantage: Increase in computational complexity 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 users (K) = 5 Number of Array Elements (M) = 12 Number of Array Elements (M) = 12 Direction of Arrival for the user of interest (the LOOK angle)=60 o Direction of Arrival for the user of interest (the LOOK angle)=60 o Direction of Arrival of the Interferers = Direction of Arrival of the Interferers = [-80 o,-15 o, 0 o, 40 o ] [-80 o,-15 o, 0 o, 40 o ] Number of iterations or data points considered (N)=1000 Number of iterations or data points considered (N)=1000

EXPERIMENTAL RESULTS [-80 o,-15 o, 0 o,40 o ] the angles of arrivals of the interferers. The RLS curve converges fastest and the best to the MMSE curve. Observe the peak at 60 o ( the LOOK angle) and nulls at [-80 o,-15 o, 0 o,40 o ] 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 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. We have also coded the algorithms in LabVIEW, because of the novelty of the idea.contd..

About LabVIEW It is an out and out graphical programming tool with an excellent and user-friendly interface. 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). 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. 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 W lms Weight Vector W lms

OBJECTIVES ACHIEVED The above described algorithms have been implemented in MATLAB. 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. The codes have also been implemented in LabVIEW, and the GUI has been developed in LabVIEW. Stand-alone codes have been written in C. 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. 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. 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. 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. 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. 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. A simple Joint Space-Time Multiple Access system has been considered.

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. 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. We have not considered Multipath fading and Rayleigh fading. We have an AWGN channel, and AWGN channel fading is taken into consideration.

Joint ST : The 3-D space and time plots The DS-CDMA signals have a 12 bit signature sequence generated by a PN generator. 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 T s =bit period of each signature bit (chip period) Thus, T=12* T s Thus, T=12* T s There are 12 antenna array elements at the receiver. 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 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