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SIMULATION OF CORDIC BASED AREA EFFICIENT EQUALIZER
Under the guidance of Dr. Arti Noor & Ms. Sunita Prasad BY
K. Sireesh Kumar & G. Pradeep Kumar M.Tech(VLSI)
The Supercomputing
People
PROBLEM STATEMENT:
Simulation of CORDIC based area efficient adaptive equalizers in MATLAB environment and writing the verilog code for DTLMS and signDTLMS algorithms and verifying their performance and convergence of the algorithms.
The Supercomputing
People
OBJECTIVE: The main objective of the project is that to reduce the inter symbol interference using DTLMS and signDTLMS algorithms in any digital communication channel
The Supercomputing
Scope: For any digital communication channel it can be applied, for suppose let us consider digital communication channel shown in the figure
People
The Supercomputing
People
Scope (contd.): In the above shown block diagram we can see a signal being transmitted from a transmitter to a receiver through a communication channel, so while signal moving from this channel we can observe noise and symbol interference being added to the signal. We are reducing this symbol interference using some well known techniques which are just advancement of the basic LMS algorithm
The Supercomputing
WHAT IS AN ADAPTIVE EQUALIZER? An adaptive equalizer is very much similar to an adaptive filter where the weights( Filter co-efficients ) are adjusted to minimize the average error power at the output with respect to the transmitted symbols.
People
The Supercomputing
People
WHY THESE ALGORITHMS HAVE BEEN CHOSEN? The LMS (least mean square) is one of the most well known adaptive algorithms, which updates the filter coefficients by a value that is proportional to the product of the input to the equalizer and the output error. And because of the special advantage of the LMS algorithm which are given below.
The Supercomputing
People
Advantage of LMS: Due to its relative computational simplicity and desirable numerical qualities the LMS algorithms received a great deal of attention in this field.
Disadvantage of LMS: Its convergence is being surpassed by several techniques. The implementation of an LMS algorithm is very simple but cannot be pipelined because of the recursive loop in its filter update formula and hence prevents it from using in systems with higher data rates.
The Supercomputing
People
Modified LMS Algorithms: A modified version of the LMS algorithm called the DLMS( Delayed- LMS) algorithm inserts certain delays in the error feed back loop and hence pipe-lined implementation can be possible with this algorithm.
WHY CORDIC IS BEING USED: The fundamental operations in almost all adaptive equalizers are suitable to be carried out by multiply-accumulate (MAC) units due to requirement of this kind of operations both in filtering as well as weight adaptation.
The Supercomputing
CORDIC Continued. On the other hand CORDIC (COordinate Rotation DIgital Computer) has received great deal of attention for its excellent performance as an elegant alternative to MAC. The CORDIC offers a unified iterative formulation to efficiently evaluate many elementary functions such as trigonometric, hyperbolic, exponential etc. The CORDIC computations are pipelinable at the micro level and are sufficiently robust against internal numerical errors.
People
The Supercomputing
People
CORDIC Continued.. Since the feedback circuits are extremely sensitive to numerical errors and an adaptive equalizer is a feedback circuit due to its adaptive nature, it would be extremely advantageous to use CORDIC based implementations rather than MAC based implementations. A new version of the LMS algorithm called the TLMS (Trigonometric LMS) algorithm has been proposed by reformulating the LMS algorithm that forcefully introduces CORDIC blocks in to the adaptive equalizer.
The Supercomputing
CORDIC Continued.. For pipelined implementation, its delayed version called the DTLMS (Delayed TLMS) algorithm can be used. The complex LMS is one of the members of the LMS family, which can be utilized efficiently for adaptive equalization in communication systems employing quadrature amplitude modulation (QAM), which is very popular in digital communications due to its high bandwidth efficiency.
People
The Supercomputing
CORDIC Continued.. Keeping this in mind, a CORDIC realization of the complex LMS based adaptive equalizer is presented by proposing modification in the basic algorithm.
People
The Supercomputing
Application Areas Any digital communication channels like • Mobile Communication • Wireless LAN
People
The Supercomputing
HARDWARE & SOFTWARE TO BE USED
Software/Hardware
Availability
Tools MATLAB Modelsim XE
Yes
Yes
People
GANTT CHART
FEB
MAR
APR
The Supercomputing
People
MAY
System study System design,Layout stimulation ,verification Minor Project Report writing
REFERENCES
The Supercomputing
People
[1]. Adaptive equalization, Shahid U. H. Qureshi; proceedings of IEEE, vol.73, no.9, September 1985, pages 1347-1389 [2]. Adaptive filter theory by Simon Haykin . [3]. Delayed least-mean-square algorithm, Wang, T.; Wang, C. L.; Electronics Letters, Volume-31, Issue: 7, 30 March 1995, Pages: 524 – 526. [4] A Trigonometric formulation of the LMS algorithm, M.Chakraborty, S.Pervin and A.S.Dhar, Proc. of the national Conference on Communications, Kanpur, India, January 2001. [5]. A Trigonometric Formulation of the LMS Algorithm for Realization on Pipelined CORDIC, M.Chakraborty, A. S. Dhar and M. H. Lee, to appear in the IEEE Trans. Circuits And Systems, part-II. August-1998. [6]. A CORDIC Arithmetic Processor Chip; Haviland, G.L.; Tuszynski, A.A.; Solid-State Circuits, IEEE Journal of, Volume: 15, Issue: 1, Feb 1980,Pages: 4 – 15.
The Supercomputing
People
[7]. The quantization effects of the CORDIC algorithm, Hu, Y.H.; IEEE Transactions on Signal Processing, [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on], Volume: 40, Issue: 4, April 1992,Pages: 834 – 844. [8]. Samir Palnitkar, VerilogHDL, Pearson education, 2004(ISBN 81- 297- 0092- 1)
THANKYOU
Under the guidance of Dr. Arti Noor & Ms. Sunita Prasad BY
K. Sireesh Kumar & G. Pradeep Kumar M.Tech(VLSI)
The Supercomputing
People
PROBLEM STATEMENT:
Simulation of CORDIC based area efficient adaptive equalizers in MATLAB environment and writing the verilog code for DTLMS and signDTLMS algorithms and verifying their performance and convergence of the algorithms.
The Supercomputing
People
OBJECTIVE: The main objective of the project is that to reduce the inter symbol interference using DTLMS and signDTLMS algorithms in any digital communication channel
The Supercomputing
Scope: For any digital communication channel it can be applied, for suppose let us consider digital communication channel shown in the figure
People
The Supercomputing
People
Scope (contd.): In the above shown block diagram we can see a signal being transmitted from a transmitter to a receiver through a communication channel, so while signal moving from this channel we can observe noise and symbol interference being added to the signal. We are reducing this symbol interference using some well known techniques which are just advancement of the basic LMS algorithm
The Supercomputing
WHAT IS AN ADAPTIVE EQUALIZER? An adaptive equalizer is very much similar to an adaptive filter where the weights( Filter co-efficients ) are adjusted to minimize the average error power at the output with respect to the transmitted symbols.
People
The Supercomputing
People
WHY THESE ALGORITHMS HAVE BEEN CHOSEN? The LMS (least mean square) is one of the most well known adaptive algorithms, which updates the filter coefficients by a value that is proportional to the product of the input to the equalizer and the output error. And because of the special advantage of the LMS algorithm which are given below.
The Supercomputing
People
Advantage of LMS: Due to its relative computational simplicity and desirable numerical qualities the LMS algorithms received a great deal of attention in this field.
Disadvantage of LMS: Its convergence is being surpassed by several techniques. The implementation of an LMS algorithm is very simple but cannot be pipelined because of the recursive loop in its filter update formula and hence prevents it from using in systems with higher data rates.
The Supercomputing
People
Modified LMS Algorithms: A modified version of the LMS algorithm called the DLMS( Delayed- LMS) algorithm inserts certain delays in the error feed back loop and hence pipe-lined implementation can be possible with this algorithm.
WHY CORDIC IS BEING USED: The fundamental operations in almost all adaptive equalizers are suitable to be carried out by multiply-accumulate (MAC) units due to requirement of this kind of operations both in filtering as well as weight adaptation.
The Supercomputing
CORDIC Continued. On the other hand CORDIC (COordinate Rotation DIgital Computer) has received great deal of attention for its excellent performance as an elegant alternative to MAC. The CORDIC offers a unified iterative formulation to efficiently evaluate many elementary functions such as trigonometric, hyperbolic, exponential etc. The CORDIC computations are pipelinable at the micro level and are sufficiently robust against internal numerical errors.
People
The Supercomputing
People
CORDIC Continued.. Since the feedback circuits are extremely sensitive to numerical errors and an adaptive equalizer is a feedback circuit due to its adaptive nature, it would be extremely advantageous to use CORDIC based implementations rather than MAC based implementations. A new version of the LMS algorithm called the TLMS (Trigonometric LMS) algorithm has been proposed by reformulating the LMS algorithm that forcefully introduces CORDIC blocks in to the adaptive equalizer.
The Supercomputing
CORDIC Continued.. For pipelined implementation, its delayed version called the DTLMS (Delayed TLMS) algorithm can be used. The complex LMS is one of the members of the LMS family, which can be utilized efficiently for adaptive equalization in communication systems employing quadrature amplitude modulation (QAM), which is very popular in digital communications due to its high bandwidth efficiency.
People
The Supercomputing
CORDIC Continued.. Keeping this in mind, a CORDIC realization of the complex LMS based adaptive equalizer is presented by proposing modification in the basic algorithm.
People
The Supercomputing
Application Areas Any digital communication channels like • Mobile Communication • Wireless LAN
People
The Supercomputing
HARDWARE & SOFTWARE TO BE USED
Software/Hardware
Availability
Tools MATLAB Modelsim XE
Yes
Yes
People
GANTT CHART
FEB
MAR
APR
The Supercomputing
People
MAY
System study System design,Layout stimulation ,verification Minor Project Report writing
REFERENCES
The Supercomputing
People
[1]. Adaptive equalization, Shahid U. H. Qureshi; proceedings of IEEE, vol.73, no.9, September 1985, pages 1347-1389 [2]. Adaptive filter theory by Simon Haykin . [3]. Delayed least-mean-square algorithm, Wang, T.; Wang, C. L.; Electronics Letters, Volume-31, Issue: 7, 30 March 1995, Pages: 524 – 526. [4] A Trigonometric formulation of the LMS algorithm, M.Chakraborty, S.Pervin and A.S.Dhar, Proc. of the national Conference on Communications, Kanpur, India, January 2001. [5]. A Trigonometric Formulation of the LMS Algorithm for Realization on Pipelined CORDIC, M.Chakraborty, A. S. Dhar and M. H. Lee, to appear in the IEEE Trans. Circuits And Systems, part-II. August-1998. [6]. A CORDIC Arithmetic Processor Chip; Haviland, G.L.; Tuszynski, A.A.; Solid-State Circuits, IEEE Journal of, Volume: 15, Issue: 1, Feb 1980,Pages: 4 – 15.
The Supercomputing
People
[7]. The quantization effects of the CORDIC algorithm, Hu, Y.H.; IEEE Transactions on Signal Processing, [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on], Volume: 40, Issue: 4, April 1992,Pages: 834 – 844. [8]. Samir Palnitkar, VerilogHDL, Pearson education, 2004(ISBN 81- 297- 0092- 1)
THANKYOU
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