20-04-2012, 11:45 AM
Performance Of LMS, NLMS and RLS Algorithms for Adaptive Equalizer
[attachment=20417]
. INTRODUCTION
Adaptive algorithms have been extensively studied in the past few decades and have been widely used in many arenas including biomedical, image and speed processing, communication signal processing and many other applications. Figure 1 shows the block diagram of the system used to carry out the study of adaptive equalizer experiment. Random number generator 1 provides the text signal u(n) used for probing the channel , whereas random generator 2 serves as the source of additive white noise v(n) that corrupts the channel output x(n). The adaptive equalizer has the task of correcting for the distortions produced by the channel in the presence of the additive white noise. Random generator 1, after suitable delay, also supplies the desired response applied to the adaptive equalizer in the form of a training sequence.
LMS ALGORITHM
LMS algorithm has become one of the most widely used algorithms in adaptive filtering. The LMS algorithm is a type of adaptive filter known as stochastic gradient-based algorithms as it utilizes the gradient vector of the filter tap weights to converge on the optimal wiener solution. It is well known and widely used due to its computational simplicity.
x(n) is the vector of tap inputs at time n, d(n) is denoted as the desired response, y(n) is the estimate of the desired response (output of the filter) and e(n) is the estimation error.
CONCLUSIONS
A comparison on the adaptive filtering algorithms (namely LMS, NLMS & RLS) with respect to adaptive equalizer has been carried out based on their convergence rates, MSE and computational complexity.
The computational complexity of LMS algorithm required 2N+1 multiplication and 2N addition. In case of NLMS 3N+1 multiplication only N multiplication is more but incase of RLS 3N2 addition and 4N2 are multiplication required and this is more compare from both.
The results show that the LMS algorithm has the least computational complexity but a poor convergence rate. This is especially the case when the input signal has a high Eigen value spread. The NLMS algorithm has an improved convergence rate while maintaining low computational complexity.
.
[attachment=20417]
. INTRODUCTION
Adaptive algorithms have been extensively studied in the past few decades and have been widely used in many arenas including biomedical, image and speed processing, communication signal processing and many other applications. Figure 1 shows the block diagram of the system used to carry out the study of adaptive equalizer experiment. Random number generator 1 provides the text signal u(n) used for probing the channel , whereas random generator 2 serves as the source of additive white noise v(n) that corrupts the channel output x(n). The adaptive equalizer has the task of correcting for the distortions produced by the channel in the presence of the additive white noise. Random generator 1, after suitable delay, also supplies the desired response applied to the adaptive equalizer in the form of a training sequence.
LMS ALGORITHM
LMS algorithm has become one of the most widely used algorithms in adaptive filtering. The LMS algorithm is a type of adaptive filter known as stochastic gradient-based algorithms as it utilizes the gradient vector of the filter tap weights to converge on the optimal wiener solution. It is well known and widely used due to its computational simplicity.
x(n) is the vector of tap inputs at time n, d(n) is denoted as the desired response, y(n) is the estimate of the desired response (output of the filter) and e(n) is the estimation error.
CONCLUSIONS
A comparison on the adaptive filtering algorithms (namely LMS, NLMS & RLS) with respect to adaptive equalizer has been carried out based on their convergence rates, MSE and computational complexity.
The computational complexity of LMS algorithm required 2N+1 multiplication and 2N addition. In case of NLMS 3N+1 multiplication only N multiplication is more but incase of RLS 3N2 addition and 4N2 are multiplication required and this is more compare from both.
The results show that the LMS algorithm has the least computational complexity but a poor convergence rate. This is especially the case when the input signal has a high Eigen value spread. The NLMS algorithm has an improved convergence rate while maintaining low computational complexity.
.