Design of Lrls Adaptive Filter with Low Adaptation Delay in Efficient Mode

In this paper, we present an efficient architecture for the implementation of a normalized lattice recursive least square adaptive filter. The adaptive process involves the use of a cost function, which is a criterion for optimum performance of the filter, to feed an algorithm, which determines how to modify filter transfer function to minimize the cost on the next iteration. For achieving lower adaptation-delay and area, delay power implementation, we use a partial product generator and a super scalar concept which uses an optimized balanced structure across the timeconsuming combinational blocks of the proposed structure. For synthesis, we find that the proposed structure allows nearly 19% less area and the power consumption is reduced to 15%, than the convention least mean square adaptive filter. We propose an efficient fixed point implementation structure of the proposed architecture and have derived an expression for steady-state error. We have shown that the steady-state error obtained from the Theoretical result matches with the simulated result. We also have proposed a variable filter structure, provides 19% savings in the total power and 10% saving in area before pruning without compromising the steady-state-error performance. Index Term: Lattice recursive least square(LRLS)algorithm, Floating Point arithmetic operation, Circuit organization and Adaptive filter. I.INTRODUCTION Recursive least squares (RLS) was discovered by Gauss but lay unused or ignored until 1950 when Plackett rediscovered the original work of Gauss from 1821. In general, the RLS can be used to solve any problem that can be solved by adaptive filters. The Recursive least squares (RLS) adaptive filters is an algorithm which recursively finds the filter coefficients that minimize a weighted linear least squares cost function relating to the input signals. This is in contrast to other algorithms such as the least mean squares (LMS) that aim to reduce the mean square error. In the derivation of the RLS, the input signals are considered deterministic, while for the LMS and similar algorithm they are considered stochastic.[1],[2] Compared to most of its competitors, the RLS exhibits extremely fast convergence. However, this benefit comes at the cost of high computational complexity .Since the convention RLS algorithm does not support super scalar concept because of its recursive behaviour, it is modified to a form called the lattice recursive least square algorithm(LRLS) [3],[4]which supports super scalar concept which allows super scalar concept implementation of the filter. The Modified LRLS adaptive filter is related to the standard RLS except that it requires fewer arithmetic operations (order N). It offers additional advantages over conventional LMS algorithms such as faster convergence rates, modular structure, and insensitivity to variations in Eigen-value spread of the input correlation matrix. The LRLS algorithm described is based on a posterior errors. A lot of work has been done to implement the LRLS algorithm in systolic architecture to increase the maximum usable frequency, but they have complex adaptation delay, which is quite high for largeorder filter.In the next section, we review the Modified LRLS algorithm, and in section 3, we describe the proposed optimized architecture for its implementation. Section 4 deals with the fixed point implementation and the synthesis of the proposed architecture and the comparison with the existing architecture, Conclusion is given in section 5. International Journal of Inventions in Computer Science and Engineering ISSN (Online): 2348 – 3539, ISSN (Print): 2348 – 3431 Volume 1 Issue 2 2014. 03.2014-12CSE16 www.ijicse.com II.RELATED WORK Review Of The Modified Lattice Recursive Least Square Algorithm The Lattice Recursive Least Squares adaptive filter is related to the standard RLS except that it requires fewer arithmetic operations (order N). It offers additional advantages over conventional LMS algorithms such as faster convergence rates, modular structure, and insensitivity to variations in eigenvalue spread of the input correlation matrix. The LRLS algorithm described is based on a posterior errors and includes the normalized form. The derivation is similar to the standard RLS algorithm and is based on the definition of . In the forward prediction case, we have with the input signal as the most up to date sample. The backward prediction case is , where i is the index of the sample in the past we want to predict, and the input signal is the most recent sample. Fig 1.Structure of the Existing System Fig 2.Structure of the Modified Lrls The idea behind RLS filters is to minimize a cost function by appropriately selecting the filter coefficients , updating the filter as new data arrives. The error signal and desired signal are defined in the negative feedback diagram above, the error implicitly depends on the filter coefficients through the estimate :