Design and Implementation of Efficient LMS Adaptive Filter with Low Adaptation Delay
Advancements in mobile computing and real time applications gives high performances low power VLSI Digital signal processing (DSP) systems. Most widely used operation in DSP is Finite Impulse Response (FIR) filtering. The most of the problem occurs while designing the filter at the receiver. Least Mean Square (LMS) adaptive filter is the most widely used adaptive filter because of its satisfactory convergence performance. Perfect solution cannot be obtained using conventional linear filters. In order to obtain perfect solution parallel computing is used in contradiction. Delayed Least Mean Square (DLMS) algorithm is used to minimize approximately the mean square error by recursively altering the weight vector at each sampling instance in order to obtain minimum mean square error updated value of weight vector effectively. Adaptive filter is simulated using Matlab and the results are analyzed. Key wordsLow power VLSI, DSP, DLMS, LMS. I.INTRODUCTION The filter is an important component in the communication world. In which unwanted signals are eliminated from useful information. However obtaining an optimal filtering performance requires a prior knowledge of both the signal and its embedded noise statistical information. One of the approaches to this problem is to design frequency selective filters, which approximate the band of frequency of the signal of interest and reject signals outside this frequency band. The unwanted signals are removed through the use of optimization theory which is becoming more popular, particularly in the area of adaptive filtering. Adaptive filters have attracted considerable attention because of their inherent capacity of adaptation. Adaptive filters are essential in wide range of signal processing control and communications including 1) signal detection 2) echo cancellation 3) noise cancellation 4) system identification and inverse modeling of unknown systems and adaptive tracking and 6) spectral analysis. These adaptive filters minimize the mean square of the error signal, which is the difference between the reference signal and the estimated filter output, by removing unwanted signals according to statistical parameters. Adaptive filters are widely used in several Digital signal processing (DSP) applications. The tap delay line finite impulse response (FIR) filter whose weights are updated by the famous Widrow Hoff least mean square algorithm, which is the most widely used adaptive filter not only due to its simplicity but also due to its satisfactory convergence performance. The aim of adaptive filter is to estimate a sequence of scalars from an observation sequence filtered by a system in which coefficients vary. The direct form FIR filter configuration for the implementation of LMS adaptive filter results in either zero or lower adaptation delay. The direct form LMS adaptive filter involves a long critical path due to an inner product computation to obtain the output. The critical path is required to be reduced by pipelined implementation when it exceeds the desired sample period. Since the conventional LMS algorithm does not support pipelined implementation because of its recursive nature, it is modified to a form called the Delayed Least Mean Square (DLMS) algorithm, where pipelined implementation of the filter is allowed. The least mean square adaptive filter is the widely used adaptive filter because of its simplicity and performance. The least mean square adaptive filter is used here because it differs from a traditional digital filter in many waysA traditional digital filter has only one input signal x(n) and one output signal y(n) An adaptive filter need an additional input signal d(n) and returns an additional output signal e(n) The coefficients of a traditional digital filter change over time. Therefore, adaptive filters have a self adjusting character whereas traditional digital filters do not have this character. International Journal of Emerging Technology in Computer Science Electronics (IJETCSE) ISSN: 0976 1353 Volume 14 Issue 2 APRIL 2015 738 II. RELATED WORK AND CONTRIBUTIONS Hanan Herzberg et.al designed a systolic array of an adaptive filter which is based on the least mean square algorithm. But due to problem in implementation of the systolic array, a modified algorithm, a special case of the delayed LMS (DLMS) is used. The DLMS algorithm introduces a delay in the updating of the filter coefficients. The convergence and steady state behavior of the systolic array are analyzed. This paper shows that the systolic array is similar to that of a conventional LMS implementation in a wide range of practical conditions. This paper utilizes algebra for the design of a systolic array implementation for adaptive filters based on LMS algorithm. Since the LMS algorithm contains feedback loop, the delays created in the decomposition and retiming process prohibit the exact implementation of the algorithm. The design procedure leads to a systolic array which implements a special case of the so called delayed LMS algorithm. The systolic array presented in this paper shows faster throughput than the other structures. It is shown that delay has a negligible effect on the convergence and the steady state behavior of the adaptive filters [1] Lan Da Van et.al proposed an interesting efficient N tap systolic DLMS adaptive FIR digital filter using a new tree systolic large PE for reducing the adaptation delay in order to achieve faster convergence compared to the other DLMS systolic structures with critical path of one MAC operation. The proposed systolic array architecture is verified through the simulation of adaptive equalization and system identification applications. This efficient architecture amenable to VLSI implementation furnishes the lowest critical period with finite driving, local connections, and satisfactory convergence at no extra cost of area. The systolic structure proposed takes account of minimum delay and high regularity and an efficient N tap systolic adaptive FIR digital filter can be easily determined under the constraint of maximum driving of the feedback error signal [2] Sudha.S.A et.al proposed FIR filter using an efficient multiplication stage technique in order to investigate area, speed, power trade offs for the implementation of FIR filtering using MCM and digital serial arithmetic. Multiple constant multiplications are the efficient of implementing several constant multiplications with the data of same input. The multiplier coefficients are expressed using shifts, adders and subtractions and these can be reduced by introducing Wallace tree multiplier, which can be used to reduce the amount of embedded multipliers in large MCM blocks. The results of the proposed method shows the better performance rate and helps in reducing delay product and in reducing area, power consumption in FIR filtering. The advantage of the proposed method is simplicity in implementation and is stable and robust against different signal conditions [3] Romuald Rocher et.al proposed the implementation of adaptive filter with fixed point arithmetic which is required to evaluate the computational quality. The accuracy is determined by calculating the global quantization noise power in the system output. In this paper a new model for evaluating analytically the global noise power in the LMS algorithm and in the NLMS algorithm is developed. Two existing models are presented and the proposed model is detailed and compared with before ones. The accuracy of the model is analyzed by simulations for evaluating fixed point noise power in LMS algorithm. In the newly developed model analysis error is done at the steady state, once the filter coefficients have converged. The advantage of new model is more tractable than other models and to be valid for all types of quantization [4] S.Ramanathan et.al presented a systolic architecture with minimal adaptation delay and input/output latency, thereby improving the convergence behavior to near that of the original LMS algorithm. The architecture synthesis is done by using a number of function preserving transformations on the signal flow graph representation of the delayed LMS algorithm. With the use of carry save arithmetic the systolic folded pipelined architecture can support very high sampling rate, eliminated only by the delay of full adder [5] Basant k et.al proposed Delayed Block LMS (DBLMS) algorithm which takes a block of L input samples and yields a block of L outputs in every training cycle. The simulation results shows that the performance of DBLMS algorithm is equivalent to that of the DLMS algorithm. This method utilizes the inherent parallelism in DBLMS algorithm to derive a highly concurrent systoliclike architecture for high speed implementation of adaptive FIR filter. The proposed structure can provide L times higher throughput compared with the existing pipelined structures [6] III. SYSTEM DESIGN There are many methods for performing weight update of an adaptive filter. Least mean square algorithm developed by Widrow Hoff originally for use in artificial neural network. This algorithm is similar to the method of steepest descent method in which it adapts weights by iteratively approaching the MSE minimum. The structure of LMS adaptive filter is shown in fihure1.