Comparison of TDLMS and FDLMS Adaptive Filtering Algorithms for Noise Cancellation

This paper investigates the tracking characteristics of Frequency domain least-mean-square (FDLMS) adaptive filters and Time domain least-mean square (TDLMS) adaptive filters and compares the convergence performance of TDLMS and FDLMS adaptive algorithms for both real and complex valued signals. We simulated the adaptive filter using MATLAB, and the results validate the better performance of FDLMS algorithm over TDLMS for both real and complex coefficient case. Keywords— Adaptive filters, LMS, Noise Cancellation. 1-INTRODUCTION Adaptive Filters are self adjusting filters that can vary their response in accordance with the varying signal characteristics and optimally separates the speech from the noise that has complicated spectrum and rapidly varying characteristics [1]. It uses the filter parameters of a moment ago to automatically adjust the filter parameters of the present moment, to adapt to the statistical properties that signal and noise [2]. Least-Mean-Square (LMS) adaptive algorithm is widely used for noise cancellation in adaptive signal processing for both real-valued and complex-valued signals. Real coefficient adaptive filters have been widely used in the areas such as biomedical engineering, communications and control. One example is to reject narrowband interference in the BPSK spread-spectrum communication system and to control the howling in speakerphone systems [3]. On the other hand, when the signal consists of in-phase and Quadrature-phase components, its sample values are complex numbers. In this situation, the complex coefficient adaptive filters must be developed that find applications in radar and communications system. One example is to reject narrowband interference in the QPSK spread-spectrum system by complex ANF [5]. The LMS algorithm can be used in both time domain (TD) and frequency domain (FD) [4]. Based on in-depth study of adaptive filter, least mean square (LMS) algorithm are applied to the adaptive filter technology in noise cancellation, and simulation results prove that FDLMS adaptive algorithms provides better convergence performance than TDLMS adaptive algorithms for both real and complex valued signals. II. ADAPTIVE NOISE CANCELLATION We considered consider a case of an airplane where the pilot speaks into a microphone and produces a voice signal r, the engine noise n in the cockpit is added to the voice signal, and the resultant signal heard by passengers would be of low quality. The goal is to obtain a signal that contains the pilot's voice, but not the engine noise. We can do this with adaptive filter algorithms as shown in Figure 1. IJECSE,Volume1,Number 2 Rahul Vijayet al. ISSN-2277-1956/V1N2-375-379 Figure 1: Noise in an airplane Figure 2 shows the solution of above problem using generalized adaptive filter algorithm where the input signal x (n) produce output signal y (n) when applied to a digital filter. Adaptive algorithm adjusts the filter coefficient included in the input vector w (n), in order to let the error signal e (n) to be the smallest. Error signal is the difference of useful signal d (n) and the filter output y (n). Therefore, adaptive filter automatically carry on a design based on the characteristic of the input signal x (n) and the useful signal d(n) . Using this method, adaptive filter can be adapted to the environment set by these signals. When the environment changes, filter through a new set of factors, adjusts for new features [6]. Figure 2: Adaptive Noise Cancellation III. LMS ALGORITHMS LMS algorithm for noise cancellation-Basic Idea: Adjustment of the filter parameters, let the mean squares error between the filter output signal and the expectations output signals be smallest, such as system output is the best estimate of useful signal. LMS algorithm can be derived in both time domain TDLMS and frequency domain FDLMS. 377 Comparison of TDLMS and FDLMS Adaptive Filtering Algorithms for Noise Cancellation ISSN-2277-1956/V1N2-375-379 Based on the steepest decline of the least mean square error (TDLMS) algorithm iterative formula is as shown in table1. Fig. 3 shows the flow graph for FDLMS algorithm, the basic operation underlying a frequency domain adaptive filter is the transformation of the input signal into a more desirable form before the adaptive processing this is accomplished by one or more discrete Fourier transform or filter banks where by the input signal is transformed to the frequency domain . In frequency domain adaptive filtering first we apply the block LMS algorithm [7] where filter convolution and correlation operation are computationally demanding. They can be implemented more efficiently in the frequency domain using fast convolution techniques, i.e. overlap-save/overlap add method also known as Fast Block LMS. The Overlap-Add and the Overlap-Save are the two main fixed frequency domain algorithms. In this work we used Overlap-Save method since the Fast-LMS algorithm which is used for the adaptive frequency domain filter is based on it. Table 1: TDLMS Adaptive Algorithm for Noise Cancellation IJECSE,Volume1,Number 2 Rahul Vijayet al. ISSN-2277-1956/V1N2-375-379 Figure 3: FDLMS Adaptive Algorithm for Noise Cancellation IV. SIMULATION RESULTS AND DISCUSSION All simulations are done using MATLAB v.7.5. The noise source is taken as Additive White Gaussian noise (AWGN) signal for real case and Complex Gaussian Circular noise for complex case. The upper bound for step size parameter μ is taken as 0.05 and filter length is taken as 10. The mean square error for each case is plotted for the first 200 iterations. Figure 4 Compares FDLMS and TDLMS for real signal case and shows that FDLMS converges faster than TDLMS and it has low steady state error compared to TDLMS. Figure 5 compares FDLMS for real signal and complex signal case and shows that FDLMS shows better performance hence faster converges if coefficients are real. In Figure 6 we compared the overall simulation results for FDLMS (real and complex) v/s TDLMS (real and complex). Simulation results show the improved performance of FDLMS over TDLMS adaptive filtering algorithm for both real and complex input signals. 379 Comparison of TDLMS and FDLMS Adaptive Filtering Algorithms for Noise Cancellation ISSN-2277-1956/V1N2-375-379 Figure 4: TDLMS v/s FDLMS Real signal case Figure 5: FDLMS Real v/s FDLMS Complex Figure 6: TDLMS and FDLMS (Real v/s Complex) V. CONCLUSIONS Our work shows that the FDLMS achieves faster convergence rate i.e. smaller Mean Square Error (MSE) for both real-valued and complex-valued signals when compared to TDLMS. As a future work it can be used in many signal IJECSE,Volume1,Number 2 Rahul Vijayet al. ISSN-2277-1956/V1N2-375-379processing applications such as channel equalization, acoustic echo cancellation, and Active noise cancellation.Further Complex FDLMS finds application in QAM and QPSK based communication system. REFERENCES[1] A. H. Sayed, Fundamentals of Adaptive Filtering. New York:Wiley,2003.[2] Ying He,Hong He,Li Li,Yi Wu, “The Application and simulation of Adaptive filter in noise cancellation” IEEE InternationalConference on Computer Science and Software Engineering, Oct, 2008[3] S. C. Pei and C. C. Tseng, “Complex adaptive IIR notch filter algorithm and its applications,” IEEE Trans. Circuits Syst., vol.CAS-41,no.2, pp.158-163, Feb. 1994.[4] Simon Haykin, “The Principle of Adaptive filter”, the electronics industrial publisher, vol. 2, Beijing, 2003, pp.159-398.[5] L.M.Li and L.B.Milstein, “Rejection of pulsed CW interference in PN spread-spectrum systems using complex adaptive filters,” IEEETrans.Comm., vol. COM-31, pp. 10-20, Jan. 1983.[6] He Zhenya, “Adaptive Signal Processing”, Science publisher, vol. 1, Beijing, 2002, pp.102-164.[7] J. J. Shynk, “Frequency-domain and multirate adaptive filtering,” IEEE Signal Process. Mag., vol. 9, pp. 14–37, Jan. 1992.