Abstract
Adaptive filters that self-adjust their transfer functions according to optimizing algorithms are powerful adaptive systems with numerous applications in the fields of signal processing, communications, radar, sonar, seismology, navigation systems and biomedical engineering. An adaptive signal processing algorithm, e.g., the least mean squares (LMS) algorithm and the recursive least square (RLS) algorithm, is used to deal with adaptation of adaptive filters. The adaptive algorithms are expected to be computationally simple, numerically robust, fast convergent and low fluctuant. Unfortunately, none of the adaptive algorithms developed so far perfectly fulfils these requirements. The stability and convergence performance of the widely-used adaptive algorithms also haven't been fully explored. This work aims to deal with performance analysis and enhancements for the adaptive algorithms and their applications. 4.3 Plot of the MSD for the various algorithms with white input and uncorrelated noise for constantly varying channel. . . . . . . . . . . . . . . . . 4.4 Plot of the MSD for the various algorithms with nonwhite Gaussian input AR(1) and uncorrelated noise. . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Plot of the MSD for the various algorithms with nonwhite Gaussian input AR(3) and uncorrelated noise. . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Block diagram of transform-domain LMS algorithm. . We first develop a new variable step-size adjustment scheme for the LMS algorithm using a quotient form of filtered quadratic output errors. Compared to the existing approaches, the proposed scheme reduces the convergence sensitivity to the power of the measurement noise and improves the steady-state performance and tracking capability for comparable transient behavior, with negligible increase in the computational costs. We then develop variable step-size approaches for the normalized least mean squares (NLMS) algorithm. We derive the optimal step-size which minimizes the mean square deviation at each iteration, and propose four approximated step-sizes according to the correlation properties of the additive noise and the variations of the input excitation. We next analyze the stability and performance of the transform-domain LMS algorithms which preprocess the inputs with a fixed data-independent orthogonal transform such as i the discrete Fourier transform (DFT), discrete Hartley transform (DHT), discrete cosine transform (DCT), discrete sine transform (DST) and power normalization. For the particular second-order autoregressive inputs, we derive the eigenvalue distributions of the autocorrelation matrices obtained after the transformations of DFT, DHT, DCT, DST and power normalization, and we make comparisons on the convergence performance of the transform-domain LMS algorithms. Finally, we enhance the performance of the conjugate gradient (CG) algorithms by presenting a generalized data windowing scheme. We analyze that the misadjustment of the new CG algorithms can reduce to zero, which is comparable to that of the RLS algorithm. In addition, we demonstrate the performance of the enhanced algorithms and verify the analytical results by computer simulations in system identification, noise cancelation and channel equalization.
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