Envelope-constrained Filtering Research Articles

Low-PAPR Hybrid Filter for SC-FDMA

We propose a hybrid filter to reduce the peak-to-average power ratio (PAPR) on the transmitter side in a long-term evolution uplink scheme. The design of the proposed filter is based on two key components: a finite impulse response filter and a Nyquist-I pulse. We consider an envelope-constrained filter design to optimize the impulse response of the proposed filter in terms of PAPR reduction. Moreover, we propose a new family of Nyquist-I pulses, the exponential linear pulse, which has a new design parameter that helps reduce PAPR for a given roll-off factor and transmission scheme. Theoretical and numerical results show that the proposed filter outperforms existing filters in terms of PAPR and symbol error rate, and it has a less computationally complex impulse response expression than existing filters for the interleaved subcarrier mode of single-carrier frequency-division multiple access.

Robust envelope-constrained filter with orthonormal bases and semi-definite and semi-infinite programming

In this paper, the equivalence relation between a semi-infinite quadratically constrained convex quadratic programming problem and a combined semi-definite and semi-infinite programming problem is considered. Then, an efficient and reliable discretization algorithm for solving a general class of combined semi-definite and semi-infinite programming problems is developed. Both the continuous-time envelope-constrained optimal equalization filter and the corresponding robust envelope-constrained filter for a communication channel are solved by using the proposed algorithm.

Adaptive filter design subject to output envelope constraints and bounded input noise

This transactions brief is concerned with designing adaptive filters subject to output envelope constraints in the presence of bounded noise at the input channel. The bound on the noise is used to form the input mask that contains all possible input signals corrupted by noise. The optimal envelope-constrained filter is designed with respect to the entire input mask. A cubic smoothing function is applied to implement the constraint approximation, which paves the way for establishing adaptive algorithms. The adaptive envelope-constrained filter thus designed, achieves guaranteed satisfaction of the output envelope constraints as long as it has converged. Computer simulations that support the theoretical findings are given.

Mean square convergence of adaptive envelope-constrained filtering

A new type of adaptive filtering scheme for solving an envelope-constrained filter design problem in a stochastic environment has been presented. The steady-state stochastic analysis of the adaptive scheme is established in the sense of the mean square. It is shown that if a given initial point is in a neighborhood of the origin, the adaptive scheme with a fixed step-size produces a filter that converges in the mean square sense to within an upper boundary of the noise-free optimum filter. Numerical examples involving pulse compression and channel equalization are presented to illustrate the convergence characteristics of the adaptive scheme operating in a stochastic environment.

Application of cubic constraint approximation in the recursive design of FIR filters subject to output envelope constraints

The smoothing function used in the constraint approximation plays an important role in the adaptive envelope-constrained (EC) filtering algorithms presented. In this paper, a cubic smoothing function is proposed to implement the constraint approximation and the simplified line search technique is introduced to speed up the convergence rate. It is shown that the performance of the adaptive EC filtering algorithms can be greatly improved due to the use of the cubic constraint approximation and simplified line searches. In particular, the second-order convergence is established for the Newton-Raphson type algorithm. Numerical results are included to illustrate the effectiveness of these adaptive EC filtering algorithms.

Continuous-time envelope-constrained filter design via DSP approach

In envelope-constrained (EC) filter design, the effect of input noise is minimised subject to the constraint that the filter's response to a specified signal fits into a prescribed envelope. The continuous-time version of this problem has been addressed using orthonormal analogue filters. The paper addresses the EC filter-design problem using a filter comprised of an A/D converter, a digital processor, a D/A converter and an analogue interpolation filter. Numerical results are presented for a number of design examples.

Design of adaptive envelope-constrained filters in the presence of impulsive noise

The problem of designing adaptive filters subject to output envelope constraints in the presence of impulsive noise at the input channel is investigated. Median smoothing is incorporated into the recently developed adaptive envelope-constrained filtering algorithms with a view to suppressing the effect of impulsive noise. It is demonstrated that the proposed adaptive filtering algorithms can provide notable improvements in the performance. In particular, the output envelope constraints of primary interest can be more easily satisfied by the filter weight estimate obtained with the median smoothing than with the average smoothing in impulsive noise situations. Numerical simulations are included to show the effectiveness of the proposed adaptive filtering algorithms.

Envelope-constrained filters: adaptive algorithms

We consider an envelope-constrained (EC) optimal filter design problem involving a quadratic cost function and a number of linear inequality constraints. Using the duality theory and the space transformation function, the optimal solution of the dual problem can be computed by finding the limiting point of an ordinary differential equation given in terms of the gradient flow. An iterative algorithm is developed via discretizing the differential equation. From the primal-dual relationship, the corresponding sequence of approximate solutions in the original EC filtering problem is obtained. Based on these results, an adaptive algorithm is constructed for solving the stochastic EC filtering problem in which the input signal is corrupted by an additive random noise. For illustration,a practical example is solved for both noise-free and noisy cases.

The effect of noise on adaptive envelope-constrained filters

The performance of the envelope-constrained filters designed by the newly developed adaptive algorithms may deteriorate when the input signal is contaminated by noise. The average window with a growing window size, and the exponentially weighted average window are presented. It is shown that the noise-induced bias in the augmented cost function will be reduced because applying such an averaging scheme helps increase values of the signal-to-noise ratio at the filter input channel. With this, the noise effect on the adaptive envelope-constrained filters can be depressed. Simulation results are given to illustrate the improved performance of the adaptive envelope-constrained filters designed in conjunction with the average window.

Gradient flow approach to discrete-time envelope-constrained filter design via orthonormal filters

Using digital orthonormal filters and Lagrangian duality theory, the envelope-constrained (EC) filtering problem has been formulated as a dual quadratic programming (QP) problem with simple constraints. Applying the barrier-gradient and barrier-Newton methods based on the space transformation and gradient flow technique, two efficient design algorithms are constructed for solving this QP problem. An adaptive algorithm, based on the barrier-gradient algorithm, is developed to solve the EC filtering problem in a stochastic environment. The convergence properties are established in the mean and mean square error senses. To demonstrate the effectiveness of the proposed algorithms, a practical example using the Laguerre networks is solved for both the deterministic and stochastic cases.

Design of robust envelope-constrained filter with orthonormal bases

In the continuous-time envelope-constrained (EC) filtering problem using an orthonormal filter structure, the aim is to synthesize an orthonormal filter such that the noise enhancement is minimized while the noiseless output response of the filter with respect to a specified input signal stays within the upper and lower bounds of the envelope. The noiseless output response of the optimum filter to the prescribed input signal touches the output boundaries at some points. Consequently, any disturbance in the prescribed input signal or error in the implementation of the optimal filter will result in the output constraints being violated. In this paper, we review a semi-infinite envelope-constrained filtering problem in which the constraint robustness margin of the filter is maximized, subject to a specified allowable increase in the optimal noisy power gain. Using a smoothing technique, it is shown that the solution of the optimization problem can be obtained by solving a sequence of strictly convex optimization problems with integral cost. An efficient optimization algorithm is developed based on a combination of the golden section search method and the quasi-Newton method.

Continuous-time envelope constrained filter design with input uncertainty

In envelope constrained (EC) filter design, the effect of input noise is minimized subject to the constraint that the filter's response to a specified signal fits into a prescribed envelope. It is always the case that the response of the optimal EC filter touches the output envelope, at some instances. Consequently, any disturbance in the prescribed input or implementation error could violate the output constraints. In an EC-filtering problem with uncertain input (ECUI), the set of possible inputs and the set of permissible outputs are defined by envelopes or masks. The objective is to design the filter to minimize the noise enhancement, while satisfying the constraint that every signal in the input envelope evokes a response, which stays in the output envelope. This paper formulates the ECUI for analog filters, and presents a number of key results, which enable this problem to be solved.

Cubic constraint approximation based adaptive algorithms for envelope-constrained filtering

The design of envelope-constrained filters is formulated as a constrained optimization problem. In this paper the constraint approximation is realized through a cubic natural spline, which results in an unconstrained optimization problem for envelope-constrained filter design. The solution of this unconstrained problem is suitable for real-time update. It is shown that, compared with the previously used quadratic natural spline, the cubic natural spline leads to the establishment of the adaptive algorithms with much more desirable performance. In particular, the step size of the cubic constraint approximation based adaptive algorithms can be chosen in a more flexible manner so as to achieve faster convergence. Numerical examples illustrate the main results.

A dual approach to continuous-time envelope-constrained filter design via orthonormal filters

The envelope-constrained (EC) filtering problem was initially posed in the continuous-time domain as a constrained L/sup 2/ space optimization problem. However, only the discretized version has been solved, using various approaches. In this paper we consider the continuous-time EC filtering problem formulated using an orthonormal basis defined on a Hilbert vector space. Caratheodory's theorem and the dual parametrization method are used to obtain a dual finite-dimensional optimization problem. Two iterative algorithms based on the gradient flow technique are then developed for solving this dual problem. The design of an EC optimal equalization filter for a communication channel is solved to illustrate the effectiveness of the proposed algorithm.

Iterative algorithms for envelope constrained recursive filter design via Laguerre functions

The envelope constrained (EC) filtering problem is concerned with the design of a time-invariant filter to process a given input pulse such that the output waveform is guaranteed to lie within a prescribed output mask. Using the orthonormal Laguerre functions the EC filtering problem can be posed as a quadratic programming (QP) problem with affine inequality constraints. An iterative algorithm for solving this QP problem is proposed. We also show that for the EC filtering problem, filters based on Laguerre functions offer a more robust and low-order alternative to finite impulse response (FIR) filters. A numerical example, concerned with the design of an equalization filter for a digital transmission channel, is presented to illustrate the effectiveness of the iterative algorithm and the Laguerre filter.

Minimax approach to envelope constrained filter design

A novel approach to envelope constrained filter (ECF) design is proposed, based on modifications of minimax algorithms, originally developed for mismatched filter design for sidelobe suppression in radar applications. The proposed approach introduces error control in the nonfeasible solution case, thereby allowing for an improved performance.

Continuous-time envelope-constrained filter design via Laguerre filters and ℋ/sub ∞/ optimization methods

The envelope-constrained filtering problem is concerned with the design of a time-invariant filter to process a given input signal such that the noiseless output of the filter is guaranteed to lie within a specified output mask while minimizing the noise gain of the filter. An algorithm is developed to solve the continuous-time envelope-constrained filter design problem with the /spl Hscr//sub /spl infin// norm of the filter as the cost and an orthonormal set of basis filters. It is shown that the problem can be reformulated and solved as a constrained /spl Hscr//sub /spl infin// model-matching problem. To illustrate the effectiveness of the design method, two numerical examples are presented that deal with the design of equalization filters for digital transmission channels.

Applications of H∞ optimization method to envelope-constrained IIR filter design

Applications of H∞ optimization method to envelope-constrained IIR filter design

Further Investigation of Adaptive Envelope-Constrained Filtering Algorithms

A new type of recursive algorithms were proposed recently for designing an adaptive envelope-constrained filter, and the corresponding convergence properties were established. In this paper, the effect of noise at the input channel on the proposed adaptive algorithms is studied. It is shown that the presence of noise which corrupts the input signal causes a bias in the filter weight estimate. An averaging window technique is applied to reduce the noise effect and its properties are evaluated in simulation experiments.

Robust design of envelope-constrained filters in the presence of input uncertainty

The maximum robustness design of envelope-constrained filters with uncertain input (ECUI) is formulated as a minimax optimization problem in which the set of feasible filters is characterized by nonsmooth matrix inequalities. An efficient design algorithm is developed to solve this problem by use of a newly developed transformation technique. The attractive feature of this algorithm is that the ECUI filter thus designed can allow for the greatest uncertainty in the input signal while still achieving the acceptable filter performance.