Peak-constrained least-squares optimization

Adams, John W.; Sullivan, Josephine

doi:10.1109/78.655417

Cited by 104 publications

(51 citation statements)

References 28 publications

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“…When pulse amplitude modulation (PAM) is used, the transmitted PAM UWB waveform is given by (1) The power spectral density (PSD) of is then given by (2) where is the Fourier transform (FT) of and depends on both and the TH code . Specifically, can be expressed as (3) where is the FT of . Equation (2) now becomes…”

Section: Signal Modelmentioning

confidence: 99%

“…Therefore, any algorithm for the solution of (14) must be able to deal with the intricacies of locally optimal solutions. 3 However, both the objective and the constraints in (14) are linear functions of the autocorrelation of . In particular, by exploiting the fact that , it can be shown that , where and .…”

Section: A Direct Maximization Of Nespmentioning

confidence: 99%

“…Once again, (27) can be efficiently solved using general purpose convex optimization tools, e.g., [22]. The problem in (27) is also particularly amenable to solution methods that employ multiple exchange techniques; e.g., [3] and [21].…”

Section: Constrained Frequency Response Approximation With Linear mentioning

confidence: 99%

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Optimal waveform design for UWB radios

Tian

Davidson

et al.

2004 IEEE International Conference on Acoustics, Speech, and Signal Processing

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Abstract-With transmit power spectra strictly limited by regulatory spectral masks, the emerging ultra-wideband (UWB) communication systems call for judicious pulse shape design in order to achieve optimal spectrum utilization, spectral mask compatibility, and coexistence with other wireless services. Meanwhile, orthogonal pulse sets are often desired in order to apply high-rate multidimensional modulation and (carrier-free) orthogonal frequency-division multiple access. Motivated by these considerations, we suggest a digital finite impulse response (FIR) filter approach to synthesizing UWB pulses and propose filter design techniques by which optimal waveforms that satisfy the spectral mask can be efficiently obtained. For single pulse design, we develop a convex formulation for the design of the FIR filter coefficients that maximize the spectrum utilization efficiency in terms of both the bandwidth and power allowed by the spectral mask. For orthogonal pulse design, a sequential strategy is derived to formulate the overall pulse design problem as a set of convex subproblems, which are then solved in a sequential manner to yield a set of mutually orthogonal pulses. Our design techniques not only provide waveforms with high spectrum utilization and guaranteed spectral mask compliance but also permit simple modifications that can accommodate several other system objectives.Index Terms-Digital pulse design, finite impulse response (FIR) filter, ultra-wide-band communications.

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Section: Signal Modelmentioning

confidence: 99%

Section: A Direct Maximization Of Nespmentioning

confidence: 99%

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Optimal waveform design for UWB radios

Tian

Davidson

et al.

2004 IEEE International Conference on Acoustics, Speech, and Signal Processing

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“…Note that in contrast to standard peak-constrained least-squares filter design [39], our design criteria do not include an explicit lower bound on the magnitude spectrum in the pass-band of the prototype filter. However, by generalizing Nyquist's first criterion for intersymbol-interference-free pulse amplitude modulation, it can be shown that the distortion and maximum stop-band level constraints [(30c) and (30b), respectively] implicitly control the pass-band 'ripple' [34, Appendix A].…”

mentioning

confidence: 99%

“…This is important because the objective and the constraints in (30) are competing criteria. For example, it is well known that there is a trade-off between the maximum stop-band level and the stop-band energy (e.g., [39]). Achieving a good design involves an exploration of the trade-offs between these criteria, followed by the design of a filter which achieves a desired position on the trade-off surface.…”

mentioning

confidence: 99%

Efficient design of oversampled NPR GDFT filter banks

Wilbur

Davidson

Reilly

2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).

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In this paper, we present a flexible, efficient design technique for the prototype filter of an oversampled near perfect reconstruction (NPR) generalized Discrete Fourier Transform (GDFT) filter bank. Such filter banks have several desirable properties for subband processing systems which are sensitive to aliasing, such as subband adaptive filters. Our design criteria for the prototype filter are explicit bounds (derived herein) on the aliased components in the subbands and the output, the distortion induced by the filter bank, and the imaged subband errors in the output. It is shown that the design of an optimal prototype filter can be transformed into a convex optimization problem which can be efficiently solved. Our design technique provides an efficient and effective tool for exploring many of the inherent trade-offs in the design of the prototype filter, including the trade-off between aliasing in the subbands and the distortion induced by the filter bank. In our examples we calculate several of these trade-offs and demonstrate that our method can generate filters with significantly better performance than filters obtained using current design methods. * A condensed version of this report has been accepted, subject to minor revisions, for publication in the IEEE Transactions on Signal Processing

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Specification parameters for finite word length linear‐phase FIR single‐band PCLS filters

Ling

2018

Adaptive Control & Signal

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SummaryFinite word length linear‐phase finite impulse response filters can be implemented using low‐cost devices. Among them, the single‐band peak‐constrained least squares filters are the most common one employed in many engineering applications. To design these filters, it is required to define the specifications on the maximum passband ripple magnitude, the maximum stopband ripple magnitude, and the number of bits for representing the filter coefficients. Most of the existing works on the filter design are on the determination of the filter coefficients based on a given set of these specification parameters. However, very few works are on the determination of these specification parameters. Hence, this paper establishes the analytical relationships among these specification parameters. In particular, the relationship between the total ripple energy and the maximum ripple magnitude of the filter, the relationship between the number of bits for representing the filter coefficients and the total ripple energy of the filter, and the relationship between the number of bits for representing the filter coefficients and the maximum ripple magnitude of the filter are established. Computer numerical simulations are presented for verifying the obtained results.

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Peak-constrained least-squares optimization

Abstract: Abstract-We presented the basic concepts for peakconstrained least-squares (PCLS) optimization in previous papers. We present advanced PCLS optimization concepts in this paper.

Cited by 104 publications

References 28 publications

Optimal waveform design for UWB radios

Optimal waveform design for UWB radios

Efficient design of oversampled NPR GDFT filter banks

Specification parameters for finite word length linear‐phase FIR single‐band PCLS filters

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