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54
Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a number of ideas and approaches to approximate processing as currently being formulated in the computer science community. We then present four examples of signal processing algorithms/systems that are structured with these goals in mind. These examples may be viewed as partial inroads toward the ultimate objective of developing, within the context of signal processing design and implementation,...
A fast randomized algorithm for the approximation of matrices
, 2007
"... We introduce a randomized procedure that, given an m×n matrix A and a positive integer k, approximates A with a matrix Z of rank k. The algorithm relies on applying a structured l × m random matrix R to each column of A, where l is an integer near to, but greater than, k. The structure of R allows u ..."
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Cited by 62 (7 self)
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We introduce a randomized procedure that, given an m×n matrix A and a positive integer k, approximates A with a matrix Z of rank k. The algorithm relies on applying a structured l × m random matrix R to each column of A, where l is an integer near to, but greater than, k. The structure of R allows us to apply it to an arbitrary m × 1 vector at a cost proportional to m log(l); the resulting procedure can construct a rankk approximation Z from the entries of A at a cost proportional to mn log(k)+l 2 (m+n). We prove several bounds on the accuracy of the algorithm; one such bound guarantees that the spectral norm ‖A − Z ‖ of the discrepancy between A and Z is of the same order as √ max{m, n} times the (k + 1) st greatest singular value σk+1 of A, with small probability of large deviations. In contrast, the classical pivoted “Q R ” decomposition algorithms (such as GramSchmidt or Householder) require at least kmn floatingpoint operations in order to compute a similarly accurate rankk approximation. In practice, the algorithm of this paper is faster than the classical algorithms, as long as k is neither very small nor very large. Furthermore, the algorithm operates reliably independently of the structure of the matrix A, can access each column of A independently and at most twice, and parallelizes naturally. The results are illustrated via several numerical examples.
BLENDENPIK: SUPERCHARGING LAPACK'S LEASTSQUARES SOLVER
"... Several innovative randomsampling and randommixing techniques for solving problems in linear algebra have been proposed in the last decade, but they have not yet made a significant impact on numerical linear algebra. We show that by using an high quality implementation of one of these techniques w ..."
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Cited by 38 (4 self)
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Several innovative randomsampling and randommixing techniques for solving problems in linear algebra have been proposed in the last decade, but they have not yet made a significant impact on numerical linear algebra. We show that by using an high quality implementation of one of these techniques we obtain a solver that performs extremely well in the traditional yardsticks of numerical linear algebra: it is significantly faster than highperformance implementations of existing stateoftheart algorithms, and it is numerically backward stable. More speci cally, we describe a leastsquare solver for dense highly overdetermined systems that achieves residuals similar to those of direct QR factorization based solvers (lapack), outperforms lapack by large factors, and scales significantly better than any QRbased solver.
An efficient implementation of NCOFDM transceivers for cognitive radios
 in Proc. of 1st Conf. on Cognitive Radio Oriented Wireless Networks and Commun., Mykonos
, 2006
"... In this paper, we present an efficient implementation of a noncontiguous orthogonal frequency division multiplexing (NCOFDM) transceiver for cognitive radio systems. NCOFDM is designed to transmit information in the presence of incumbent users, deactivating subcarriers located in the vicinity of ..."
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Cited by 29 (1 self)
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In this paper, we present an efficient implementation of a noncontiguous orthogonal frequency division multiplexing (NCOFDM) transceiver for cognitive radio systems. NCOFDM is designed to transmit information in the presence of incumbent users, deactivating subcarriers located in the vicinity of these users to avoid interference. Given that the core component of an NCOFDM transceiver is the fast Fourier transform (FFT), and that several of the subcarriers are deactivated, it is possible to reduce the execution time by “pruning ” the FFT. We propose an algorithm that efficiently and quickly prunes the FFT for NCOFDM transceivers. Results show that the proposed algorithm substantially outperforms other FFT pruning algorithms when a medium to large number of subcarriers have been deactivated. 1
A lowcomplexity ML channel estimator for OFDM
 IEEE Commun. Lett
, 2003
"... Abstract—Orthogonal frequencydivision multiplexing with cyclic prefix enables lowcost frequencydomain mitigation of multipath distortion. However, to determine the equalizer coefficients, knowledge of the channel frequency response is required. While a straightforward approach is to measure the ..."
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Cited by 20 (3 self)
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Abstract—Orthogonal frequencydivision multiplexing with cyclic prefix enables lowcost frequencydomain mitigation of multipath distortion. However, to determine the equalizer coefficients, knowledge of the channel frequency response is required. While a straightforward approach is to measure the response to a known pilot symbol sequence, existing literature reports a significant performance gain when exploiting the frequency correlation properties of the channel. Expressing this correlation by the finite delay spread, we build a deterministic model parametrized by the channel impulse response and, based on this model, derive the maximumlikelihood channel estimator. In addition to being optimal (up to the modeling error), this estimator receives an elegant time–frequency interpretation. As a result, it has a significantly lower complexity than previously published methods. Index Terms—Equalizers, orthogonal frequencydivision multiplexing (OFDM). I.
Constrained least squares detector for OFDM/SDMAbased wireless networks
 IEEE Trans. Wireless Commun
, 2003
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 12 (1 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
and A Ortega, "DCT Computation based on Variable Complexity Fast Approximations
 Proc. ICIP98
, 1998
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Wavelet transform based fast approximate fourier transform
 in Proc. IEEE Intl. Conf. Acoustics, Speech, and Signal Processing
, 1997
"... We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The CooleyTukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. If no intermediate coecients are dropped and no approxi ..."
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Cited by 11 (1 self)
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We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The CooleyTukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. If no intermediate coecients are dropped and no approximations are made, the proposed algorithm computes the exact result, and its computational complexity is on the same order of the FFT, i.e. O(N log 2 N). The main advantage of the proposed algorithm is that the good time and frequency localization of wavelets can be exploited to approximate the Fourier transform for many classes of signals resulting in much less computation. Thus the new algorithm provides an ecient complexity v.s. accuracy tradeo. When approximations are allowed, under certain sparsity conditions, the algorithm can achieve linear complexity, i.e. O(N). The proposed algorithm also has builtin noise reduction capability. 1.
An efficient FFT for OFDM based cognitive radio on a reconfigurable architecture
 in Communications, ICC '07. IEEE International Conference
, 2007
"... Abstract — Cognitive Radio is a promising technology to utilize nonused parts of the spectrum that actually are assigned to licensed services. An adaptive OFDM based Cognitive Radio system has the capacity to nullify individual carriers to avoid interference to the licensed user. Therefore, there c ..."
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Cited by 11 (3 self)
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Abstract — Cognitive Radio is a promising technology to utilize nonused parts of the spectrum that actually are assigned to licensed services. An adaptive OFDM based Cognitive Radio system has the capacity to nullify individual carriers to avoid interference to the licensed user. Therefore, there could be a considerably large number of zerovalued inputs/outputs for the IFFT/FFT in the OFDM transceiver. Due to the wasted operations on zero values, the standard FFT is no longer efficient. Based on this observation, we propose to use a computationally efficient IFFT/FFT as an option for OFDM based Cognitive Radio. Mapping this algorithm onto a reconfigurable architecture is discussed. I.