A Pipeline for the QR Update in Digital Signal Processing

[EN] The input and output signals of a digital signal processing system can often be represented by a rectangular matrix as it is the case of the beamformer algorithm, a very useful particular algorithm that allows extraction of the original input signal once it is cleaned from noise and room reverberation. We use a version of this algorithm in which the system matrix must be factorized to solve a least squares problem. The matrix changes periodically according to the input signal sampled; therefore, the factorization needs to be recalculated as fast as possible. In this paper, we propose to use parallelism through a pipeline pattern. With our pipeline, some partial computations are advanced so that the final time required to update the factorization is highly reducedThis work was supported by the Spanish Ministry of Economy and Competitiveness under MINECO and FEDER projects TIN2014-53495-R and TEC2015-67387-C4-1-R.Dolz, MF.; Alventosa, FJ.; Alonso-Jordá, P.; Vidal Maciá, AM. (2019). A Pipeline for the QR Update in Digital Signal Processing. Computational and Mathematical Methods. 1:1-13. https://doi.org/10.1002/cmm4.1022S113

A pipeline structure for the block QR update in digital signal processing

[EN] There exist problems in the field of digital signal processing, such as filtering of acoustic signals that require processing a large amount of data in real time. The beamforming algorithm, for instance, is a process that can be modeled by a rectangular matrix built on the input signals of an acoustic system and, thus, changes in real time. To obtain the output signals, it is required to compute its QR factorization. In this paper, we propose to organize the concurrent computational resources of a given multicore computer in a pipeline structure to perform this factorization as fast as possible. The pipeline has been implemented using both the application programming interface OpenMP and GrPPI, a library interface to design parallel applications based on parallel patterns. We tackle not only the performance challenge but also the programmability of our idea using parallel programming frameworks.This work was supported by the Spanish Ministry of Economy and Competitiveness under MINECO and FEDER projects TIN2014-53495-R and TEC2015-67387-C4-1-R.Dolz, MF.; Alventosa, FJ.; Alonso-Jordá, P.; Vidal Maciá, AM. (2019). A pipeline structure for the block QR update in digital signal processing. The Journal of Supercomputing. 75(3):1470-1482. https://doi.org/10.1007/s11227-018-2666-1S14701482753Huang Y, Benesty J, Chen J (2006) Acoustic MIMO signal processing (signals and communication technology). Springer, BerlinRamiro C, Vidal AM, González A (2015) MIMOPack: a high performance computing library for MIMO communication systems. J Supercomput 71:751–760Alventosa FJ, Alonso P, Piñero G, Vidal AM (2016) Implementation of the Beamformer algorithm for the NVIDIA Jetson. In: Actas de la Conferencia, Granada, Spain, pp 201–211. ISBN 978-3-319-49955-0Alventosa FJ, Alonso P, Vidal AM, Piñero G, Quintana-Ortí ES (2018) Fast block QR update in digital signal processing. J Supercomput. https://doi.org/10.1007/s11227-018-2298-5del Rio D, Dolz MF, Fernández J, García JD (2017) A generic parallel pattern interface for stream and data processing. Concurr Comput Pract Exp 29(24):e4175Benesty J, Chen J, Huang Y, Dmochowski J (2007) On microphone-array Beamforming from a MIMO acoustic signal processing perspective. IEEE Trans Audio Speech Lang Process 15(3):1053–1065Lorente J, Piñero G, Vidal AM, Belloch JA, González A (2011) Parallel implementations of Beamforming design and filtering for microphone array applications. In: 19th European Signal Processing Conference (EUSIPCO), Barcelona, Spain, pp 501–505Belloch JA, Ferrer M, González A, Martínez-Zaldívar FJ, Vidal AM (2013) Headphone-based virtual spatialization of sound with a GPU accelerator. J Audio Eng Soc 61:546–561Belloch JA, González A, Martínez-Zaldívar FJ, Vidal AM (2011) Real-time massive convolution for audio applications on GPU. J Supercomput 58(3):449–457Golub GH, Van Loan CF (2013) Matrix computations. Johns Hopkins studies in the mathematical sciences. Johns Hopkins University Press, BaltimoreGunter BC, van de Geijn RA (2005) Parallel out-of-core computation and updating the QR factorization. ACM Trans Math Softw 31(1):60–78Buttari A, Langou J, Kurzak J, Dongarra J (2009) A class of parallel tiled linear algebra algorithms for multicore architectures. Parallel Comput 35(1):38–53Dolz MF, Alventosa FJ, Alonso-Jordá P, Vidal AM (2018) A pipeline for the QR update in digital signal processing. In: Proceedings of the 18th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2018), Rota, Cádiz, Spain, pp 1–5Quintana-Ortí G, Quintana-Ortí ES, Van De Geijn RA, Van Zee FG, Chan E (2009) Programming matrix algorithms-by-blocks for thread-level parallelism. ACM Trans Math Softw 36(3):14:1–14:2