Efficient and Stable Algorithms to Extend Greville's Method to Partitioned Matrices Based on Inverse Cholesky Factorization

Greville's method has been utilized in (Broad Learn-ing System) BLS to propose an effective and efficient incremental learning system without retraining the whole network from the beginning. For a column-partitioned matrix where the second part consists of p columns, Greville's method requires p iterations to compute the pseudoinverse of the whole matrix from the pseudoinverse of the first part. The incremental algorithms in BLS extend Greville's method to compute the pseudoinverse of the whole matrix from the pseudoinverse of the first part by just 1 iteration, which have neglected some possible cases, and need further improvements in efficiency and numerical stability. In this paper, we propose an efficient and numerical stable algorithm from Greville's method, to compute the pseudoinverse of the whole matrix from the pseudoinverse of the first part by just 1 iteration, where all possible cases are considered, and the recently proposed inverse Cholesky factorization can be applied to further reduce the computational complexity. Finally, we give the whole algorithm for column-partitioned matrices in BLS. On the other hand, we also give the proposed algorithm for row-partitioned matrices in BLS

Two Ridge Solutions for the Incremental Broad Learning System on Added Nodes

The original Broad Learning System (BLS) on new added nodes and its existing efficient implementation both assume the ridge parameter is near 0 in the ridge inverse to approximate the generalized inverse, and compute the generalized inverse solution for the output weights. In this paper, we propose two ridge solutions for the output weights in the BLS on added nodes, where the ridge parameter can be any positive real number. One of the proposed ridge solutions computes the output weights from the inverse Cholesky factor, which is updated by extending the existing inverse Cholesky factorization. The other proposed ridge solution computes the output weights from the ridge inverse, and updates the ridge inverse by extending the Greville method that can only computes the generalized inverse of a partitioned matrix. The proposed BLS algorithm based on the ridge inverse requires the same complexity as the original BLS algorithm, while the proposed BLS algorithm based on the inverse Cholesky factor requires less complexity and training time than the original BLS and the existing efficient BLS. Both the proposed ridge solutions for BLS achieve the same testing accuracy as the standard ridge solution in the numerical experiments. The difference between the testing accuracy of the proposed ridge solutions and that of the existing generalized inverse solutions is negligible when the ridge parameter is very small, and becomes too big to be ignored when the ridge parameter is not very small. When the ridge parameter is not near 0, usually the proposed two ridge solutions for BLS achieve better testing accuracy than the existing generalized inverse solutions for BLS, and then the former are more preferred than the latter

Design and Implementation of an Universal Lattice Decoder on FPGA

In wireless communication, MIMO (multiple input multiple output) is one of the promising technologies which improves the range and performance of transmission without increasing the bandwidth, while providing high rates. High speed hardware MIMO decoders are one of the keys to apply this technology in applications. In order to support the high data rates, the underlying hardware must have significant processing capabilities. FPGA improves the speed of signal processing using parallelism and reconfigurability advantages. The objective of this thesis is to develop an efficient hardware architectural model for the universal lattice decoder and prototype it on FPGA. The original algorithm is modified to ensure the high data rate via taking the advantage of FPGA features. The simulation results of software, hardware are verified and the BER performance of both the algorithms is estimated. The system prototype of the decoder with 4-transmit and 4-receive antennas using a 4-PAM (Pulse amplitude modulation) supports 6.32 Mbit/s data rate for parallelpipeline implementation on FPGA platform, which is about two orders of magnitude faster than its DSP implementation

Combined data detection scheme for zero-padded OFDM signals in MMF links

© © 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this letter, we propose a receiver scheme for zero-padded orthogonal frequency division multiplexing (OFDM) that combines low complexity from overlap-and-add equalizer and low error rate provided by successive interference cancellation data detection from optimal ordering vertical Bell Laboratories layered space-time (V-BLAST) architecture. Results of numerical simulations on multimode optical fiber links show that the proposed scheme improves the error rate performance of zero forcing (ZF) equalization receiver, reaching results similar to V-BLAST. For example, the proposed scheme can reach 33.9 Gb/s in a 600-m link, whereas the ZF receiver would reach 29.06 Gb/s and cyclic prefix OFDM only 19.37 Gb/s. These results are obtained with a reduction in computational complexity (measured in number of real products) of 86% in detection and 66% in preprocessing with respect to the ZF receiver, and 75% and 97% with respect to the V-BLAST receiver.Manuscript received May 6, 2015; accepted May 24, 2015. Date of publication June 1, 2015; date of current version July 10, 2015. This work was supported by the Spanish Ministerio de Economia y Competitividad under Project TEC2012-38558-C02-02 and Project TEC2012-38558-C02-01, both with FEDER funds. The work of P. Medina was supported by the Formacion de Personal Investigador Grant Program of the Universitat Politecnica de Valencia.Medina Sevila, P.; Almenar Terré, V.; Corral, JL. (2015). Combined data detection scheme for zero-padded OFDM signals in MMF links. IEEE Photonics Technology Letters. 27(16):1753-1756. https://doi.org/10.1109/LPT.2015.2439158S17531756271

Efficient detection algorithms for Multiple-Input Multiple-Output (MIMO) systems

[EN] In the last ten years, one of the most significant technological developments that will lead to the new broadband wireless generation is the communication via Multiple-Input Multiple-Output (MIMO) systems. MIMO systems are known to provide an increase of the maximum rate, reliability and coverage of current wireless communications. Maximum-Likelihood (detection over Gaussian MIMO channels is shown to get the lowest Bit Error Rate for a given scenario. However, it has a prohibitive complexity which grows exponentially with the number of transmit antennas and the size of the constellation. Motivated by this, there is a continuous search for computationally efficient optimal or suboptimal detectors. In this work, we carry out an state of the art review of detection algorithms and propose the combination of a suboptimal MIMO detector called K-Best Sphere Decoder with a channel matrix condition number estimator to obtain a versatile combined detector with predictable performance and suitable for hardware implementation. The effect of the channel matrix condition number in data detection is exploited in order to achieve a decoding complexity lower than the one of already proposed algorithms with similar performance. Some practical algorithms for finding the 2-norm condition number of a given channel matrix and for performing the threshold selection are also presented and their computational costs and accuracy are discussed[ES] Uno de los desarrollos tecnol'ogicos m'as significativos de la ' ultima d'ecada que llevar'an a la nueva generaci'on de banda ancha en movilidad es la comunicaci'on mediante sistemas de m' ultiples entradas y m' ultiples salidas (MIMO). Los sistemas MIMO proporcionan un notable incremento en la capacidad, fiabilidad y cobertura de las comunicaciones inal'ambricas actuales. Se puede demostrar que la detecci'on 'optima o dem'axima verosimilitud (ML) en canales MIMO Gaussianos proporciona la m'¿nima tasa de error de bit (BER) para un escenario dado pero tiene el inconveniente de que su complejidad crece exponencialmente con el n'umero de antenas y el tama¿no de la constelaci'on utilizada. Por este motivo, hay una cont'¿nua b' usqueda de detectores 'optimos o sub'optimos que sean m'as eficientes computacionalmente. En este trabajo, se ha llevado a cabo una revisi 'on del estado del arte de los principales algoritmos de detecci'on para sistemas MIMO y se ha propuesto la combinaci'on de un detector MIMO sub'optimo conocido como K-Best Sphere Decoder con un estimador del n'umero de condici'on de la matriz de canal, para conseguir un detector combinado basado en umbral con complejidad predecible y adecuado para implementaci'on en hardware. Se ha explotado el efecto del n'umero de condici'on en la detecci'on de datos para disminuir la complejidad de los algoritmos de detecci 'on existentes sin apenas alterar sus prestaciones. Por ' ultimo tambi'en se presentan distintos algoritmos pr'acticos para encontrar el dos n'umero de condici'on as'¿ como para realizar la selecci 'on del umbral.Roger Varea, S. (2008). Efficient detection algorithms for Multiple-Input Multiple-Output (MIMO) systems. http://hdl.handle.net/10251/12200Archivo delegad

Improved Recursive Algorithms for V-BLAST to Reduce the Complexity and Save Memories

Improvements I-IV were proposed to reduce the computational complexity of the original recursive algorithm for vertical Bell Laboratories layered space-time architecture (VBLAST). The existing recursive algorithm with speed advantage and that with memory saving incorporate Improvements I-IV and only Improvements III-IV into the original algorithm, respectively. To the best of our knowledge, the algorithm with speed advantage and that with memory saving require the lowest complexity and the least memories, respectively, among the existing recursive V-BLAST algorithms. We propose Improvements V and VI to replace Improvements I and II, respectively. Instead of the lemma for inversion of partitioned matrix applied in Improvement I, Improvement V uses another lemma to speed up the matrix inversion step by the factor of 1.67. Then the formulas adopted in our Improvement V are applied to deduce Improvement VI, which includes the improved interference cancellation scheme with memory saving. In the existing algorithm with speed advantage, the proposed algorithm I with speed advantage replaces Improvement I with Improvement V, while the proposed algorithm II with both speed advantage and memory saving replaces Improvements I and II with Improvements V and VI, respectively. Both proposed algorithms speed up the existing algorithm with speed advantage by the factor of 1.3, while the proposed algorithm II achieves the speedup of 1.86 and saves about half memories, compared to the existing algorithm with memory saving