Fast Kurtosis Maximization Algorithm Research Articles

Non-Cancellation Multistage Kurtosis Maximization with Prewhitening for Blind Source Separation

Chi et al. recently proposed two effective non-cancellation multistage (NCMS) blind source separation algorithms, one using the turbo source extraction algorithm (TSEA), called the NCMS-TSEA, and the other using the fast kurtosis maximization algorithm (FKMA), called the NCMS-FKMA. Their computational complexity and performance heavily depend on the dimension of multisensor data, that is, number of sensors. This paper proposes the inclusion of the prewhitening processing in the NCMS-TSEA and NCMS-FKMA prior to source extraction. We come up with four improved algorithms, referred to as the PNCMS-TSEA, the PNCMS-FKMA, the PNCMS-TSEA(p), and the PNCMS-FKMA(p). Compared with the existing NCMS-TSEA and NCMS-FKMA, the former two algorithms perform with significant computational complexity reduction and some performance improvements. The latter two algorithms are generalized counterparts of the former two algorithms with the single source extraction module replaced by a bank of source extraction modules in parallel at each stage. In spite of the same performance of PNCMS-TSEA and PNCMS-TSEA(p) (PNCMS-FKMA and PNCMS-FKMA(p)), the merit of this parallel source extraction structure lies in much shorter processing latency making the PNCMS-TSEA(p) and PNCMS-FKMA(p) well suitable for software and hardware implementations. Some simulation results are presented to verify the efficacy and computational efficiency of the proposed algorithms.

A Block-by-Block Blind Post-FFT Multistage Beamforming Algorithm for Multiuser OFDM Systems Based on Subcarrier Averaging

Chi et al. proposed a computationally efficient fast kurtosis maximization algorithm for blind equalization of multiple-input multiple-output linear time-invariant systems. This algorithm is also an iterative batch processing algorithm and has been applied to blind source separation. This paper considers blind beamforming of multiuser orthogonal frequency division multiplexing (OFDM) systems. Assuming that the channel is static within one OFDM block, a blind post-FFT multistage beamforming algorithm (MSBFA) based on subcarrier averaging is proposed. The algorithm basically comprises:( i) source (path signal) extraction using a hybrid beamforming algorithm composed of a Fourier beamformer and a kurtosis maximization beamformer, (ii) time delay estimation and compensation, (iii) classification (path-to-user association) and blind maximum ratio combining (of path signals). The designed beamformer is exactly the same for all the subcarriers, effectively utilizes multipath diversity for performance gain, and works well even in an environment with spatially correlated sources. Some simulation results are presented to demonstrate the effectiveness of the proposed MSBFA.

Blind Multiuser Detection by Kurtosis Maximization for Asynchronous Multirate DS/CDMA Systems

Chi et al. proposed a fast kurtosis maximization algorithm (FKMA) for blind equalization/deconvolution of multiple-input multiple-output (MIMO) linear time-invariant systems. This algorithm has been applied to blind multiuser detection of single-rate direct-sequence/code-division multiple-access (DS/CDMA) systems and blind source separation (or independent component analysis). In this paper, the FKMA is further applied to blind multiuser detection for multirate DS/CDMA systems. The ideas are to properly formulate discrete-time MIMO signal models by converting real multirate users into single-rate virtual users, followed by the use of FKMA for extraction of virtual users' data sequences associated with the desired user, and recovery of the data sequence of the desired user from estimated virtual users' data sequences. Assuming that all the users' spreading sequences are given a priori, two multirate blind multiuser detection algorithms (with either a single receive antenna or multiple antennas), which also enjoy the merits of superexponential convergence rate and guaranteed convergence of the FKMA, are proposed in the paper, one based on a convolutional MIMO signal model and the other based on an instantaneous MIMO signal model. Some simulation results are then presented to demonstrate their effectiveness and to provide a performance comparison with some existing algorithms.

Turbo Source Extraction Algorithm and Noncancellation Source Separation Algorithms by Kurtosis Maximization

The kurtosis maximization criterion has been effectively used for blind spatial extraction of one source from an instantaneous mixture of multiple non-Gaussian sources, such as the kurtosis maximization algorithm by Ding and Nguyen, and the fast kurtosis maximization algorithm (FKMA) by Chi and Chen. By empirical studies, we found that the smaller the normalized kurtosis magnitude of the extracted source signal, the worse the performance of these algorithms. In this paper, with the assumption that each source is a non-Gaussian linear process, a novel blind source extraction algorithm, called turbo source extraction algorithm (TSEA), is proposed. The ideas of the TSEA are to exploit signal temporal properties for increasing the normalized kurtosis magnitude, and to apply spatial and temporal processing in a cyclic fashion to improve the signal extraction performance. The proposed TSEA not only outperforms the FKMA, but also shares the convergence and computation advantages enjoyed by the latter. This paper also considers the extraction of multiple sources, also known as source separation, by incorporating the proposed TSEA into the widely used multistage successive cancellation (MSC) procedure. A problem with the MSC procedure is its susceptibility to error propagation accumulated at each stage. We propose two noncancellation multistage (NCMS) algorithms, referred to as NCMS-FKMA and NCMS-TSEA, that are free from the error propagation effects. Simulation results are presented to show that the NCMS-TSEA yields substantial performance gain compared with some existing blind separation algorithms, together with a computational complexity comparison. Finally, we draw some conclusions