Ching-Yung Chen

Batch processing algorithms for blind equalization using higher-order statistics

Statistical signal processing has been one of the key technologies in the development of wireless communication systems, especially for broadband multiuser communication systems which severely suffer from intersymbol interference (ISI) and multiple access interference (MAI). This article reviews batch processing algorithms for blind equalization using higher-order statistics for mitigation of the ISI induced by single-input, single-output channels as well as of both the ISI and MAI induced by multiple-input, multiple-output channels. In particular, this article reviews the typical inverse filter criteria (IFC) based algorithm, super-exponential algorithm, and constant modulus algorithm along with their relations, performance, and improvements. Several advanced applications of these algorithms are illustrated, including blind channel estimation, simultaneous estimation of multiple time delays, signal-to-noise ratio (SNR) boost by blind maximum ratio combining, blind beamforming for source separation in multipath, and multiuser detection for direct sequence/code division multiple access (DS/CDMA) systems in multipath.

Blind MAI and ISI suppression for DS/CDMA systems using HOS-based inverse filter criteria

Cumulant-based inverse filter criteria (IFC) using second-and higher order statistics (HOS) proposed by Tugnait et al. (1993) have been widely used for blind deconvolution of discrete-time multi-input multi-output (MIMO) linear time-invariant systems with non-Gaussian measurements through a multistage successive cancellation procedure, but the deconvolved signals turn out to be an unknown permutation of the driving inputs. A multistage blind equalization algorithm (MBEA) is proposed for multiple access interference (MAI) and intersymbol interference (ISI) suppression of multiuser direct sequence/code division multiple access (DS/CDMA) systems in the presence of multipath. The proposed MBEA, which processes the chip waveform matched filter output signal without requiring any path delay information, includes blind deconvolution processing using IFC followed by identification of the estimated symbol sequence with the associated user through a user identification algorithm (UIA). Then, some simulation results are presented to support the proposed MBEA and UIA. Finally, some conclusions are drawn.

Blind beamforming and maximum ratio combining by kurtosis maximization for source separation in multipath

Ding and Nguyens (2000) kurtosis maximization algorithm (KMA) for blind signal separation and antenna beamforming assumes the absence of multipath channels. This paper proposes a multistage source separation (MSS) algorithm assuming that source signals are independent identically distributed (iid) non-Gaussian and received in the presence of multiple paths (as practically happens in wireless communications). The proposed MSS algorithm includes extraction and blind maximum ratio combing (BMRC) of a source signal from different paths using a fast KMA (FKMA), besides signal classification, time delay estimation, and cancellation of the contribution of the extracted source signal from the received signal at each stage. The proposed MSS algorithm with no need of prior information about the array configuration and direction of arrival (DOA) is supported through computer simulation.

Blind identification of SIMO systems and simultaneous estimation of multiple time delays from HOS-based inverse filter criteria

Higher order statistics-based inverse filter criteria (IFC) have been effectively used for blind equalization of single-input multiple-output (SIMO) systems. Recently, Chi and Chen reported a relationship between the unknown SIMO system and the optimum equalizer designed by the IFC for finite signal-to-noise ratio (SNR). In this paper, based on this relationship, an iterative fast Fourier transform (FFT)-based nonparametric blind system identification (BSI) algorithm and an FFT-based multiple-time-delay estimation (MTDE) algorithm are proposed with a given set of non-Gaussian measurements. The proposed BSI algorithm allows the unknown SIMO system to have common subchannel zeros, and its performance (estimation accuracy) is superior to that of the conventional IFC-based methods. The proposed MTDE algorithm can simultaneously estimate all the (P-1) time delays (with respect to a reference sensor) with space diversity of sensors exploited; therefore, its performance (estimation accuracy) is robust to the nonuniform distribution of SNRs of P /spl ges/ 2 sensors (due to channel fading). Some simulation results are presented to support the efficacy of the proposed BSI algorithm and MTDE algorithm.

Turbo source separation algorithm using HOS based inverse filter criteria

Ding and Ngugen proposed a kurtosis maximization algorithm and Chi arid Chen proposed a fast kurtosis maximization algorithm (FKMA) for blind separation of a instantaneous mixture of colored non-Gaussian sources. Their algorithms only involve spatial processing, but their performance may significantly degrade for finite signal-to-noise ratio as kurtosis magnitudes of source signals are not sufficiently large. This paper proposes a novel iterative blind source separation algorithm, called a turbo source separation algorithm (TSSA), which alternatively involves spatial processing as the FKMA, and temporal processing (blind deconvolution) using Chi and Cheris fast inverse filter criteria algorithm at each iteration. Some simulation results are presented to support that the proposed TSSA works well with better performance than the FKMA and some existing second-order statistics based algorithms.

Performance of super-exponential algorithm for blind equalization

Shalvi and Weinstein (1990, 1993, 1994) proposed a computationally efficient iterative super-exponential algorithm (SEA) using higher-order cumulants for blind equalization. For practical situations of finite signal-to-noise ratio (SNR) and channels allowed to have zeros on the unit circle, it can be shown that the linear equalizer obtained using the SEA is stable with a nonlinear relation to the nonblind minimum mean square error (MMSE) equalizer, that it is a perfect phase equalizer for some cumulant orders, and that it is the same as the linear equalizer associated with Shalvi and Weinsteins blind deconvolution criteria for some cumulant orders. Then some simulation results are presented to justify the analytic results followed by some conclusions.

Blind identification of MIMO systems by a system to HOS based inverse filter relationship

Higher-order statistics based inverse filter criteria (HOS-IFC) proposed by Tugnait (1997) and Chi et al. (2002) have been widely used for blind identification and deconvolution of multiple-input multiple-output (MIMO) linear time-invariant systems with a set of nonGaussian measurements. Based on a relationship, that holds true for finite signal-to-noise ratio, between the optimum inverse filter associated with the HOS-IFC and the unknown MIMO system, an iterative FFT-based blind system identification (BSI) algorithm for MIMO systems is proposed in this paper, for which common subchannel zeros are allowed and the system order information is never needed, and meanwhile its performance is superior to the performance of Tugnaits HOS-IFC approach. Some simulation results are presented to support the efficacy of the proposed BSI algorithm.

Two-dimensional Fourier series-based model for nonminimum-phase linear shift-invariant systems and texture image classification

In this paper, Chis (1997, 1999) real one-dimensional (1-D) parametric nonminimum-phase Fourier series-based model (FSBM) is extended to two-dimensional (2-D) FSBM for a 2-D nonminimum-phase linear shift-invariant system by using finite 2-D Fourier series approximations to its amplitude response and phase response, respectively. The proposed 2-D FSBM is guaranteed stable, and its complex cepstrum can be obtained from its amplitude and phase parameters through a closed-form formula without involving complicated 2-D phase unwrapping and polynomial rooting. A consistent estimator is proposed for the amplitude estimation of the 2-D FSBM using a 2-D half plane causal minimum-phase linear prediction error filter (modeled by a 2-D minimum-phase FSBM), and then, two consistent estimators are proposed for the phase estimation of the 2-D FSBM using the Chien et al. (1997) 2-D phase equalizer (modeled by a 2-D all-pass FSBM). The estimated 2-D FSBM can be applied to modeling of 2-D non-Gaussian random signals and 2-D signal classification using complex cepstra. Some simulation results are presented to support the efficacy of the three proposed estimators. Furthermore, classification of texture images (2-D non-Gaussian signals) using the estimated FSBM, second-, and higher order statistics is presented together with some experimental results. Finally, we draw some conclusions.

On super-exponential algorithm, constant modulus algorithm and inverse filter criteria for blind equalization

The super-exponential algorithm (SEA), constant modulus algorithm (CMA) and inverse filter criteria (IFC) using higher-order statistics have been widely used for blind equalization. Chi et al., (2000) have reported that SEA and IFC are equivalent under certain conditions. We further prove that SEA, IFC and CMA are equivalent under certain conditions, and their convergence speed and computational load can be significantly improved as the given data are preprocessed by the well-known lattice linear prediction error (LPE) filter for both off-line processing and adaptive processing. Some simulation results are presented to support the analytic results and the proposed off-line and adaptive implementations.

Blind identification of MIMO FIR systems for colored inputs by HOS based inverse filter criteria and GCD

A novel two-step algorithm is proposed for blind identification (BID) of a discrete-time K-input P-output (P /spl ges/ K and P > 1) finite impulse response system F(z) = (F/sub 1/(z), ...,F/sub K/ (z)) driven by K stationary nonGaussian inputs which are spatially independent but temporally colored. With each input modelled as a moving-average process with model Bk(z), Chi et al.s (2003) BID algorithm using higher-order statistics based inverse filter criteria is utilized to estimate the combined system H(z) = (F/sub 1/(z)B/sub 1/(z),...,F/sub K/(z)B/sub K/(Z)) in the first step. In the second step, Qiu et al.s (1997) greatest common divisor computation method is employed to obtain F/sub k/(z) and B/sub k/(z) from the estimated H(z). Some simulation results are presented to support the efficacy of the proposed 2-step BID algorithm.