Chii-Horng Chen

Cumulant-based inverse filter criteria for MIMO blind deconvolution: properties, algorithms, and application to DS/CDMA systems in multipath

Tugnait (1995) and Chi and Chen proposed multi-input multi-output inverse filter criteria (MIMO-IFC) using higher order statistics for blind deconvolution of MIMO linear time-invariant systems. This paper proposes three properties on the performance of the MIMO linear equalizer associated with MIMO-IFC for any signal-to-noise ratio, including (P1) perfect phase equalization property, (P2) a relation to MIMO minimum mean square error (MIMO-MMSE) equalizer, and (P3) a connection with the one obtained by MIMO super-exponential algorithm (MIMO-SEA) that usually converges fast but does not guarantee convergence for finite data. Based on (P2), a fast algorithm for computing the theoretically optimum MIMO equalizer is proposed. Moreover, based on (P3), a fast MIMO-IFC based algorithm with performance similar to that of the MIMO-SEA and with guaranteed convergence is proposed as well as its application to suppression of multiple access interference and intersymbol interference (ISI) for multiuser asynchronous DS/CDMA systems in multipath. Finally, some simulation results are presented to support the analytic results and the proposed algorithms.

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.

Two-dimensional frequency-domain blind system identification using higher order statistics with application to texture synthesis

In this paper, Shalvi and Weinsteins (1993) super-exponential (SE) algorithm using higher order statistics for blind deconvolution of one-dimensional (1-D) linear time-invariant systems is extended to a two-dimensional (2-D) SE algorithm. Then, a 2-D frequency-domain blind system identification (BSI) algorithm for 2-D linear shift-invariant (LSI) systems using the computationally efficient 2-D SE algorithm and the 2-D linear prediction error filter is proposed. In addition to the LSI system estimate, the proposed BSI algorithm also provides a minimum mean square error (MMSE) equalizer estimate and an MMSE signal enhancement filter estimate. Then, a texture synthesis method (TSM) using the proposed BSI algorithm is presented. Some simulation results to support the efficacy of the proposed BSI algorithm and some experimental results to support the efficacy of the proposed TSM are presented. Finally, some conclusions are drawn.

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.

New cumulant-based inverse filter criteria for deconvolution of nonminimum phase systems

This work proposes a new family of cumulant-based inverse filter criteria J/sub M,m/, which require a single slice of Mth-order (M/spl ges/3) cumulants, a (2m)th-order cumulant, and a (2M-2m)th-order cumulant of the inverse filter output where 1/spl les/m/spl les/M-1, for deconvolution of linear time invariant (LTI) nonminimum phase systems with only non-Gaussian output measurements contaminated by Gaussian noise. Some simulation results are then presented for a performance comparison of the proposed criteria, Tugnaits (1993) criteria, and Chi and Kungs (1992) criteria. Finally, conclusions are presented.

MIMO inverse filter criteria and blind maximum ratio combining using HOS for equalization of DS/CDMA systems in multipath

Tugnaits multi-input multi-output inverse filter criteria (MIMO-IFC) using either second- and third-order or second- and fourth-order cumulants for blind deconvolution are extended to those using second- and higher-order (/spl ges/ 3) cumulants. Next, a blind maximum ratio combining (BMRC) method using the MIMO-IFC is proposed. Then a blind equalization algorithm for multiuser DS/CDMA systems in multipath channels is proposed using the proposed BMRC method and MIMO-IFC. Finally, some simulation results are provided to support the proposed algorithm.

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.

Performance of cumulant based inverse filter criteria for blind deconvolution of multi-input multi-output linear time-invariant systems

Tugnait (1997), and Chi and Chen proposed multi-input multi-output inverse filter criteria (MIMO-IFC) using higher-order statistics for blind deconvolution of multi-input multi-output (MIMO) linear time-invariant (LTI) systems. This paper proposes a performance analysis for the MIMO linear equalizer associated with MIMO-IFC for finite SNR, including (P1) perfect phase equalization property, (P2) a relation to MIMO minimum mean square error (MIMO-MMSE) equalizer, and (P3) a connection with the one obtained by Yeung and Yaus MIMO super-exponential algorithm (MIMO-SEA) that usually converges fast but has no guarantee of convergence for finite data. Furthermore, based on (P3), a MIMO-IFC based algorithm with performance similar to that of the MIMO-SEA and with guaranteed convergence is proposed. Finally, some simulation results are presented to support the analytic results and the proposed algorithm.

Peak filter and notch filter for harmonic retrieval using higher-order statistics

In this paper, an algorithm using the well-known notch filter and an algorithm using a peak filter are proposed to estimate the frequencies of sinusoidal signals with a given set of Gaussian noise corrupted measurements y(n) provided that the number of sinusoids is known in advance. The former processes y(n) such that a single fourth-order cumulant of the notch filter output is minimum in absolute value, while the latter processes y(n) such that the same fourth-order cumulant of the peak filter output is maximum in absolute value. Then the unknown frequencies are obtained from the optimum notch filter and the optimum peak filter, respectively. A performance analysis of the two proposed algorithms is then presented followed by some simulation results for a performance comparison of the proposed algorithms and Swami and Mendels (1991) SVD low-rank approximation method.