Chih-Chun Feng

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.

Embedding and detection of side information for peak-to-average power ratio reduction of an OFDM signal using partial transmit sequences

The peak-to-average power ratio (PAPR) problem of OFDM systems can be efficiently resolved using the partial transmit sequences (PTS) method, for which data recovery requires side information (SI) about the phase rotation factors used at the transmitter. With no loss of spectrum efficiency, two embedded SI transmission schemes (I and II), including frequency-domain marking algorithms and decision statistics, are proposed for PSK data and one (III) for QAM data. A time-domain implementation of the proposed marking algorithms is presented for reducing complexity. Simulation results demonstrate the good performance of the proposed schemes, especially for scheme III.

Design of Wiener filters using a cumulant based MSE criterion

This paper proposes a cumulant (higher-order statistics) based mean-square-error (MSE) criterion for the design of Wiener filters when both the given wide-sense stationary random signal x(n) and the desired signal d(n) are non-Gaussian and contaminated by Gaussian noise sources. It is theoretically shown that the designed Wiener filter associated with the proposed criterion is identical to the conventional correlation (second-order statistics) based Wiener filter as if both x(n) and d(n) were noise-free measurements. As the latter, the former can also be obtained by solving a cumulant-based Wiener-Hopf equation associated with a (cumulant-based) orthogonality principle. Then a generalized cumulant projection theorem is proposed which includes the projection of cumulants to correlations associated with the proposed cumulant-based MSE criterion and that associated with Delopoulos and Giannakis’ cumulant-based MSE criterion as special cases. Moreover, the proposed cumulant-based MSE criterion and Delopoulos and Giannakis’ cumulant-based MSE criterion are equivalent for cumulant order M = 3. Some simulation results for system identification and time delay estimation are then provided to demonstrate the good performance of the proposed cumulant-based Wiener filter. Finally, we draw some conclusions. Zusammenfassung Wir schlagen fi,ir den Entwurf von Wiener-Filtern ein Kumulanten(Statistiken hiiherer Ordnung)-basiertes mittleres quadratisches Fehlerkriterium (mean-square-error, MSE) fi.ir den Fall vor, da13 das gegebene, im weiten Sinne stationgre Zufallssignal x(n) und das gewiinschte Signal d(n) beide nicht GauD-verteilt sind und durch GauO-Rauschquellen gestijrt sind. Es wird theoretisch gezeigt, dafi das mit dem vorgeschlagenen Kriterium entworfene Wiener-Filter identisch ist mit dem konventionellen Korrelations(Statistiken zweiter Ordnung)-basierten Wiener-Filter, wenn sowohl x(n) als such d(n) rauschfreie Messungen sind. Wie im letzten Fall, kann such der vorhergehende Fall durch L&en einer Kumulantenbasierten Wiener-Hopf-Gleichung, verbunden mit einem (Kumulanten-basierten) Orthogonalitlitsprinzip, erzielt werden. Sodann wird ein verallgemeinertes Kumulanten-Projektionstheorem vorgeschlagen, welches die Projektion von Kumulanten auf Korrelationen, sowohl auf der Basis des vorgeschlagenen Kumulanten-basierten MSE-Kriteriums, als such in Verbindung mit dem Kumulanten-basierten MSE-Kriterium von Delopoulos und Giannakis als Spezialfdle, einschliel3t. DarEberhinaus sind das vorgeschlagene Kumulanten-basierte MSE-Kriterium und das Kumulanten-basierte MSE-Kriterium von Delopoulos und Giannakis lquivalent fiir Kumulanten der Ordnung M = 3. Einige Simulationsergebnisse zur Systemidentifikation und VerzGgerungszeit-Schgtzung werden gegeben, urn das gute Verhalten des vorgeschlagenen Kumulanten-basierten Wiener-Filter zu demonstrieren. AbschlieRend ziehen wir einige Schltifolgerungen.

Performance of Shalvi and Weinstein's deconvolution criteria for channels with/without zeros on the unit circle

This correspondence shows that the Shalvi and Weinstein (1994) blind deconvolution criteria are applicable for finite SNR regardless of channels having zeros on the unit circle or not. The associated deconvolution filter is stable with a nonlinear relation to the nonblind MMSE equalizer and capable of performing perfect phase equalization for finite SNR.

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.

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.

Performance of Shalvi and Weinstein's blind deconvolution criteria for channels with/without zeros on the unit circle

In this paper, we show that Shalvi and Weinsteins (1994) blind deconvolution criteria are applicable for finite SNR regardless of channels having zeros on the unit circle or not. The associated deconvolution filter is stable with a nonlinear relation to the nonblind MMSE equalizer and capable of performing perfect phase equalization for finite SNR.