New approach to equalizing antenna elements: analysis and performance evaluation

The antenna face of a phased array radar typically consists of several hundred of antenna elements, and they degrade independently.  This poses a challenging problem to radar target detection, discrimination, and classification, which rely on adaptive beamforming and assume that the channels are matched to each other.  In this research, a channel equalization algorithm is developed compensating for the mismatch between the reference and testing channels using the least-squares error (LSE) criterion. The equalized output is precisely the projection of the reference channel data onto the columns of the equalization matrix, which is solely a function of the testing channel output.  Through the analysis of the equalization matrix, the performance metrics including the squares error, instantaneous correlation coefficient, and cancellation ratio (CR) of the proposed equalizer are expressed in closed forms.  The analysis also allows us to postulate on the effect of system parameters including: window size, equalizer length, and input signal-to-noise ratio (SNR) on the performance metrics. Extensive Monte Carlo simulations show that higher values of the equalizer length, input SNR, or window size improves the CR; however, once a system parameter approaches a certain threshold, further incrementing the size of these parameters has a diminishing return on system performance.  Simulations also reveal that an equalizer with good CR or correlation coefficient results into the equalized testing channel output being almost a replica of the reference channel’s output. Correspondingly, degradation in the CR or correlation coefficient affects the equalized testing channel output.  The simulation results agree closely with known theoretical analyses. The research in this paper demonstrates the importance of channel equalization and system parameter selection in obtaining a satisfactory antenna elements/subarrays output

Robust equalization of multichannel acoustic systems

In most real-world acoustical scenarios, speech signals captured by distant microphones from a source are reverberated due to multipath propagation, and the reverberation may impair speech intelligibility. Speech dereverberation can be achieved by equalizing the channels from the source to microphones. Equalization systems can be computed using estimates of multichannel acoustic impulse responses. However, the estimates obtained from system identification always include errors; the fact that an equalization system is able to equalize the estimated multichannel acoustic system does not mean that it is able to equalize the true system. The objective of this thesis is to propose and investigate robust equalization methods for multichannel acoustic systems in the presence of system identification errors. Equalization systems can be computed using the multiple-input/output inverse theorem or multichannel least-squares method. However, equalization systems obtained from these methods are very sensitive to system identification errors. A study of the multichannel least-squares method with respect to two classes of characteristic channel zeros is conducted. Accordingly, a relaxed multichannel least- squares method is proposed. Channel shortening in connection with the multiple- input/output inverse theorem and the relaxed multichannel least-squares method is discussed. Two algorithms taking into account the system identification errors are developed. Firstly, an optimally-stopped weighted conjugate gradient algorithm is proposed. A conjugate gradient iterative method is employed to compute the equalization system. The iteration process is stopped optimally with respect to system identification errors. Secondly, a system-identification-error-robust equalization method exploring the use of error models is presented, which incorporates system identification error models in the weighted multichannel least-squares formulation

Blind MultiChannel Identification and Equalization for Dereverberation and Noise Reduction based on Convolutive Transfer Function

This paper addresses the problems of blind channel identification and multichannel equalization for speech dereverberation and noise reduction. The time-domain cross-relation method is not suitable for blind room impulse response identification, due to the near-common zeros of the long impulse responses. We extend the cross-relation method to the short-time Fourier transform (STFT) domain, in which the time-domain impulse responses are approximately represented by the convolutive transfer functions (CTFs) with much less coefficients. The CTFs suffer from the common zeros caused by the oversampled STFT. We propose to identify CTFs based on the STFT with the oversampled signals and the critical sampled CTFs, which is a good compromise between the frequency aliasing of the signals and the common zeros problem of CTFs. In addition, a normalization of the CTFs is proposed to remove the gain ambiguity across sub-bands. In the STFT domain, the identified CTFs is used for multichannel equalization, in which the sparsity of speech signals is exploited. We propose to perform inverse filtering by minimizing the $\ell_1$-norm of the source signal with the relaxed $\ell_2$-norm fitting error between the micophone signals and the convolution of the estimated source signal and the CTFs used as a constraint. This method is advantageous in that the noise can be reduced by relaxing the $\ell_2$-norm to a tolerance corresponding to the noise power, and the tolerance can be automatically set. The experiments confirm the efficiency of the proposed method even under conditions with high reverberation levels and intense noise.Comment: 13 pages, 5 figures, 5 table