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Supervised identification and removal of common filter components in adaptive blind SIMO system identification
Abstract
Adaptive blind system identification with LMS-type algorithms is prone to misconvergence in the presence of noise. In this paper we consider the hypothesis that such misconvergence is due to the introduction of a common filter to the estimated impulse respones. A technique is presented for identifying and removing the common filter using prior knowledge of the true channels. Experimental results with this approach show an improved rate of convergence and reduced system error. Furthermore, misconvergent behaviour is no longer observed, offering a plausible explanation as to the source of misconvergence in adaptive blind system identification.
... Further identification problems arise with observation noise since the cross-relation does not hold exactly in such cases. The authors of [6, 7] demonstrated that the NPM of the normalized multichannel frequency-domain LMS (NMCFLMS) algorithm [4] from the class of adaptive CRapproaches thus indicates divergence in noisy conditions. For an in-depth evaluation of the estimated impulse responses, the idea of a common filter error in blind SIMO identification was recently introduced in [7, 8]. ...
... The authors of [6, 7] demonstrated that the NPM of the normalized multichannel frequency-domain LMS (NMCFLMS) algorithm [4] from the class of adaptive CRapproaches thus indicates divergence in noisy conditions. For an in-depth evaluation of the estimated impulse responses, the idea of a common filter error in blind SIMO identification was recently introduced in [7, 8]. In this paper, we strengthen the notion of a convolutive BCI error . ...
... These problems usually arise from a lack of channel diversity, i.e., from channels with near-common or exact common zeros, e.g., due to channel delays. Current research in the area of blind SIMO identification further indicates that the estimation error in noisy conditions cannot be described by a gain factor either [6, 7, 8], which naturally causes the NPM to fail. In all such cases, we are interested in a more versatile distance measure absorbing a broader range of misidentifications. ...
The blind identification of single-input multiple-output (SIMO) systems suffers in the presence of near-common and exact common zeros between the channels, particularly in conjunction with observation noise. In general, we notice an ambiguity of the identification which cannot be resolved without further a priori information on the channel coefficients. In order to enable an adequate evaluation of blind SIMO identification in such cases, we develop the normalized filter-projection misalignment (NFPM), which represents a multichannel squared-error distance between true and estimated channels, while absorbing a common filter error due to a possible lack of identifiability. Using the NFPM measure, we demonstrate experimentally that the steady-state performance of the blind multichannel least mean-square (MCLMS) algorithm in the presence of missing channel diversity and noise is in line with the results obtained from supervised least mean-square (LMS) system identification.
... Of particular interest is the common filter that appears in systems estimated from noisy observations, so-called because the solutions to all estimated channels are equivalent to the true channels convolved with a single, common, filter. Studies in [7][8][9] have shown that supervised identification and removal of the common filter improves ...
The effect of additive sensor noise on single-input-multiple-output (SIMO) blind system identification (BSI) algorithms based upon cross-relation (CR) error is investigated. Previous studies have shown that additive noise in the observed signal results in systems comprising the true estimated channels convolved with an erroneous 'common filter', and additionally that identification and removal of this filter significantly improves estimation error. However, the source of the common filter remained an open question. This paper explains the common filter through a first-order perturbation analysis of the CR matrix, showing that it be estimated from the perturbation and the eigenvectors of the noiseless CR matrix. The analysis given in this paper provides a new insight into the effect of noise on SIMO BSI algorithms and forms the first step towards an overall noise robust solution.
An important prerequisite for acoustic multi-channel equalization for speech dereverberation involves the identification of the acoustic channels between the source and the microphones. Blind System Identification (BSI) algorithms based on cross-relation error minimization are known to mis-converge in the presence of noise. Although algorithms have been proposed in the literature to improve robustness to noise, the estimated room impulse responses are usually constrained to have a flat magnitude spectrum. In this paper, noise robust algorithms based on a Rayleigh quotient cost function are proposed. Unlike the traditional algorithms, the estimated impulse responses are not always forced to have unit norm. Experimental results using simulated room impulse responses and several SNRs show that one of the proposed algorithms outperforms competing algorithms in terms of normalized projection misalignment.
This paper introduces a new binaural noise estimator based on the target cancellation technique. The left and right source-to-microphone transfer functions (channels) are blindly estimated by means of the constrained least-mean-square algorithm, minimizing the cross-relation error between left and right microphone signals. This blind channel identification (BCI) thus implies a blocking of the target signal and a biased noise estimation in the error signal. The related noise power is then corrected using the estimated chan-nels. The performance of the proposed algorithm is investigated in comparison to different single and dual channel noise power estima-tors. The investigations show that the proposed algorithm is capable of estimating and tracking the noise power fast and accurately. The suitability of the noise power spectral density (PSD) estimator is finally confirmed within a speech enhancement framework.
Blind identification and equalization of single-input/multiple-output (SIMO) systems already received a great deal of sustainable interest. This paper directs the attention towards the characteristics of common channel zeros and in particular the common phantom zeros of blindly estimated channels. The understanding facilitates the major contribution of the paper which is a method for the separation of the common phantom-zeros part of blindly estimated channels. The method is supposed to have application in the removal of common phantom zeros after blind channel identification (BCI) and before multichannel equalization, i.e., to improve the signal processing conditions at the interface of identification and equalization.
The blind identification of single-input multiple-output (SIMO) systems is often performed by exploiting a cross-relation (CR) between channel pairs. It has been shown that this property allows an estimation of channel impulse responses up to a common gain factor if certain identifiability conditions are met. In this case, the estimated channels can be evaluated by a gain-compensated system distance known as normalized projection misalignment (NPM). Current algorithms for blind channel identification, however, suffer in the presence of insufficient channel diversity and observation noise. In this paper, we first demonstrate that in the absence of noise the CR identification error for channels with exact common zeros is given by a single-channel pole-zero transfer function. Next, we extend our analysis to the realistic case of near-common zeros and noise for which we show that the effective error can still be approximated by a common transfer function as long as the distance between the channel zeros remains below a signal-to-noise ratio-dependent threshold. A finite impulse response (FIR) modeling of the error then enables us to define a common-filter-error-compensated system distance, termed normalized filter-projection misalignment (NFPM), which establishes a natural extension to the NPM analysis. By finally considering realistic channels, which we blindly estimate with the adaptive multichannel least mean-square (MCLMS) algorithm, we demonstrate that the NFPM reliably reaches the noise floor, confirming that the effective error can be approximated by a common FIR filter.
Image methods are commonly used for the analysis of the acoustic properties
of enclosures. In this paper we discuss the theoretical and practical
use of image techniques for simulating, on a digital computer, the
impulse response between two points in a small rectangular room.
The resulting impulse response, when convolved with any desired input
signal, such as speech, simulates room reverberation of the input
signal. This technique is useful in signal processing or psychoacoustic
studies. The entire process is carried out on a digital computer
so that a wide range of room parameters can be studied with accurate
control over the experimental conditions. A FORTRAN implementation
of this model has been included.
The least-squares and the subspace methods are two well-known
approaches for blind channel identification/equalization. When the order
of the channel is known, the algorithms are able to identify the
channel, under the so-called length and zero conditions. Furthermore, in
the noiseless case, the channel can be perfectly equalized. Less is
known about the performance of these algorithms in the practically
inevitable cases in which the channel possesses long tails of
“small” impulse response terms. We study the performance of
the mth-order least-squares and subspace methods using a perturbation
analysis approach. We partition the true impulse response into the
mth-order significant part and the tails. We show that the mth-order
least-squares or subspace methods estimate an impulse response that is
“close” to the mth-order significant part. The closeness
depends on the diversity of the mth-order significant part and the size
of the tails. Furthermore, we show that if we try to model not only the
“large” terms but also some “small” ones, then
the quality of our estimate may degrade dramatically; thus, we should
avoid modeling “small” terms. Finally, we present
simulations using measured microwave radio channels, highlighting
potential advantages and shortcomings of the least-squares and subspace
methods
Conventional blind channel identification algorithms are based on
channel outputs and knowledge of the probabilistic model of channel
input. In some practical applications, however, the input statistical
model may not be known, or there may not be sufficient data to obtain
accurate enough estimates of certain statistics. In this paper, we
consider the system input to be an unknown deterministic signal and
study the problem of blind identification of multichannel FIR systems
without requiring the knowledge of the input statistical model. A new
blind identification algorithm based solely on the system outputs is
proposed. Necessary and sufficient identifiability conditions in terms
of the multichannel systems and the deterministic input signal are also
presented
An analysis of the noise effect on the convergence charac-teristic of the least-mean-squares (LMS) type adaptive al-gorithms for blind channel identification is presented. It is shown that the adaptive blind algorithms misconverge in the presence of noise. A novel technique for ameliorating such misconvergence characteristic, using a frequency domain en-ergy constraint in the adaptation rule, is proposed. Exper-imental results demonstrate that the robustness of the blind adaptive algorithms can be significantly improved using such constraints.
This paper shows that the robustness of the normalized mul-tichannel frequency-domain LMS algorithm reported in [1] can be improved using constraints in the adaptation rule. In the identification of acoustic impulse responses with lead-ing bulk zeros from noisy observations the proposed con-straint shows significant performance improvement in terms of normalized projection misalignment. Experimental results for various simulated conditions are presented to justify our claim.
A new method of measuring reverberation time is described. The method
uses tone bursts (or filtered pistol shots) to excite the enclosure.
A simple integral over the tone-burst response of the enclosure yields,
in a single measurement, the ensemble average of the decay curves
that would be obtained with bandpass-filtered noise as an excitation
signal. The smooth decay curves resulting from the new method improve
the accuracy of reverberation-time measurements and facilitate the
detection of nonexponential decays.
We discuss the philosophy of evaluating estimated impulse responses for applications in which the overall scaling or gain is irrelevant, as, for example, in blind channel identification. We argue that no matter how the estimate is obtained, the performance should be independently evaluated using an error measure that is appropriate for a problem of this class. Of several possible error measures, the normalized projection error, which is obtained by minimizing the l/sub 2/ norm over all possible gain values, seems to be the most natural and consistent. An example demonstrates that using an inappropriate error measure can produce misleading results.
We extend our previous studies on adaptive blind channel identification from the time domain into the frequency domain. A class of frequency-domain adaptive approaches, including the multichannel frequency-domain LMS (MCFLMS) and constrained/unconstrained normalized multichannel frequency-domain LMS (NMCFLMS) algorithms, are proposed. By utilizing the fast Fourier transform (FFT) and overlap-save techniques, the convolution and correlation operations that are computationally intensive when performed by the time-domain multichannel LMS (MCLMS) or multichannel Newton (MCN) methods are efficiently implemented in the frequency domain, and the MCFLMS is rigorously derived. In order to achieve independent and uniform convergence for each filter coefficient and, therefore, accelerate the overall convergence, the coefficient updates are properly normalized at each iteration, and the NMCFLMS algorithms are developed. Simulations show that the frequency-domain adaptive approaches perform as well as or better than their time-domain counterparts and the cross-relation (CR) batch method in most practical cases. It is remarkable that for a three-channel acoustic system with long impulse responses (256 taps in each channel) excited by a male speech signal, only the proposed NMCFLMS algorithm succeeds in determining a reasonably accurate channel estimate, which is good enough for applications such as time delay estimation.
The least-squares and the subspace methods are well known approaches for blind channel identification /equalization. When the order of the channel is known, the algorithms are able to identify the channel, under the so-called length and zero conditions. Furthermore, in the noiseless case, the channel can be perfectly equalized. Less is known about the performance of these algorithms in the cases in which the channel order is underestimated. We partition the true impulse response into the significant part and the tails. We show that the m-th order least-squares or subspace methods estimate an impulse response which is "close" to the m-th order significant part of the true impulse response. The closeness depends on the diversity of the m-th order significant part and the size of the "unmodeled" part. 1 INTRODUCTION The recent development of second order statistics (SOS) based blind channel identification methods under a single-input/multiple-output (SIMO) channel setting [1], derived ...