Algorithms for blind equalization with multiple antennas based on frequency domain subspaces (original) (raw)
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A subspace based blind identification and equalization algorithm
A subspace based blind channel identification algorithm is proposed here. This algorithm operates directly on the data domain and therefore avoids the problems associated with other algorithms which use t h e statistical information contained in t h e received signal directly. In the noiseless case, this algorithm uses t h e least number of symbols that can possibly be used t o identify the channel exactly. In t h e noisy case, simulations have shown that almost exact identification can be obtained by using a few more symbols than the theoretical minimum. This is orders of magnitude better than the other blind algorithms. Once t h e channel has been identified by using this procedure, any of the existing equalization techniques can be used along with it to obtain the symbols.
Error correcting least-squares Subspace algorithm for blind identification and equalization
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A subspace based blind channel identiÿcation algorithm using only the fact that the received signal can be oversampled is proposed. No direct use is made in this algorithm of either the statistics of the input sequence or even of the fact that the symbols are from a ÿnite set and therefore this algorithm can be used to identify even channels in which arbitrary symbols are sent. Using this algorithm as a base and using the extra information which becomes available when the transmitted symbols are from a known ÿnite set, the EC-LS-Subspace algorithm is derived. The EC-LS-Subspace algorithm operates directly on the data domain and therefore avoids the problems associated with other algorithms which use the statistical information contained in the received signal directly. In the noiseless case, if some conditions are met, it is possible for the proposed Basic Subspace algorithm to identify the channel exactly using an observation interval of just (J +2)T , if the length of the impulse response of a channel is JT; T being the symbol interval. In the noisy case, simulations have shown that the channel can be identiÿed accurately by using a very small observation interval (comparable to (J + 2)T).
9Th European Signal Processing Conference, 1998
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 m m mth-order least-squares and subspace methods using a perturbation analysis approach. We partition the true impulse response into the m m mth-order significant part and the tails. We show that the m m mth-order least-squares or subspace methods estimate an impulse response that is "close" to the m m mth-order significant part. The closeness depends on the diversity of the m m 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.
Methods for blind equalization and resolution of overlapping echoes of unknown shape
IEEE Transactions on Signal Processing, 1999
This paper considers the related problems of using an uncalibrated antenna array to (1) recover an unknown signal transmitted over an unknown (but stationary) multipath channel, and (2) resolve overlapping pulse echoes with unknown shape. Unlike recently proposed multichannel blind equalization techniques, the methods described herein employ a model based on physical channel parameters rather than unstructured single-input, multi-output FIR lters. The algorithms exploit similarities between a model for the data in the frequency domain and the standard direction-of-arrival estimation problem. This connection between the two problems suggests several di erent approaches based on, for example, maximum likelihood, MODE, IQML, and ESPRIT. These approaches are developed in some detail, and the results of several simulation examples are included to compare their performance. channel parameters. The term \blind" implies that the signal recovery and channel estimation is to be achieved with neither the aid of known training sequences, prior knowledge concerning the channel, nor array calibration information.
Blind Radio Channel Identification and Equalization based on Oversampling and/or Antenna Arrays
Equalization for digital communications constitutes a very particular blind deconvolution problem in that the received signal is cyclostationary. Oversampling (OS) (w.r.t. the symbol rate) of the cyclostationary received signal leads to a stationary vector-valued signal (polyphase representation (PR)). OS also leads to a fractionally-spaced channel model and equalizer. In the PR, channel and equalizer can be considered as an analysis and synthesis lter bank. Zero-forcing (ZF) equalization corresponds to a perfect-reconstruction lter bank. We show that in the OS case FIR ZF equalizers exist for a FIR channel. In the PR, the noise-free multichannel power spectral density matrix has rank one and the channel can be found as the (minimumphase) spectral factor. The multichannel linear prediction of the noiseless received signal becomes singular eventually, reminiscent of the single-channel prediction of a sum of sinusoids. As a result, a ZF equalizer can be determined from the received signal second-order statistics by linear prediction in the noise-free case, and by using a Pisarenko-style modi cation when there is additive noise. In the given data case, Music (subspace) or ML techniques can be applied. We also present some Cramer-Rao bounds and compare them to the case of channel identi cation using a training sequence.
IEEE Transactions on Signal Processing, 1999
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 m m mth-order least-squares and subspace methods using a perturbation analysis approach. We partition the true impulse response into the m m mth-order significant part and the tails. We show that the m m mth-order least-squares or subspace methods estimate an impulse response that is "close" to the m m mth-order significant part. The closeness depends on the diversity of the m m 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.
Deterministic Blind Subspace MIMO Equalization
EURASIP Journal on Advances in Signal Processing, 2002
A subspace based approach for the blind multiple signal separation and recovery for MIMO systems is proposed in this paper. Instead of using the statistics of the received signal, the proposed algorithm exploits the received signal structure and the finite alphabet property of the desired signals. The finite alphabet property is used to remove the unknown unitary matrix that is associated with most of the statistics-based MIMO system identification algorithms. The proposed algorithm also incorporates an error-correcting procedure; therefore, it has more accuracy than the existing algorithms. Computer simulation results demonstrate that the algorithm can detect the signals and estimate channel parameters accurately with very few symbols, even under high noise and bad channel conditions.
Further results on blind identification and equalization of multiple FIR channels
1995 International Conference on Acoustics, Speech, and Signal Processing, 1995
In previous work, we have shown that in the case of multiple antennas and/or oversampling, FIR ZF equalizers exist for FIR channels and can be obtained from the noise-free linear prediction (LP) problem. The LP problem also lead to a minimal parameterization of the noise subspace, which was used to solve the deterministic maximum likelihood (DML) channel estimation problem. Here we present further contributions along two lines. One is a number of blind equalization techniques of the adaptive ltering type. We also present some robustifying modi cations of the DML problem.
Blind multichannel equalization using a novel subspace method
IEEE Transactions on Signal Processing, 2000
This correspondence develops a new blind multichannel equalization (BME) scheme and proposes an appropriate cost function by the exploitation of some shifting properties of the autocorrelation matrices of the source. In addition, an efficient programming is considered based on a generalized rayleigh quotient formulation using a conjugate gradient algorithm.
Blind Channel Estimation and Equalization
International Journal of Multimedia and Ubiquitous Engineering, 2016
This paper resolves the problem of channel estimation and identification of a nonminimum phase system using three algorithms. These algorithms play an important role for estimating blindly the parameters of radio mobile channel. Thus studying the blind's problem channel equalization based on the following, Proposed Algorithm, CMA and SKMAA equalizers. The simulation results in the noisy environment and for different SNR values demonstrate that Proposed Algorithm is more performing than the other algorithms. In addition, the Sign Kurtosis Maximization Adaptive Algorithm (SKMAA) is more powerful compared to Constant Modulus Algorithm (CMA), that is to say it gives the right blind channel equalization.