D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," IEEE Trans. on Signal Processing, vol. 45, no. 9, pp. 2307--2317, September 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a set of linear transformations that relate the receiver weights for each user, then these transformations are used to augment the standard ACMA equations. The algorithm is similar in spirit to that described in [12] where the CM property was combined with Mutually Referenced Equalizer algorithm [13, 14, 15] for blind equalization. However, in this paper, additional structure is exploited so that only a single receiver is estimated for each user. The data model assumed in this paper is presented in the next section, together with a brief description of the STBC framework of [7] The ACMA approach of ....

D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line Blind Multichannel Equalization Based on Mutually Referenced Filters," IEEE Trans. Sig. Proc., vol. 45, no. 9, pp. 2307--2317, Sept. 1997.

....P n . P oqp r fPd (16) Assume that fP for given which is valid for most modulation schemes such as BPSK, QPSK, and QAM. Notice that each row of scaled by a known interpolation coefficient (P H , which makes it possible to eliminate the unknown by cross referencing [9] . Specifically, multiplying row respectively gives the same value (P P fP . Taking difference between two rows related to th symbol data, we obtain the following equation fP (17) 7 F F R 9 q 5 q 5 q 5 q 5 q . ....

D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," IEEE Trans. Signal Processing, vol.45, pp.2307-2317, Sept. 1997.

....often makes blind estimation approaches tractable in time varying channels [15] The proposed scheme consists of front end processing and blind identification of an equalizer matrix which is associated with estimating points. The elimina tion of unknown symbols is based on the cross referencing [16]. A new identifiability is established for noiseless case and new detection schemes are proposed based on the estimated equalizer matrix. For multiuser scenario, decorrelating or regularized decorrelating front end can be used. The fast inversion of code matrix can be implemented with a ....

....model III. BLIND CHANNEL TRACKING ALGORITHM In this section, propose a blind estimator for equalizer bed on a line interpolation model exploiting the multipath diversity of propagation channel The proposed gorithm is bed on the cross reference technique to eliminate the unknown data symbols [16] 2The orparameterization of N makes the parameter matrix i poorly con ditioned which induces sere noise enhancement in step (19) for noisy cases. A. Front end processing We consider the conventional matched filter (Hermitian of the code matrix) decorrelator, and regularized decorrelator as ....

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D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," IEEE Trans. Signal Processing, vol.45, pp.2307-2317, Sept. 1997.

.... subspace techniques such as the subspace channel estimation algorithm [8] the cross relation algorithm [18] and the least squares smoothing (LSS) algorithm [12] 19] The dual of the column space methods is the row space techniques for symbol estimations [14] or direct equalizer construction [3], 4] Manuscript received July 24, 2000; revised September 26, 2001. This work was supported in part by the National Science Foundation under Contract CCR9804019 and the Multidisciplinary University Research Initiative (MURI) under the Office of Naval Research Contract N00014 00 1 0564. The ....

D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," IEEE Trans. Signal Processing, vol. 45, pp. 2307--2317, Sept. 1997.

....often makes blind estimation approaches tractable in time varying channels [16] The proposed scheme consists of front end processing and blind identi cation of a parameter matrix which is associated with the estimating points. The elimination of unknown symbols is based on the cross referencing [17]. A new identi ability is established for noiseless case and new detection schemes are proposed based on the estimated parameter matrix. For multiuser scenario, decorrelating or regularized decorrelating front end can be used. The fast inversion of code matrix can be implemented with a ....

....Blind Channel Tracking Algorithm In this section, we propose a blind estimator for an equalizer based on a linear interpolation model exploiting the multipath diversity of propagation channel. The proposed algorithm is based on the cross reference technique to eliminate the unknown data symbols [17]. A. Front end processing We consider the conventional matched lter, decorrelator, and regularized decorrelator as the front end. The regularized decorrelator can be used to mitigate the noise enhancement for an improved performance. When the spreading factor is large and the multiuser ....

[Article contains additional citation context not shown here]

D. Gesbert, P. Duhamel, and S. Mayrargue, \On-line blind multichannel equalization based on mutually referenced lters," IEEE Trans. Signal Processing, vol.45, pp.2307-2317, Sept. 1997.

....1053 587X(99)04656 5. desired features, filterbank precoders and blind equalizers were proposed in [14] to minimize the rate reduction and obviate channel zero restrictions imposed by spatio temporal output diversity methods that rely on fractional sampling (FS) and or multiple antenna reception [13], 15] 22] 28] 33] However, identifiability in [14] was established only for white inputs and linear equation or subspace algorithms were developed for simple precoders (see also [19] In a deterministic multirate framework, filterbanks for nonblind channel equalization were also proposed ....

....applicable in TDMA and CDMA systems for the blind equalization of the downlink channel. Consistency analysis and modifications needed at low SNR are given in Section IV. In Section V, the proposed methods are tested via simulations and compared with alternative methods that employ space diversity [13], 15] 22] 33] fractional sampling (FS) 28] or they exploit a priori knowledge of the symbol constellation, e.g. the constant modulus algorithm (CMA) 16] II. PRELIMINARIES We will consider the same discrete time multirate transmitter model presented in [24] for the baseband ....

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D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," IEEE Trans. Signal Processing, vol. 45, pp. 2307--2317, Sept. 1997.

....for the definition of the delay) Therefore, there exist a relationship between equalizers with different delays. This property can be exploited to obtain a bank of equalizers known as blind mutually referenced equalizers (MRE) This approach again requires either oversampling or multiple antennas [102]. 9 The reason why the algorithms are known as Bussgang algorithms is that the output of the transversal filter y(n) after convergence of the adaptive algorithm is approximately a Bussgang process, i.e. Ey(n)y(n k) Ey(n)g(y(n k) 8 k where g( Delta) is the memoryless nonlinear operator [96, ....

D. Gesbert, P. Duhamel and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," IEEE Trans. on Sig. Proc., pp. 2307--2317, September 1997.

....of the row span of the data matrix are intersected. This procedure is such that only the symbol sequence that is present in all shifts will remain, thus removing the ISI. As shown in [6] the algorithm is essentially identical to the mutually referenced equalizer (MRE) technique by Gesbert e.a. [7]. The MRE idea is illustrated in figure 1: if the received data vector x i at time i is obtained by the convolution of a source symbol sequence by a filter of length 2, then there are two possible equalizer outputs, z (0) i and z (1) i , one a delay of the other. By forcing this property, ....

....in the null space of X, in all algorithms to follow a preprocessing is necessary, consisting of a prewhitening and dimension reduction to the rank of X. The processing consists of computing a singular value decomposition of X =US S SV, and replacing X by the first 2Q rows of V. Refer to [8, 5, 7] for further details. 3. Algorithm derivation 3.1. Mutually referenced equalizers We consider Q = 1 for now, and drop the index q for readability. An equalizer can be viewed as a vector w acting on X (i) to produce an output sequence z = w X (i) Since S (i) has two rows, there are ....

D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters, " IEEE Trans. Signal Proc., vol. 45, pp. 2307--2317, Sept. 1997.

....possible shifts. Blind estimation of equalizers corresponding to all possible shifts was also suggested (without uniqueness proofs) in [15] using an interesting linear prediction framework. An algorithm for the direct estimation of all possible equalizers was also derived independently in [2] and [3] by estimating the equalizer taps via second order statistics of the output. 2 In contrast, this paper s framework invokes no statistical assumptions on the input and, at moderate SNR s ( dB) yields operational equalizers using as few as 50 to 100 samples. This is because the equalizing ....

....for , allowing to be either deterministic, or (non )white random; 3) identifiability proofs revealing the role of persistenceof excitation; 4) methods to optimally combine the outputs of all equalizers corresponding to different delays . 2 Reference [2] assumes white inputs, whereas [3], which appeared after the conference version of this paper [6] dispenses with the whiteness assumption. A conference version of the results here can be found in [6] and extensions to time varying channels appeared in [4] II. DIRECT BLIND EQUALIZERS We will assume carrier synchronization ....

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D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," IEEE Trans. Signal Processing, vol. 45, pp. 2307--2317, Sept. 1997. 3

....equalization. In fact, for SIMO subchannels without common zeros, several FSE methods, such as the CMA and the super exponential algorithm, can converge globally to ISI free settings [58] Direct SIMO blind equalization algorithms based on SOS can also be more robust to channel modeling errors [81], 86] Practical applications of blind equalization and blind identification can be found mostly in wireless microwave digital links [245] Commercially, blind equalization has found new applications in the digital HDTV system and the digital cable modem [246] More recently, promising results ....

.... other hand, second order or deterministic blind solutions based on fractional sampling and or multiple antennas capitalize on their single input multi output (SIMO) equivalent structures, and require shorter data records for channel estimation and noise resilient equalization [238] 161] 293] [81], 91] However, their restrictions on channel nulls are (close to being) systematically violated when fractional sampling is not accompanied with sufficient excess bandwidth. This testifies to the fact that, similar to training, these blind methods require redundancy in the form of excess ....

[Article contains additional citation context not shown here]

D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," IEEE Trans. Signal Processing, vol. 45, no. 9, pp. 2307-2317, Sept. 1997.

....(e.g. CF, LP and TXK assume i.i.d. data) while others do not (e.g. SS , LS and TSML methods) Most of the approaches are batch channel identification methods. The equalizers (inverse filters) are obtained indirectly. Adaptive algorithms directly resulting equalizers are also proposed (e.g. [10]) as well as methods that perform direct symbol estimation (e.g. 11] 12] The latter two papers [11] 12] are targeted at the more complicated multi user case, where both adopt a two step approach removing ISI first and then separating users. Existing BE (or blind channel identification) ....

D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," IEEE Trans. Signal Process., vol. 45, pp. 2307--2317, Sept. 1997.

.... (LP) methods [53, 54] and deterministic subspace based methods working directly on X and exploiting either the Hankel structure of H [52, 53, 55] or the Toeplitz structure of S [56, 57] Closely related to these are the CrossRelation method [58] and the Mutually Referenced Equalizer method [59]. It is possible to incorporate partial knowledge of the channel into some of the methods, in particular the fact that the pulse shape function is usually known [60 62] This puts an additional linear constraint on the channel impulse response vector h and may lead to important improvements in ....

D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," IEEE Trans. Signal Proc., vol. 45, no. 9, pp. 2307--2317, Sept. 1997.

....sources are highly correlated (polyphase components of the same signal) Our algorithm consists of two stages : 2 D MIMO partial deconvolution and separation of polyphase components. For the deconvolution stage we have extended the generalized MRE method, previously proposed by Gesbert et. al [4], from 1 D to 2 D signals. For the separation stage we propose a source separation algorithm that minimizes out of band spectral energy resulting from instantaneous mixture of polyphasecomponents. The deconvolution method using multiple FIR filters we propose belongs to the class of algebraic ....

....Although this is not easily characterized in terms of the blurring filter [7, 8] assume this holds in the sequel. The 1 D MRE algorithm, from which we developed its 2 D version, was proposed for the first time to address 1 D blind multichannel equalization problem with only one input signal [4], and subsequently extended to multi input case [5] The basic principle of the MRE method is the exploitation of simple relationships that reveal the information redundancy at the outputs of different deconvolver filters (equalizers) with different restoration delays. We wish to compute different ....

[Article contains additional citation context not shown here]

D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters, " IEEE Trans. Signal Proc., vol. 45, no. 9, pp. 13071317, Sep. 1997.

....step, and this can result in increased robustness. The direct symbol estimation methods [8, 9] have sometimes been called row span methods as they exploit the row span information of the data matrix to find the vector of unknown symbols. Following a seemingly different strategy, MRE techniques [6] estimate a collection of channel equalizers by forcing them to produce the same (unknown) output sequence, up to fixed equalization lags. The goal of this paper is to demonstrate that these two methods are in fact identical, with small differences arising only due to variations in the ....

....in the noise free case, all equalizers return the same output sequence [s 0 s 1 ] up to a common scaling. Note that this is true only in the case of the constraint specified in (8) C. The MRE method The idea behind the mutually referenced equalizer (MRE) method for blind equalization [6] is to exploit the the relations in (3) by finding a vector of n equalizers w= w 0 w n 1 ] that simultaneously minimizes all differences kw i X (i) w k X (k) k 2 . This can be written as a least squares problem 1 w X mre = 0 ; X mre : 2 6 6 6 6 6 4 X ....

D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," IEEETrans. Signal Processing, vol. 45, no. 9, pp. 2307--2317, Sept. 1997.

....sources are highly correlated (polyphase components of the same signal) Our algorithm consists of two stages : 2 D MIMO partial deconvolution and separation of polyphase components. For the deconvolution stage we have extended the generalized MRE method, previously proposed by Gesbert et. al [4], from 1 D to 2 D signals. For the separation stage we propose a source separation algorithm that minimizes out of band spectral energy resulting from instantaneous mixture of polyphasecomponents. The deconvolution method using multiple FIR filters we propose belongs to the class of algebraic ....

....rank. Although this is not easily characterized in terms of the blurring filter [7, 8] assume this holds in the sequel. The 1 D MRE algorithm, from which we developed its 2 D version, was proposed for the first time to address 1 D blind multichannel equalization problem with only one input signal [4], and subsequently extended to multi input case [5] The basic principle of the MRE method is the exploitation of simple relationships that reveal the information redundancy at the outputs of different deconvolver filters (equalizers) with different restoration delays. We wish to compute different ....

[Article contains additional citation context not shown here]

D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters, " IEEE Trans. Signal Proc., vol. 45, no. 9, pp. 13071317, Sep. 1997.

....methods [6, 4] In most communications applications however, low complexity, design flexibility, and tracking ability are highly desirable properties and, as a consequence, simpler and potentially adaptive deconvolution algorithms are to be favored. Few examples of these are available, found in [16, 5, 11, 18, 19]. Unlike most second order based techniques, the Prediction Error (PE) approach [5] is still exactly consistent in the presence of channel length mismatch 1 [7] This makes the PE technique very attractive, from a practical point of view, since it is known that channel order estimation errors ....

....of the noise variance. In addition, it can be implemented using a low cost Gradient Projection Algorithm. In section 4, the use of a similar quadratic constraint for adaptive denoising is studied in the context of the Mutually Referenced Equalizers (MRE) criterion for channel equalization [16]. Here, a modification of the MRE algorithm is introduced, in order to allow the computation of adaptive unbiased channel FIR inverses (zero forcing i.e. removing all ISI) in a noisy environment. The performances of the proposed algorithms are evaluated in a wireless communications context with ....

[Article contains additional citation context not shown here]

D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," in IEEE Trans. on ASSP. To appear. Shorter version in [15].

....in the so called second order statistics and algebraic methods for the SIMO identification problem [1] At least three classes can be identified. The first addresses the problem of estimating the channels, viz. e.g. 2 4] the second considers the estimation of channel inverses (equalizers) [5 7], and the third attempts to recover the transmitted symbols directly from a (typically small) batch of output samples without resorting to channel equalizer estimates [8, 9] Categories 2 and 3 have the advantage of by passing the channel estimation and inversion step, which in cases results in ....

....step, which in cases results in increased robustness. The direct symbol estimation methods [8, 9] have sometimes been called row span methods as they exploit the row span information of the data matrix to find the vector of unknown symbols. Following a seemingly different strategy, MRE techniques [5] estimate a collection of channel equalizers by forcing them to produce the same (unknown) output sequence, up to fixed equalization lags. As we show here, these two methods are in fact more or less identical, with small differences depending on the implementation. We first review the row span ....

[Article contains additional citation context not shown here]

D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters, " IEEE Trans. Signal Processing, vol. 45, no. 9, pp. 2307-- 2317, Sept. 1997.

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D. Gesbert, P. Duhamel, and S. Mayrargue, "On-line blind multichannel equalization based on mutually referenced filters," IEEE Trans. on Signal Processing, vol. 45, no. 9, pp. 2307--2317, September 1997.

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