A Toeplitz displacement method for blind multipath estimation forlong code DS/CDMA signals

The problem of blind channel identification for direct-sequence/code-division multiple-access (DS/CDMA) multiuser systems is explored. For wideband DS/CDMA signals, multipath distortion is well modeled by a finite-impulse response filter. In this work, a blind channel identification technique based on second-order statistics is investigated. The method exploits knowledge of the spreading code of the user of interest via matched filtering, as well as properties of spreading codes. The current scheme focuses on a method appropriate for randomized long sequence DS/CDMA. This access scheme poses special challenges as the spreading codes are time varying. An analytical approximation of the mean-squared error is derived using perturbation techniques. The performance of the algorithm is studied via simulation and through the mean-squared error approximation, which is observed to be tight     

A fast RLS transversal filter for adaptive linear phase filtering

A fast transversal filter algorithm is presented for the adaptive recursive least-squares design of filters with linear phase. Connections with a popular method of spectrum estimation are explored. The algorithm is derived in a new framework, for the prewindowed given data case. Exact and soft-constraint initialization are discussed and an improved rescue procedure is proposed. Data sequence weighting is introduced to allow for arbitrarily time-varying weighting strategies, facilitating the tracking of arbitrarily non-stationary phenomena.     

A theoretical high-rate analysis of causal versus unitary online transform coding

Backward adaptive or "online" transform coding (TC) of Gaussian sources is investigated. The Karhunen-Loe/spl grave/ve transform (KLT, unitary approach) and the causal transform (CT, causal approach) are compared in this context. When the covariance matrix R_/sub x/ of the source is used in the TC scheme, KLT and CT present similar coding gains at high rates. The aim of this study is to model analytically the behavior of these two coding structures when the ideal TC scheme gets perturbed, that is, when only a perturbed value R_/sub x/+/spl Delta/R is known at the encoder. In the online TC schemes considered here, this estimate is used to compute both the transform and the bit assignment. /spl Delta/R is caused by two noise sources: estimation noise (finite set of available data at the encoder) and quantization noise (quantized data at the decoder). Furthermore, not only does the transformation itself get perturbed, but also the bit assignment does as well. In this framework, theoretical expressions for the coding gains in both the unitary and the causal cases are derived under the high-rate assumption.     

Achieving the Optimal Diversity-Versus-Multiplexing Tradeoff for MIMO Flat Channels With QAM Space–Time Spreading and DFE Equalization

The use of multiple transmit (Tx) and receive (Rx) antennas allows to transmit multiple signal streams in parallel and hence to increase communication capacity. We have previously introduced simple convolutive linear precoding schemes that spread transmitted symbols in time and space, involving spatial spreading, delay diversity and possibly temporal spreading. In this paper we show that the use of the classical multiple-input-multiple-output (MIMO) decision feedback equalizer (DFE) (but with joint detection) for this system allows to achieve the optimal diversity-versus-multiplexing tradeoff introduced in Zheng and Tse, "Diversity and multiplexing: A fundamental tradeoff in multiple-antenna channels," IEEE Trans. Inf. Theory, May 2003, when a minimum mean squared error (MMSE) design is used. One of the major contributions of this work is the diversity analysis of a MMSE equalizer without the Gaussian approximation. Furthermore, the tradeoff is discussed for an arbitrary number of transmit and receive antennas. We also show the tradeoff obtained for a MMSE zero forcing (ZF) design. So, another originality of this paper is to show that the MIMO optimal tradeoff can be attained with a suboptimal receiver, in this case a DFE, as opposed to optimal maximum likelihood sequence estimation (MLSE)     

On the convergence behavior of the LMS and the normalized LMSalgorithms

It is shown that the normalized least mean square (NLMS) algorithm is a potentially faster converging algorithm compared to the LMS algorithm where the design of the adaptive filter is based on the usually quite limited knowledge of its input signal statistics. A very simple model for the input signal vectors that greatly simplifies analysis of the convergence behavior of the LMS and NLMS algorithms is proposed. Using this model, answers can be obtained to questions for which no answers are currently available using other (perhaps more realistic) models. Examples are given to illustrate that even quantitatively, the answers obtained can be good approximations. It is emphasized that the convergence of the NLMS algorithm can be speeded up significantly by employing a time-varying step size. The optimal step-size sequence can be specified a priori for the case of a white input signal with arbitrary distribution     

The fast subsampled-updating fast transversal filter (FSU FTF) RLS algorithm

We present a new fast algorithm for Recursive Least-Squares(rls) adaptive filtering that uses displacement structure and subsampled updating. Thefsu ftf algorithm is based on the Fast Transversal Filter(ftf) algorithm, which exploits the shift invariance that is present in therls adaptation of afir filter. Theftf algorithm is in essence the application of a rotation matrix to a set of filters and in that respect resembles the Levinson algorithm. In the subsampled updating approach, we accumulate the rotation matrices over some time interval before applying them to the filters. It turns out that the successive rotation matrices themselves can be obtained from a Schur type algorithm which, once properly initialized, does not require inner products. The various convolutions that thus appear in the algorithm are done using the Fast Fourier Transform(fft). For relatively long filters, the computational complexity of the new algorithm is smaller than the one of the well-known lms algorithm, rendering it especially suitable for applications such as acoustic echo cancellation.     

Performance and Complexity Analysis of Blind FIR Channel Identification Algorithms Based on Deterministic Maximum Likelihood in SIMO Systems

We analyze two algorithms that have been introduced previously for Deterministic Maximum Likelihood (DML) blind estimation of multiple FIR channels. The first one is a modification of the Iterative Quadratic ML (IQML) algorithm. IQML gives biased estimates of the channel and performs poorly at low SNR due to noise induced bias. The IQML cost function can be “denoised” by eliminating the noise contribution: the resulting algorithm, Denoised IQML (DIQML), gives consistent estimates and outperforms IQML. Furthermore, DIQML is asymptotically globally convergent and hence insensitive to the initialization. Its asymptotic performance does not reach the DML performance though. The second strategy, called Pseudo-Quadratic ML (PQML), is naturally denoised. The denoising in PQML is furthermore more efficient than in DIQML: PQML yields the same asymptotic performance as DML, as opposed to DIQML, but requires a consistent initialization. We furthermore compare DIQML and PQML to the strategy of alternating minimization w.r.t. symbols and channel for solving DML (AQML). An asymptotic performance analysis, a complexity evaluation and simulation results are also presented. The proposed DIQML and PQML algorithms can immediately be applied also to other subspace problems such as frequency estimation of sinusoids in noise or direction of arrival estimation with uniform linear arrays.     

Normalized sliding window constant modulus and decision-directedalgorithms: a link between blind equalization and classical adaptivefiltering

By minimizing a deterministic criterion of the constant modulus (CM) type or of the decision-directed (DD) type, we derive normalized stochastic gradient algorithms for blind linear equalization (BE) of QAM systems. These algorithms allow us to formulate CM and DD separation principles, which help obtain a whole family of CM or DD BE algorithms from classical adaptive filtering algorithms. We focus on the algorithms obtained by using the affine projection adaptive filtering algorithm (APA). Their increased convergence speed and ability to escape from local minima of their cost function make these algorithms very promising for BE applications     

Fractionally spaced equalization of linear polyphase channels andrelated blind techniques based on multichannel linear prediction

We consider the problem of linear equalization of polyphase channels and its blind implementation. These channels may result from oversampling the single output of a transmission channel or/and by receiving multiple outputs of an antenna array. A number of previous contributions in the field of blind channel identification have shown that polyphase channels can be blindly identified using only second-order statistics (SOS) of the output. In this work, we are mostly interested in the blind linear equalization of these channels. After some elaboration on the specifics of the equalization problem for polyphase channels, we show how optimal settings of various well-known types of linear equalization structures can be obtained blindly using only the output's SOS by using multichannel linear prediction or related techniques     

Fast subsampled-updating stabilized fast transversal filter (FSUSFTF) RLS algorithm for adaptive filtering

We present a new, doubly fast algorithm for recursive least-squares (RLS) adaptive filtering that uses displacement structure and subsampled-updating. The fast subsampled-updating stabilized fast transversal filter (FSU SFTF) algorithm is mathematically equivalent to the classical fast transversal filter (FTF) algorithm. The FTF algorithm exploits the shift invariance that is present in the RLS adaptation of an FIR filter. The FTF algorithm is in essence the application of a rotation matrix to a set of filters and in that respect resembles the Levinson (1947) algorithm. In the subsampled-updating approach, we accumulate the rotation matrices over some time interval before applying them to the filters. It turns out that the successive rotation matrices themselves can be obtained from a Schur-type algorithm that, once properly initialized, does not require inner products. The various convolutions that appear In the algorithm are done using the fast Fourier transform (FFT). The resulting algorithm is doubly fast since it exploits FTF and FFTs. The roundoff error propagation in the FSU SFTF algorithm is identical to that in the SFTF algorithm: a numerically stabilized version of the classical FTF algorithm. The roundoff error generation, on the other hand, seems somewhat smaller. For relatively long filters, the computational complexity of the new algorithm is smaller than that of the well-known LMS algorithm, rendering it especially suitable for applications such as acoustic echo cancellation