Pierre Duhamel

Subspace-based blind and semi-blind channel estimation for OFDM systems

This paper proposes a new blind channel estimation method for orthogonal frequency division multiplexing (OFDM) systems. The algorithm makes use of the redundancy introduced by the cyclic prefix to identify the channel based on a subspace approach. Thus, the proposed method does not require any modification of the transmitter and applies to most existing OFDM systems. Semi-blind procedures taking advantage of training data are also proposed. These can be training symbols or pilot tones, the latter being used for solving the intrinsic indetermination of blind channel estimation. Identifiability results are provided, showing that in the (theoretical) situation where channel zeros are located on subcarriers, the algorithm does not ensure uniqueness of the channel estimation, unless the full noise subspace is considered. Simulations comparing the proposed method with a decision-directed channel estimator finally illustrates the performance of the proposed algorithm.

Orthogonal transmultiplexers in communication: a review

This paper presents conventional and emerging applications of orthogonal synthesis/analysis transform configurations (transmultiplexer) in communications. It emphasizes that orthogonality is the underlying concept in the design of many communication systems. It is shown that orthogonal filter banks (subband transforms) with proper time-frequency features can play a more important role in the design of new systems. The general concepts of filter bank theory are tied together with the application-specific requirements of several different communication systems. Therefore, this paper is an attempt to increase the visibility of emerging communication applications of orthogonal filter banks and to generate more research activity in the signal processing community on these topics.

Blind equalization of OFDM systems based on the minimization of a quadratic criterion

Classical multicarrier systems based on the discrete Fourier transform (DFT) make use of a guard interval (GI) in order to enable a low complexity equalization scheme. This guard interval consists of a redundant prefix cyclically appended to each bloc of modulated symbols so as to exploit the cyclic convolution property of the DFT. Therefore, besides decreasing the useful transmitted symbol rate, this technique is very specific to DFT-based OFDM systems. In order to implement a digital modulator, an oversampled version of the continuous signal that would be produced by the all-analog ideal modulator is often computed. This amounts to appending null symbols to the block of symbols to be modulated. This work shows that forcing the presence of these null symbols at the appropriate places on the receiver side is sufficient to equalize the channel. Here, a linear equalizer is adapted by minimizing a quadratic criterion based on the energy of the subband signals that should be zero. Since no knowledge upon the useful data is required, this method performs blind equalization. Moreover, it requires neither a guard interval nor any reference symbol. As a result, for a given channel bit-rate budget, the data rate is increased.

Prediction error methods for time-domain blind identification of multichannel FIR filters

Blind channel identification methods based on the oversampled channel output is a problem of theoretical and practical interest. It is first demonstrated that the subspace methods developed in Moulines are not robust to errors in the determination of the model order. An alternative solution is then proposed, based on a linear prediction approach. The effect of overestimating the channel order is investigated by simulations: it is demonstrated that the prediction error method is robust to over-determination.

Adaptive filtering in subbands using a weighted criterion

Transform-domain adaptive algorithms have been proposed to reduce the eigenvalue spread of the matrix governing their convergence, thus improving the convergence rate. However, a classical problem arises from the conflicting requirements between algorithm improvement requiring rather long transforms and the need to keep the input/output delay as small as possible, thus imposing short transforms. This dilemma has been alleviated by the so-called short-block transform domain algorithms but is still apparent. This paper proposes an adaptive algorithm compatible with the use of rectangular orthogonal transforms (e.g., critically subsampled, lossless, perfect reconstruction filter banks), thus allowing better tradeoffs between algorithm improvement, arithmetic complexity, and input/output delay. The method proposed makes a direct connection between the minimization of a specific weighted least squares criterion and the convergence rate of the corresponding stochastic gradient algorithm. This method leads to improvements in the convergence rate compared with both LMS and classical frequency domain algorithms.

Subspace methods for the blind identification of multichannel FIR filters

A class of methods for identifying a single input/multiple output finite impulse response system (SIMO-FIR), from the outputs of the system only is presented. These methods rely on a minimal parametric representation of the system solution. They are based on the orthogonality between a signal and a noise subspaces. This is exploited to build quadratic forms whose minimization yields the desired estimates up to a scale factor. It is shown (by numerical simulations) that these methods provide significantly better (in terms of bias and variance) estimates than the method by Tong et al. (1991), while requiring about one half the number of computations. They are thus very attractive for applications, in particular, for narrowband TDMA channel equalization.<<ETX>>

Reduced complexity equalizers for zero-padded OFDM transmissions

The widespread application of OFDM for local area mobile wireless broadband systems is strongly motivated by the simple equalization it affords. OFDMs bottleneck of channel-dependent performance was only previously addressed by replacing the cyclic prefix (CP) with trailing zeros (TZ). Such zero-padded OFDM transmissions enable FIR channel-irrespective symbol recovery which results in significant BER gains. The price paid is increased receiver complexity compared to the classical CP-OFDM. To reduce complexity, this paper proposes two novel equalizers for TZ-OFDM. One is based on an overlap and add approach and exhibits exactly the same performance and complexity as CP-OFDM. The second offers BER performance close to the TZ-OFDM MMSE equalizer and incurs a moderate complexity increase. An extension of an existing CP-OFDM pilot-based channel estimation method is also derived for the proposed equalization schemes. Simulations are conducted in a realistic HiperLAN/2 scenario comparing the various OFDM transceivers.

A pseudorandom postfix OFDM modulator - semi-blind channel estimation and equalization

This paper details a new orthogonal-frequency-division-multiplexing (OFDM) modulator based on the use of a pseudorandom postfix (PRP)-OFDM and discusses low-complexity equalization and channel estimation/tracking architectures. The main property of this new modulation scheme is the ability to estimate and track the channel variations semi-blindly using order-one statistics of the received signal. Compared with known cyclic prefix OFDM (CP-OFDM) pilot-symbol-assisted modulation (PSAM) schemes, the pilot overhead is avoided: The channel estimation is performed based on the exploitation of pseudorandomly weighted postfix sequences replacing the guard interval contents of CP-OFDM. PRP-OFDM is shown to be of advantage if the target application requires 1) a minimum pilot overhead, 2) low-complexity channel tracking (e.g., high mobility context), and 3) adjustable receiver complexity/performance trade-offs (available due to the similarities of PRP-OFDM to the zero-padded OFDM (ZP-OFDM) modulation scheme) without requiring any feedback loop to the transmitter.

Perfect reconstruction versus MMSE filter banks in source coding

Classically, the filter banks (FBs) used in source coding schemes have been chosen to possess the perfect reconstruction (PR) property or to be maximally selective quadrature mirror filters (QMFs). This paper puts this choice back into question and solves the problem of minimizing the reconstruction distortion, which, in the most general case, is the sum of two terms: a first one due to the non-PR property of the FB and the other being due to signal quantization in the subbands. The resulting filter banks are called minimum mean square error (MMSE) filter banks. Several quantization noise models are considered. First, under the classical white noise assumption, the optimal positive bit rate allocation in any filter bank (possibly nonorthogonal) is expressed analytically, and an efficient optimization method of the MMSE filter banks is derived. Then, it is shown that while in a PR FB, the improvement brought by an accurate noise model over the classical white noise one is noticeable, it is not the case for the MMSE FB. The optimization of the synthesis filters is also performed for two measures of the bit rate: the classical one, which is defined for uniform scalar quantization, and the order-one entropy measure. Finally, the comparison of rate-distortion curves (where the distortion is minimized for a given bit rate budget) enables us to quantify the SNR improvement brought by MMSE solutions.

Reduced computation blind equalization for FIR channel input Markov models

The paper deals with adaptive blind equalization for the transmission of digital modulated signals on an unknown dispersive channel with additive white gaussian noise. The observed signal being modeled as a hidden Markov model(HMM), the expectation-maximization (EM) algorithm can be used to realize both the channel identification and the estimation of the emitted symbols. The paper proposes a new on-line algorithm with reduced complexity. This algorithm, obtained as an approximate solution of the maximum likelihood (ML) problem via the EM sequential algorithm, has strong connections with decision feedback equalizers (DFE) using the recursive least square (RLS) Algorithm.