Relying on basic tools such as eigensignals of linear time-invariant systems, linear and circular block convolution, and fast Fourier transforms (FFTs), this article develops a systematic discrete-time framework and designs novel systems for single- and multiuser wireless multicarrier communications-a field rich in signal processing challenges that holds great potential in various applications including audio/video broadcasting, cable television, modem design, multimedia services, mobile local area networks, and future-generation wideband cellular systems. Wireless multicarrier (MC) communication systems utilize multiple complex exponentials as information-bearing carriers. MC transmissions thus retain their shape and orthogonality when propagating through linear time-dispersive media, precisely as eigensignals do when they pass through linear time-invariant (LTI) systems.

Wireless multicarrier communications

Fast Fourier Transform

Zero padding (ZP) of multicarrier transmissions has been proposed as an appealing alternative to the traditional cyclic prefix (CP) orthogonal frequency-division multiplexing (OFDM) to ensure symbol recovery regardless of the channel zero locations. In this paper, both systems are studied to delineate their relative merits in wireless systems where channel knowledge is not available at the transmitter. Two novel equalizers are developed for ZP-OFDM to tradeoff performance with implementation complexity. Both CP-OFDM and ZP-OFDM are then compared in terms of transmitter nonlinearities and required power backoff. Next, both systems are tested in terms of channel estimation and tracking capabilities. Simulations tailored to the realistic context of the standard for wireless local area network HIPERLAN/2 illustrate the pertinent tradeoffs.

https://www.dtc.umn.edu/s/resources/cp-zp.pdf

Cyclic prefixing or zero padding for wireless multicarrier transmissions

Techniques are described for efficiently estimating and compensating for the effects of a communication channel in a multi-carrier wireless communication system. The techniques exploit the fact that the transmitted symbols are drawn from a finite-alphabet to efficiently estimate the propagation channel for multi-carrier communication systems, such systems using OFDM modulation. A transmitter transmits data through a communication channel according to the modulation format. A receiver includes a demodulator to demodulate the data and an estimator to estimate the channel based on the demodulated data. The channel estimator applies a power-law operation to the demodulated data to identify the channel. The techniques can be used in both blind and semi-blind modes of channel estimation.

Channel estimation for wireless ofdm systems

While multipath induced phase rotations can be dealt with by differential encoding in orthogonal frequency division multiplexing (OFDM) communications, the loss of orthogonality due to the carrier offset must be compensated before discrete Fourier transform (DFT)-based demodulation can be performed. In this letter, we present a high-performance/low-complexity blind carrier offset estimation algorithm by exploiting intrinsic structure information of OFDM signals. The algorithm offers the accuracy of a super resolution subspace method, viz. MUSIC, without involving computationally intensive subspace decompositions.

A high-efficiency carrier estimator for OFDM communications

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.

/pdf/adaptive-filtering-in-subbands-using-a-weighted-criterion-3613kkynar.pdf

Adaptive filtering in subbands using a weighted 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.

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

A new subspace method performing the blind and semi-blind identification of the transmission channel suited to multicarrier systems with cyclic prefix (OFDM) is proposed in this paper. This technique has the advantage to preserve the classical OFDM emitter structure based on a cyclic prefix insertion. Therefore it applies to all existing standardized multicarrier systems (DAB, ADSL, etc.) and does not prevent the use of the classical very simple equalization scheme. Moreover the method detailed provides an unbiased channel estimation and is robust to channel order overdetermination provided that the channel frequency response has no zeroes located on a subcarrier.

A subspace based blind and semi-blind channel identification method for OFDM systems

Two new blind channel identification methods suited to multicarrier system (OFDM) exploiting the redundancy introduced by the adjunction of a cyclic prefix at the emitter and relying on the evaluation of the received signal autocorrelation matrix are presented. The proposed algorithms are able to identify any channel without any constraint on their zeroes location (including non-minimum phase channels) and are robust to the addition of white noise. Moreover a further enhancement of the estimation accuracy can easily be achieved by taking advantage of already present training symbols in current systems operating in a semi-blind context. Furthermore one of the two identification strategies has a very low arithmetical complexity which makes it particularly attractive in practice. Notice that these methods are not restricted to classical DFT-type modulators and still apply with any perfect reconstruction modulator.

Blind and semi-blind channel identification methods using second order statistics for OFDM systems

Classical transform-domain algorithms adapt the filter coefficients (in each "frequency bin") by minimizing a criterion depending on a full-band time-domain error. This paper proposes an algorithm which updates each portion of the frequency response of the adaptive filter according to the error in the same subband. For this purpose, a multirate adaptive filter is used where a subband decomposition of the error is performed using critically sampled lossless perfect reconstruction filter banks. This new algorithm is based on the minimization of a weighted criterion by a stochastic gradient algorithm and leads to improvements in the convergence rate compared to both LMS and classical frequency domain algorithms.

/pdf/adaptive-filtering-in-subbands-using-a-weighted-criterion-7qy26vw9s0.pdf

M. de Courville

Papers

Adaptive filtering in subbands using a weighted criterion

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

A subspace based blind and semi-blind channel identification method for OFDM systems

Blind and semi-blind channel identification methods using second order statistics for OFDM systems

Adaptive filtering in subbands using a weighted criterion