We propose a distributed blind equalization method for wireless sensor networks, in which a source sends data and each node performs time-domain equalization to estimate the data from a received signal that is affected by inter-symbol interference. The equalization can be performed distributively based on the mutually referenced equalization principle. Even if the nodes in the network are not fully connected to each other, the average consensus technique enables us to perform the equalization of all channels.

A class of multimodulus algorithms (MMA(p)) optimized by an optimal step-size (OS) for blind equalization are firstly investigated in this letter. The multimodulus (MM) criterion is essentially a split cost function that separately implements the real and imaginary part of the signal, hence the phase can be recovered jointly with equalization. More importantly, the step-size leading to the minimum of the MM criterion along the search direction can be obtained algebraically among the roots of a higher-order polynomial at each iteration, thus a robust optimal step-size multimodulus algorithm (OS-MMA(p)) is developed. Experimental results demonstrate improved performance of the proposed algorithm in mitigating the inter-symbol interference (ISI) compared with the OS constant modulus algorithm (OS-CMA). Besides, the computational complexity can be reduced by the proposed OS-MMA(2) algorithm.

In this paper, we first propose two batch blind source separation and equalization algorithms based on support vector regression (SVR) for linear time-invariant multiple input multiple output (MIMO) systems. The proposed algorithms combine the conventional cost function of SVR with error functions of classical on-line algorithm for blind equalization: both error functions of constant modulus algorithm (CMA) and radius directed algorithm (RDA) are contained in the penalty term of SVR. To recover all sources simultaneously, the cross-correlations of equalizer outputs are included in the cost functions. Simulation experiments show that the proposed algorithms can recover all sources successfully and compensate channel distortion simultaneously. With the use of iterative re-weighted least square (IRWLS) solution of SVR, the proposed algorithms exhibit low computational complexity. Compared with traditional algorithms, the new algorithms only require fewer samples to achieve convergence and perform a lower residual interference. For multilevel signals, the single algorithms based on constant modulus property usually show a relatively high residual error, then we propose two dual-mode blind source separation and equalization schemes. Between them, the dual-mode scheme based on SVR merely requires fewer samples to achieve convergence and further reduces the residual interference.

We propose a pre-filtering system for blind equalization in order to separate orthogonal frequency division multiplexing (OFDM) symbols in a multiple-input multiple-output (MIMO) - OFDM system. In a conventional blind MIMO-OFDM equalization without the pre-filtering system, there is a possibility that originally transmitted streams are permutated, resulting in the receiver being unable to retrieve desired signals. We also note that signal permutation is different for each subcarrier. In order to solve this problem, each transmitted stream of the proposed MIMO-OFDM system is pre-filtered by a unique allpass filter. In this paper, the pre-filter is referred to as transmit tagging filter (TT-Filter). At a receiver, an inverse filter of the TT-filter is used to blindly equalize a MIMO channel without permutation problem. Further, in order to overcome the issue of phase ambiguity, this paper introduces blind phase compensation.

In OFDM systems, residual inter-block interference can be suppressed by a time-domain equalizer that blindly shortens the effective length of a channel impulse response. To further improve the performance of blind equalizers, we propose a channel shortening method that attempts to maximize the minimum FFT output power over data subcarriers. Simulation results indicate that the max-min strategy has performance improvement over a conventional channel shortening method.

In block transmissions, inter-block interference (IBI) due to delayed waves exceeding a cyclic prefix severely limits the performance. To suppress IBI in downlink MC-CDMA systems, this paper proposes a novel channel shortening method using a time-domain equalizer. The proposed method minimizes a cost function related to equalizer output autocorrelations without the transmission of training symbols. We prove that the method can shorten a channel and suppress IBI completely. Simulation results show that the proposed method can significantly suppress IBI using relatively less number of received blocks than a conventional method when the number of users is moderate.

This letter presents the architecture of multi-gigabit parallel demodulator suitable for demodulating high order QAM modulated signal and easy to implement on FPGA platform. The parallel architecture is based on frequency domain implementation of matched filter and timing phase correction. Parallel FIFO based delete-keep algorithm is proposed for timing synchronization, while a kind of reduced constellation phase-frequency detector based parallel decision feedback PLL is designed for carrier synchronization. A fully pipelined parallel adaptive blind equalization algorithm is also proposed. Their parallel implementation structures suitable for FPGA platform are investigated. Besides, in the demonstration of 2 Gbps demodulator for 16QAM modulation, the architecture is implemented and validated on a Xilinx V6 FPGA platform with performance loss less than 2 dB.

In this paper, a novel CMA (constant modulus algorithm) algorithm employing fast convolution in the DFT (discrete Fourier transform) domain is proposed. We propose a non-linear adaptation algorithm that minimizes CMA cost function in the DFT domain. The proposed algorithm is completely new one as compared to the recently introduced similar DFT domain CMA algorithm in that, the original CMA cost function has not been changed to develop DFT domain algorithm, resulting improved convergence properties. Using the proposed approach, we can reduce the number of multiplications to O(Nlog2 N), whereas the conventional CMA has the computation order of O(N2). Simulation results show that the proposed algorithm provides a comparable performance to the conventional CMA.

A new blind adaptive equalization method for constant modulus signals based on minimizing the approximate negentropy of the estimation error for a finite-length equalizer is presented. We consider the approximate negentropy using nonpolynomial expansions of the estimation error as a new performance criterion to improve the performance of a linear equalizer using the conventional constant modulus algorithm (CMA). Negentropy includes higher order statistical information and its minimization provides improved convergence, performance, and accuracy compared to traditional methods, such as the CMA, in terms of the bit error rate (BER). Also, the proposed equalizer shows faster convergence characteristics than the CMA equalizer and is more robust to nonlinear distortion than the CMA equalizer.

This paper proposes a new blind adaptive MLSE equalizer for frequency selective mobile radio channels. The proposed equalizer performs channel estimation for each survivor path of the Viterbi algorithm (VA), and restricts the number of symbol candidates for the channel estimation in order to reduce prohibitive complexity. In such channel estimation, autocorrelation matrices of the symbol candidates are likely to become singular, which increases the estimation error. To cope with the singularity, the proposed equalizer employs a recursive channel estimation algorithm using the Moore-Penrose generalized inverse of the autocorrelation matrix. As another problem, the blind channel estimation can yield plural optimal estimates of a channel impulse response, and the ambiguity of the estimates degrades the BER performance. To avoid this ambiguity, the proposed equalizer is enhanced so that it can take advantage of the fractional sampling. The enhanced equalizer performs symbol-spaced channel estimation for each fractional sampling phase. This equalizer combines separate channel estimation errors, and provides the sum to the VA processor as the branch metric, which tremendously reduces the probability that a correct estimate turns into a false one. Computer simulation demonstrates the effectiveness of the proposed equalizers in the frequency selective fading channels.

A new receiver structure that combines the constant modulus algorithm (CMA) and the Kalman filter (KF) is investigated to exploit the advantages of both algorithms; simple implementation of blind algorithms, and excellent tracking ability, respectively. The proposed scheme achieves faster convergence and adaptability to the channel variation, which is verified through comparative simulations in doubly-selective (time- and frequency-selective) fading channels.

The present letter deals with the blind equalization problem of a single-input single-output infinite impulse response (SISO-IIR) channel with additive Gaussian noise. To solve the problem, we propose a new criterion for maximizing constrainedly a fourth-order cumulant. The algorithms derived from the criterion have such a novel property that even if Gaussian noise is added to the output of the channel, an effective zero-forcing (ZF) equalizer can be obtained with as little influence of Gaussian noise as possible. To show the validity of the proposed criterion, some simulation results are presented.

This paper proposes a direct blind equalization algorithm based on the multiple-shift correlation (MSC) property of the received data. Employing adaptive beamforming technique, we develope a partially adaptive channel equalizer (PACE) which allows the number of the adaptive weights to be less than the number of all the channel parameters. The PACE is with fast convergence speed and low implementation complexity. This paper also analyzes the effect of mismatch of channel order estimation due to small head and tail of the channel impulse response. From the analysis, we show the performance degradation is a function of the optimal output signal-to-interference plus noise ratio (SINR), the optimal output power and the control vector. We also propose a simple iterative method to reudce the performance degradation. Analysis of this proposed iterative method is also performed. Some simulation examples are demonstrated to show the effectiveness of the proposed blind channel equalizer and the performance analysis.

Recently, a cluster map based blind RBF equalizer (CM-BRE) has been proposed. By utilizing the underlying structure characteristics of RBF equalizer, the CM-BRE can be implemented by the combination of neural-gas algorithm (NGA) with several sorting operations. Although the CM-BRE is able to achieve almost identical performance with the optimal RBF equalizer, the high computational load mainly caused by NGA limits it's application. In this paper, we propose a downsizing method that employs the inter-relation among RBF centers and significantly reduces the NGA's computational load. Furthermore, a method to determine the feedback vector is derived, then CM-BRE is extended to a cluster map based blind RBF decision feedback equalizer (CM-BRDFE). The proposed CM-BRDFE also shows the close performance with the optimal RBF decision feedback equalizer in simulations.

The purpose of this paper is to propose a novel cluster map based blind RBF equalizer for received signal constellation (RSC) independent channel, which belongs to RSC based blind equalization approach. Without channel estimator, firstly, the desired numbers of unlabeled RBF centers are obtained by an unsupervised clustering algorithm. Then a cluster map generated from the known RBF equalizer structure is used to partition the unlabeled centers into appropriate subsets merely by several simple sorting operations, which corresponds to the weight initialization. Finally, the weight is adjusted iteratively by an unsupervised least mean square (LMS) algorithm. Since the process of the weight initialization using the underlying structure of RBF equalizer is very effective, the proposed blind RBF equalizer can achieve almost identical performance with the optimal RBF equalizer. The validity of the proposed equalizer is also demonstrated by computer simulations.

In this paper, we propose a blind adaptive channel identification and equalization algorithm with phase offset compensation for single-input multiple-output (SIMO) channel. It is based on the one-step forward multichannel linear prediction error method and can be implemented by an RLS algorithm. Phase offset problem is inherent part of any second-order statistics-based blind identification and equalization. To solve this problem, we use a blind adaptive algorithm called the constant modulus derotator (CMD) algorithm based on constant modulus algorithm (CMA). Moreover, unlike many known subspace (SS) methods or cross relation (CR) methods, our proposed algorithms do not require channel order estimation. Therefore, our algorithms are robust to channel order mismatch.

This paper considers a link of two problems; multichannel blind deconvolution and multichannel blind identification of linear time-invariant dynamic systems. To solve these problems, cumulant maximization has been proposed for blind deconvolution, while cumulant matching has been utilized for blind identification. They have been independently developed. In this paper, a cumulant maximization criterion for multichannel blind deconvolution is shown to be equivalent to a least-squares cumulant matching criterion after multichannel prewhitening of channel outputs. This equivalence provides us with a new link between a cumulant maximization criterion for blind deconvolution and a cumulant matching criterion for blind identification.

The problem of separating blindly independent sources from a convolutive mixture cannot be addressed in its widest generality without resorting to statistics of order higher than two. The core of the problem is in fact to identify the paraunitary part of the mixture, which is addressed in this paper. With this goal, a family of statistical contrast is first defined. Then it is shown that the problem reduces to a Partial Approximate Joint Diagonalization (PAJOD) of several cumulant matrices. Then, a numerical algorithm is devised, which works block-wise, and sweeps all the output pairs. Computer simulations show the good behavior of the algorithm in terms of Symbol Error Rates, even on very short data blocks.

In this paper, fast algorithms for the CMA (constant modulus algorithm), which is one of the widely used algorithms for blind equalizationi are presented. We propose the FBCMA (frequency domain block CMA) which takes advantage of fast linear convolution in the DFT domain by using the overlap save method. For the FBCMA, a nonlinear error function in the frequency domain is derived using Parseval's relation. Also, an adaptive algorithm in the DFT domain is introduced to adjust the frequency domain filter coefficients. For a block size and filter length of N, the multiplications required for the conventional CMA and proposed FBCMA are on the order of O(N2) and O(N log N), respectively.

In this paper, we propose a new structure of blind equalizer and its cost function. The proposed cost function is a quadratic form and has the unique solution. In addition, the proposed scheme can employ iterative algorithms which achieve less computational complexity and can be easily realized in real time processing. In order to verify the effectiveness of the proposed schemes, several computer simulations including a 64-QAM signal equalization have been shown.