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 Journal of Signal and Information Processing (JSIP) , 2014, DOI: 10.4236/jsip.2014.54018 Abstract: Recently, two expressions (for the noiseless and noisy case) were proposed for the residual inter-symbol interference (ISI) obtained by blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. However, those expressions are not applicable for biased input signals. In this paper, a closed-form approximated expression is proposed for the residual ISI applicable for the noisy and biased input case. This new proposed expression is valid for blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. The new proposed expression depends on the equalizer’s tap length, input signal statistics, channel power, SNR, step-size parameter and on the input signal’s bias. Simulation results indicate a high correlation between the simulated results and those obtained from our new proposed expression.
 Mathematics , 2005, Abstract: Sparse intersymbol-interference (ISI) channels are encountered in a variety of high-data-rate communication systems. Such channels have a large channel memory length, but only a small number of significant channel coefficients. In this paper, trellis-based equalization of sparse ISI channels is revisited. Due to the large channel memory length, the complexity of maximum-likelihood detection, e.g., by means of the Viterbi algorithm (VA), is normally prohibitive. In the first part of the paper, a unified framework based on factor graphs is presented for complexity reduction without loss of optimality. In this new context, two known reduced-complexity algorithms for sparse ISI channels are recapitulated: The multi-trellis VA (M-VA) and the parallel-trellis VA (P-VA). It is shown that the M-VA, although claimed, does not lead to a reduced computational complexity. The P-VA, on the other hand, leads to a significant complexity reduction, but can only be applied for a certain class of sparse channels. In the second part of the paper, a unified approach is investigated to tackle general sparse channels: It is shown that the use of a linear filter at the receiver renders the application of standard reduced-state trellis-based equalizer algorithms feasible, without significant loss of optimality. Numerical results verify the efficiency of the proposed receiver structure.
 Xudong Ma Mathematics , 2008, Abstract: In this paper, we consider the demodulation and equalization problem of differential Impulse Radio (IR) Ultra-WideBand (UWB) Systems with Inter-Symbol-Interference (ISI). The differential IR UWB systems have been extensively discussed recently. The advantage of differential IR UWB systems include simple receiver frontend structure. One challenge in the demodulation and equalization of such systems with ISI is that the systems have a rather complex model. The input and output signals of the systems follow a second-order Volterra model. Furthermore, the noise at the output is data dependent. In this paper, we propose a reduced-complexity joint demodulation and equalization algorithm. The algorithm is based on reformulating the nearest neighborhood decoding problem into a mixed quadratic programming and utilizing a semi-definite relaxation. The numerical results show that the proposed demodulation and equalization algorithm has low computational complexity, and at the same time, has almost the same error probability performance compared with the maximal likelihood decoding algorithm.
 Advances in Radio Science : Kleinheubacher Berichte , 2005, Abstract: Turbo equalization is a widely known method to cope with low signal to noise ratio (SNR) channels corrupted by linear intersymbol interference (ISI) (Berrou and Galvieux, 1993; Hagenauer et al., 1997). Recently in this workshop it was reported that also for nonlinear channels a remarkable turbo decoding gain can be achieved (Siegrist et al., 2001). However, the classical turbo equalization relies on code rates at 1/3 up to 1/2 which makes it quite unattractive for high rate data transmission. Considering the potential of iterative equalization and decoding, we obtain a considerable turbo decoding gain also for high rate codes of less than 7% redundancy by using punctured convolutional codes and block codes.
 Journal of Signal and Information Processing (JSIP) , 2017, DOI: 10.4236/jsip.2017.82004 Abstract: Up to now, the Mean Square Error (MSE) criteria, the residual Inter-Symbol Interference (ISI) and the Bit-Error-Rate (BER) were used to analyze the equalization performance of a blind adaptive equalizer in its convergence state. In this paper, we propose an additional tool (additional to the ISI, MSE and BER) for analyzing the equalization performance in the convergence region based on the Maximum Time Interval Error (MTIE) criterion that is used for the specification of clock stability requirements in telecommunications standards. This new tool preserves the short term statistical information unlike the already known tools (BER, ISI, MSE) that lack this information. Simulation results will show that the equalization performance of a blind adaptive equalizer obtained in the convergence region for two different channels is seen to be approximately the same from the residual ISI and MSE point of view while this is not the case with our new proposed tool. Thus, our new proposed tool might be considered as a more sensitive tool compared to the ISI and MSE method.
 Mathematics , 2011, DOI: 10.1109/JSTSP.2011.2166950 Abstract: In this paper, we deal with low-complexity near-optimal detection/equalization in large-dimension multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels using message passing on graphical models. A key contribution in the paper is the demonstration that near-optimal performance in MIMO-ISI channels with large dimensions can be achieved at low complexities through simple yet effective simplifications/approximations, although the graphical models that represent MIMO-ISI channels are fully/densely connected (loopy graphs). These include 1) use of Markov Random Field (MRF) based graphical model with pairwise interaction, in conjunction with {\em message/belief damping}, and 2) use of Factor Graph (FG) based graphical model with {\em Gaussian approximation of interference} (GAI). The per-symbol complexities are $O(K^2n_t^2)$ and $O(Kn_t)$ for the MRF and the FG with GAI approaches, respectively, where $K$ and $n_t$ denote the number of channel uses per frame, and number of transmit antennas, respectively. These low-complexities are quite attractive for large dimensions, i.e., for large $Kn_t$. From a performance perspective, these algorithms are even more interesting in large-dimensions since they achieve increasingly closer to optimum detection performance for increasing $Kn_t$. Also, we show that these message passing algorithms can be used in an iterative manner with local neighborhood search algorithms to improve the reliability/performance of $M$-QAM symbol detection.
 电子与信息学报 , 2009, Abstract: Inter Symbol Interference (ISI) will increase when transmission rate of an Impulse Radio-Ultra Wide Band (IR-UWB) system is getting larger, which will worsen Bit Error Rate (BER), restrict the highest realizable transmission rate. In order to suppress ISI and realize high transmission rate, based on the causation of ISI, a Fractionally Spaced-Decision Feedback Middle Equalization (FS-DFME) equalization receiver is proposed. The receiver can realize jointly Matched Filter (MF) and channel equalization so as to collect multipath signal energy and suppress ISI. Simulation results show that the observation window length is important parameter in mitigation of ISI. Compared with Linear Equalization (LE) and Fractionally Spaced-Decision Feedback Non-Middle Equalization (FS-DFNME) equalization receiver, ISI is mitigated more effectively by FS-DFME equalization receiver and BER performance is improved obviously.
 International Journal of Engineering Sciences & Research Technology , 2013, Abstract: The technique of compensating the effect of ISI in optical communication system described here is equalization .This technique of equalization is used for compensating the effect of ISI in the channel which causes disturbance in the signal, which is transmitted. There are various types of equalizers are used depending upon the application used and the kind of system in which it is used. The most important purpose of the equalization technique is to correct the channel frequency response. They not only correct the frequency response of the channel but also cancel the effects of multipath signal component present in the system. This paper aims at studying and simulation of equalization techniques; here two types of equalization techniques are stimulated, they are Zero Forcing Equalization and MMSE Equalization. Here in these techniques filters are used at the receiving end to cancel the effects of ISI in the received signal introduced by channel impulse response. As Inter Symbol Interference is considered to be one of the most challenging problems encountered in fiber optical communication system so as to remove the effect we can apply equalizer at the receiver to undo the effect of the channel by applying an inverse filter. The First technique used is zero forcing (ZF) equalizer to reduce the effect of inter symbol interference (ISI) introduced by the channel impulse response. The second method used Minimum Mean Square Error (MMSE) equalizer to reduce the effect of inter symbol interference (ISI) introduced by the channel impulse response. Simulation result shows that the Minimum Mean Square Error (MMSE) equalizer reduce the effect of inter symbol interference (ISI) better as compare to that of zero forcing (ZF) equalizer.
 International Journal of Advanced Computer Sciences and Applications , 2011, Abstract: The recent digital transmission systems impose the application of channel equalizers with short training time and high tracking rate. Equalization techniques compensate for the time dispersion introduced by communication channels and combat the resulting inter-symbol interference (ISI) effect. Given a channel of unknown impulse response, the purpose of an adaptive equalizer is to operate on the channel output such that the cascade connection of the channel and the equalizer provides an approximation to an ideal transmission medium. Typically, adaptive equalizers used in digital communications require an initial training period, during which a known data sequence is transmitted. A replica of this sequence is made available at the receiver in proper synchronism with the transmitter, thereby making it possible for adjustments to be made to the equalizer coefficients in accordance with the adaptive filtering algorithm employed in the equalizer design. In this paper, an overview of the current state of the art in adaptive equalization techniques has been presented.
 Mathematics , 2005, Abstract: We propose a computationally efficient multilevel coding scheme to achieve the capacity of an ISI channel using layers of binary inputs. The transmitter employs multilevel coding with linear mapping. The receiver uses multistage decoding where each stage performs a separate linear minimum mean square error (LMMSE) equalization and decoding. The optimality of the scheme is due to the fact that the LMMSE equalizer is information lossless in an ISI channel when signal to noise ratio is sufficiently low. The computational complexity is low and scales linearly with the length of the channel impulse response and the number of layers. The decoder at each layer sees an equivalent AWGN channel, which makes coding straightforward.
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