Convergence behavior of a PS-FSE in the presence of acyclostationary crosstalk interference

The convergence and steady-state behavior of a phase-splitting fractionally spaced equalizer (PS-FSE) are analyzed in the presence of a cyclostationary crosstalk interference. It is shown that the FSE in the presence of cyclostationary crosstalk has a different eigenstructure compared to the one in the presence of stationary noise. We also show that the convergence characteristic of the PS-FSE varies depending on the relative clock phase between the signal and the crosstalk     

Polynomial perceptrons and their applications to fading channelequalization and co-channel interference suppression

This paper investigates the behaviors of polynomial perceptrons and introduces a fractionally spaced recursive polynomial perceptron with low complexity and fast convergence rate. The nonlinear mapping ability of the polynomial perceptron is analyzed. It is shown that a polynomial perceptron with degree L(⩾4) satisfies the Stone-Weierstrass theorem and can approximate any continuous function to within a specified accuracy. Moreover, the nonlinear mapping ability of a polynomial perceptron with degree L is similar to that of the three-layer perceptron with one hidden layer for time same number of neurons in the input layer. The nonlinear mapping ability of the fractionally spaced recursive polynomial perceptron is also presented. Applications of polynomial perceptrons for fading channel equalization and co-channel interference suppression in a 16-level quadrature amplitude modulation receiver system are considered. Computer simulations are used to evaluate and compare the performance of polynomial perceptron (PP) and fractionally spaced bilinear perceptron (FSBLP) with that of the synchronous decision feedback multilayer perceptron (SDFMLP), fractionally spaced decision feedback multilayer perceptron (FSDFMLP), and the conventional decision feedback equalizer (DFE). The results show that the performance of the fractionally spaced bilinear perceptron is clearly superior to that of the other structures     

Decision feedback equalization for CDMA in indoor wirelesscommunications

Commercial interest in Code Division Multiple Access (CDMA) systems has risen dramatically in the last few years. It yields a potential increase in capacity over other access schemes, because it provides protection against interference, multipath, fading, and jamming. Recently, several interference cancellation schemes for CDMA have been proposed but they require information about all interfering active users or some channel parameters. The authors present an adaptive fractionally spaced decision feedback equalizer (DFE) for a CDMA system in an indoor wireless Rayleigh fading environment. This system only uses information about the desired user's spreading code and a training sequence. An analysis on the optimum performance of the DFE receiver shows the advantages of this system over others in terms of capacity improvements. A simulation of this system is also presented to study the convergence properties and implementation considerations of the DFE receiver. Effects on the performance because of sudden birth and death of users in the CDMA system and bit error rate performance of the DFE receiver is also presented     

Decision-feedback equalization of pulse-position modulation onmeasured nondirected indoor infrared channels

We examine the performance of two decision-feedback equalizers (DFEs) for pulse-position modulation (PPM) on measured nondirected indoor infrared channels with intersymbol interference. PPM offers high average-power efficiency, but on ISI channels, unequalized PPM suffers severe performance penalties. We have previously examined the performance of the maximum-likelihood sequence detector (MLSD), and found that it yields significant improvements. However, the MLSD often requires such large complexity and delay that it may be impractical. We investigate suboptimal, reduced-complexity equalization techniques for PPM, providing a performance analysis of zero-forcing chip-rate and symbol-rate DFEs. Our results show that a symbol-rate DFE provides performance that closely approaches that of the optimal MLSD     

Minimum mean-squared error decision-feedback equalization fordigital subscriber line transmission with possibly correlated line codes

The author presents a theory on MMSE (minimum mean-squared error) decision-feedback equalization which augments previously published results by allowing both a correlated symbol sequence and a fractionally spaced DFE (decision-feedback equalizer) forward filter. This theory facilitates calculating the potential DSL (digital subscriber line) transmission performance in cases of correlated line codes, especially for situations where one or both of the DFE filters are infinite in length. The situation of an infinite-length DFE is of interest because it provides information on the limit of MMSE equalization and can thus serve as a benchmark against which the performance of a finite-length DFE may be compared. The author also presents a few numerical examples of the performance of MMSE decision-feedback equalization in DSL transmission at ISDN (integrated services digital network) basic access rates with several well-known line codes     

Adaptive single-user receivers for direct-sequence spread-spectrumCDMA systems

The capacity of a direct-sequence spread-spectrum code-division multiple-access (DSSS-CDMA) system is limited by multiple-access interference (MAI) and the near-far problem. Multiuser receivers provide a solution to these problems, but they require knowledge of parameters of the MAI and are computationally complex. Adaptive single-user receivers, however, do not require knowledge of MAI parameters and need fewer computations. This paper discusses a wide range of adaptive single-user receivers found in the literature and presents their performance results under a unified framework to provide a basis of comparison. Results indicate that, compared to the conventional receiver, adaptive single-user receivers provide large gains in system capacity and are near-far resistant. It is shown that fractionally spaced adaptive receivers, which exploit spectral correlation due to the cyclostationary nature of the DSSS signal, perform better than adaptive receivers that cannot exploit this correlation. Multipath results presented for two-ray and urban channels indicate that fractionally spaced adaptive receivers act as RAKE receivers     

Digital Equalization of Chromatic Dispersion and Polarization Mode Dispersion

In this paper, we consider a fractionally spaced equalizer (FSE) for electronic compensation of chromatic dispersion (CD) and polarization-mode dispersion (PMD) in a dually polarized (polarization-multiplexed) coherent optical communications system. Our results show that the FSE can compensate any arbitrary amount of CD and first-order PMD distortion, provided that the oversampling rate is at least 3/2 and that a sufficient number of equalizer taps are used. In contrast, the amount of CD and PMD that can be corrected by a symbol-rate equalizer only approaches an asymptotic limit, and increasing the number of taps has no effect on performance due to aliasing that causes signal cancellation and noise enhancement.     

Sequence estimation techniques for digital subscriber looptransmission with crosstalk interference

The use of reduced-state sequence estimation techniques in a digital subscriber loop receiver is discussed. These techniques offer a potential performance improvement over conventional equalization techniques such as decision feedback equalization (DFE). Stationary and cyclostationary NEXT noise models are described. The theoretical performance obtainable from a Viterbi algorithm receiver with stationary white Gaussian noise, stationary NEXT, and cyclostationary NEXT noise models is estimated, and the reduced-state decision feedback sequence estimation and M algorithms are reviewed. It is shown that the improvement can be especially significant in the presence of cyclostationary crosstalk because of the freedom that sequence estimation receivers afford in the choice of receiver sampling phase. This advantage is evaluated for Viterbi algorithm receivers. By simulation of two practical reduced-state sequence estimation receivers, it is demonstrated that, in the presence of cyclostationary crosstalk, a substantial increase in maximum loop range (or equivalently, maximum bit rate) may be achievable compared to conventional DFE equalization     

Decision feedback equalization of the indoor radio channel

The measured multipath profiles from five different indoor areas are used for the performance analysis of a binary phase shift keying (BPSK) modem with a decision feedback equalizer (DFE). The performance from the measured multipath profiles is compared with the performance predictions based on a computer simulated channel model. Both average probability of error and probability of outage are calculated for a DFE with three fractionally spaced forward and three feedback taps. An equivalent delay power spectrum function, determined from the ensemble of the measured channel impulse responses, is defined. Using this function, analytical lower bounds on the average probability of error and the probability of outage of the BPSK/DFE modem with an infinite number of feedback taps and three forward taps are determined and compared with the results based on measured data and the computer generated channel impulse responses     

FRESH-DFE: A New Structure for Interference Cancellation

This paper proposes a new structure of decision feedback equalizer that exploits the cyclostationary properties of digitally modulated signals to mitigate interference. In the proposed structure, the forward filter of the conventional DFE is replaced by a cyclic filter. It is assumed that the desired and the interference signals use some mutually different signaling attributes, for example symbol rates, centre frequency etc. The resulting structure is evaluated in the presence of up to six strong interfering signals, a scenario that is typically found in wireless cellular systems. The proposed structure provides performance gains for some modulation formats but it reduces to the conventional DFE for other signal formats.     

Further Results on Adaptive Equalizer Improvements for 16 QAM and 64 QAM Digital Radio

Channel distortions due to multipath fading are a principal source of outage for high-capacity digital radio. Time domain equalization is increasingly becoming an effective means to compensate for fading induced ISI. This paper compares the performance of transversal and decision feedback equalizers used for 16 QAM and 64 QAM digital radio systems. The effect of tap spacing is examined by comparing the results of baud period spacing with fractionally spaced equalizers. The performance measure used is peak distortion. This measure is plotted against various fade parameters for the different equalizers studied, the two modulation schemes, forms of timing recovery, and the effects of joint operation of demodulation and symbol synchronization circuitry. Results clearly indicate, in terms of better signature curves, the superiority of fractionally spaced equalizers over synchronous equalizers. An additional advantage is the robustness of FSE's to timing phase errors. A decision feedback equalizer with fractional spacing on the feedforward part offers the best performance. It is shown that the performance of a DFE synchronized to the first precursor is significantly improved as compared to the conventional case of synchronizing with the main sample of the received pulse. With the new position of reference (first precursor), fractional DFE's benefit more than theirT-spaced counterpart.     

Baseband trellis-coded modulation with combinedequalization/decoding for high bit rate digital subscriber loops

The authors present a simulation study evaluating the performance of trellis-coded modulation with combined code/ISI sequence estimation for high bit rate (800 kb/s) transmission on subscriber loops. The receiver contains a fractionally spaced forward filter of a decision feedback equalizer (DFE) as a front end. This is shown to suppress phase synchronized crosstalk very effectively. The performance is further enhanced by the use of trellis code with a large number of states received with an M algorithm sequence-estimating receiver with a smaller number of states     

On training fractionally spaced equalizers using intersymbolinterpolation

The use of an intersymbol interpolation method in training fractionally spaced equalizers (FSEs) is investigated. It is shown that the optimal interpolation filter depends on the amplitude frequency response of the transmitter filter and the channel. Using a nonoptimal interpolation filter increases the stead-state mean-square error of the FSE. An interpolated complex FSE (CFSE) using a stochastic gradient, or LMS, adaptive algorithm has very little advantage over an LMS CFSE with symbol-rate updating. However, an interpolated LMS phase-splitting FSE (PS-FSE) has a convergence speed that is twice as fast as a conventional PS-FSE. Special precautions for evaluating the performance of interpolated FSEs are discussed, and a novel evaluation scheme is proposed     

Fractionally spaced blind equalization using polyperiodic linearfiltering

Performance of fractionally spaced equalizers using polyperiodic linear filtering is depicted. The fractionally sampled version of an arbitrary stable channel's outputs with stationary random inputs exhibit cyclostationarity with cycle frequencies being integer multiples of the reciprocal of the oversampling factor. By optimally polyperiodic linear filtering the oversampled outputs, we can fully utilize the cyclostationary property. With some traditional Bussgang techniques, such as stop-and-go decision-directed method, to adaptively update the filter coefficients, the convergence rate of the fractionally spaced equalizers proposed is improved, while the complexity retains in the same order as original Bussgang ones. Some computer simulation results are shown to demonstrate the improvement we can achieve     

Error-rate evaluation of linear equalization and decision feedbackequalization with error propagation

We propose applying an approximate Fourier series to evaluate efficiently the bit-error-rate (BER) performance of finite-length linear equalization (LE) and decision feedback equalization (DFE). By extending the Fourier series, we enable BER calculations for quadrature phase-shift keying (QPSK) transmission on complex channels with in-phase and crosstalk intersymbol interference (ISI). The BER calculation is based on determining the residual ISI samples and background Gaussian noise variance at the equalizer output for static channels or for realizations of quasi-static fading channels. A simple bound on the series error magnitude in terms of the Fourier series parameters ensures the required accuracy and precision. Improved state transition probability estimates are derived and verified by simulation for an approximate Markov model of the DFE error propagation for the case in which residual ISI exists even when the previous decisions stored in the feedback filter (FBF) are correct. We demonstrate the ease and widespread applicability of our approach by producing results which elucidate a variety of equalization tradeoffs. Our analysis includes symbol-spaced and fractionally spaced minimum mean-square error (MMSE)-LE, zero-forcing (ZF)-LE, and MMSE-DFE (with and without error propagation) on static ISI channels and multipath channels with quasi-static Rayleigh fading; a comparison between suboptimum and optimum receiver filtering in conjunction with equalization; and an assessment of the accuracy of some widely used equalization BER approximations and bounds     

GCMAC-based predistortion for digital modulations

The subject of this paper is the compensation for nonlinearities in digital communication systems by means of predistortion. In this work, we apply the generalized cerebellar model articulation controller (GCMAC) to simplify and accelerate the predistorter convergence. The range of analyzed predistorters includes: 1) a symbol-rate data predistorter that, for a given time span, achieves a similar level of compensation provided by present techniques, but with faster convergence; 2) a fractionally spaced data predistorter that controls, at the same time, the signal constellation and the transmitted spectrum; 3) a decision-feedback scheme that compensates for remote nonlinearities; and 4) a digital signal data predistorter. The performance of the proposed data and signal predistorters is evaluated using typical linear and nonlinear modulated transmitted signals such as QAM and GMSK     

Blind equalization and estimation of FIR communications channelsusing fractional sampling

We consider the problem of blind estimation and equalization of digital communication finite impulse response (FIR) channels using fractionally spaced samples. Fractionally sampled data are cyclostationary rather than stationary. The problem is cast into a mathematical framework of parameter estimation for a vector stationary process with single input (information sequence) and multiple outputs, by using a time-series representation of a cyclostationary process. The channel parameters are estimated by first estimating various subchannels using the second- and the fourth-order cumulant function of the received data, and then appropriately aligning and scaling them. The estimated channel impulse response is then used to construct a linear equalizer. Two illustrative simulation examples using four- and 16-QAM signals are presented where effect of symbol-timing-phase offset is studied via simulations     

Performance of trellis codes for a class of equalized ISI channels

The performance of trellis codes is examined for a class of intersymbol interference (ISI) channels that occur in high-frequency radio systems. The channels considered are characterized by in-band spectral nulls and by a rapid time variation. The baseline modulation technique is 4QAM (four-point quadrature amplitude modulation). When spectral nulls are absent, performance of fractionally spaced linear equalizers and trellis decoders is found to be near ideal and to be better than using symbol-spacing in the equalizer. However, error propagation in the feedback path, resulting from equalizer-based decisions, ruins the performance of the combination of decision-feedback equalizers and trellis decoders when spectral nulls are present. Their performance can be improved by using fractionally spaced feedforward equalizer sections and by designing the decoder to compensate for ISI. Rate 2/3 codes are found to outperform rate 1/2 codes in error performance     

On blind identifiability of multipath channels using fractionalsampling and second-order cyclostationary statistics

The problem of blind identifiability of digital communication multipath channels using fractionally spaced samples is considered. Fractionally sampled data are cyclostationary rather than stationary. The problem is cast into a mathematical framework of parameter estimation for a vector stationary process with single input (information sequence) and multiple outputs, by using a time-series representation of a cyclostationary process. A necessary and sufficient condition for channel identifiability from the correlation function of the vector stationary process is derived. This result provides an alternative but equivalent statement of an existing result. Using this result, it is shown that certain class of multipath channels cannot be identified from the second-order statistics irrespective of how the sampling rate is chosen     

Adaptive Equalization Techniques for HF Channels

Data transmission at rates of 1.2 kbits/s or higher through voiceband ionospheric channels is subject to impairment from severe linear distortion, fast channel time variations, and severe fading. In this paper, we have focused on the performance of DFE (decision feedback equalization) receivers for communication over 3 kHz bandwidth HF channels. We describe the results of simulations for a wide range of fading rates on simulated and real recorded HF channels, using fractionally spaced DFE receivers. Both LMS (least mean square) and FRLS (fast recursive least squares) adaptation algorithms with periodic restart were evaluated, and both ideal-reference and decision-directed operation was observed. The results indicate that FRLS adaptation yields superior performance to LMS in rapid fading conditions, but that this performance advantage diminishes at low signal-to-noise ratios. Also, fade rates greater than about 1 Hz produced relatively high error rates, irrespective of which adaptation method was employed. Finally, a novel modification of the simple LMS algorithm which improves its tracking ability was evaluated. This involved preceding the LMS DFE receiver with an adaptive lattice whitening filter.