MAP selection-diversity DFE for indoor wireless data communications

Indoor high-speed wireless data networks encounter signal fading and delay-spread multipath propagation. Hence, the realization of low error rate transmission requires measures to combat the performance degradation due to both signal fading and intersymbol interference (ISI). Receiver diversity has been known to be an efficient way of coping with the former problem, while adaptive equalization could be used to mitigate the effects of the latter. Incorporation of receiver diversity with adaptive equalization is therefore desirable. We propose a novel selection-diversity approach with an adaptive decision-feedback equalizer (DFE). In this method, selection is done on a symbol-by-symbol basis such that the output of the branch with the lowest estimated a posteriori probability of error is used as the final decision. This final (and hence more reliable) decision is used to adapt the DFE for all diversity branches. It is shown in this paper that the proposed selection rule is optimal for selection-diversity in the maximum a posteriori probability (MAP) sense. A very simple selection metric can be derived from this selection rule and practical ways of computing the selection metric are also presented. Simulation results show that the proposed method is very efficient. It is capable of achieving almost the same performance as an optimal [least squares (LS)], but computationally intensive, combining diversity approach. Furthermore, at an average bit error rate (BER) of 10^-4, a gain of approximately 1.25 dB can be achieved over a previously proposed selection-diversity equalization approach     

Digital Transmission Performance on Fading Dispersive Diversity Channels

The reception and detection of a single digit under known channel conditions are investigated. The probability of error for an optimum one-shot receiver instantaneously matched to the channel state is averaged over an ensemble of dispersive diversity channels. The average probability of error as a function of energy to noise ratio is found to be solely dependent on the ratio of rms dispersion width to data symbol width. For these dispersive channels an implicit diversity effect is qualitatively explained in terms of eigenvalues that depend on the ensemble statistic. The one-shot receiver performance provides a bound for practical receivers. In a comparison with a decision feedback equalizer, it is shown that on moderately dispersive channels the equalizer nearly achieves optimum one-shot performance. Since an adaptive version of this equalizer exists, this means data transmission on slowly fading channels is possible at rates above the natural rate suggested by the channel dispersion spread without bandwidth expansion and with small intersymbol interference penalty. The use of one-shot receiver performance curves can also be used as estimates of equalizer performance in situations where computation of the latter is impractical.     

An upper bound on the error probability in decision-feedback equalization

An upper bound on the error probability of a decision-feedback equalizer which takes into account the effect of error propagation is derived. The bound, which assumes independent data symbols and noise samples, is readily evaluated numerically for arbitrary tap gains and is valid for multilevel and nonequally likely data. One specific result for equally likely binary symbols is that if the worst case intersymbol interference when the firstJfeedback taps are Set to zero is less than the original signal voltage, then the error probability is multiplied by at most a factor of2^Jrelative to the error probability in the absence of decision errors at highS/Nratios. Numerical results are given for the special case of exponentially decreasing tap gains. These results demonstrate that the decision-feedback equalizer has a lower error probability than the linear zero-forcing equalizer when there is both a highS/Nratio and a fast roll-off of the feedback tap gains.     

Turbo equalization via constrained-delay APP estimation with decision feedback

We consider turbo equalization for intersymbol interference (ISI) channels, wherein soft symbol decisions generated by the channel detector are iteratively exchanged with the outer error-correction decoder based on the turbo principle. Our work is based on low-complexity suboptimal soft-output channel detection using a constrained-delay (CD) a posteriori probability (APP) algorithm. Central to the proposed idea is the incorporation of effective decision-feedback schemes, which significantly reduce complexity while providing immunity against error propagation that typically plagues decision-feedback schemes. We observe that the effect of decision feedback is quite different on turbo equalization versus traditional, hard-decision-generating and noniterative equalization. In particular, we demonstrate that when the feedback scheme applied is inadequate for the given equalizer parameters and ISI condition, the extrinsic information generated by the equalizer becomes distinctly non-Gaussian, and the quality of soft information, as monitored by the trajectory of mutual information, fails to improve in the iterative process. We identify parameters of feedback-based CD-APP schemes that offer favorable complexity/performance tradeoffs, compared with existing turbo-equalization techniques.     

Comparison of precoding schemes for digital subscriber lines

Precoding at the transmitter side is a practicable method for transmission over intersymbol interference channels. In contrast to decision-feedback equalization no error propagation occurs and coded modulation can be applied as for the intersymbol interference free channel. Tomlinson-Harashima (1971, 1972) precoding and flexible precoding are analyzed and compared. The dualities and differences are discussed. The focus of interest is the application of precoding to fast digital transmission over twisted pair lines, such as high-rate or asymmetric digital subscriber lines. It turns out that flexibility-which is not necessary in the specific application, digital subscriber lines-of flexible precoding is paid with a performance loss compared to Tomlinson-Harashima precoding     

Theoretical and Measured Performance of a DFE Modem on a Fading Multipath Channel

A decision-feedback equalizer (DFE) is the basis of a recent development of a quadruple diversity troposcatter modem which can operate up to a data rate of 12.6 Mbit/s in a 99% bandwidth of 15 MHz. In this paper a theoretical approach is developed for the calculation of average bit error rate (ABER), including the effects of intersymbol interference due to multipath and the finiteness of the transversal filters used to realize the DFE. By omitting the intersymbol interference effect, the calculation provides a lower bound which can be used to assess the intersymbol interference penalty for a particular DFE structure. The paper includes calculations of a DFE configuration which has a three tap forward filter with tap spacing equal to one-half a symbol interval. Measured performance results from fading channel simulator tests of a three tap forward filter DFE are presented for data rates from 1.5 to 12.6 Mbit/s and for a wide range of multipath statistical conditions. The results for this DFE configuration show (1) excellent agreement between calculated and measured ABER, (2) a small intersymbol interference penalty when the 2σ multipath spread is less than approximnately one-half the data symbol interval, and (3) successful operation at values of multipath spread up to twice the data symbol interval. In a sequel to this paper, the results of a field test of the DFE modem are presented. These live links test results are consistent with both the calculated and simulator measured data presented here.     

Analytical Study on the Effect of Cochannel Interference on Partially Coherent Diversity Systems

In this paper, we study the effect of cochannel interference (CCI) on the performance of partially coherent BPSK and QPSK in uncorrelated L-branch equal-gain combining systems. We consider a generalized propagation model wherein the desired and interfering signals undergo Nakagami-m or Rician fading with different amounts of fading severity. Further, the interfering signals are assumed to be asynchronous symbol timing with the desired signal, so that the effect of cross-signal intersymbol interference (ISI) is taken into account. Using a convergent Fourier series method, we derive extensive analytical results for the average bit error probability and the SNR gain penalty caused by the interference signals for different signal to-interference ratio levels. The numerical results presented in this paper demonstrate the system performance under very realistic propagation and detection conditions including CCI, carrier phase error recovery, cross-signal ISI, generalized fading channels, and AWGN. Hence our results are expected to be of significant practical use for such scenarios.     

时域自适应均衡技术的分析与应用

概述了频率选择性衰落信道的传输特性,论述了采用均衡技术的必要性。通过对各种均衡器结构和自适应均衡算法在抵抗符号间干扰能力、收敛速度以及运算复杂度等方面的分析与比较,选择了判决反馈作为均衡器结构、最小均方自适应算法作为自适应准则的均衡器方案。仿真及试验结果证实了设计的时域自适应均衡器不仅具有较强的抵抗符号间干扰能力,而且能够获得隐分集增益,在频率选择性衰落信道中具有良好的应用效果。     

MMSE Equalization of Interference on Fading Diversity Channels

Adaptive equalization is used in digital transmission systems with parallel fading channels. The equalization combines the diversity channels and reduces intersymbol interference due to multipath returns. When interference is present and correlated from channel to channel, the equalizer can also reduce its effect on the quality of information transfer, important applications for interference cancellation occur in diversity troposcatter systems in the presence of jamming, diversity high frequency (HF) systems which must cope with interfering skywaves, and space diversity line-of-sight (LOS) radio systems where adjacent channel interference is a problem. In this paper we develop the general formulation for minimum mean square error (MMSE) equalization of interference in digital transmission diversity systems. The problem formulation includes the use of available receiver decisions to assist in MMSE processing. The effects of intersymhol interference are included in the analysis through a critical approximation which assumes sufficient processor capability to reduce ISI effects to levels small enough for satisfactory communication. The analysis also develops he concept of additional implicit or intrinsic diversity which results from channel multipath dispersion. It shows how the MMSE processor sacrifices diversity to suppress interference even when the interference arrives in the main beams of the receiver antenna patterns. The condition of near synchronous same-path interference is also addressed. Because the spatial angle of arrival of the interference may result in delay differences between interference signals in different antenna channels, interference delay compensation may be required. We show that this effect is compensated for with a small number of appropriately spaced equalizer taps.     

A reduced-complexity algorithm for combined equalization and decoding

This paper presents a new application of a suboptimal trellis decoding algorithm for combined equalization and decoding. The proposed algorithm can outperform the reduced-state sequence estimator (RSSE) of the same order of complexity. The algorithm, termed estimated future decision-feedback algorithm (EFDFA), was originally proposed for the problem of noncoherent decoding with multiple-symbol overlapped observations and is now reformulated for the problem of intersymbol interference inflicted channels. The EFDFA uses the RSSE as a building block. The performance improvement is achieved by using estimated future symbols in the decision process. The estimated future symbols are obtained by RSSE decoding time-reversed blocks of the input. The same technique can be used to greatly enhance the performance of the conventional decision-feedback equalizer. An analysis of the performance of the EFDFA based on the performance of the RSSE is described. The EFDFA can be configured as an adaptive equalizer capable of operating in a time-varying environment, and is shown to perform well in fading conditions. With only minor additional complexity, the EFDFA is also capable of producing soft outputs.     

Adaptive noncoherent DFE for MDPSK signals transmitted over ISIchannels

A novel noncoherent decision-feedback equalization (NDFE) scheme for M-ary differential phase shift-keying signals transmitted over intersymbol interference channels is presented. A suboptimum version with lower computational complexity and a noncoherent linear equalizer (NLE) are derived from the original NDFE scheme. Furthermore, the relation of the novel NLE to a previously proposed NLE is investigated. In contrast to known NDFE schemes, the novel scheme can approach the performance of coherent minimum mean-squared error decision-feedback equalization. For adaptation of the feedforward and feedback filters, efficient novel modified least mean-square and recursive least squares algorithms are presented. Finally, it is shown that the proposed adaptive NDFE scheme is robust against frequency offset     

Linear Minimum Mean-Square Error Estimators Applied to Channel Equalization

This concise paper investigates various aspects of the application of unbiased linear minimum mean-square error (ULMMSE) estimators to the equalization of channels used for digital data transmission. One application is to the equalization of the channel to a response free from intersymbol interference. Previous results regarding this application are clarified and extended. The other application is to the equalization of the channel to a finite short memory response. This stems from an interest in reducing the complexity of the Viterbi algorithm. Various new results on the optimum ULMMSE equalizer and its performance are presented. In both applications, the optimum ULMMSE equalizer is a stable, realizable, finite dimensional recursive filter.     

Turbo Equalization with Prediction and Iterative Estimation of Time-Varying Frequency-Selective Channels

Turbo equalization that cooperates with channel prediction and iterative channel estimation is investigated for mobile wireless communications. Frames of information bits are encoded, interleaved, and mapped to symbols for transmission over time-varying frequency-selective fading channels. At the receiver, the Turbo equalizer consists of a maximum a posteriori probability equalizer/demapper and a soft-input soft-output maximum a posteriori probability decoder. With initial channel estimates and sparse pilot insertion across a number of frames, the receiver predicts the channel of the current frame. The effect of error propagation of channel prediction is mitigated by the de-interleaver that is embedded in the Turbo equalizer. The predicted and interpolated channel is refined through a channel estimator that uses the soft estimates of data symbols at each Turbo iteration. Due to the bandlimiting feature of channel variation, the channel estimation error can be smoothed by low-pass filters that follow the channel estimator. Simulation results show that incorporating Turbo equalization with channel prediction and iterative channel estimation can combat time- and frequency-selective fading and improve reception performance.     

Phase precoding for frequency-selective Rayleigh and Rician slowlyfading channels

This paper presents a novel phase precoding (pre-equalization) technique to equalize frequency-selective Rayleigh and Rician slowly fading channels for personal communication systems using phase modulation. In order to achieve intersymbol interference (ISI)-free transmission, the precoding technique pre-distorts the signal transmitted from a base station to a portable unit. The novelty of the technique lies in using a spiral curve design: (1) to ensure the stability of the precoder even in equalizing a non-minimum-phase channel; (2) to obtain an ISI-free received signal; and (3) to keep a constant transmitted signal amplitude. Using the precoder can improve the bit-error-rate (BER) transmission performance without increasing the complexity of the portable unit receiver. The BER performance of coherent quadrature phase-shift-keying (QPSK) with the channel pre-equalization is analyzed theoretically for both Rayleigh and Rician fading channels. Analytical and simulation results demonstrate that coherent QPSK using the proposed channel precoder has a significantly lower BER than that using a conventional decision-feedback equalizer (DFE) because the precoder does not suffer from error propagation     

Nonlinear equalization of multipath fading channels withnoncoherent demodulation

A nonlinear decision-based adaptive equalizer compatible with differentially coherent phase shift keying (PSK) is proposed for frequency-selective fading channels. This equalization scheme is appropriate whenever conventional equalizers are not capable of tracking phase variations in selective fading channels. The received signal is first converted to a baseband signal and then sent through a differential detector. A nonlinear processor before the equalizer generates the needed nonlinear terms that are weighted and summed in the equalizer. Nonlinear intersymbol interference at the output of the differential detector is dealt with by minimizing an error signal between the output of the equalizer and the detected data. The adaptation algorithm can be any algorithm currently used for conventional equalizers. Our simulation results confirm that for channels with spectral nulls, equalization is achieved successfully with the proposed scheme, whereas, linear equalizers, either with coherent or noncoherent detection, fail     

Wide-band digital subscriber access with multidimensional blockmodulation and decision-feedback equalization

The author investigates the potential transmission performance of pair-wire subscriber lines at the higher rate of 800 kb/s, with particular reference to digital subscriber line transmission for ISDN (integrated services digital network) basic access. Block modulation schemes of 1-4 dimensions, at a rate of 2 bits per dimension, are considered. Time-division multiplexing is used to combine the multiple dimensions for transmission over a single-waveform channel, namely, the subscriber line. The channel noise is assumed to be additive and dominated by near-end crosstalk. MMSE (minimum mean-squared error) decision-feedback equalization is used to deal with the noise and the intersymbol interference. Using the theory developed, the potential performance of some simple lines is calculated. The coding gain of a multidimensional modulation scheme is found to be fully preserved after transmission if the equalizer is infinite in length. However, the gain realized can be much lower, or none at all, if the equalizer is only moderate in length. This latter phenomenon is due to the fact that the noise at the decision point is coloured, due to the inability of the equalizer to whiten it sufficiently     

Modulation diversity for frequency-selective fading channels

In this article, modulation diversity (MD) for frequency-selective fading channels is proposed. The achievable performance with MD is analyzed and a simple design criterion for MD codes for Rayleigh-fading channels is deduced from an upper bound on the pairwise error probability (PEP) for single-symbol transmission. This design rule is similar to the well-known design rule for MD codes for flat fading and does not depend on the power-delay profile of the fading channel. Several examples for MD codes with prescribed properties are given and compared. Besides the computationally costly optimum receiver, efficient low-complexity linear equalization (LE) and decision-feedback equalization (DFE) schemes for MD codes are also introduced. Simulations for the widely accepted COST fading models show that performance gains of several decibels can be achieved by MD combined with LE or DFE at bit-error rates (BERs) of practical interest. In addition, MD also enables the suppression of cochannel interference.     

Valuation of the effects of intersymbol interference indecision-feedback equalizers

For channels which suffer predominantly from additive noise and intersymbol interference, the decision-feedback equalizer has provided a relatively simple solution for reducing the effects of interfering symbols at the input to the decision device. A technique is developed that enables fast, accurate calculation of the error performance of decision-feedback equalization for a number of channel models. The method is to calculate the n-step transition probability for an associated Markov process and then use this transition probability as an approximation to the stationary probability distribution. For systems with finite memory, it is proved that the method converges. If the signal-to-noise ratio (SNR) is high and the signal amplitude is more than twice the worst-case interference, it is shown that the convergence is rapid. Numerical results indicate that the convergence is rapid enough to make this an efficient method of calculation, even for channels for which the interference does not fully satisfy this condition. Two examples are given here, but the technique has been tested on most of the examples that have been presented in the literature. The method yields results in closer agreement with simulation results than previous results obtained using bounding techniques, especially at low to moderate SNRs, and requires less computation     

Performance evaluation of experimental 50-Mb/s diffuse infraredwireless link using on-off keying with decision-feedback equalization

We report an experimental nondirected optical link for short-range, indoor data transmission at 50 Mb/s. The system uses on-off keying (OOK) and achieves low bit-error rates (BERs) in the presence of intersymbol interference, background light noise, and shadowing, with a range of 2.9 m in a skylit room. The transmitter produces an eye-safe Lambertian pattern at 806 nm with an average power of 474 mW. The receiver utilizes a hemispherical concentrator with a hemispherical bandpass optical filter, a 1-cm² silicon p-i-n photodiode, and a high-impedance hybrid preamplifier to achieve a high signal-to-noise ratio (SNR). A high-pass filter is used to mitigate fluorescent light noise, with quantized feedback removing the resulting baseline wander. A decision-feedback equalizer provides resistance to intersymbol interference due to multipath. The system and its components are characterized, and compared to theory. We observe that decision-feedback equalization yields a reduction of multipath power penalties that is in good agreement with theory     

An information-theoretic framework for deriving canonical decision-feedback receivers in Gaussian channels

A framework is presented that allows a number of known results relating feedback equalization, linear prediction, and mutual information to be easily understood. A lossless, additive decomposition of mutual information in a general class of Gaussian channels is introduced and shown to produce an information-preserving canonical decision-feedback receiver. The approach is applied to intersymbol interference (ISI) channels to derive the well-known minimum mean-square error (MMSE) decision-feedback equalizer (DFE). When applied to the synchronous code-division multiple-access (CDMA) channel, the result is the MMSE (or signal-to-interference ratio (SIR) maximizing) decision-feedback detector, which is shown to achieve the channel sum-capacity at the vertices of the capacity region. Finally, in the case of the asynchronous CDMA channel we are able to give new connections between information theory, decision-feedback receivers, and structured factorizations of multivariate spectra.