Chip-Level MMSE Equalization for CDMA Downlink

1IntroductionNext generation standards support high data rate ser-vices,in which users are only assigned a smaller-orderspreading code . This leads to a necessity for the tech-niques that suppress Inter-Chip Interference (ICI) aswell as Multi-Access Interference ( MAI) . The tradi-tional RAKE receiver experiences difficulty because theorthogonality decays when signal transmits over multi-path frequency selective fading channels . The RAKEreceiver cannot overcome the serious MAI and I…     

Zero forcing and minimum mean-square-error equalization formultiuser detection in code-division multiple-access channels

In code-division multiple-access (CDMA) systems transmitting over time-varying multipath channels, both intersymbol interference (ISI) and multiple-access interference (MAI) arise. The conventional suboptimum receiver consisting of a bank of matched filters is often inefficient because interference is treated as noise. The optimum multiuser detector is too complex to be implemented at present. Four suboptimum detection techniques based on zero forcing (ZF) and minimum mean-square-error (MMSE) equalization with and without decision feedback (DF) are presented and compared. They combat both ISI and MAI. The computational complexity of all four equalizers is essentially the same. All four equalizers are independent of the size of the data symbol alphabet. It is shown that the performance of the MMSE equalizers is better than that of the corresponding ZF equalizers. Furthermore, the performance of the equalizers with DF is better than that of the corresponding equalizers without DF. The impairing effect of error propagation on the equalizers with DF is reduced by channel sorting     

Modified design of high-order 1-D all-pass recursive digital filters

An optimization method is proposed for the design of high-order all-pass delay equalizers for a prescribed group-delay characteristic by using the cascade form realization of digital filters. Unlike other methods, in the proposed method stability is guaranteed by imposing certain mild constraints on the filter coefficients so that the unconstrained optimization technique of Fletcher and Powell is used. To reduce the function minimization time, design values of the parameters of the delay equalizers, obtained by Bernhardt's simplified method, are used as the initial vector in the optimization technique of the proposed method. It is shown that the proposed method for the design of optimal delay equalizers results in all classes of equalizers with real and complex poles and approximates the prescribed group delay more accurately.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant A-7739.     

基于最低误码率准则的奇次三阶Volterra均衡器用于干扰抑制

该文针对通信系统中的干扰抑制问题,提出一种基于最低误码率准则的Volterra均衡器.区别于以往研究中采用最小均方误差准则估计Volterra核,本文采用最低误码率准则.仿真表明:对于扩展的二元相移键控信号,在相对强的窄带干扰下,匹配滤波器和基于最小均方误差准则的线性均衡器已失效,而基于最低误码率准则的Volterra均衡器仍能表现出良好的性能,也大大优于最小均方误差准则的Volterra均衡器;并且在计算复杂度与误码率性能的权衡中,奇次三阶Volterra均衡器更有实用价值.     

MLSE Equalizers for Frequency Discrimination Receiver of MSK Optical Transmission System

We propose maximum-likelihood sequence estimator (MLSE) equalizers based on either Viterbi algorithm or template matching temple matching (TM) for the equalization of impairments imposed on the minimum shift keying (MSK) modulation formats in long haul transmission without optical dispersion compensation. The TM-MLSE equalizer is proposed as a simplified alternative for the Viterbi-MLSE equalizer. It is verified that the Viterbi-MLSE equalizer can operate optimally when noise approaches a Gaussian distribution. Simulation results of the performances of the two MLSE equalizers for optical frequency discrimination receiver-based optical MSK systems are described. The transmission performance is evaluated in terms of: (1) the chromatic dispersion (CD) tolerance for both Viterbi-MLSE and TM-MLSE equalizers; (2) transmission distance limits of Viterbi-MLSE equalizers with various number of states; (3)the robustness to fiber polarization mode dispersion (PMD) of Viterbi-MLSE equalizers; and (4) performance improvements for Viterbi-MLSE equalizers when utilizing sampling schemes with two and four samples per bit over the conventional single sample per bit. With a small number of states (64 states), the non-compensating optical link can equivalently reach up to approximately 928 km SSMF for 10 Gb/s transmission or 58 km SSMF for 40 Gb/s. The performance of 16-state Viterbi-MLSE equalizers for optical frequency discrimination receiver (OFDR)-based optical MSK transmission systems for PMD mitigation is also numerically investigated. The performance of Viterbi-MLSE equalizers can be further improved by using the sampling schemes with multiple samples per bit compared to the conventional single sample bit. The equalizer also offers high robustness to fiber PMD impairment.     

The application of nonlinear structures to the reconstruction ofbinary signals

The problem of reconstructing digital signals which have been passed through a dispersive channel and corrupted with additive noise is discussed. The problems encountered by linear equalizers under adverse conditions on the signal-to-noise ratio and channel phase are described. By considering the equalization problem as a geometric classification problem the authors demonstrate how these difficulties can be overcome by utilizing nonlinear classifiers as channel equalizers. The manner in which neural networks can be utilized as adaptive channel equalizers is described, and simulation results which suggest that the neural network equalizers offer a performance which exceeds that of the linear structures, particularly in the high-noise environment, are presented     

Diversity–Multiplexing Tradeoff in ISI Channels

The optimal diversity–multiplexing tradeoff curve for the intersymbol interference (ISI) channel is computed and various equalizers are analyzed using this performance metric. Maximum-likelihood signal decoding (MLSD) and decision feedback equalization (DFE) equalizers achieve the optimal tradeoff without coding, but zero forcing (ZF) and minimum mean-square-error (MMSE) equalizers do not. However if each transmission block is ended with a period of silence lasting the coherence time of the channel, both ZF and MMSE equalizers become diversity-multiplexing optimal. This suggests that the bulk of the performance gain obtained by replacing linear decoders with computationally intensive ones such as orthogonal frequency-division multiplexing (OFDM) or Viterbi, can be realized in much simpler fashion—with a small modification to the transmit scheme.      

Analysis of predistortion, equalization, and ISI cancellationtechniques in digital radio systems with nonlinear transmit amplifiers

An analysis made of the performance of predistortion, equalization, and intersymbol interference (ISI) cancellation techniques in compensating for the transmit amplifier nonlinearity in digital microwave radio systems. The study is carried out using the 64 QAM and 256 QAM signal formats and two values of the roll-off factor in the Nyquist pulse shaping. The simulated compensation techniques include three types of predistortion, two ISI cancellers, and several nonlinear equalizers with or without decision feedback. A basic result is that decision-feedback equalizers do not offer any significant advantage over nonrecursive equalizers. It is also shown that ISI cancelers with a memoryless equalizer as first-stage decision device do not perform any better than nonlinear equalizers of similar complexity. Another contribution an improved fifth-order analog signal predistortion technique is analyzed. The gain that can be achieved using a modified 256 QAM signal constellation that is more robust to nonlinear distortion is quantified     

Deterministic approaches for blind equalization of time-varyingchannels with antenna arrays

In this paper, we study the blind equalization problem of time-varying (TV) systems where the channel variations are too rapid to be tracked with conventional adaptive equalizers. We show that using a finite Fourier basis expansion, a TV antenna array system can be cast into a time-invariant multi-input, multi-output (MIMO) framework. The multiple inputs are related through the bases, thereby allowing blind equalization to be accomplished without the use of higher order statistics. Two deterministic blind equalization approaches are presented: one determines the channels first and then the equalizers, whereas the other estimates the equalizers directly. Related issues such as order determination are addressed briefly. The proposed algorithms are illustrated using simulations     

Nonlinear Electrical Equalization for Different Modulation Formats With Optical Filtering

Based on bit-error-ratio simulations, we investigate electrical-dispersion-compensation performance by using a nonlinear electrical equalizer based on nonlinear Volterra theory for different modulation formats. This nonlinear equalizer is compared to conventional decision-feedback equalizer as well as to maximum-likelihood sequence estimation. Especially, we show that nonlinear equalizers, in conjunction with narrowband optical filtering of the light signal, result in improved performance. First of all, the system can benefit from the noise reduction due to narrowband filtering. Second, interacting with chromatic dispersion, nonlinear equalizers benefit from the improved dispersion tolerance through spectrum reshaping by narrowband optical filtering. Finally, nonlinear equalizers can efficiently mitigate the distortion resulting from strong optical filtering     

On fractionally spaced blind adaptive equalization under symboltiming offsets using Godard and related equalizers

The problem of fractionally spaced (FS) blind adaptive equalization under symbol-timing-phase offsets is considered. In the case of trained (nonblind) equalizers, the performance of FS equalizers is known to be independent of the timing-phase unlike that of baud-rate equalizers. Moreover, trained FS equalizers synthesize optimal filters in the minimum mean-square error sense, and hence are superior to baud-rate trained equalizers. It is an open question whether such properties hold true for FS Godard blind equalizers. We present a simulation example where such advantages do not materialize. We also present a solution based upon a parallel multimodel Godard baud-rate filter bank approach which yields a performance almost invariant w.r.t. symbol-timing-phase and superior to that of baud-rate equalizers     

Equalizers for multiple input/multiple output channels and PAMsystems with cyclostationary input sequences

The author studies minimum mean square error (MMSE) linear and decision feedback (DF) equalisers for multiple input/multiple output (MIMO) communication systems with intersymbol interference (ISI) and wide-sense stationary (WSS) inputs. To derive these equalizers, one works in the D-transform domain and uses prediction theory results. Partial-response MMSE equalizers are also found. As an application, the author considers a pulse amplitude modulation (PAM) communication system with ISI and cyclostationary inputs. The MMSE linear and DF equalizers are determined by studying an equivalent MIMO system. The resulting filters are expressed in compact matrix notation and are time-invariant, whereas the corresponding single input/single output filters are periodically time-invariant. The author also considers MMSE equalizers for a wide-sense stationary process by introducing a `random phase'. To aid in the performance evaluation of various equalizers, the author derives their mean square errors     

Digital Subscriber-Loop Performance Using Echo-Cancellation with WAL I and WAL II Coding

The performance of the echo-cancelling method of transmission using the WAL I and WAL II line codes is investigated for a loop model which is based on a statistical survey of the subscriber loopnetwork in New Zealand. Extensive simulation results are given for linear equalizers and decision-feedback equalizers operating at 144 kbit/s. It is found that, provided a good sampling phase can be assumed, simple DFE's and WAL I line code are generally adequate for a loop population penetration of over 95 percent.     

Convergence analysis of finite length blind adaptive equalizers

The paper presents some new analytical results on the convergence of two finite length blind adaptive channel equalizers, namely, the Godard equalizer and the Shalvi-Weinstein equalizer. First, a one-to-one correspondence in local minima is shown to exist between the Godard and Shalvi-Weinstein equalizers, hence establishing the equivalent relationship between the two algorithms. Convergence behaviors of finite length Godard and Shalvi-Weinstein equalizers are analyzed, and the potential stable equilibrium points are identified. The existence of undesirable stable equilibria for the finite length Shalvi-Weinstein equalizer is demonstrated through a simple example. It is proven that the points of convergence for both finite length equalizers depend on an initial kurtosis condition. It is also proven that when the length of equalizer is long enough and the initial equalizer setting satisfies the kurtosis condition, the equalizer will converge to a stable equilibrium near a desired global minimum. When the kurtosis condition is not satisfied, generally the equalizer will take longer to converge to a desired equilibrium given sufficiently many parameters and adequate initialization. The convergence analysis of the equalizers in PAM communication systems can be easily extended to the equalizers in QAM communication systems     

Non-uniformly spaced tapped-delay-line equalizers

A systematic way to design nonuniformly spaced tapped-delay-line (TDL) equalizers is described, and the performance of such equalizers is compared to that of uniformly spaced TDL equalizers with the same number of tap coefficients. It is shown that the signal-to-mean-squared-error ratio at the output of a TDL equalizer can be improved by optimally choosing the positions of the tap weights. An algorithm to find both the tap positions and the corresponding tap weights for a given delay span and a given minimum tap spacing of the equalizer is presented. Typical results are illustrated by using, as an example, the magnetic recording channel. For two target waveforms at different densities of recording, it is shown that there is a potential for saving up to seven equalizer taps     

盲均衡算法抵抗水声信道多途干扰的实验研究

介绍了盲均衡器对具有多途效应的BPSK相干水声通信数据均衡的实验结果。采用Matlab编程，获得了符合盲均衡要求的信源信号，通过在水池发射具有低频载波的信号，获得了具有多途水声信道特性的BPSK数据，经过解调、同步等处理后，检验了隐含和直接使用高阶统计量的盲均衡算法对实际多途水声信道的均衡效果，并与传统的自适应均衡算法进行了性能对比。结果表明，一种常数模判决反馈盲均衡算法，获得了与自适应算法很接近的性能。     

Capacity bound analysis for FIR Be/spl acute/zout equalizers in ISI MIMO channels

We provide a quantitative analysis for the capacity performance of zero-forcing equalizers, also known as Be/spl acute/zout equalizers, in a multiple antenna, frequency-selective fading environment with either parallel or sequential structure. The capacity upper bound of the equalizers, when there is no restriction on the filter length, is derived by directly extending the flat-fading results in a previous paper by the present authors. The parallel structure presents an inherent capacity loss quantified as a function of the channel couplings, which can be avoided by adopting an interference cancellation procedure in the sequential structure. For practical implementation, two approaches are investigated for finite impulse response (FIR) sequential equalizers-truncated LaBe/spl acute/st (Layered Be/spl acute/zout Space-Time) and perfect LaBe/spl acute/st equalizers. For truncated LaBe/spl acute/st equalizers, the percentage of achievable capacity is derived as a function of the filter length in analytical form, and the empirical optimum delay is also provided. For perfect LaBe/spl acute/st equalizers, we demonstrate that the filter choice that yields an optimum signal-to-noise ratio (SNR) can also asymptotically achieve the optimum infinite impulse response (IIR) capacity bound. Both of the two designs can approach the IIR capacity upper bound arbitrarily closely, provided there are an adequate number of FIR taps.     

Blind fractionally spaced equalization of noisy FIR channels:direct and adaptive solutions

Blind fractionally spaced equalizers reduce intersymbol interference using second-order statistics without the need for training sequences. Methods for finding FIR zero-forcing blind equalizers directly from the observations are described, and adaptive versions are developed. In contrast, most current methods require channel estimation as a first step to estimating the equalizer. The direct methods can be zero-forcing, minimum mean-square error, or even minimum mean square error (MMSE) within the class of zero-forcing equalizers. Performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels, including an empirically measured digital microwave channel     

复值的MBER非线性均衡器用于QAM信号

本文提出一种复值的最低误码率非线性滤波器用于非线性信道中QAM信号的均衡.推导了针对QAM信号的最低误码率准则训练算法的目标函数,并用Voherra序列来实现复值的非线性均衡器.为使非线性均衡器能在线自适应训练并增加训练算法的数值稳定性,提出～种滑窗随机梯度算法.大量仿真表明,对于非线性信道中QAM信号的均衡,最低误码率非线性均衡器的性能优于最小均方误差准则.     

On Mean-Square Decision Feedback Equalization and Timing Phase

We analyze the effect of timing phase on the performance of digital data receivers which employ decision feedback equalization. It has long been conjectured, and verified by computer simulations, that decision feedback equalizers are considerably less sensitive to the choice of timing phase than are conventional transversal linear equalizers. We develop the theoretical machinery which provides a rationale for these observations. It follows from our results that for typical operating conditions a 1-2 dB penalty can be incurred by choosing a bad timing phase in decision feedback, while the penalty can be an order of magnitude greater than this (in dB) in conventional linear equalizers.