Blind equalization for correlated input symbols: A Bussgang approach

This paper addresses the problem of blind equalization in the case of correlated input symbols, and it shows how the knowledge of the symbol sequence probability distribution can be directly incorporated in a Bussgang blind equalization scheme. Numerical results pertaining to both linear and nonlinear modulation schemes show that a significant improvement in equalization performance is obtained by exploiting the symbol sequence probability distribution using the approach herein described.     

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     

Blind equalization for broadband access

This article discusses the general principles of blind equalization and its use in emerging broadband access applications such as FTTC and xDSL. New results obtained for these applications are also presented     

Blind FSR-LPTV equalization and interference rejection

We address the problem of synthesizing blind channel identification and equalization methods for digital communications systems, aimed at counteracting the presence of cochannel or adjacent-channel interference. Owing to the presence of the interfering signal, the minimum mean-square error equalizer turns out to be linear periodically time-varying, which is implemented by resorting to its Fourier series representation. Moreover, by exploiting the cyclic conjugate second-order statistics of the channel output, we propose a new weighted subspace-based channel identification method, which is asymptotically immune to the presence of high-level interference. Computer simulation results confirm the effectiveness of the proposed identification/equalization technique.     

Blind equalization using least-squares lattice prediction

Second-order statistics of the received signal can be used to equalize a communication channel without knowledge of the transmitted sequence. Blind zero-forcing (ZF) and minimum mean-square error (MMSE) equalization can be achieved with linear prediction error filtering. The equivalence with the equalizers derived by Giannakis and Halford (see ibid., vol.45, p.2277-92, 1997) is shown, and adaptive predictors that result in a lattice filtering structure are applied. The required channel coefficient vector is obtained with adaptive eigen-pair tracking. Either forward or backward prediction errors can be used. The performance of the blind equalizer is examined by simulations. The MMSE of the optimum FSE is approached, and the algorithm exhibits robustness to channels with common subchannel zeros     

Blind equalization using a tricepstrum-based algorithm

An adaptive blind equalization method is introduced for nonminimum phase communication channels. The method estimates the inverse channel impulse response, by using the complex cepstrum of the fourth-order cumulants (tricepstrum) of the synchronously sampled received signal. As such, the proposed adaptive method depends only on the statistics of the received sequence, and is capable of reconstructing separately both the minimum and maximum phase response of the channel. It is demonstrated, by means of extensive simulations, that the proposed tricepstrum-based equalization scheme performs well and outperforms other existing blind equalizers, at the expense of higher computational complexity     

Blind equalization of nonlinear channels from second-orderstatistics

This paper addresses the blind equalization problem for single-input multiple-output nonlinear channels, based on the second-order statistics (SOS) of the received signal. We consider the class of "linear in the parameters" channels, which can be seen as multiple-input systems in which the additional inputs are nonlinear functions of the signal of interest. These models include (but are not limited to) polynomial approximations of nonlinear systems. Although any SOS-based method can only identify the channel to within a mixing matrix (at best), sufficient conditions are given to ensure that the ambiguity is at a level that still allows for the computation of linear FIR equalizers from the received signal SOS, should such equalizers exist. These conditions involve only statistical characteristics of the input signal and the channel nonlinearities and can therefore be checked a priori. Based on these conditions, blind algorithms are developed for the computation of the linear equalizers. Simulation results show that these algorithms compare favorably with previous deterministic methods     

基于有色信源MIMO-FIR信道的盲均衡准则

针对有色信源具有的统计特性,分析了该类信源的二阶与四阶相关统计量在时间和空间上所呈现的规律,提出了一种在对信源要求比较弱的条件下MIMO-FIR信道的新盲均衡准则,并构建了基于该准则的盲均衡算法。通过计算机仿真验证了提出算法的有效性。     

Redundant filterbank precoders and equalizers. II. Blind channelestimation, synchronization, and direct equalization

For pt.I see ibid., vol.47, no.7, p.1988-2006 (1999). Transmitter redundancy introduced using finite impulse response (FIR) filterbank precoders offers a unifying framework for single- and multiuser transmissions. With minimal rate reduction, FIR filterbank transmitters with trailing zeros allow for perfect (in the absence of noise) equalization of FIR channels with FIR zero-forcing equalizer filterbanks, irrespective of the input color and the channel zero locations. Exploiting this simple form of redundancy, blind channel estimators, block synchronizers, and direct self-recovering equalizing filterbanks are derived in this paper. The resulting algorithms are computationally simple, require small data sizes, can be implemented online, and remain consistent (after appropriate modifications), even at low SNR colored noise. Simulations illustrate applications to blind equalization of downlink CDMA transmissions, multicarrier modulations through channels with deep fades, and superior performance relative to CMA and existing output diversity techniques relying on multiple antennas and fractional sampling     

Blind constant modulus equalization via convex optimization

In this paper, we formulate the problem of blind equalization of constant modulus (CM) signals as a convex optimization problem. The convex formulation is obtained by performing an algebraic transformation on the direct formulation of the CM equalization problem. Using this transformation, the original nonconvex CM equalization formulation is turned into a convex semidefinite program (SDP) that can be efficiently solved using interior point methods. Our SDP formulation is applicable to baud spaced equalization as well as fractionally spaced equalization. Performance analysis shows that the expected distance between the equalizer obtained by the SDP approach and the optimal equalizer in the noise-free case converges to zero exponentially as the signal-to-noise ratio (SNR) increases. In addition, simulations suggest that our method performs better than standard methods while requiring significantly fewer data samples.     

Blind channel identification and equalization withmodulation-induced cyclostationarity

Recent results have pointed out the importance of inducing cyclostationarity at the transmitter for blind identification and equalization of communication channels. This paper addresses blind channel identification and equalization relying on the modulation-induced cyclostationarity, without introducing redundancy at the transmitter. It is shown that single-input single-output channels can be identified uniquely from output second-order cyclic statistics, irrespective of the location of channel zeros, color of additive stationary noise, or channel order overestimation errors, provided that the period of modulation-induced cyclostationarity is greater than half the channel length. Linear, closed-form, nonlinear correlation matching, and subspace-based approaches are developed for channel estimation and are tested using simulations. Necessary and sufficient blind channel identifiability conditions are presented. A Wiener cyclic equalizer is also proposed     

Blind decision feedback equalization for terrestrial televisionreceivers

In December 1996 the Federal Communications Commission (FCC) adopted the Grand Alliance (GA) system as the digital television broadcasting standard for the United States ending a seven-year-long search for a fully digital television standard. MPEG-2 was chosen as the video compression standard, and trellis-coded 8-vestigial sideband (VSB) with a training sequence was chosen as the transmission standard. The laboratory tests that were performed on the final two competing systems, 8-VSB with training sequence and 32-quadrature amplitude modulation (QAM) with blind equalization, showed a need for blind equalization in dynamic channels that could not be adequately handled by an equalizer training on the training sequence alone. Hence, the final GA system recommended the use of blind equalization in the receiver. In this paper, we describe the U.S. digital television transmission standard as it pertains to the equalization problem, typical transmission channel characteristics and the need for blind equalization in terrestrial television receivers     

Blind equalization algorithms for dual-mode CAP-QAM reception

We propose a dual-mode receiver capable of blindly demodulating both carrierless amplitude modulation/phase modulation (CAP) and quadrature amplitude modulation (QAM) line codes. Our work is motivated by some emerging broad-band access standards which require a receiver that can first blindly start up, then blindly distinguish between CAP and QAM, and finally decode the signal. The “brute force” solution to this problem would be to implement CAP and QAM receivers in parallel. However, we propose a single novel receiver based on a single equalizer that accommodates both line codes, yielding significant computational savings. We describe the receiver architecture, blind start-up methods, and line code identification algorithms, as well as computer simulations and a laboratory experiment to verify the theoretical receiver behavior     

基于BP神经网络的盲均衡

针对基于以往前馈神经网络（BP模型）的盲均衡算法中CMA中代价函数收敛速度慢,函数仿真曲线振荡明显,信号恢复出来的误码率相对较高,本文提出了利用一个新的代价函数并在此基础上利用以往权值的调节值来调节当前的权值,从而降低了算法对局部极值点的敏感性。运用MATLAB工具对新的算法性能进行了仿真,仿真结果表明,该算法在一定程度上加快了代价函数的收敛速度,函数的仿真曲线振荡缓慢趋于平坦,在信号的恢复性能上降低了信号的剩余误差与误码率。     

Blind channel equalization using chirp modulating signals

This paper addresses the problem of blind channel equalization in the context of digital communications. Recent results have shown that certain operations applied to the source signal at the transmitter help in the blind identification and equalization of the channel at the receiver. In this paper, the baseband data signal is multiplied with a chirp sequence. Exploiting certain structural properties arising from this operation, a batch-type algorithm is obtained for calculating the equalizer's coefficients. Conditions on the chirp sequence parameters are obtained that guarantee an equalization solution. A low-complexity adaptive algorithm is also proposed. Finally, extensive simulations, and comparisons with other well-known blind techniques, illustrate the excellent performance of this algorithm.     

Blind equalization for short burst wireless communications

In this paper, we propose a dual mode blind equalizer based on the constant modulus algorithm (CMA). The blind equalizer is devised for short burst transmission formats used in many current wireless TDMA systems as well as future wireless packet data systems. Blind equalization is useful for such short burst formats, since the overhead associated with training can be significant when only a small number of bits are transmitted at a time. The proposed equalizer overcomes the common problems associated with classic blind algorithms, i.e., slow convergence and ill-convergence, which are detrimental to applying blind equalization to short burst formats. Thus, it can eliminate the overhead associated with training sequences. Also, the blind equalizer is extended to a two branch diversity combining blind equalizer. A new initialization for fractionally spaced CMA equalizers is introduced. This greatly improves the symbol timing recovery performance of fractionally spaced CMA equalizers with or without diversity, when applied to short bursts. Through simulations with quasi-static or time-varying frequency selective wireless channels, the performance of the proposed equalizer is compared to selection diversity and conventional equalizers with training sequences. The results indicate that its performance is far superior to that of selection diversity alone and comparable to the performance of equalizers with short training sequences. Thus, training overhead can be removed with no performance degradation for fast time-varying channels, and with slight performance degradation for static channels     

Blind equalization in antenna array CDMA systems

Multipath induced interchip-interference (ICI) alters waveforms of transmitted signals and presents a major obstacle to direct-sequence (DS) code-division-multiple-access (CDMA) communications. For systems with aperiodic pseudorandom (PN) spreading sequences, the primary way to counter fading is through employing RAKE receivers that enhance the signal-to-interference ratio (SIR) by combining multipath signals from the desired user. In this paper, we formulate a discrete-time model for antenna array CDMA systems and study the 2-D RAKE receiver problem by casting it into an optimum vector FIR equalizer design and estimation framework. A novel aspect of the present work is the full exploitation of the potential of 2-D RAKE receivers without requiring any detailed knowledge of the multipath channels     

Blind detection of equalization errors in communication systems

In adaptive channel equalization, transmitted symbol estimates at the equalizer output may be in error because of excessive channel noise, convergence of the equalizer to a “closed-eye” local minimum, or error propagation if the equalizer has a decision feedback structure. This paper is concerned with the detection of equalization errors (i.e., errors in transmitted symbol estimates) in a blindfolded manner whereby no direct access to the channel input is required. The detection problem is cast into a binary hypothesis testing framework. Assuming a linear communication channel that is time-invariant during the test interval, a relationship between the presence of equalization errors and time variations in the underlying linear model taking the transmitted symbol estimates to the equalizer input is established. Based on this relationship, a uniformly most powerful test is constructed to detect the presence of equalization errors in finite-length observations. Finite sample size and asymptotic detection performance of the test is studied. A method for estimating the equalization delay without direct access to the channel input is developed. The effectiveness of the test is illustrated by way of computer simulations     

Blind zero forcing equalization of multichannel nonlinear CDMAsystems

Code division multiple access (CDMA) has emerged as a popular format for wireless communication systems. As a result of intersymbol interference (ISI) and nonlinearities, the performance of CDMA systems can suffer. In this paper, we propose a blind equalizer for CDMA systems with Volterra (nonlinear) channels. The equalizer requires multiple observations at the receiver, which are obtained through oversampling or an antenna array, and a knowledge of the code of the desired user. Zero forcing equalization is possible in the noise-free case. Simulations demonstrate the performance of the equalizer under a variety of operating conditions     

联合多脉冲检测的PSWF正交调制信号盲自适应均衡

卫星通信信道的复杂时变特性,使基于椭圆球面波函数(Prolate Spheroidal Wave Function,PSWF)的正交调制信号脉冲组的正交性受到破坏,已有均衡方法未能充分利用多脉冲干扰中的有用信息,效果有限。针对该问题,结合信道均衡与多脉冲检测各自的优势,提出一种联合多脉冲检测的PSWF时域正交调制信号自适应均衡方法,利用多脉冲检测消除脉冲间干扰的能力,降低均衡模块的阶数及算法难度;同时,利用均衡模块对信道的部分补偿作用,为多脉冲检测改善信道环境。在相同信道条件下,所提方法获得同等量级误比特率所需信噪比较自适应判决反馈均衡算法降低约2 dB。