Robust Interference Management via Linear Precoding and Linear/Non-Linear Equalization

This work studies the robust design of linear precoding and linear/ non-linear equalization for multi-cell MIMO systems in the presence of imperfect channel state information (CSI). A worst-case design approach is adopted whereby the CSI error is assumed to lie within spherical sets of known radius. First, the optimal robust design of linear precoders is tackled for a MIMO interference broadcast channel (MIMO-IBC) with general unicast/multicast messages in each cell and operating over multiple time-frequency resources. This problem is formulated as the maximization of the worst-case sum-rate assuming optimal detection at the mobile stations (MSs). Then, symbol-by-symbol non-linear equalization at the MSs is considered. In this case, the problem of jointly optimizing linear precoding and decision-feedback (DF) equalization is investigated for a MIMO interference channel (MIMO-IC) with the goal of minimizing the worst-case sum-mean squared error (MSE). Both problems are addressed by proposing iterative algorithms with descent properties. The algorithms are also shown to be implementable in a distributed fashion on processors that have only local and partial CSI by means of the Alternating Direction Method of Multipliers (ADMM). From numerical results, it is shown that the proposed robust solutions significantly improve over conventional non-robust schemes in terms of sum-rate or symbol error rate. Moreover, it is seen that the proposed joint design of linear precoding and DF equalization outperforms existing separate solutions.     

Noncoherent space-time equalization

In this paper, noncoherent equalization is combined with multiple receive antennas. The resulting noncoherent space-time equalization (NSTE) schemes are analyzed and compared with the corresponding coherent receivers. In particular, noncoherent linear equalization (NLE), noncoherent decision-feedback equalization (NDFE), and noncoherent sequence estimation (NSE) are considered. For NLE and NDFE novel approximations for the signal-to-distortion ratio (SDR) are derived and verified by simulations. It is shown that NSTE can suppress interfering users and exploit diversity as efficiently as coherent STE. However, NSTE is more robust against channel phase variations than the combination of coherent STE and synchronization. Robust noncoherent recursive least squares (NC-RLS) algorithms, which compare favorably with the conventional RLS algorithm with additional carrier synchronization loop, are proposed for fast filter adaptation.     

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     

Equalization algorithms in the frequency domain for continuous phase modulations

In this paper, novel equalization algorithms for continuous phase modulations (CPMs) are illustrated. Both conventional (linear and decision-feedback) and turbo equalization techniques are derived using the Laurent decomposition of CPM signals. All of them operate in the frequency domain and process two samples of the received signal per channel symbol. Numerical results show that on one hand, conventional equalization strategies offer good performance for binary partial response signaling over severely frequency-selective wireless channels at a moderate complexity. On the other hand, there is evidence that turbo techniques provide a small energy saving at the price of a substantial computational burden.     

频选快衰落信道的Turbo均衡算法

针对频选快衰落信道,本文提出卡尔曼滤波信道跟踪、软输出判决反馈均衡及软输入软输出信道解码迭代处理的Turbo均衡算法以充分利用已获得的信息,实现信道估计、信道均衡与信道解码的迭代更新,并克服传统判决反馈均衡器误差传播的缺陷.仿真表明,本算法能有效地跟踪快衰落信道,经两次迭代就可获得较为满意的码间干扰消除效果.     

Detection of coded modulation signals on linear, severely distortedchannels using decision-feedback noise prediction with interleaving

On linear bandlimited Gaussian noise channels with sufficiently high SNR, channel capacity can be approached by combining powerful coded modulation schemes designed for Nyquist channels with the equalization power of decision-feedback equalization (DFE). However, this combination may not be realized in a straightforward manner, since, in general, DFE requires delay-free decisions for feedback, and in a coded system such decisions are not sufficiently reliable. A technique is proposed that combines periodic interleaving with noise-predictive DFE, so that delayed reliable decisions can be used for feedback. When sufficient delay in the interleavers can be tolerated, this technique can attain the DFE performance. On severely distorted channels, modest delays can be sufficient to obtain respectable gains over linear equalization     

频选衰落MIMO信道的Turbo均衡

针对Turbo编码频选慢衰落MIMO信道,提出基于滑窗式概率数据辅助(Probabilistic Data Association)的软输出判决反馈均衡和软输入软输出Turbo信道解码器间迭代处理的Turbo均衡算法。充分利用已获得的信息,实现信道均衡与信道解码的迭代更新,克服传统判决反馈均衡器误差传播的缺陷。仿真表明,该系统经3次迭代就可获得较为满意的符号间干扰消除效果。     

Kalman Filter-Trained Recurrent Neural Equalizers for Time-Varying Channels

Recurrent neural networks have been successfully applied to communications channel equalization because of their modeling capability for nonlinear dynamic systems. Major problems of gradient-descent learning techniques commonly employed to train recurrent neural networks are slow convergence rates and long training sequences required for satisfactory performance. This paper presents decision-feedback equalizers using a recurrent neural network trained with Kalman-filtering algorithms. The main features of the proposed recurrent neural equalizers, using the extended Kalman filter and the unscented Kalman filter, are fast convergence and good performance using relatively short training symbols. Experimental results for various time-varying channels are presented to evaluate the performance of the proposed approaches over a conventional recurrent neural equalizer.     

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.     

Adaptive Equalization of the Slow Fading Channel

This paper considers equalization of the slow fading channel for a serial data transmission application. Linear and decision-feedback adaptive equalization techniques are contrasted. The error propagation effect in decision-feedback equalizers is analyzed by a Markov process model. The error probability magnification is computed for both fixed and fading channels and for both binary and quaternary phase-shift-keying (PSK) transmission. The results show that the error propagation effect is small and in regions of practical error probabilities the decision-feedback equalizer is superior to its linear counterpart. Parameters of a practical decisionfeedback equalizer are estimated and a performance evaluation is performed. The implicit diversity gain is shown to be significant and the intersymbol interference penalty is found to be less than 1 dB. Because the intersymbol interference penalty is small, more complex nonlinear processors such as the Viterbi algorithm cannot be recommended for this application. Time jitter effects for the equalizer are included in a calculation of average error probability.     

Optimized Delay Diversity for Suboptimum Equalization

The optimization of delay diversity (DD) for linear equalization (LE) and decision-feedback equalization (DFE) is presented. The general case of transmission over a correlated multiple-input–multiple-output frequency-selective fading channel is considered. The proposed optimization requires the knowledge of the statistical properties of the wireless channel at the transmitter, but channel state information is only required at the receiver side. Based on an approximation of the bit error rate for LE and DFE, a stochastic gradient algorithm for optimization of the DD transmit filters is derived. Simulation results for the Global System for Mobile Communications (GSM)/Enhanced Data Rates for GSM Evolution system show significant performance gains of the proposed optimized DD scheme over the DD schemes reported by Gore (Proc. IEEE Inter. Conf. Commun., 2002) and Hehn (IEEE Trans. Wireless Commun., vol. 4, p. 2289, 2005) if LE and DFE are used at the receiver.     

Pipelined adaptive DFE architectures using relaxed look-ahead

Fine-grain pipelined adaptive decision-feedback equalizer (ADFE) architectures are developed using the relaxed look-ahead technique. This technique, which is an approximation to the conventional look-ahead computation, maintains functionality of the algorithm rather than the input-output behavior. Thus, it results in substantial hardware savings as compared to either parallel processing or look-ahead techniques. Pipelining of the decision feedback loop and the adaptation loop is achieved by the use of delay relaxation and sum relaxation. Both the conventional and the predictor form of ADFE have been pipelined. Results of the convergence analysis of the proposed algorithms are also provided. The performance of the pipelined algorithms for the equalization of a magnetic recording channel is studied. It is shown that the conventional ADFE results in an SNR loss of about 0.6 dB per unit increase in the speed-up factor. The predictor form of ADFE is much more robust and results in less than 0.1 dB SNR loss per unit increase in the speed-up factor. Speed-ups of up to 8 and 45 have been demonstrated for the conventional and predictor forms of ADFE     

Blind channel estimation via combining autocorrelation and blind phase estimation

Symbol spaced blind channel estimation methods are presented which can essentially use the results of any existing blind equalization method to provide a blind channel estimate of the channel. Blind equalizer's task is reduced to only phase equalization (or identification) as the channel autocorrelation is used to obtain the amplitude response of the channel. Hence, when coupled with simple algorithms such as the constant modulus algorithm (CMA) these methods at baud rate processing provide alternatives to blind channel estimation algorithms that use explicit higher order statistics (HOS) or second-order statistics (subspace) based fractionally-spaced/multichannel algorithms. The proposed methods use finite impulse response (FIR) filter linear receiver equalizer or matched filter receiver based infinite impulse response+FIR linear cascade equalizer configurations to obtain blind channel estimates. It is shown that the utilization of channel autocorrelation information together with blind phase identification of the CMA is very effective to obtain blind channel estimation. The idea of combining estimated channel autocorrelation with blind phase estimation can further be extended to improve the HOS based blind channel estimators in a way that the quality of estimates are improved.     

Equalization strategies for transmission over space and time

An overview of equalization schemes applicable to point-to-point communication over MIMO ISI channels is given, i.e., channels which suffer from both multiuser interference between the data streams transmitted in parallel and intersymbol interference due to the dispersive (frequency-selective) nature of the channel. Spatial, temporal, and combined spatial/temporal equalization strategies for dealing with these types of interferences are discussed. In particular, linear and decision-feedback equalization, and equalization based on singular value/eigenvector decomposition and lattice basis reduction, respectively, are treated. The underlying mathematical principle, utilized in these schemes, is stated in each case. Via numerical simulations, the performance of selected equalization strategies is compared.     

Iterative decoding of convolutionally encoded signals overmultipath Rayleigh fading channels

We analyze and compare several strategies for iteratively decoding trellis-encoded signals over channels with memory. Soft-in/soft-out extensions of reduced-complexity trellis search algorithms such as delayed decision-feedback sequence estimating (DDFSE) or parallel decision-feedback decoding (PDFD) algorithms are used instead of conventional BCJR and min-log-BCJR algorithms. It has been shown that for long channel impulse responses and/or high modulation orders where the BCJR algorithm becomes prohibitively complex, the proposed algorithms offer very good performance with low complexity. The problem of channel estimation in practical implementation of turbo detection schemes is studied in the second part. Two methods of channel reestimation are proposed: one based on the expectation-maximization (EM) algorithm and the second on a simple Bootstrap technique. Both algorithms are shown to dramatically improve the performance of the classical pseudo inverse channel estimation performed initially on a training sequence     

Multi-input multi-output fading channel tracking and equalizationusing Kalman estimation

This paper addresses the problem of channel tracking and equalization for multi-input multi-output (MIMO) time-varying frequency-selective channels. These channels model the effects of inter-symbol interference (ISI), co-channel interference (CCI), and noise. A low-order autoregressive model approximates the MIMO channel variation and facilitates tracking via a Kalman filter. Hard decisions to aid Kalman tracking come from a MIMO finite-length minimum-mean-squared-error decision-feedback equalizer (MMSE-DFE), which performs the equalization task. Since the optimum DFE for a wide range of channels produces decisions with a delay Δ > 0, the Kalman filter tracks the channel with a delay. A channel prediction module bridges the time gap between the channel estimates produced by the Kalman filter and those needed for the DFE adaptation. The proposed algorithm offers good tracking behavior for multiuser fading ISI channels at the expense of higher complexity than conventional adaptive algorithms. Applications include synchronous multiuser detection of independent transmitters, as well as coordinated transmission through many transmitter/receiver antennas, for increased data rate     

Equalization concepts for EDGE

An equalization concept for the novel radio access scheme Enhanced Data rates for GSM Evolution (EDGE) is proposed by which high performance can be obtained at moderate computational complexity. Because high-level modulation is employed in EDGE, optimum equalization as usually performed in Global System for Mobile Communications (GSM) receivers is too complex and suboptimum schemes have to be considered. It is shown that delayed decision-feedback sequence estimation (DDFSE) and reduced-state sequence estimation (RSSE) are promising candidates. For various channel profiles, approximations for the bit error rate of these suboptimum equalization techniques are given and compared with simulation results for DDFSE. It turns out that a discrete-time prefilter creating a minimum-phase overall impulse response is indispensable for a favorable tradeoff between performance and complexity. Additionally, the influence of channel estimation and of the receiver input filter is investigated and the reasons for performance degradation compared to the additive white Gaussian noise channel are indicated. Finally, the overall system performance attainable with the proposed equalization concept is determined for transmission with channel coding     

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.     

Reduced-complexity equalization techniques for broadband wirelesschannels

This paper presents reduced-complexity equalization techniques for broadband wireless communications, both outdoors (fixed or mobile wireless asynchronous transfer mode (ATM) networks) and indoors [high-speed local-area networks (LANs)]. The two basic equalization techniques investigated are decision-feedback equalization (FE) and delayed decision-feedback sequence estimation (DDFSE). We consider the use of these techniques in highly dispersive channels, where the impulse response can last up to 100 symbol periods. The challenge is in minimizing the complexity as well as providing fast equalizer start-up for transmissions of short packets. We propose two techniques which, taken together, provide an answer to this challenge. One is an open-loop timing recovery approach (for both DFE and DDFSE) which can be executed prior to equalization; the other is a modified DFE structure for precanceling postcursors without requiring training of the feedback filter. Simulation results are presented to demonstrate the feasibility of the proposed techniques for both indoor and outdoor multipath channel models. The proposed open-loop timing recovery technique plays a crucial role in maximizing the performance of DFE and DDFSE with short feedforward spans (the feedforward section of DDFSE is a Viterbi sequence estimator). A feedforward span of only five is quite sufficient for channels with symbol rate-delay spread products approaching 100. The modified DFE structure speeds up the training process for these channels by 10-20 times, compared to the conventional structure without postcursor precancellation. The proposed techniques offer the possibility of practical equalization for broadband wireless systems     

Filtered multitone modulation for very high-speed digitalsubscriber lines

A filter-bank modulation technique called filtered multitone (FMT) and its application to data transmission for very high-speed digital subscriber line technology are described. The proposed scheme leads to significantly lower spectral overlapping between adjacent subchannels than for known multicarrier techniques such as discrete multitone (DMT) or discrete wavelet multitone. FMT modulation mitigates interference due to echo and near-end crosstalk signals, and increases the system throughput and reach. Signal equalization in an FMT receiver is accomplished in the form of per-subchannel symbol-spaced or fractionally spaced linear or decision-feedback equalization. The problem of channel coding for this type of modulation is also addressed, and an approach that allows combined removal of intersymbol-interference via precoding and trellis coding is described. Furthermore, practical design aspects regarding filter-bank realization, initial transceiver training, adaptive equalization, and timing recovery are discussed. Finally, simulation results of the performance achieved by FMT modulation for very high-speed digital subscriber line systems, where upstream and downstream signals are separated by frequency-division duplexing, are presented and compared with DMT modulation