Adaptive turbo reduced-rank equalization for MIMO channels

An adaptive iterative (turbo) decision-feedback equalizer (DFE) for channels with intersymbol interference (ISI) is presented. The filters are computed directly from the soft decisions and received data to minimize a least-squares (LS) cost function. Numerical results show that this method gives a substantial improvement in performance relative to a turbo DFE computed from an exact channel estimate, assuming perfect feedback. Adaptive reduced-rank estimation methods are also presented, based on the multistage Wiener filter (MSWF). The adaptive reduced-rank turbo DFE for single-input/single-output channels is extended to multiple-input/multiple-output (MIMO) channels with ISI and multiple receive antennas. Numerical results show that for MIMO channels with limited training, the reduced-rank turbo DFE can perform significantly better than the full-rank turbo DFE.     

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。     

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.     

Iterative Equalization using Improved Block DFE for Synchronous CDMA Systems

Iterative equalization using optimal multiuser detector and optimal channel decoder in coded CDMA systems improves the bit error rate (BER) performance tremendously. However, given large number of users employed in the system over multipath channels causing significant multiple-access interference (MAI) and intersymbol interference (ISI), the optimal multiuser detector is thus prohibitively complex. Therefore, the sub-optimal detectors such as low-complexity linear and non-linear equalizers have to be considered. In this paper, a novel low-complexity block decision feedback equalizer (DFE) is proposed for the synchronous CDMA system. Based on the conventional block DFE, the new method is developed by computing the reliable extrinsic log-likelihood ratio (LLR) using two consecutive received samples rather than one received sample in the literature. At each iteration, the estimated symbols by the equalizer is then saved as a priori information for next iteration. Simulation results demonstrate that the proposed low-complexity block DFE algorithm offers good performance gain over the conventional block DFE.     

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     

Unsupervised receiver processing techniques for linear space-time equalization of wideband multiple input / multiple output channels

In this paper, we address the problem of unsupervised (blind) space-time equalization of frequency-selective multiple-input multiple-output (MIMO) channels. The motivation behind this work is that in order to provide the high transmission rates that data-demanding applications require, wireless multiple antenna (MIMO) systems will have to operate in wide bandwidths. In such scenarios, frequency selectivity may induce important intersymbol interference (ISI), in addition to the interuser interference (IUI) that each antenna's transmitted stream of data suffers from the other antennas. Under these conditions, channel estimation of the frequency-selective MIMO channel may become a daunting task that ultimately reduces the effective transmission rate. We present a family of globally convergent blind space-time equalization techniques, developed from multiuser kurtosis output-based criteria, which allow the recovery of the MIMO channel inputs without the training overhead that channel estimation typically requires, thus improving the MIMO channel's spectral efficiency.     

A Method of Time-Varying Rayleigh Channel Tracking in MIMO Radio System

Multi-input multi-output (MIMO) technique, which uses multiple antennas at transmitter and receiver, is the essential technique of the next generation mobile communication system. It can greatly increase the system capacity and spectral efficiency without additional bandwidth[1]. Because of the time-varying nature of the wireless channels and the interference (including inter-symbol interference and inter-user interference), the equalization at the receiver is more difficult to achieve. Amon…     

Near-optimum soft decision equalization for frequency selective MIMO channels

In this paper, we develop soft decision equalization (SDE) techniques for frequency selective multiple-input multiple-output (MIMO) channels in the quest for low-complexity equalizers with error performance competitive to that of maximum likelihood (ML) sequence detection. We demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered and linear in the signal constellation size. Building on the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. The first SDE algorithm adopts a zero-padded transmission structure to convert the challenging sequence detection problem into a block-by-block least-square formulation. It introduces key enhancement to the original PDA to enable applications in rank-deficient channels and for higher level modulations. The second SDE algorithm takes advantage of the Toeplitz channel matrix structure embodied in an equalization problem. It processes the data samples through a series of overlapping sliding windows to reduce complexity and, at the same time, performs implicit noise tracking to maintain near-optimum performance. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Simulation comparisons of our SDE methods with minimum-mean-square error (MMSE)-based MIMO DFE and sphere decoded quasi-ML detection are presented.     

Joint coding and decision feedback equalization for broadbandwireless channels

This paper introduces a new approach for joint convolutional coding and decision feedback equalization (DPE). To minimize error propagation, the DFE uses a combination of soft decisions and delayed tentative decisions to cancel intersymbol interference (ISI). Soft decisions are obtained by passing the DFE output through a (soft) nonlinear device. This simple method is shown to perform almost as well as an optimum soft feedback approach on wireless channels with diversity. Tentative decisions from the Viterbi decoder are used to cancel ISI due to multipath with large delays, thus remedying the increasing effect of error propagation in channels with large delay spreads. We consider the use of this soft/delayed feedback DFE (S/D-DFE) technique in broadband wireless channels (with delay spreads up to several tens of the symbol period) typical in high-bitrate mobile data applications. Simulation results indicate that the proposed joint coding and S/D-DFE technique performs to within 1-2 dB [in required signal-to-noise ratio (SNR)] of an ideal coded DFE without error propagation. When combined with antenna diversity and a reduced-complexity DFE concept with adaptive feedforward tap assignment, it provides high packet throughput against Rayleigh fading, severe delay spreads, and high Doppler rates     

Adaptive Techniques for Joint Optimization of XTC and DFE Loop Gain in High‐Speed I/O

High‐speed I/O channels require adaptive techniques to optimize the settings for filter tap weights at decision feedback equalization (DFE) read channels to compensate for channel inter‐symbol interference (ISI) and crosstalk from multiple adjacent channels. Both ISI and crosstalk tend to vary with channel length, process, and temperature variations. Individually optimizing parameters such as those just mentioned leads to suboptimal solutions. We propose a joint optimization technique for crosstalk cancellation (XTC) at DFE to compensate for both ISI and XTC in high‐speed I/O channels. The technique is used to compensate for between 15.7 dB and 19.7 dB of channel loss combined with a variety of crosstalk strengths from 60 mV_p‐p to 180 mV_p‐p adaptively, where the transmit non‐return‐to‐zero signal amplitude is a constant 500 mV_p‐p.     

An adaptive RAM-DFE for storage channels

A modification of the decision feedback equalizer (DFE), RAM-DFE, is presented and analyzed for use in channels with trailing nonlinear intersymbol interference, especially binary saturation-recording channels. In the RAM-DFE, a look-up table, which can be easily implemented with random access memory, (RAM), replaces the transversal filter feedback section of the DFE. The feedforward section of the equalizer remains linear. A general nonlinear Markov (or finite-state machine) model is used to model the nonlinear intersymbol interference (ISI) channel. With this Markov model, a method is introduced for computing the minimum-mean-squared-error settings of the feedforward filter coefficients and the feedback filter and look-up table contents for the linear DFE and the RAM-DFE, respectively. RAM-DFE with these settings can be significantly better than the linear DFE for channels with trailing nonlinear ISI. Globally convergent gradient-type algorithms for updating the feedforward section coefficients and the contents of the feedback table are introduced and analyzed. Results based on data taken from disk storage units are discussed     

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.     

On the equivalence of the simultaneous and separate MMSEoptimizations of a DFE FFF and FBF

There is great interest in the use of decision feedback equalization (DFE) to mitigate the effects of intersymbol interference (ISI) on wireless multipath fading channels. The coefficients of a DFE feedforward filter (FFF) and feedback filter (FBF) are usually adjusted based on the minimum mean square error (MMSE) criterion. The equalizer coefficients can be calculated by recursive adaptation or by direct computation based on a channel estimate. The equivalence of the simultaneous and separate MMSE optimization of the FFF and FBF of a finite-length DFE is established     

Decision feedback sequence estimation for unwhitened ISI channelswith applications to multiuser detection

Decision feedback sequence estimation (DFSE), which is a reduced-complexity alternative to maximum likelihood sequence estimation (MLSE), can be used effectively for equalization of intersymbol interference (ISI) as well as for multiuser detection. The algorithm performs very well for whitened (minimum-phase) channels. For nonminimum-phase channels, however, the algorithm is not very effective. Moreover, DFSE requires a noise-whitening filter, which may not be feasible to compute for time-varying channels such as a multiuser direct-sequence code division multiple access (DS-CDMA) channel. Noise-whitening is also cumbersome for applications that involve bidirectional equalization such as the global system for mobile communication (GSM) system. In such conditions, it is desirable to use the Ungerboeck (1974) formulation for sequence estimation, which operates directly on the discrete-time unwhitened statistic obtained from conventional matched filtering. Unfortunately, DFSE based on matched filter statistics is severely limited by untreated interference components. We identify the anticausal interference components, using an error probability analysis. This leads us to a modified unwhitened decision feedback sequence estimator (MUDFSE) in which the components are canceled, using tentative decisions. We obtain approximate error probability bounds for the proposed algorithm. Performance results indicate that the modified algorithm, used on unwhitened channels with relatively small channel correlations, provides similar performance/complexity tradeoffs as the DFSE used on the corresponding whitened minimum-phase channels. The algorithm is especially attractive for multiuser detection for asynchronous DS-CDMA channels with long spreading codes, where it can achieve near-MLSE performance with exponentially lower complexity     

Diversity Combining and Equalization with TCM for Wireless Communications

This paper presents an equalization structure in which antennadiversity, adaptive decision feedback equalization (DFE), interleavingand trellis-coded modulation (TCM) can be effectively combined to combatboth ISI and cochannel interference in cellular mobile radioenvironments. The feedback filter of the DFE can use either tentative orfinal decision symbols of the TCM Viterbi decoding to cancel tail ISIwith the square root Kalman algorithm. A performance bound on theaverage pairwise error probability for TCM under perfect interleavingand equalization is obtained by analysis. Some simulation results whichillustrate the potential of the proposed system will also be given. Inparticular, a performance comparison between the proposed method anduncoded QPSK modulation will be undertaken.     

A multistep linear prediction approach to blind asynchronous CDMAchannel estimation and equalization

A multistep linear prediction approach is presented for blind channel estimation, multiuser interference (MUI) suppression, and detection of asynchronous short-code direct sequence code division multiple access signals in multipath channels. Only the spreading code of the desired user is assumed to be known; its transmission delay may be unknown. We exploit the previously proposed multistep linear prediction approach for blind multiple-input multiple-output channel estimation in conjunction with the structure imposed by the desired user's spreading code sequence. With the knowledge of the desired user's code sequence, only the second-order statistics of the data are needed under certain sufficient conditions on the underlying multiuser MIMO transfer function. Based on the desired user's channel estimate, a linear minimum mean square error filter is designed for simultaneous equalization and MUI suppression. Three illustrative simulation examples are presented     

Performance of sequence estimation scheme of narrowband digital FMsignals with limiter-discriminator detection

A communication scheme using binary FM with noncoherent limiter-discriminator detection has been well known. Up to now, the improvement of bit error rate at the receiver side has been carried out through the bandwidth optimization of the IF filter, the decision feedback equalization (DFE), or simple two-state maximum likelihood sequence estimator (MLSE). This channel is inherently the intersymbol interference (ISI) channel due to the premodulation baseband filtering as well as the narrowband IF filtering. So the sequence estimation scheme using the Viterbi algorithm can be applied successfully, although the channel is not additive white Gaussian and maximum likelihood in the strict sense. In this paper, through computer simulations, we examine the actual BER improvement of the sequence estimation scheme with multiple-state trellis especially for MSK and GMSK signals. We mainly consider static AWGN and frequency nonselective Rician fading channels. Consequently, by adjusting the IF filter bandwidth, very large estimation gains are obtained compared to the conventional DFE or MLSE detector for AWGN and Rician fading channels. This scheme does not produce large demodulation delay and is implemented only by adding the signal processing part to the final stage of the receiver. This scheme seems to be very useful for any applications including satellite mobile channels     

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     

Blind equalization and multiuser detection in dispersive CDMAchannels

The problem of blind demodulation of multiuser information symbols in a high-rate code-division multiple-access (CDMA) network in the presence of both multiple-access interference (MAI) and intersymbol interference (ISI) is considered. The dispersive CDMA channel is first cast into a multiple-input multiple-output (MIMO) signal model framework. By applying the theory of blind MIMO channel identification and equalization, it is then shown that under certain conditions the multiuser information symbols can be recovered without any prior knowledge of the channel or the users' signature waveforms (including the desired user's signature waveform), although the algorithmic complexity of such an approach is prohibitively high. However, in practice, the signature waveform of the user of interest is always available at the receiver. It is shown that by incorporating this knowledge, the impulse response of each user's dispersive channel can be identified using a subspace method. It is further shown that based on the identified signal subspace parameters and the channel response, two linear detectors that are capable of suppressing both MAI and ISI, i.e., a zero-forcing detector and a minimum-mean-square-error (MMSE) detector, can be constructed in closed form, at almost no extra computational cost. Data detection can then be furnished by applying these linear detectors (obtained blindly) to the received signal. The major contribution of this paper is the development of these subspace-based blind techniques for joint suppression of MAI and ISI in the dispersive CDMA channels     

基于粒子群优化的MIMO系统判决反馈均衡研究

为了更好地消除多输入多输出(MIMO)系统中的码间干扰(ISI),提出了一种基于粒子群优化(PSO)的判决反馈均衡(DFE)算法;将该算法与基于最小均方(LMS)算法的判决反馈均衡进行了比较.仿真结果表明,PSO DFE的误码率性能明显优于LMS DFE,且收敛速度快.