Multichannel signal processing for data communications in thepresence of crosstalk

Transceiver designs for multiple coupled channels typically treat the crosstalk between adjacent twisted pairs as random noise uncorrelated with the transmitted signal. The authors propose a transmitter/receiver pair that compensates for crosstalk by treating an entire bundle of twisted pairs as a single multi-input/multi-output channel with a (slowly varying) matrix transfer function. The proposed transceiver uses multichannel adaptive FIR filters to cancel near- and far-end crosstalk, and to pre- and postprocess the input/output of the channel. Linear pre- and postprocessors that minimize mean squared error between the received and transmitted signal in the presence of both near- and far-end crosstalk are derived. The performance of an adaptive near-end crosstalk canceller using the stochastic gradient (least-mean-square) transversal algorithm is illustrated by numerical simulation. Plots of mean squared error versus time and eye diagrams are presented, assuming a standard transmission line model for the channel. A signal design algorithm that maps a vector input bit stream to a stream of channel symbol vectors is also presented and illustrated explicitly for s simple model of two coupled channels     

On a whitening approach to partial channel estimation and blindequalization of FIR/IIR multiple-input multiple-output channels

Channel estimation and blind equalization of multiple-input multiple-output (MIMO) communications channels is considered using primarily the second-order statistics of the data. Such models arise when a single receiver data from multiple sources is fractionally sampled (assuming that there is excess bandwidth) or when an antenna array is used with or without fractional sampling. We consider estimation of (partial) channel impulse response and design of finite-length minimum mean-square error (MMSE) blind equalizers. The basis of the approach is the design of a zero-forcing equalizer that whitens the noise-free data. We allow infinite impulse response (IIR) channels. Moreover, the multichannel transfer function need not be column reduced. Our approaches also work when the “subchannel” transfer functions have common zeros as long as the common zeros are minimum-phase zeros. The channel length or model orders need not be known. The sources are recovered up to a unitary mixing matrix and are further “unmixed” using higher order statistics of the data. A linear prediction approach is also considered under the above conditions of possibly IIR channels, common subchannel zeros/factors, and not-necessarily column reduced channels. Four illustrative simulation examples are provided     

Adaptive minimum bit-error rate equalization for binary signaling

We consider the design and adaptation of a linear equalizer with a finite number of coefficients in the context of a classical linear intersymbol-interference channel with Gaussian noise and a memoryless decision device. If the number of equalizer coefficients is sufficient, the popular minimum mean-squared-error (MMSE) linear equalizer closely approximates the optimal linear equalizer that directly minimizes bit-error rate (BER). However, when the number of equalizer coefficients is insufficient to approximate the channel inverse, the minimum-BER equalizer can outperform the MMSE equalizer by as much as 16 dB in certain cases. We propose a simple stochastic adaptive algorithm for realizing the minimum-BER equalizer. Compared to the least-mean-square algorithm, the proposed algorithm can provide a substantial reduction in BER with no increase in complexity     

Time-varying FIR equalization for doubly selective channels

We propose a time-varying (TV) finite impulse response (FIR) equalizer for doubly selective (time- and frequency-selective) channels. We use a basis expansion model (BEM) to approximate the doubly selective channel and to design the TV FIR equalizer. This allows us to turn a complicated equalization problem into an equivalent simpler equalization problem, containing only the BEM coefficients of both the doubly selective channel and the TV FIR equalizer. The minimum mean-square error (MMSE) as well as the zero-forcing (ZF) solutions are considered. Comparisons with the block linear equalizer (BLE) are made. The TV FIR equalization we propose here unifies and extends many previously proposed serial equalization approaches. In contrast to the BLE, the proposed TV FIR equalizer allows a flexible tradeoff between complexity and performance. Moreover, through computer simulations, we show that the performance of the proposed MMSE TV FIR equalizer comes close to the performance of the ZF and MMSE BLE, at a point where the design as well as the implementation complexity are much lower.     

Blind estimation and equalization of MIMO channels via multidelaywhitening

Blind channel estimation and blind minimum mean square error (MMSE) equalization of multiple-input multiple-output (MIMO) communications channels arising in multiuser systems is considered, using primarily the second-order statistics of the data. The basis of the approach is the design of multiple zero-forcing equalizers that whiten the noise-free data at multiple delays. In the past such an approach has been considered using just one zero-forcing equalizer at zero-delay. Infinite impulse response (IIR) channels are allowed. Moreover, the multichannel transfer function need not be column-reduced. The proposed approach also works when the “subchannel” transfer functions have common zeros so long as the common zeros are minimum-phase zeros. The channel length or model orders need not be known. Using second-order statistics, the sources are recovered up to a unitary mixing matrix, and are further “unmixed” using higher order statistics of the data. Two illustrative simulation examples are provided where the proposed method is compared with its predecessors and an existing method to show its efficacy     

应用于LTE上行链路的D-MMSE-FE 均衡算法

为克服线性均衡性能的局限性及避免传统判决反馈均衡器的高复杂度,提出了一种判决反馈均衡算法D-MMSE-FE。该均衡器先是分析线性MMSE均衡的结果成分,并根据最小均方误差准则计算出均衡器的前、后向传递函数,形成反馈链路,提高均衡器性能。将该种均衡器应用于TDD-LTE 1×2 SIMO上行链路中,在协议中常用的信道下进行了计算机仿真,仿真结果表明,TDD-LTE 1×2 SIMO均衡器相对于线性均衡器使系统性最多可提高达2 dB。     

A quaternary partial-response class-IV transceiver for 125 Mbit/sdata transmission over unshielded twisted-pair cables: principles ofoperation and VLSI realization

The paper describes an experimental transceiver for full-duplex transmission at a rate of 125 Mbit/s over unshielded twisted-pair cables of ordinary voice-grade quality, intended for use in a fiber distributed data interface (FDDI) network. Quaternary partial-response class-IV (QPRIV) overall-channel signaling with near-end crosstalk (NEXT) cancellation and maximum-likelihood sequence detection is employed. The spectral shape of the QPRIV signals facilitates equalization and achieving compliance with EMC regulations. Since in an FDDI system each transmitter can be clocked independently, the receiver must cope with phase drift between NEXT signals to be cancelled and signals received from the remote transmitter. With the chosen transceiver architecture, digital-to-analog conversion of transmit signals, analog-to-digital conversion of receive signals, and adaptive NEXT cancellation are performed synchronously with the transmitter clock. The rate change from transmit timing to controlled receive timing is accomplished by an adaptive equalizer in conjunction with an elastic buffer and occasional coefficient shifts. The equalizer is adjusted rapidly enough to allow for a maximal phase drift of ±100 ppm. The implementation of all digital signal-processing functions in a single 0.5 μm CMOS VLSI prototype chip is discussed. The employed standard-cell design resulted in a power consumption of 6 W. Significantly lower power consumption can be achieved by custom design of highly repetitive processing elements     

A multidelay whitening approach to blind identification andequalization of SIMO channels

Blind channel estimation and blind equalization of single-input multiple-output communications channels is considered using only the second-order statistics of the data. Estimation of (partial) channel impulse response and design of finite-length minimum mean-square error blind equalizers is investigated. The basis of the approach is the design of multiple zero-forcing equalizers that whiten the noise-free data at multiple delays. In the past such an approach has been considered using just one zero-forcing equalizer at zero-delay. Infinite-impulse response channels are allowed. The proposed approach also works when the "subchannel" transfer functions have common zeros so long as the common zeros are minimum-phase zeros. The channel length or model orders need not be known. Three illustrative simulation examples using 4-QAM and 16-QAM signals are provided where the proposed approach is compared with several existing approaches     

Adaptive Interference Suppression for the Downlink of a Direct Sequence CDMA System with Long Spreading Sequences

A simple approach for adaptive interference suppression for the downlink (base-to-mobile link) of a direct sequence (DS) based cellular communication system is presented. The base station transmits the sum of the signals destined for the different mobiles, typically attempting to avoid intra-cell interference by employing orthogonal spreading sequences for different mobiles. However, the signal reaching any given mobile passes through a dispersive channel, thus destroying the orthogonality. In this paper, we propose an adaptive linear equalizer at the mobile that reduces interference by approximately restoring orthogonality. The adaptive equalizer uses the pilot's spreading sequence (which observes the same channel as the spreading sequence for the desired mobile) as training. Simulation results for the linear Minimum Mean Squared Error (MMSE) equalizer are presented, demonstrating substantial performance gains over the RAKE receiver. Long spreading sequences (which vary from symbol to symbol) are employed, so that the equalizer adapts not to the time-varying spreading sequences, but to the slowly varying downlink channel. Since the inter-cell interference from any other base station also has the structure of many superposed signals passing through a single channel, the adaptive equalizer can also suppress inter-cell interference, with the tradeoff between suppression of intra- and inter-cell interference and noise enhancement depending on their impact on the Mean Squared Error (MSE).     

Low-Complexity Block Turbo Equalization for OFDM Systems in Time-Varying Channels

We propose low-complexity block turbo equalizers for orthogonal frequency-division multiplexing (OFDM) systems in time-varying channels. The presented work is based on a soft minimum mean-squared error (MMSE) block linear equalizer (BLE) that exploits the banded structure of the frequency-domain channel matrix, as well as a receiver window that enforces this banded structure. This equalization approach allows us to implement the proposed designs with a complexity that is only linear in the number of subcarriers. Three block turbo equalizers are discussed: two are based on a biased MMSE criterion, while the third is based on the unbiased MMSE criterion. Simulation results show that the proposed iterative MMSE BLE achieves a better bit error rate (BER) performance than a previously proposed iterative MMSE serial linear equalizer (SLE). The proposed equalization algorithms are also tested in the presence of channel estimation errors.      

基于导频序列信道缩短的超宽带信道估计

针对多频带超宽带系统,提出一种基于导频序列信道缩短的信道估计方法,解决了循环前缀长度小于信道最大多径延迟时难于估计信道参数的问题。首先在发送信号中插入块状导频,利用最小均方误差准则（MMSE）,在接收机前端设计信道缩短均衡器,然后根据均衡器输出序列估计出复合信道,最后通过反卷积解出原信道参数。仿真实验表明：该算法具有良好性能。     

Filter Bank precoding for FIR equalization in high-rate MIMO communications

In this paper, the problem of designing finite-impulse-response (FIR) equalizers for multiple-input multiple-output (MIMO) FIR channels is considered. It is shown that an arbitrary MIMO frequency-selective channel can be rendered FIR equalizable by a suitable filter bank (FB) precoding operation that introduces redundancy at the transmitter. The expression for the minimum redundancy required to ensure FIR invertibility is derived. The analysis is extended to the case of MIMO multicarrier modulation. Optimum zero-forcing (ZF) and minimum mean-squared error (MMSE) solutions for the FIR equalizer are derived. Simulation results are provided to demonstrate that the proposed scheme achieves better performance than the block-processing methods while supporting a higher data rate.     

Frequency-Division Bidirectional Communication Over Chip-to-Chip Channels

Frequency division multiple access is applied to bidirectional communication over chip-to-chip links. Frequency division is implemented by dividing the spectrum into low-frequency (dc) and high-frequency (ac) bands using a simple LC filter. The nonidealities that this filter introduces are compensated for with a transmitter/receiver pair that can recover signals in both bands. The receiver uses a dual-path topology that includes hysteresis to recover data from a signal with no dc content. The transmitter is a 6-tap (FIR) pre-emphasis equalizer with variable tap spacing. In simulation, the transmitter and receiver simultaneously communicate error-free at 8 Gb/s over the ac channel and at 500 Mb/s over the dc channel. Measurements shows that the ac and dc signals can be individually recovered and that the two signals occupy distinct frequency bands.      

Iterative Channel Estimation and Successive ICI Cancellation for OFDM Systems over Doubly Selective Channels

In orthogonal frequency division multiplexing systems, significant inter-carrier interference (ICI) caused by doubly selective channels make challenge for reliable reception. In this paper, channel estimation and ICI cancellation are considered jointly. Relying on the basis expansion model (BEM) of time-varying channel, the linear system model of transceiver is established, and the corresponding joint optimization of the transmitted data and BEM coefficients is formulated. Due to the separability of the data and BEM coefficients, we use cyclic minimizing technique to perform channel estimation and equalization alternately. This yields a linear minimum mean square-error (LMMSE) channel estimator and a block MMSE equalizer respectively. The block MMSE equalizer has complexity O(N ³), where N is the number of data subcarriers. To reduce the complexity, instead of equalizing all the data simultaneously, we consider estimating each data symbol successively. This idea results in the per subcarrier interference canceller with lower complexity O(N ²). Finally, an iterative receiver consisting of the data-aided LMMSE channel estimator and the successive interference canceller is developed. Simulation results show the scheme is effective over the channel with relatively large Doppler spread.     

Decision-Feedback Equalization for Pulse-Position Modulation

In this paper, we propose a minimum mean squared error (MMSE) decision feedback equalizer (DFE) for pulse position modulated (PPM) signals in the presence of intersymbol interference (ISI). While traditional uses of PPM may not have had ISI, PPM is increasingly being considered for use in situations where ISI is an issue, such as high-performance optical communication systems and ultrawideband communications. First, we review previous work on the subject which used the zero-forcing criterion under strict assumptions about the channel and equalizer lengths. Then, we derive a computationally efficient MMSE equalizer which removes these restrictions, and is suitable for use with training-based stochastic gradient-descent algorithms. Finally, we demonstrate the performance of the proposed equalizer with simulations.     

无人机数据链信道线性Turbo均衡研究

Turbo均衡是一种基于Turbo迭代解码原理的均衡技术,利用的是均衡器与解码器之间信息的迭代使用来达到消除码间干扰的目的。Turbo均衡技术中通常采用基于最大后验概率的最大后验概率(MAP)均衡器,虽然性能较好,但计算量较大,系统延时较长。为降低延时,保证均衡性能,针对无人机遥控遥测数据链信道,设计了一种相对于MAP均衡器计算量较少的线性最小均方误差(MMSE)均衡器,通过仿真验证了这种线性Turbo均衡的性能,分析了其应用的可行性。     

Time Compression Multiplexing for Loop Transmission of Speech Signals

This paper considers the use of time compression multiplexing (TCM) for telephone loop communications. The analysis treats TCM transmission degradations in general, and applies the results to telephone speech transmission. To gain an understanding of the nature of TCM degradations, transmission through a linear, time invariant network and demultiplexing is considered. The channel signals are then assumed to be wide-sense stationary random processes, and expressions for the spectral properties of the TCM distortion and interchannel crosstalk are determined. To accurately evaluate the performance of a TCM system, a practical and economical equalizer is proposed. It is designed to meet speech transmission requirements for the telephone loop plant. A worst case application is chosen to evaluate the system performance. The evaluation of the TCM transmission performance utilizes both the random signal model and a computer simulation using digitized speech. The random signal analysis shows that the spectra of the distortion and crosstalk are significant for human speech. Results of the digitized speech simulation demonstrate that the subjective effect of the signal distortion is not severe, but the crosstalk is somewhat intelligible and more severe than expected.     

Decision feedback equalization

As real world communication channels are stressed with higher data rates, intersymbol interference (ISI) becomes a dominant limiting factor. One way to combat this effect that has recently received considerable attention is the use of a decision feedback equalizer (DFE) in the receiver. The action of the DFE is to feed back a weighted sum of past decision to cancel the ISI they cause in the present signaling interval. This paper summarizes the work in this area beginning with the linear equalizer. Three performance criteria have been used to derive optimum systems; 1) minimize the noise variance under a "zero forcing" (ZF) constraint i.e., insist that all intersymbol interference is cancelled, 2) minimize the mean-square error (MMSE) between the true sample and the observed signal just prior to the decision threshold, and 3) minimize the probability of error (Min Pe). The transmitter can be fixed and the receiver optimized or one can obtain the joint optimum transmitter and receiver. The number of past decisions used in the feedback equalization can be finite or infinite. The infinite case is easier to handle analytically. In addition to reviewing the work done in the area, we show that the linear equalizer is in fact a portion of the DFE receiver and that the processing done by the DFE is exactly equivalent to the general problem of linear prediction. Other similarities in the various system structures are also shown. The effect of error propagation due to incorrect decisions is discussed, and the coaxial cable channel is used as an example to demonstrate the improvement available using DFE.     

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.     

Doubly Iterative Equalization of Continuous-Phase Modulation

In this paper, a doubly iterative receiver is proposed for joint turbo equalization, demodulation, and decoding of coded binary continuous-phase modulation (CPM) in multipath fading channels. The proposed receiver consists of three soft-input soft-output (SISO) blocks: a front-end soft-information-aided minimum mean square error (MMSE) equalizer followed by a CPM demodulator and a back-end channel decoder. The MMSE equalizer, combined with an a priori soft-interference canceler (SIC) and an a posteriori probability mapper, forms a SISO processor suitable for iterative processing that considers discrete-time CPM symbols which belong to a finite alphabet. The SISO CPM demodulator and the SISO channel decoder are both implemented by the a posteriori probability algorithm. The proposed doubly iterative receiver has a central demodulator coupled with both the front-end equalizer and the back-end channel decoder. A few back-end demodulation/decoding iterations are performed for each equalization iteration so as to improve the a priori information for the equalizer. As presented in the extrinsic information transfer (EXIT) chart analysis and simulation results for different multipath fading channels, this provides not only faster convergence to low bit error rates, but also lower computational complexity.