Discrete multiple tone modulation with coset coding for thespectrally shaped channel

A discrete approach to multiple tone modulation is developed for digital communication channels with arbitrary intersymbol interference (ISI) and additive Gaussian noise. Multiple tone modulation is achieved through the concatenation of a finite block length modulator based on discrete Fourier transform (DFT) code vectors, and high gain coset or trellis codes. Symbol blocks from an inverse DFT (IDFT) are cyclically extended to generate ISI-free channel-output symbols that decompose the channel into a group of orthogonal and independent parallel subchannels. Asymptotic performance of this system is derived, and examples of asymptotic and finite block length coding gain performance for several channels are evaluated at different values of bits per sample. This discrete multiple tone technique is linear in both the modulation and the demodulation, and is free from the effects of error propagation that often afflict systems employing bandwidth-optimized decision feedback plus coset codes     

Block coding capacity of high bit rate digital subscriber lines bythe structured channel signaling technique

Self near-end crosstalk (NEXT) is assumed to be the dominant source of impairment, and the subscriber loop configuration is governed by carrier serving area (CSA) design rules. The structured channel signaling (SCS) technique decomposes the physical channel into multiple parallel independent signaling subchannels by exploiting the combined eigenstructure of the channel and the correlation of the (NEXT) interference. Computer performance evaluation studies reveal two distinct patterns. For a given loop configuration, as the block length increases, the coding gain usually increases, and for a fixed block code length, the coding gain degrades as the loop length (including bridged taps) increases. For loops at the extreme range of a CSA, block codes of at least 20 symbols are required to achieve a performance commensurate with that of a decision feedback equalizer (DFE) composed of an optimal nine-tap minimum mean-square error (MMSE) feedforward filter and an ideal feedback canceler     

Space–Time Codes From Structured Lattices

We present constructions of space–time (ST) codes based on lattice coset coding. First, we focus on ST code constructions for the short block-length case, i.e., when the block length is equal to or slightly larger than the number of transmit antennas. We present constructions based on dense lattice packings and nested lattice (Voronoi) shaping. Our codes achieve the optimal diversity–multiplexing tradeoff (DMT) of quasi-static multiple-input multiple-output (MIMO) fading channels for any fading statistics, and perform very well also at practical, moderate values of signal-to-noise ratios (SNR). Then, we extend the construction to the case of large block lengths, by using trellis coset coding. We provide constructions of trellis coded modulation (TCM) schemes that are endowed with good packing and shaping properties. Both short-block and trellis constructions allow for a reduced complexity decoding algorithm based on minimum mean-squared error generalized decision feedback equalizer (MMSE-GDFE) lattice decoding and a combination of this with a Viterbi TCM decoder for the TCM case. Beyond the interesting algebraic structure, we exhibit codes whose performance is among the state-of-the art considering codes with similar encoding/decoding complexity.      

Quantized feedback information in orthogonal space-time block coding

This work considers how the presence of quantized channel information obtained from a feedback link may be utilized for determining a transmit weighting matrix that improves the performance of a predetermined orthogonal space-time block (OSTB) code. To reduce the effects of feedback delay, quantization errors and feedback channel bit errors, methods based on vector quantization for noisy channels are used in the design of the feedback link. The resulting transmission scheme and feedback link take the imperfect nature of the channel information into account while combining the benefits of conventional beamforming with those provided by OSTB coding.     

Transformation of a Rayleigh fading channel into a set of parallelAWGN channels and its advantage for coded transmission

The authors consider transmission over a memoryless Rayleigh fading channel. It is shown that an appropriate orthogonal transformation at the transmit side and block decision feedback equalisation at the receive side transform the Rayleigh fading channel into a set of AWGN channels. The advantage for coded transmission is demonstrated     

On the Capacity and Design of Limited Feedback Multiuser MIMO Uplinks

The theory of multiple-input–multiple-output (MIMO) technology has been well developed to increase fading channel capacity over single-input–single-output (SISO) systems. This capacity gain can often be leveraged by utilizing channel state information at the transmitter and the receiver. Users make use of this channel state information for transmit signal adaptation. In this correspondence, we derive the capacity region for the MIMO multiple access channel (MIMO MAC) when partial channel state information is available at the transmitters, where we assume a synchronous MIMO multiuser uplink. The partial channel state information feedback has a cardinality constraint and is fed back from the basestation to the users using a limited rate feedback channel. Using this feedback information, we propose a finite codebook design method to maximize the sum rate. In this correspondence, the codebook is a set of transmit signal covariance matrices. We also derive the capacity region and codebook design methods in the case that the covariance matrix is rank one (i.e., beamforming). This is motivated by the fact that beamforming is optimal in certain conditions. The simulation results show that when the number of feedback bits increases, the capacity also increases. Even with a small number of feedback bits, the performance of the proposed system is close to an optimal solution with the full feedback.      

Fast adaptive equalization/diversity combining for time-varyingdispersive channels

We examine adaptive equalization and diversity combining methods for fast Rayleigh-fading frequency selective channels. We assume a block adaptive receiver in which the receiver coefficients are obtained from feedforward channel estimation. For the feedforward channel estimation, we propose a novel reduced dimension channel estimation procedure, where the number of unknown parameters are reduced using a priori information of the transmit shaping filter's impulse response. Fewer unknown parameters require a shorter training sequence. We obtain least-squares, maximum-likelihood, and maximum a posteriori (MAP) estimators for the reduced dimension channel estimation problem. For symbol detection, we propose the use of a matched filtered diversity combining decision feedback equalizer (DFE) instead of a straightforward diversity combining DFE. The matched filter form has lower computational complexity and provides a well-conditioned matrix inversion. To cope with fast time-varying channels, we introduce a new DFE coefficient computation algorithm which is obtained by incorporating the channel variation during the decision delay into the minimum mean square error (MMSE) criterion. We refer to this as the non-Toeplitz DFE (NT-DFE). We also show the feasibility of a suboptimal receiver which has a lower complexity than a recursive least squares adaptation, with performance close to the optimal NT-DFE     

An analytical comparison of partial power-feedback designs for MIMO block fading channels

It has been shown that with perfect feedback (CSIT), the optimal multiple input/multiple output (MIMO) transmission strategy is a cascade of channel encoder banks, power control matrix, and eigen-beamforming matrix. However, the feedback capacity requirement for perfect CSIT is 2n/sub T//spl times/n/sub R/, which is not scalable with respect to n/sub T/ or n/sub R/. In this letter, we shall compare the performance of two levels of partial power-feedback strategies, namely, the scalar symmetric feedback and the vector feedback, for MIMO block fading channels. Unlike quasi-static fading, variable rate encoding is not needed for block fading channels to achieve the optimal channel capacity.     

Application of quasi-orthogonal space-time block codes in beamforming

It is well known that when channel information is available at the transmitter, transmit beamforming scheme can be employed to enhance the performance of a multiple-antenna system. Recently, Jongren et al. and Zhou-Giannakis proposed a new performance criterion based on partial channel side information at the transmitter. With this criterion, an optimal beamforming matrix was constructed for the orthogonal space-time block codes. However, the same method has not been applied to the recently proposed quasi-orthogonal space-time block codes (QSTBCs) due to the nonorthogonal nature of the quasi-orthogonal designs. In this paper, the issue of combining beamforming with QSTBCs is addressed. Based on our asymptotic analysis, we extend the beamforming scheme from Jongren et al. and construct the beamforming matrices for the quasi-orthogonal designs. The proposed beamforming scheme accomplishes high transmission rate as well as high-order spatial diversity. The new QSTBC beamformer can be presented as a novel four-directional or eight-directional eigen-beamformer that works for systems with four or more transmit antennas. Simulations for systems with multiple transmit antennas demonstrate significant performance improvement over several other widely used beamforming methods at various SNRs and for channels with different quality of feedback.     

A decision feedback equalizer with time-reversal structure

This work describes the use of a receiver with a time-reversal structure for low-complexity decision feedback equalization of slowly fading dispersive indoor radio channels. Time-reversal is done by storing each block of received signal samples in a buffer and reversing the sequential order of the signal samples in time prior to equalization. As a result, the equivalent channel impulse response as seen by the equalizer is a time-reverse of the actual channel impulse response. Selective time-reversal operation, therefore, allows a decision feedback equalizer (DFE) with a small number of forward filter taps to perform equally well for both minimum-phase and maximum-phase channel characteristics. The author evaluates the theoretical performance bounds for such a receiver and quantifies the possible performance improvement for discrete multipath channels with Rayleigh fading statistics. Two extreme cases of DFE examples are considered: an infinite-length DFE; and a DFE with a single forward filter tap. Optimum burst and symbol timing recovery is addressed and several practical schemes are suggested. Simulation results are presented. The combined use of equalization and diversity reception is considered     

Signal space detection for recording channels with jitter noise

A delay-constrained sequence detector is considered for recording channels whose major impediments include intersymbol interference (ISI) and magnetic transition jitter noise. The jitter noise is data-dependent, and a given noise sample is correlated with neighboring noise samples. A sequence detector with a finite decision delay can be formulated in a finite dimensional vector space. For a correlated noise channel, the decision boundary is generally quadratic. We present a technique for obtaining a minimal set of hyperplanes approximating a quadratic decision boundary with a negligible performance loss. In this process, a distance measure, which is consistent with the notion of the effective SNR, is defined and used as a design parameter to trade the complexity and performance. As an achievable performance bound, we derive the effective SNR for the maximum-likelihood sequence detector (MLSD) for these channels. The performance of the partial response maximum likelihood (PRML) detector commonly adopted for current data storage channels as well as the Viterbi algorithm (VA) based on the traditional Euclidean metric, which serves as the MLSD for additive white Gaussian noise, are also analyzed and compared with that of the proposed signal space detector     

On channel orthogonalization using space-time block coding with partial feedback

Orthogonal space-time block codes (OSTBCs) yield full diversity gain even while requiring only a linear receiver. Such full-rate (rate-one) orthogonal designs are available for complex symbol constellations only for N=2 transmit antennas. In this paper, we propose a new family of full-rate space-time block codes (STBCs) using a single parameter feedback for communication over Rayleigh fading channels for N=3,4 transmit antennas and M receive antennas. The proposed rate-one codes achieve full diversity, and the performance is similar to maximum receiver ratio combining. The decoding complexity of these codes are only linear even while performing maximum-likelihood decoding. The partial channel information is a real phase parameter that is a function of all the channel gains, and has a simple closed-form expression for N=3,4. This feedback information enables us to derive (channel) orthogonal designs starting from quasi-orthogonal STBCs. The feedback complexity is significantly lower than conventional closed-loop transmit beamforming. We compare the proposed codes with the open-loop OSTBCs and also with the closed-loop equal gain transmission (EGT) scheme which uses equal power loading on all antennas. Simulated error-rate performances indicate that the proposed channel orthogonalized STBCs significantly outperform the open-loop orthogonal designs, for the same spectral efficiency. Moreover, even with significantly lower feedback and computational complexity, the proposed scheme outperforms the EGT technique for M>N.     

Reduced-state sequence estimation with set partitioning anddecision feedback

A reduced-state sequence estimator for linear intersymbol interference channels is described. The estimator uses a conventional Viterbi algorithm with decision feedback to search a reduced-state subset trellis that is constructed using set-partitioning principles. The complexity of maximum-likelihood sequence estimation (MLSE) due to the length of the channel memory and the size of the signal set is systematically reduced. An error probability analysis shows that a good performance/complexity tradeoff can be obtained. In particular, the results indicate that the required complexity to achieve the performance of MLSE is independent of the size of the signal set for large enough signal sets. Simulation results are provided for two partial-response systems. A simple technique for quadrature partial-response signaling (QPRS) is described that eliminates the quasicatastrophic nature of the ML trellis     

Transmit signal design for optimal estimation of correlated MIMO channels

We address optimal estimation of correlated multiple-input multiple-output (MIMO) channels using pilot signals, assuming knowledge of the second-order channel statistics at the transmitter. Assuming a block fading channel model and minimum mean square error (MMSE) estimation at the receiver, we design the transmitted signal to optimize two criteria: MMSE and the conditional mutual information between the MIMO channel and the received signal. Our analysis is based on the recently proposed virtual channel representation, which corresponds to beamforming in fixed virtual directions and exposes the structure and the true degrees of freedom in the correlated channel. However, our design framework is applicable to more general channel models, which include known channel models, such as the transmit and receive correlated model, as special cases. We show that optimal signaling is in a block form, where the block length depends on the signal-to-noise ratio (SNR) as well as the channel correlation matrix. The block signal corresponds to transmitting beams in successive symbol intervals along fixed virtual transmit angles, whose powers are determined by (nonidentical) water filling solutions based on the optimization criteria. Our analysis shows that these water filling solutions identify exactly which virtual transmit angles are important for channel estimation. In particular, at low SNR, the block length reduces to one, and all the power is transmitted on the beam corresponding to the strongest transmit angle, whereas at high SNR, the block length has a maximum length equal to the number of active virtual transmit angles, and the power is assigned equally to all active transmit angles. Consequently, from a channel estimation viewpoint, a faster fading rate can be tolerated at low SNRs relative to higher SNRs.     

Limited feedback unitary precoding for orthogonal space-time block codes

Orthogonal space-time block codes (OSTBCs) are a class of easily decoded space-time codes that achieve full diversity order in Rayleigh fading channels. OSTBCs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information. When channel state information is available at the transmitter, though, precoding the space-time codeword can be used to support different numbers of transmit antennas and to improve array gain. Unfortunately, transmitters in many wireless systems have no knowledge about current channel conditions. This motivates limited feedback precoding methods such as channel quantization or antenna subset selection. This paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver. The receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error-free, zero-delay feedback channel. A criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system. Low average distortion codebooks are derived based on the optimal codeword selection criterion. The resulting design is found to relate to the famous applied mathematics problem of subspace packing in the Grassmann manifold. Codebooks designed by this method are proven to provide full diversity order in Rayleigh fading channels. Monte Carlo simulations show that limited feedback precoding performs better than antenna subset selection.     

Design of transmit FIR filters for FDM data transmission systems

The design of transmit finite-impulse response (FIR) filters with few coefficients in frequency division multiplexing data transmission systems is considered. In these systems, quality objectives are imposed for transmission over channels affected by additive white Gaussian noise (AWGN) and over channels affected by AWGN plus adjacent channel interference (ACI). The goal of this letter is: given that an adaptive receive filter, possibly cooperating with an adaptive decision feedback equalizer, is used for the AWGN channel and for the AWGN plus ACI channel, what is the best fixed FIR transmit filter to use for both channel cases? This goal is achieved by optimizing the compromise between the performance of the system on the two mentioned channels. Also, the advantages of the proposed design over a rival method based on a fixed receive filter are demonstrated.     

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.      

Optimal decision strategies for acquisition of spread-spectrumsignals in frequency-selective fading channels

The focus of this paper is on the initial acquisition of a direct sequence (DS) spread-spectrum signal utilizing a purely parallel search strategy. A parallel search strategy is utilized because it reduces the acquisition time compared to either serial or partially parallel strategies. In particular, the purpose of this paper is to derive the optimal decision rule, based on the maximum-likelihood criterion, for frequency-selective fading channels. The performance of the conventional decision rule, optimized for additive white Gaussian noise and flat-fading channels, the optimal decision rule derived, and a suboptimal decision rule, also presented in this paper, are compared. It is shown that the optimal and suboptimal decision rules for Rayleigh-fading channels outperform the conventional decision rule. For Rician-fading channels, it is shown both that the optimal decision rule outperforms the conventional decision rule, and that the optimum decision rule for Rayleigh-fading channels, when implemented on a Rician-fading channel, yields approximately optimum performance     

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.     

Feedback capacity of finite-state machine channels

We consider a finite-state machine channel with a finite memory length (e.g., finite length intersymbol interference channels with finite input alphabets-also known as partial response channels). For such a finite-state machine channel, we show that feedback-dependent Markov sources achieve the feedback capacity, and that the required memory length of the Markov process matches the memory length of the channel. Further, we show that the whole history of feedback is summarized by the causal posterior channel state distribution, which is computed by the sum-product forward recursion of the Bahl-Cocke-Jelinek-Raviv (BCJR) (Baum-Welch, discrete-time Wonham filtering) algorithm. These results drastically reduce the space over which the optimal feedback-dependent source distribution needs to be sought. Further, the feedback capacity computation may then be formulated as an average-reward-per-stage stochastic control problem, which is solved by dynamic programming. With the knowledge of the capacity-achieving source distribution, the value of the capacity is easily estimated using Markov chain Monte Carlo methods. When the feedback is delayed, we show that the feedback capacity can be computed by similar procedures. We also show that the delayed feedback capacity is a tight upper bound on the feedforward capacity by comparing it to tight existing lower bounds. We demonstrate the applicability of the method by computing the feedback capacity of partial response channels and the feedback capacity of run-length-limited (RLL) sequences over binary symmetric channels (BSCs).