Maximum Likelihood Sequence Detection Research Articles

Improved lower bounds on the symbol error probability for ISI channels

A lower bound on the symbol error probability obtained with maximum likelihood sequence detection on the intersymbol interference channel is derived. It is recognised that the bound can be substantially improved by considering every possible transmitted sequence and not only the ones generating the well-known dmin2. Also, a method is devised which finds the additive components of the bound using a trellis search. It is demonstrated that for many channels, using a truncated upper bound as a lower bound yields incorrect results. This might be the case even if the upper bound is truncated to its first term corresponding to dmin2.

Autocovariance preserving estimator (APE) interpretation of the MLSD metric for Rayleigh fading channels

This paper describes a new interpretation of the maximum-likelihood sequence detector metric for a linearly modulated signal and an unknown time-varying, dispersive, Rayleigh fading channel. The metric, which involves the channel and noise autocovariances, is transformed into the intuitive Mahalanobis distance (squared Euclidean distance in white noise) between the observations and a reference estimated from them. A novel estimator, called the autocovariance preserving estimator, is obtained that trades off increased estimation bias for reduced sequence-error probability.

Innovations-based MAP detection for time-varying frequency-selective channels

By using the innovations process, this paper provides a unification and extension of the existing maximum a posteriori (MAP) detectors (MAPDs). The practically important topics of linear modulations, time-varying frequency-selective channels, differential phase detection, and fractional sampling are accounted for. The MAPDs are derived under different conditions of optimality and a priori knowledge as follows: when the MAP criterion is applied to the constellation mapper's input bits or output symbols, when all observations or only a fixed number of future observations (i.e. fixed-lag MAPDs) from a transmission are available, when the time-varying channel impulse response is perfectly known, and when only the Gaussian-distributed channel's mean and autocovariance and the noise variance are known. As these quantities are actually unknown, their estimation in the context of MAP detection is also discussed. The MAPDs are characterized through simulation and a novel, unified analysis. Although MAPDs are less suited to hardware implementation than the traditional maximum-likelihood sequence detectors, the MAPDs can accept nonuniform a priori bit or symbol probabilities and provide soft outputs. In this way, the MAPDs are well suited to iterative decoding, and so they will become increasingly integral to high-performance receiver designs.

Transition detector for CD and DVD

This bit detector for d=2 modulation codes is remarkably simple, supports very high data rates, can be adaptive, and is capable of handling nonlinearities. The performance approaches that of a full-fledged maximum-likelihood sequence detector.

A structured channel estimator for maximum likelihood sequence detection in multipath fading channels

This paper describes a channel estimator using known prior information about the transmit and receive filters, it is shown that the composite channel lies in a certain subspace obtained from the impulse responses of these filters. A structured linear channel model is then developed that is linearly parameterized by an unknown vector. To illustrate the potential usefulness of such an approach, the estimated structured channel is used in a multisensor and oversampled maximum likelihood sequence estimation (MLSE) receiver. We also present expressions on the pairwise error probability for the MLSE receiver based on the structured channel model. Using these results, we investigate the phenomenon of error flooring.

Decision-feedback equalization of pulse-position modulation on measured nondirected indoor infrared channels

We examine the performance of two decision-feedback equalizers (DFEs) for pulse-position modulation (PPM) on measured nondirected indoor infrared channels with intersymbol interference. PPM offers high average-power efficiency, but on ISI channels, unequalized PPM suffers severe performance penalties. We have previously examined the performance of the maximum-likelihood sequence detector (MLSD), and found that it yields significant improvements. However, the MLSD often requires such large complexity and delay that it may be impractical. We investigate suboptimal, reduced-complexity equalization techniques for PPM, providing a performance analysis of zero-forcing chip-rate and symbol-rate DFEs. Our results show that a symbol-rate DFE provides performance that closely approaches that of the optimal MLSD.

Partitioning of spreading sequences for increased minimum distance using CPFSK modulation

By using continuous-phase frequency shift keying (CPFSK) in a direct-sequence code-division multiple-access (DS-CDMA) system, and by partitioning the spreading sequence so that differing patterns of plus and minus chips are multiplied onto successive data bits, the net phase change will differ from bit to bit, giving an apparent variation in modulation index similar to multi-h CPFSK. This gives similar coding gain effects as multi-h CPFSK when maximum-likelihood sequence detection is used. Improved probability of error performance in terms of increased minimum distance has been demonstrated when the spreading sequence of a CDMA system is properly overlaid on outgoing data bits in the CPFSK modulation scheme. At the best modulation index observed, h=5/7, a computer search shows /spl sim/1.4-dB advantage over binary phase shift keying, and a /spl sim/0.6-dB advantage over the best fixed-h CPFSK.

Adaptive state allocation algorithm in MLSD receiver for multipath fading channels: structure and strategy

This paper presents the adaptive state allocation (ASA) algorithm, a new scheme based on maximum likelihood sequence detection (MLSD) of signals transmitted over Rayleigh fading channels. Although MLSD is an optimal scheme, its computational complexity limits many applications. The ASA algorithm is a detection method whose performance is close to that of MLSD, but with greatly reduced computational complexity. Adaptive state partitioning in the trellis diagram is used in this algorithm by measuring the short-term received signal power. Also, an adaptive threshold for selecting only a few states of the trellis is employed in this algorithm based on the Chernoff distance between the probability density functions (PDFs) of correct and incorrect branch metrics. The ASA-DF, a special case of ASA using decision feedback, shows a very good tradeoff between the performance and computational complexity for selective fading channels. Using ASA with diversity reception not only improves the performance, but also decreases the computational complexity in comparison with the computational complexity of using MLSD with diversity reception.

Receiver structures for time-varying frequency-selective fading channels

Several receiver structures for linearly modulated signals are proposed for time-varying frequency-selective channels. Their channel estimators explicitly model the time variation of the channel taps via polynomials. These structures are constructed from the following building blocks: (i) sliding or fixed block channel estimators; (ii) maximum likelihood sequence detectors (MLSDs) or decision feedback equalizers (DFEs); and (iii) single or multiple passes. A sliding window channel estimator uses a window of received samples to estimate the channel taps within or at the end of the window. Every symbol period, the window of samples is slid along another symbol period, and a new estimate is calculated. A fixed block channel estimator uses all received samples to estimate the channel taps throughout the packet, all at once. A single pass receiver estimates the channel and detects data once only. A multipass receiver performs channel estimation and data detection repetitively. The effect of the training symbol positions on the performance of the block multipass approach is studied. The bit error rate (BER) performance of the MLSD structures is characterized through simulation and analysis. The proposed receivers offer a range of performance/complexity tradeoffs, but all are well suited to time-varying channels. In fast fading channels, as the signal-to-noise ratio (SNR) increases, they begin to significantly outperform the per-survivor processing-based MLSD receivers which employ the least mean-squares (LMS) algorithm for channel estimation.

Breadth-first maximum likelihood sequence detection: basics

The problem of performing breadth-first maximum likelihood sequence detection (MLSD) under given structural and complexity constraints is solved and results in a family of optimal detectors. Given a trellis with S states, these are partitioned into C classes where B paths into each class are selected recursively in each symbol interval. The derived result is to retain only those paths which are closest to the received signal in the Euclidean (Hamming) distance sense. Each member in the SA(B, C) family of sequence detectors (SA denotes search algorithm) performs complexity constrained MLSD for the additive white Gaussian noise (AWGN) (BSC) channel. The unconstrained solution is the Viterbi algorithm (VA). Analysis tools are developed for each member of the SA(B, C) class and the asymptotic (SNR) probability of losing the correct path is associated with a new Euclidean distance measure for the AWGN case, the vector Euclidean distance (VED). The traditional Euclidean distance is a scalar special case of this, termed the scalar Euclidean distance (SED). The generality of this VED is pointed out. Some general complexity reductions exemplify those associated with the VA approach.

Adaptive MLSDE using the EM algorithm

The theory of adaptive sequence detection incorporating estimation of channel and related parameters is studied in the context of maximum-likelihood (ML) principles in a general framework based on the expectation and maximization (EM) algorithm. A generalized ML sequence detection and estimation (GMLSDE) criterion is derived based on the EM approach, and it is shown how the per-survivor processing and per-branch processing methods emerge naturally from GMLSDE. GMLSDE is developed into a real time detection/estimation algorithm using the online EM algorithm with coupling between estimation and detection. By utilizing Titterington's (1984) stochastic approximation approach, different adaptive ML sequence detection and estimation (MLSDE) algorithms are formulated in a unified manner for different channel models and for different amounts of channel knowledge available at the receiver. Computer simulation results are presented for differentially encoded quadrature phase-shift keying in frequency flat and selective fading channels, and comparisons are made among the performances of the various adaptive MLSDE algorithms derived earlier.

Coding and equalization for PPM on wireless infrared channels

We analyze the performance of trellis-coded pulse-position modulation with block decision-feedback equalization (BDFE) and parallel decision-feedback decoding (PDFD) on indoor, wireless infrared channels. We show that the reduced complexities of BDFE and PDFD as compared to maximum-likelihood sequence detection allow for better codes whose increased coding gain more than compensates for the penalty due to suboptimal detection. We quantify these net gains in performance over a range of dispersive channels, indicating where BDFE and PDFD provide the best performance. Finally, we present Monte Carlo simulation results to verify our analysis.

Equalization techniques for high-density magnetic recording

The advent of digital computers spurred the development of magnetic tape and disk-drive storage systems capable of storing large amounts of digital information. Since the early development of such systems in the 1950s, we have experienced a phenomenal growth in the use of digital storage systems and an equally large increase in storage capacity and storage density. Over the past four decades, the major factor contributing to the large increases in storage density and capacity has been the continuous technological improvements in the design and development magnetic media and heads. As the storage densities increase, signal processing becomes an important tool in the reconstruction of the digital information in the readback process. We present a tutorial treatment of signal-processing techniques for combating intersymbol interference inherent in high-density digital magnetic recording systems. We focus primarily on magnetic disk systems. We observed that the optimum detector for the ISI-corrupted signal is a maximum-likelihood sequence detector (MLSD) that can be efficiently implemented by means of the Viterbi algorithm.

A compact neural network for partial-response maximum-likelihood detectors: algorithmic study

A compact neural network algorithm for partial-response maximum-likelihood (PRML) sequence detection is presented. Compact neural networks are a class of locally connected neural networks suitable for very large scale integration (VLSI) implementation. The hardware complexity for VLSI implementation of the proposed algorithm grows linearly with the level of the deliberately designed symbol interference effects of the partial-response (PR) signalling scheme. Large dedicated memory for storage of likelihood matrices in digital Viterbi-algorithm-based detectors is not needed for the proposed detector. Detailed analysis on network stability for network topology and time constant of an analog neuron is described. This detector algorithm has competitive bit-error rate performance when compared with the digital Viterbi algorithm under the noise condition for many real-world applications. The proposed algorithm is suitable for analog VLSI implementation because of its low time complexity and linear area complexity for the detection of PRML signalling schemes.

The condition for the applicability of the Viterbi algorithm with implications for fading channel MLSD

The general condition for the optimality of the Viterbi algorithm (VA) as a method for implementing maximum-likelihood sequence detection (MLSD) is described. It is shown that this folding condition is not met for the fading linear Gaussian channel. This clarifies previously published results and allows approaches for approximate MLSD to be viewed as an attempt to force the VA as a suboptimal solution.

2.8 V asynchronous high-speed current comparator for sequence detection applications

A low voltage, low power current-mode comparator is described. The circuit features a wide dynamic range and very high-speed asynchronous operation and is intended for use in maximum likelihood sequence detection (MLSD) applications.

Linear predictive receivers for fading channels

The authors discuss maximum likelihood sequence detection (MLSD) based on prediction techniques for linearly modulated digital signals transmitted over fading channels. Efficient implementations of the sequence detector are investigated and a general formulation for computing the prediction coefficients is derived. Furthermore, the equivalence of different existing prediction-based receivers is shown.

Detection of stochastic processes

This paper reviews two streams of development, from the 1940's to the present, in signal detection theory: the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance. This treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous-time stochastic processes. The mathematics and intuition behind such developments as the matched filter, the RAKE receiver, the estimator-correlator, maximum-likelihood sequence detectors, multiuser detectors, sequential probability ratio tests, and cumulative-sum quickest detectors, are described.

Design of equalized maximum-likelihood receiver

A receiver structure referred to as equalized maximum likelihood (EML) is proposed to reduce the complexity of the maximum-likelihood sequence detector (MLSD). Performance of EML is evaluated through the bit-error rate (BER) measurement for a magnetic recording channel. EML exhibits 1-dB gain over the conventional partial response maximum likelihood (PRML) for 10/sup -5/ BER.

Architecture and Design of 1-D Enhanced Cellular NeuralNetwork Processors for Signal Detection

One-dimensional cellular array processor architecture and design for neural-based partial response (PR) signal detection are presented. Analog parallel computing approaches have many attractive advantages in achieving low power, low cost, and faster processing speed by its uniquely coupled parallel and distributed processing nature. In this paper, we describe the maximum likelihood sequence estimation (MLSE) algorithm for PR signals, the enhanced Cellular Neural Network (CNN) processor array architecture to realize the detection algorithm, and system performance evaluation. Analytical models and simulations on a design example of the detector have been employed to demonstrate the advantages of this scalable VLSI architecture. A processing rate of 265 Mbps was achieved for a prototype detector on a silicon area of 5.14 mm by 5.81 mm is a 1.2 µm CMOS technology. The processing rate can be beyond 1Gbps if it is implemented in the same amount of silicon area by using 0.5 µm CMOS technology. Such promising results clearly demonstrate the ability to meet the needs in future high speed data communication by VLSI realization of maximum likelihood sequence detectors based on the enhanced cellular neural network paradigm.