Wireless Communications

The Viterbi algorithm (VA) is a recursive optimal solution to the problem of estimating the state sequence of a discrete-time finite-state Markov process observed in memoryless noise. Many problems in areas such as digital communications can be cast in this form. This paper gives a tutorial exposition of the algorithm and of how it is implemented and analyzed. Applications to date are reviewed. Increasing use of the algorithm in a widening variety of areas is foreseen.

The viterbi algorithm

A maximum-likelihood sequence estimator for a digital pulse-amplitude-modulated sequence in the presence of finite intersymbol interference and white Gaussian noise is developed, The structure comprises a sampled linear filter, called a whitened matched filter, and a recursive nonlinear processor, called the Viterbi algorithm. The outputs of the whitened matched filter, sampled once for each input symbol, are shown to form a set of sufficient statistics for estimation of the input sequence, a fact that makes obvious some earlier results on optimum linear processors. The Viterbi algorithm is easier to implement than earlier optimum nonlinear processors and its performance can be straightforwardly and accurately estimated. It is shown that performance (by whatever criterion) is effectively as good as could be attained by any receiver structure and in many cases is as good as if intersymbol interference were absent. Finally, a simplified but effectively optimum algorithm suitable for the most popular partial-response schemes is described.

Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference

Consider a Gaussian multiple-access channel shared by K users who transmit asynchronously independent data streams by modulating a set of assigned signal waveforms. The uncoded probability of error achievable by optimum multiuser detectors is investigated. It is shown that the K -user maximum-likelihood sequence detector consists of a bank of single-user matched filters followed by a Viterbi algorithm whose complexity per binary decision is O(2^{K}) . The upper bound analysis of this detector follows an approach based on the decomposition of error sequences. The issues of convergence and tightness of the bounds are examined, and it is shown that the minimum multiuser error probability is equivalent in the Iow-noise region to that of a single-user system with reduced power. These results show that the proposed multiuser detectors afford important performance gains over conventional single-user systems, in which the signal constellation carries the entire burden of complexity required to achieve a given performance level.

Minimum probability of error for asynchronous Gaussian multiple-access channels

Space-time codes (STC) are a class of signaling techniques, offering coding and diversity gains along with improved spectral efficiency. These codes exploit both the spatial and the temporal diversity of the wireless link by combining the design of the error correction code, modulation scheme and array processing. STC are well suited for improving the downlink performance, which is the bottleneck in asymmetric applications such as downstream Internet. Three original contributions to the area of STC are presented in this dissertation. First, the development of analytic tools that determine the fundamental limits on the performance of STC in a variety of channel conditions. For trellis-type STC, transfer function based techniques are applied to derive performance bounds over Rayleigh, Rician and correlated fading environments. For block-type STC, an analytic framework that supports various complex orthogonal designs with arbitrary signal cardinalities and array configurations is developed. In the second part of the dissertation, the Virginia Tech Space-Time Advanced Radio (VT-STAR) is designed, introducing a multi-antenna hardware laboratory test bed, which facilitates characterization of the multiple-input multiple-output (MIMO) channel and validation of various space-time approaches. In the third part of the dissertation, two novel space-time architectures paired with iterative processing principles are proposed. The first scheme extends the suitability of STC to outdoor wireless communications by employing iterative equalization/decoding for time dispersive channels and the second scheme employs iterative interference cancellation/decoding to solve the error propagation problem of Bell-Labs Layered Space-Time Architecture (BLAST). Results show that remarkable energy and spectral efficiencies are achievable by combining concepts drawn from space-time coding, multiuser detection, array processing and iterative decoding.

Space-Time Codes for High Data Rate Wireless Communications

A linear correspondence is developed between the states of a rate- k/n convolutional encoder G and the states of a corresponding syndrome former H^T , where H is an encoder of the code dual to the code generated by G . This correspondence is used to find an expression for the number of all-zero paths of length \tau in the code trellis; the answer depends only on the constraint lengths of the dual code. A partial answer to the resynchronization problem also falls out of this development.

Structural analysis of convolutional codes via dual codes

A lower bound on the symbol error probability achieved by any estimator of a digital pulse-amplitude-modulated sequence in the presence of white Gaussian noise and intersymbol interference is presented. The bound reduces to the well-known single-pulse error probability bound when intersymbol interference is small, but is tighter when interference is large. For example, on the singlepole ( RC ) channel, the effective signal-to-noise ratio for any estimator is shown to decrease by at least 3 dB for every doubling in pulse rate T-1as T \rightarrow 0 and, on the double-pole channel, by at least 9 dB, thus disproving a recent conjecture [2] on the performance of nonlinear receivers.

Jr. G. Forney

Papers

Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference

Structural analysis of convolutional codes via dual codes

Lower Bounds on Error Probability in the Presence of Large Intersymbol Interference