A computational cost reduction scheme for a post-distortion type nonlinear distortion compensator of OFDM signals is proposed, and compared with the conventional sub-optimum detection scheme. The proposed scheme utilizes the principle that a complex OFDM signal can be demodulated with not only both I-phase (real part) and Q-phase (imaginary part) components, but also either of them. Usually each phase of an OFDM signal exhibits different signal envelope and they are distorted differently by the nonlinearity of a power amplifier. Consequently, three output sequence patterns can be obtained at the receiver. By comparing these outputs, we can know the erroneous positions of these sequences to some extent. By the aid of this comparison, we need to evaluate only a limited number of replicas for the compensation process of the post-distortion type nonlinear distortion compensator, which results in the computational cost reduction. We have proposed four new compensation schemes based on this idea and derived their performance in terms of the bit error rate and the average number of calculations.

Conventional approach for frequency estimation usually assume a single tone without data modulation. In many applications such an assumption, realized by using either a separate pilot beacon or synchronization preamble is not feasible. This paper deals with frequency estimation of phase-modulated carriers in the absence of timing information and known data pattern. We introduce new frequency estimators that are based on the generalized maximum likelihood principle. The communication channels under consideration include both additive white Gaussian noise (AWGN) channels and correlated Rician fading channels. For the latter class, we distinguish between the case when the fading (amplitude) process is tracked and that when it is not tracked.

Recently, a trellis-based recursive maximum likelihood decoding (RMLD) algorithm has been proposed for decoding binary linear block codes. This RMLD algorithm is computationally more efficient than the Viterbi decoding algorithm. However, the computational complexity of the RMLD algorithm depends on the sectionalization of a code trellis. In general, minimization of the computational complexity results in non-uniform sectionalization of a code trellis. From implementation point of view, uniform sectionalization of a code trellis and regularity among the trellis sections are desirable. In this paper, we apply the RMLD algorithm to a class of codes which are transitive invariant. This class includes Reed-Muller (RM) codes, the extended and permuted BCH (EBCH) codes and their subcodes. For this class of codes, the binary uniform sectionalization of a code trellis results in the following regular structure. At each step of decoding recursion, the metric table construction procedure is applied uniformly to all the sections and the size and structure of each metric table are the same. This simplifies the implementation of the RMLD algorithm. Furthermore, for all RM codes of lengths 64 and 128 and EBCH codes of lengths 64 and 128 with relatively low rate, the computational complexity of the RMLD algorithm based on the binary uniform sectionalization of a code trellis is almost the same as that based on an optimum sectionalization of a code trellis.

We consider methods to locate sync words in packet or frame transmission over the additive white Gaussian noise channel. Our starting point is the maximization of the probability of correctly locating the sync word. We extend Massey's original result to the specific synchronization problem, where the sync words is prefixed to the data stream and each packet is preceded by idle transmission or additive white Gaussian noise. We give simulation results for several interesting sync words such as Barker sequences of length 7 and 13 and a sync word of length 17 with good cross-correlation properties. One of the conclusions is that the newly derived formula for the probability of correctly locating the sync word enables the reduction of the false sync detection probability.

Adaptive maximum likelihood (ML) detection implemented by the Viterbi algorithm (VA) is proposed for the reception of MPSK signals in frequency nonselective fast Rayleigh fading. M-state VA, each state in the VA trellis represents a signal constellation point, is used. Diversity reception is incorporated into the structure of Viterbi decoding. The pilot symbol (unmodulated carrier) is periodically inserted to terminate the trellis so that the phase ambiguity of the detected data sequence is avoided. Applying the per-survivor processing principle (PSPP), adaptive ML detection performs adaptive channel estimation using a simple linear predictor at all trellis states in parallel. The predictor coefficient is stochastically adapted without requiring a priori knowledge of fading channel statistics, based on a recursive least-squares (RLS) adaptation algorithm, to match changes in the statistical properties of the channel (i.e., AWGN of fast/slow fading) using both data and pilot symbols. Simulations of 4PSK signal transmission demonstrate that the proposed adaptive ML detection scheme can track fast fading, thus significantly reducing the irreducible bit error rate (BER) due to Doppler spread in the fading channel. It is also shown that adaptive ML detection provides BER performance close to ideal coherent detection (CD) in AWGN channels.

Approximate maximum likelihood (ML) detection implemented by a reduced state Viterbi algorithm (VA), called the reduced state Viterbi coherent detection (RSVCD) algorithm in this paper, is described for the reception of uncoded M-ary PSK (MPSK) signals transmitted over additive white Gaussian noise (AWGN) channels. An M-state trellis, each state representing one of M signal constellation points, is used. The RSVCD algorithm performs parallel channel estimation based on the per-survivor processing principle (PSPP). Simple decision feedback CD (DFCD) is deduced as a special case of RSVCD. Unified BER expressions are derived for RSVCD, DFCD, and approximate ML detection implemented as an ML-state Viterbi algorithm (referred to as VACD) [6] as well as ideal CD and differential detection (DD). Computer simulation results are also presented and compared with theoretical results.

The present paper clarifies that the variance of the maximum likelihood estimator (MLE) of a parameter does not reach the Cramer-Rao lower bound (CRLB) when fitting a straight-line to observed two-dimensional data. In addition, the variance of the MLE can be shown to be equal to the CRLB only if observed noise reduces to a one-dimensional Gaussian variable. For most practical applications, it can be assumed that noise is added only to the range direction. In this case, the MLE is clearly an asymptotically effective estimator. However, even if we assume such a noise model, ML line-fitting to the data from many points of view has a high computational cost. The present paper proposes an alternative fitting method in order to provide a cost-effective unbiased estimator. The reliability of this new method is analyzed statistically and by computer simulation.

A joint estimator for carrier phase, symbol timing, and data sequence is proposed. This fully digital scheme is systematically derived from the maximum likelihood estimation (MLE) theory. The simulation and the analytical results demonstrate that the scheme is asymptotical to the optimum in AWGN channel.

The estimation of model parameter is essentially important for an MRF image model to work well. Because the maximum likelihood estimate (MLE), which is statistically optimal, is too difficult to implement, the conventional estimates such as the maximum pseudo-likelihood estimate (MPLE), the coding method estimate (CME), and the least-squares estimate (LSE) are all based on the (conditional) pixel probabilities for simplicity. However, the conventional pixel-based estimators are not very satisfactorily accurate, especially when the interactions of pixels are strong. We therefore propose two window-based estimators to improve the estimation accuracy: the adjoining-conditional-window (ACW) scheme and the separated-conditional-window (SCW) scheme. The replacement of the pixel probabilities by the joint probabilities of window pixels was inspired by the fact that the pixels in an image present information in a joint way and hence the more pixels we deal with the joint probabilities of, the more accurate the estimate should be. The window-based estimators include the pixel-based ones as special cases. We present respectively the relationship between the MLE and each of the two window-based estimates. Through the relationships we provide a unified view that the conventional pixel-based estimates and our window-based estimates all approximate the MLE. The accuracy of all the estimates can be described by two types of superiority: the cross-scheme superiority that an ACW estimate is more accurate than the SCW estimate with the same window size, and the in-scheme superiority that an ACW (or SCW) estimate more accurate than another ACW (or SCW) estimate which uses smaller window size. The experimental results showed the two types of superiority and particularly the significant improvement in estimation accuracy due to using window probabilities instead of pixel probabilities.

The robust statistics has recently been adopted by the computer vision community. Various robust approaches in the computer vision research have been proposed in the last decade for analyzing the image motion from the image sequence. Because of the frequent violation of the Gaussian assumption of the noise and the motion discontinuities due to multiple motions, the motion estimates based on the straightforward approaches such as the least squares estimator and the regularization often produces unsatisfactory result. Robust estimation is a promising approach to deal with these problems because it recovers the intrinsic characteristics of the original data with the reduced sensitivity to the contamination. Several previous works exist and report some isolated results, but there has been no comprehensive analysis. In this paper robust approaches to the optical flow estimation based on the maximum likelihood estimators are proposed. To evaluate the performance of the M-estimators for estimating the optical flow, comparative studies are conducted for every possible combinations of the parameters of three types of M-estimators, two types of residuals, two methods of scale estimate, and two types of starting values. Comparative studies on synthetic data show the superiority of the M-estimator of redescending ψ-function using the starting value of least absolute residuals estimator using Huber scale iteration, in comparison with the other M-estimators and least squares estimator. Experimental results from the real image experiments also confirm that the proposed combinations of the M-estimators handle the contaminated data effectively and produce the better estimates than the least squares estimator or the least absolute residuals estimator.

In the usual optical flow detection, the gradient constraint, which expresses the relationship between the gradient of the image intensity and its motion, is combined with the least-squares criterion. This criterion means assuming that only the time derivative of the image intensity contains noise. In this paper, we assume that all image derivatives contain noise and derive a new optical flow detection technique. Since this method requires the knowledge about the covariance matrix of the noise, we also discuss a method for its estimation. Our experiments show that the proposed method can compute optical flow more accurately than the conventional method.

The uncertainty involved in the gradient constraint for optical flow detection is often modeled as constant Gaussian noise added to the time-derivative of the image intensity. In this paper, we examine this modeling closely and investigate the error behavior by experiments. Our result indicates that the error depends on both the spatial derivatives and the image motion. We propose alternative uncertainty models based on our experiments. It is shown that the optical flow computation algorithms based on them can detect more accurate optical flow than the conventional least-squares method.

In this paper, we study three-dimensional motion estimation using optical flow. We construct a weighted quotient-form objective function that provides an unbiased estimator. Using this objective function with a certain projection operator as a weight drastically reduces the computational cost for estimation compared with using the maximum likelihood estimator. To reduce the variance of the estimator, we examine the weight, and we show by theoretical evaluations and simulations that, with an appropriate projection function, and when the noise variance is not too small, this objective function provides an estimator whose variance is smaller than that of the maximum likelihood estimator. The use of this projection is based on the knowledge that the depth function has a positive value (i. e., the object is in front of the camera) and that it is generally smooth.

This paper presents a new method for solving the structure-from-motion problem for optical flow. The fact that the structure-from-motion problem can be simplified by using the linearization technique is well known. However, it has been pointed out that the linearization technique reduces the accuracy of the computation. In this paper, we overcome this disadvantage by correcting the linearized solution in a statistically optimal way. Computer simulation experiments show that our method yields an unbiased estimator of the motion parameters which almost attains the theoretical bound on accuracy. Our method also enables us to evaluate the reliability of the reconstructed structure in the form of the covariance matrix. Real-image experiments are conducted to demonstrate the effectiveness of our method.

The tandem structure of a matched filter (MF) and a maximum likelihood sequence estimator (MLSE) using the Viterbi algorithm (VA) has been considered to be an optimal receiver for digital pulse-amplitude sequences in the presence of intersymbol interference (ISI) and additive white Gaussian noise (AWGN). An adaptive array antenna has the capability of filtering received signals in the spatial domain as well as in the temporal one. In this paper, we propose a receiver structure using an adaptive array antenna, a digital filter and the VA that is spatially and temporally optimal for multi-user detection in a direct sequence code division multiple access (DS/CDMA) environment. This receiver uses a tapped delay line (TDL) array antenna and the VA, which provides a maximum likelihood sequence estimate from the spatially and temporally whitened matched filter (ST-WMF) output. Performance of the proposed receiver is evaluated by theoretical analysis and computer simulations.

This letter is concerned with the evaluation of the average computational complexity of the maximum likelihood decoding of a linear block code using its trellis diagram. Each section of the L-section minimal trellis diagram for a linear block code consists of parallel components which are structurally identical subgraphs without cross connection between them. A parallel component is also known to be decomposed into subgraphs, and a decoding algorithm by using the structure of the subgraphs of parallel components was proposed, and an upper bound on the worst case computational complexity was derived. In this letter, the average computational complexity of the decoding algorithm is evaluated by computer simulation. We evaluated the average numbers of additions and comparisons performed in the decoding algorithm for example codes, (64,45) extended and permuted binary primitive BCH code, the third order Reed-Muller (64,42) code and its (64,40) subcode. It is shown that the average numbers are much smaller than those for the worst case, and hence the decoding algorithm is efficient when the number of sections, L, is small, say 4 or 8, for the example codes. Especially, for the (64,45) extended binary primitive BCH code with L4, the average numbers of additions and comparisons in the decoding algorithm for finding the survivor's metric of each state after finding the smallest metric among parallel branches are about 1/50 and 17/100 of those in the conventional exhaustive search, respectively. The number of additions and comparisons by the conventional search for all the example codes is smallest when L is 4. As a result, the decoding algorithm with L4 gives the smallest number of operations among those decoding methods considered here.

A new upper hound on the error probability for maximum likelihood sequence estimation of digital signaling on intersymbol interference channels with additive white Gaussian noise is presented. The basic idea is to exclude all parallel error sequences and to exclude some of the overlapping error events from the union bound. It is shown that the new upper bound can be easily and efficiently computed by using a properly labeled error-state diagram and a one-directional stack algorithm. Several examples are presented that compare the new upper bound with bounds previously reported in the literature.

We prove that the maximum likelihood estimator for estimating 3-D motion from noisy optical flow is not optimal", i.e., there is an unbiased estimator whose covariance matrix is smaller than that of the maximum likelihood estimator when a Gaussian noise distribution is assumed for a sufficiently large number of observed points. Since Gaussian assumption for the noise is given, the maximum likelihood estimator minimizes the mean square error of the observed optical flow. Though the maximum likehood estimator's covariance matrix usually reaches the Cramér-Rao lower bound in many statistical problems when the number of observed points is infinitely large, we show that the maximum likelihood estimator's covariance matrix does not reach the Cramér-Rao lower bound for the estimation of 3-D motion from noisy optical flow under such conditions. We formulate a superior estimator, whose covariance matrix is smaller than that of the maximum likelihood estimator, when the variance of the Gaussian noise is not very small.

This paper proposes a new adaptive Interference Cancelling Equalizer (ICE) with a blind algorithm. From a received signal, ICE not only eliminates inter-symbol interference, but also cancels co-channel interference. Blind ICE can operate well even if training signals for the interference are unknown. First, training signal conditions for applying blind ICE are considered. Next, a theoretical derivation for blind ICE is developed in detail by applying the maximum likelihood estimation theory. It is shown that RLS-MLSE with diversity, which is derived for mobile radio equalizers, is also effective for blind ICE. Computer simulations demonstrate the 40kb/s QDPSK transmission performance of Blind ICE as a blind canceller with two branch diversity reception under Rayleigh fading in a single interference environment. The simulations assume synchronous training; the canceller is trained for the desired signal but not for the interference signals. Blind ICE can be successfully achieved at more than -10dB CIR values when average Eb/N0 is 15dB and a maximum Doppler frequency is 40Hz.

Upper bounds on the bit error probability and repeat request probability, and lower bounds on the throughput are derived for a Hybrid-ARQ scheme that employs trellis-coded modulation on a fading dispersive channel. The receiver employs a modified Viterbi algorithm to perform joint maximum likelihood sequence estimation (MLSE) equalization and decoding. Retransmissions are generated by using the approach suggested by Yamamoto and Itoh. The analytical bounds are extended to trellis-coded modulation on fading dispersive channels with code combining. Comparison of the analytical bounds with simulation results shows that the analytical bounds are quite loose when diversity reception is not employed. However, no other analytical bounds exist in the literature for the trellis-coded Hybrid ARQ system studied in this paper. Therefore, the results presented in this paper can provide the basis for comparison with more sophisticated analytical bounds that may be derived in the future.