Reduced state MAP algorithm with modified branch metric

An iterative receiver with soft decision feedback is derived to yield a maximum a posteriori (MAP) estimate of fast Rayleigh flat fading channels. The derivation is based on the expectation-maximization (EM) algorithm. Simulation results indicate that the derived receiver performs better than an iterative receiver with hard decision feedback, for both uncoded data and convolutionally coded data. The combination with turbo codes is also investigated. Three kinds of decision feedback are proposed and compared namely, re-encoder, soft decision feedback and quantizer. It is shown via simulation that soft decision feedback is the best while the quantizer has similar performance. The re-encoder, on the other hand has performance degradation.

The large-system performance of iterative multiuser decision-feedback detectors (DFDs) is studied for synchronous coded direct-sequence code-division multiple access. Both successive and parallel demodulation of users are considered. The filters are optimized according to the minimum mean-squared error criteria, assuming perfect feedback. We first consider Viterbi decoding with hard decision feedback, and compute union bounds on the large-system error rate. We then consider maximum a posteriori (MAP) decoding with soft decision feedback, and evaluate the error rate semianalytically by assuming the log-likelihood ratios computed by the MAP decoder are Gaussian random variables. Performance is studied numerically as a function of noise level, spectral efficiency, and code rate. Results show that soft decision feedback gives substantial gains relative to hard decision feedback. At moderate spectral efficiencies (users divided by bandwidth expansion less than 0.9), the iterative DFDs with soft decision feedback based on a posteriori probabilities can achieve near-single-user performance at an E/sub b//N/sub 0/ close to the large-system capacity bound.

A detection scheme built on a combination of a simplified branch metric based search and refined calculation is proposed in this work to reduce the computational complexity of the quasi-maximum-likelihood (QML) detectors, such as the QR-decomposition combined with M-algorithm (QRD-M), list sequential sphere decoder (LISS) and list sphere decoding (LSD), for multiple-input multiple-output (MIMO) multiplexing systems, while maintaining similar performance to the original methods. More specifically, the proposed method utilizes a multiplication-free accumulated branch metric to first identify the potential candidates with significantly reduced search complexity. The optimal solution is then determined by the standard squared Euclidean distance metric from the initial candidates. The key idea of the proposed method lies in the fact that the best candidate identified by the simplified branch metric coincides with that of which is based on the conventional one with a high probability for a properly designed parameter. Numerical results demonstrates that the QRD-M detector using the proposed method achieves significantly better performance than the conventional one with comparable (or even less) computational complexity.

: Reception of one or more signals, overlapping in frequency and time with the desired signal, is commonly called cochannel interference. Joint detection is the optimal minimum probability of error decision rule for cochannel interference. This dissertation investigates the optimum approach and a number of suboptimum approaches to joint detection when a priori information based in fields, or sets of transmitted symbols, is available. In the general case the solution presents itself as a time-varying estimation problem that may be efficiently solved with a modified Bahl, Cocke, Jelinek and Raviv (BCJR) algorithm. The low-entropy properties of a particular signal of interest, the Automatic Identification System (AIS), are presented. Prediction methods are developed for this signal to be used as a priori information for a joint field-based maximum a posteriori (MAP) detector. Advanced joint detection techniques to mitigate cochannel interference are found to have superior bit error rate (BER) performance than can be obtained compared to traditional methods.

This paper relates to the application method of channel state information (CSI) to the Viterbi (maximum likelihood) decoder in the digital terrestrial television broadcasting system. The proposed Viterbi decoder uses the CSI derived from the pilots inserted in the transmitter of the COFDM (coded orthogonal frequency division multiplexing) system. The CSI is calculated by interpolation using the pilots in the receiver. The active real (I) and imaginary (Q) data after equalization are transferred to the branch metric calculation block that decides the euclidean distance for soft decision decoding and also the estimated CSI values are transferred to the same block. After calculating the euclidean distance for the soft decision decoding, the euclidean distance of the branch metric is multiplied by CSI. To do so, new branch metric values that consider each carrier state information are obtained. We simulated this method in Rayleigh fading defined in the ETSI standard. From the simulation, this method has better performance of about 0.15 dB to 0.7 dB and 2.2 dB to 2.9 dB in the Rayleigh channel than that of conventional soft decision Viterbi decoding with or without a bit interleaver where the constellation is QPSK, l6-QAM and 64-QAM.

Three-dimensional maximum a posteriori (MAP) imaging with radiopharmaceuticals labeled with three Cu radionuclides

Super-resolution (SR) aims at generating a high resolution image or image sequence from several slightly different low-resolution images. In previous work, we have showed that a Maximum A Posteriori (MAP) SR algorithm can yield significant image quality enhancement of the individual respiratory gated PET frames. However, in the past it has been also argued that image-based motion correction algorithms yield sub-optimal results, particularly when images are reconstructed using iterative methods. Here, we evaluate the results incorporating MAP SR directly as part of the One-Step-Late (OSL) reconstruction algorithm. The evaluation used GATE simulated data. The IEC phantom with lesions between 10–37mm (contrast 8/1) was used to simulate 200 noise realizations of 6 frames, each shifted by 3mm along the z-axis relative to each other. The algorithm was also tested on four realistic phantoms. Gated respiratory images were reconstructed with the OPL-EM algorithm. Superresolution was performed through a MAP algorithm either as part of the reconstruction process or as a post-processing step applied to the individually reconstructed gated frames. A Huber prior was used as regularization term while the function yielded by the MAP method was optimized through a quasi-Newton algorithm. We compared signal-to-noise ratio (SNR) and contrast, as well as the bias-variance tradeoff for each algorithm. SR incorporated reconstruction led to 9% and 14% higher SNR and contrast respectively compared to the image-based SR. The bias-variance tradeoff showed that reconstruction-incorporated SR has a bias and variance of 39% lower and 60% higher respectively compared to image-based SR.

This paper presents a quantitative performance evaluation method for the maximum a posteriori (MAP) state estimate fusion algorithm. Under ideal conditions where data association is assumed to be perfect, it has been shown that the MAP or best linear unbiased estimate (BLUE) fusion formula provides the best linear minimum mean squared estimate (LMMSE) given local estimates under the linear Gaussian assumption for a static system. However, for a dynamic system where fusion is recursively performed by the fusion center on local estimates generated from local measurements, it is not obvious how the MAP algorithm will perform. In the past, several performance evaluation methods have been proposed for various fusion algorithms, including simple convex combination, cross-covariance combination, information matrix, and MAP fusion. However, not much has been done to quantify the steady state behavior of these fusion methods for a dynamic system. The goal of this work is to present analytical fusion performance results for MAP state estimate fusion without extensive Monte Carlo simulations, using an approach developed for steady state performance evaluation for track fusion. Two different communication strategies are considered: fusion with and without feedback to the sensors. Analytic curves for the steady state performance of the fusion algorithm for various communication patterns are presented under different operating conditions.

This paper compares a number of decision feedback schemes that improve the initial channel estimates provided by the pilot symbols alone. The decision feedback scheme that feeds back the systematic bits achieves about the same performance as feeding back both the systematic and parity bits at the low fading rate. Its performance is slightly degraded at the higher fading rate. The advantage of this scheme is its lower complexity as the LLRs of the systematic bits are readily available in the turbo decoding process. Soft decision feedback does not always provide large improvement in performance. Noticeable gain in performance using soft decision feedback is seen only when the bits to be fed back are not reliable during the first few iterations.

Maximum likelihood (ML) detection algorithm for multiple input multiple output (MIMO) systems provided the best bit error rate (BER) performance with heavy calculating complexity. The use of QR decomposition with M-algorithm (QRD-M) had been proposed to provide near-ML detection performance and lower calculating complexity. However, its complexity still grew exponentially with increasing dimension of the transmitted signal. To reduce the problem, an improved detection scheme was proposed here. After constructing the tree detecting model of MIMO systems, the ML search of one layer was done, the branch metrics were calculated and sorted, which gave an ordered set of the layer, then depth-first search were used to search the left layers with termination methods. The proposed algorithm provides near QRD-M detection performance.

Limited-data tomography, to which electromagnetic geotomography belongs, is analyzed in this paper. In this technique, a discrete forward projection model may be expressed by a rank-deficient system of linear equations whose the nullspace is non-trivial. This means that some image components may fall into the nullspace, and hence the minimal-norm least-square solution, to which many image reconstructions methods converge, may be different from the true one. The Algebraic Reconstruction Technique (ART), Simultaneous Iterative Reconstruction Technique (SIRT), or Conjugate Gradients Least Squares (CGLS) are examples of such methods. In this paper, we deal with the question of how to partially recover the missing image components. First, we analyze the advantages of using the iterative Tikhonov regularization and the Maximum A Posteriori (MAP) algorithm with Gibbs prior. Then, we conclude that the missing (nullspace) image components can be partially recovered if the MAP algorithm is implemented through a multigrid technique. The results, which are presented for synthetic noise-free and noisy data, demonstrate the validity of our assumption. The problem of estimating the regularization and scaling parameters in the MAP algorithm is also addressed.

The maximum a posteriori (MAP) probability algorithm and the soft output Viterbi algorithm (SOVA), usually known as soft in soft out (SISO) algorithms are used for data detection in non minimum phase channels representative of an outdoor cellular wireless environment. The performance of combinations of MAP and SOVA based equalizer and decoder is evaluated by simulation experiment. The performance does not improve much for more than five iterations in a severe ISI channel. The results obtained for 1 dB to 4 dB bit energy to noise power show that almost identical results are obtained for two other combinations of the SOVA and MAP in a serial concatenated scheme to take care of ISI. Theoretical analysis seems to support the viewpoint that all 4 possible combinations of MAP and SOVA algorithms result in an almost identical performance towards higher iteration numbers. Hence, SOVA-SOVA combination may be more suitable from implementation point of view than the other 3 combinations

This paper considers the joint design of bit loading, precoding and receive filters for a multiple-input multiple-output (MIMO) digital communication system employing decision feedback (DF) detection at the receiver. Both the transmitter as well as the receiver are assumed to know the channel matrix perfectly. It is well known that, for linear MIMO transceivers, a diagonal transmission (i.e., orthogonalization of the matrix channel) is optimal for some criteria. Surprisingly, it was shown five years ago that for the family of Schur-convex functions an additional rotation of the symbols is necessary. However, if the bit loading is optimized jointly with the linear transceiver, then the rotation is unnecessary. Similarly, for DF MIMO transceivers, a rotation of the symbols is sometimes needed. The main result of this paper shows that for a DF MIMO transceiver where the bit loading is jointly optimized with the transceiver filters, the rotation of the symbols becomes unnecessary and, consequently, also the DF part of the receiver is not required.

Emission tomography imaging modality has given a new dimension to the field of medicine and biology. The maximum a posteriori (MAP) and maximum likelihood (ML) algorithms are the widely used reconstruction algorithms for emission tomography. However, the images reconstructed by MAP and ML methods still suffer from artifacts such as noise, over-smoothing and streaking artifacts. These algorithms often fail to recognize the density class in the reconstruction and hence result in over penalization causing blurring effect. A good knowledge of prior distribution is a must for MAP-based method. Recently proposed median root prior (MRP) algorithm preserves the edges in the image, but the reconstructed image suffers from step like streaking artifact. In this work, a fuzzy logic based approach is proposed for the pixel-pixel nearest neighborhood interaction. The proposed algorithm consists of two elementary steps: (1) edge detection-fuzzy rule based derivatives are used for the detection of edges in the nearest neighborhood window; (2) fuzzy smoothing penalization is performed only for those pixels for which edges are missing in the neighborhood window. Analysis shows that the proposed fuzzy rule based reconstruction algorithm is capable of producing better estimates compared to the images reconstructed by MAP and MRP algorithms. The reconstructed images are sharper with small features being better resolved due to the nature of the fuzzy potential function.

In this correspondence, we study algorithmic approach to solving the problem of maximum a posteriori (MAP) estimation of Markov sequences transmitted over noisy channels, which is also known as the MAP decoding problem. For the class of memoryless binary channels that produce independent substitution and erasure errors, the MAP sequence estimation problem can be formulated and solved as one of the longest path in a weighted directed acyclic graph. But for algorithm efficiency, we transform the graph problem to one of matrix search. If the underlying matrix is totally monotone, then the complexity of MAP sequence estimation can be greatly reduced. We give a sufficient condition for the matrix induced by MAP sequence estimation to be totally monotone, which is indeed the case if the input sequence is Gaussian Markov. Under this condition, the complexity of MAP decoding can be reduced from O(N/sup 2/M) to O(NM), where N is the size of source alphabet and M is the length of input sequence. Furthermore, for Markov sequences of fixed-length code we propose a block parsing strategy to reduce the complexity of MAP sequence estimation to O(M+N/sup 2/M/logM) or to O(M+NM/logM), depending on if the total monotonicity holds. Another significance of this correspondence lies in the applicability of the presented algorithmic approach, which has been thoroughly studied in computer science literature, to many other discrete optimization problems encountered in both source and channel coding, ranging from optimal multiresolution and multiple-description quantizer design, to context quantization for minimum conditional entropy, and to optimal packetization with uneven error protection.