Maximum A Posteriori Probability Detection Research Articles

Compensation Schemes for Transmitter- and Receiver-Based Pattern-Dependent Distortion

A nonlinear pre-distorter (NLPD) at the transmitter, and a maximum-a-posteriori probability (MAP) detector, time-domain Volterra nonlinear equalizer (VNLE), or sparse-VNLE at the receiver are compared for compensation of the pattern-dependent distortion that can occur in high baud rate transmitters and receivers. Experimental results are presented for a 1.206-Tb/s dual-polarization 16-ary quadrature amplitude-modulation (16-QAM) superchannel signal with three subcarriers. The NLPD with iterative calculation of the pre-distortion provides the best performance in back-to-back systems and transmission systems followed by the MAP detector, VNLE, and sparse-VNLE. At the FEC threshold of 1.9 × 10 -2 , the NLPD provides an increase in the transmission distance of 300 km compared with the sparse-VNLE, VNLE, and MAP detector. For transmission over 1500 km of SMF, the VNLE and MAP detector exhibit additional optical signal-to-noise ratio margins of 0.16 and 0.47 dB relative to the sparse-VNLE. Compared with the VNLE, the sparse-VNLE exhibits a 55% reduction in number of kernel coefficients.

Lattice reduction‐based iterative receivers: using partial bit‐wise MMSE filter with randomised sampling and MAP‐aided integer perturbation

For iterative detection and decoding (IDD) in multiple-input multiple-output systems, the maximum a posteriori probability (MAP) detector would be ideal in terms of the performance. However, due to its high computational complexity, various suboptimal low-complexity approximate MAP detectors have been studied. In this study, a lattice reduction (LR)-based detector is considered for a near-optimal performance for IDD. The authors improve further the performance by employing a partial bit-wise minimum mean square error (MMSE) approach with randomised sampling, which has a lower complexity than that of the full bit-wise MMSE method. Moreover, the list of candidate vectors obtained by randomised sampling is extended using a MAP-aided integer perturbation algorithm for a better performance with low additional complexity. Through simulation results, it is shown that a near-optimal performance can be obtained which is better than that of the LR-based randomised successive interference cancellation and the full bit-wise MMSE methods.

Optimal Detector Randomization in Cognitive Radio Systems in the Presence of Imperfect Sensing Decisions

In this study, optimal detector randomization is developed for secondary users in a cognitive radio system in the presence of imperfect spectrum sensing decisions. It is shown that the minimum average probability of error can be achieved by employing no more than four maximum a-posteriori probability (MAP) detectors at the secondary receiver. Optimal MAP detectors and generic expressions for their average probability of error are derived in the presence of possible sensing errors. Also, sufficient conditions are presented related to improvements due to optimal detector randomization.

Lattice Reduction-Based Approximate MAP Detection with Bit-Wise Combining and Integer Perturbed List Generation

For iterative detection and decoding (IDD) in multiple-input multiple-output (MIMO) systems, the log-likelihood ratio (LLR) of each coded bit can be found by an optimal bit-wise maximum a posteriori probability (MAP) detector. However, since this MAP detector requires a prohibitively high computational complexity, low-complexity suboptimal detectors are desirable. In this paper, lattice reduction (LR)-based MIMO detection is investigated to derive a low-complexity detector that can achieve near MAP performance for IDD. In order to approximate LLR values incorporating the extrinsic information provided by a soft-input soft-output (SISO) decoder, bit-wise LR-based minimum mean square error (MMSE) filters are derived. Furthermore, in order to minimize the performance degradation due to quantization (or rounding) errors in the LR-based detection, a low-complexity integer perturbed list generation method is proposed, where no tree search is used by taking advantage of a near orthogonal channel basis obtained by LR. Through a complexity analysis and simulations, it is shown that the proposed approach achieves near optimal performance, while the complexity is comparable with that of the MMSE soft cancellation method, which is known to be computationally efficient. As a bit-wise detector, a parallel implementation of the proposed method would be straightforward, which lowers the detection delay.

Approximate MAP Detection With Ordering and Successive Processing for Iterative Detection and Decoding in MIMO Systems

For iterative detection and decoding (IDD) in multiple-input multiple-output (MIMO) systems, the MIMO detector needs to provide soft-decisions. Since the complexity of the maximum a posteriori probability (MAP) detector grows exponentially with the number of transmit antennas, various suboptimal detectors are proposed to exploit the tradeoff between complexity and performance. Among them, the minimum mean square error (MMSE)-soft cancellation (SC) detector has an excellent tradeoff. In this paper, by noting that the MMSE-SC detector is an approximate MAP detector, another approximate MAP detector that uses successive processing is proposed. The proposed successive detector can provide a better performance than the MMSE-SC detector, while its complexity is comparable with that of the MMSE-SC detector. An interesting feature of the proposed successive detector is that the tradeoff between complexity and performance can be exploited by a single parameter, which could be an important control parameter in practical implementations.

A maximum a-posteriori identification criterion for wavelet domain watermarking

A detector based on Maximum A-posteriori Probability (MAP) criterion has been introduced for identifying image watermark in the Discrete Cosine Transform (DCT) domain. This type of detector has been shown to be optimum and robust to common image processing operations. In this paper, an MAP detector in the Discrete Wavelet Transform (DWT) domain is proposed. It is based on modelling the wavelet coefficients by a generalised Gaussian distribution. Simulations are used to compare the proposed detector with the conventional correlation detector in terms of detection effectiveness.

A Correlation Based Analysis for Approximate MAP Detectors and Iterative Receivers

In this paper, we consider two approximate maximum a posteriori probability (MAP) detectors for code division multiple access (CDMA) systems. We show that if the sum of multiple access interferences (MAI) is Gaussian (with certain mean and variance from the extrinsic information), the (well-known) minimum mean square error (MMSE) detector with soft interference cancellation (SIC), called the MMSE-SIC detector, becomes the MAP detector. Thus, for a large number of users, the MMSE-SIC detector becomes asymptotically the MAP detector. In addition, we consider a correlation based analysis for the iterative detection with the approximate MAP detectors to see the performance limit. Then, the correlation analysis is further generalized to analyze the performance of the iterative receiver consisting of an approximate MAP detectors and channel decoders for coded signals

Metric Selection for Reduced-Complexity MAP Detectors in MIMO Systems

Reduced-complexity maximum a posteriori probability (MAP) signal detection is a promising technique for multiple-input multiple-output space division multiplexing (MIMO-SDM) transmission. These detectors avoid exhaustive searches for all possible transmitted symbol vectors by generating a set of candidate symbol vectors. One problem with the reduced-complexity MAP detectors when used in conjunction with soft input decoders is the inaccuracy of log likelihood ratio (LLR) values since they are computed from a handful of candidate symbol vectors, which degrades the subsequent decoding process. To rectify this weakness, this paper proposes an LLR computation scheme for reduced complexity MAP detectors. The unique feature of the proposed scheme is that it utilizes the statistical property of the MIMO channel metric to narrow down further the number of candidate symbol vectors. Toward this goal, metric selection is performed to select only a statistically good portion of the candidate symbol vectors. Computer simulation results show that the proposed LLR computation scheme is more effective than the existing schemes especially when the number of candidate symbol vectors becomes smaller in reduced-complexity MAP detection.

Advanced detection and coding techniques for nonlinear intersymbol interference cancellation in 40 Gb/s systems

To mitigate the fibre nonlinearities in high-speed transmission (at 40 Gb/s or higher), the use of maximum a posteriori probability (MAP) symbol decoding supplemented with iterative decoding is proposed. The MAP detector operates on the channel trellis to correct the corrupted data and to provide soft outputs processed further in an iterative decoder. Impressive performance improvement is demonstrated.

Nonlinear BCJR equalizer for suppression of intrachannel nonlinearities in 40 Gb/s optical communications systems

A maximum a posteriori probability (MAP) symbol decoding supplemented with iterative decoding is proposed as an effective mean for suppression of intrachannel nonlinearities. The MAP detector, based on Bahl-Cocke-Jelinek-Raviv algorithm, operates on the channel trellis, a dynamical model of intersymbol interference, and provides soft-decision outputs processed further in an iterative decoder. A dramatic performance improvement is demonstrated. The main reason is that the conventional maximum-likelihood sequence detector based on Viterbi algorithm provides hard-decision outputs only, hence preventing the soft iterative decoding. The proposed scheme operates very well in the presence of strong intrachannel intersymbol interference, when other advanced forward error correction schemes fail, and it is also suitable for 40 Gb/s upgrade over existing 10 Gb/s infrastructure.

The heuristic, GLRT, and MAP detectors for double differential Modulation are identical

We consider the relationship between several single-symbol detectors for double differential modulation. We have shown in a previous paper that a simple heuristic detector is identical to the generalized likelihood ratio test (GLRT) detector. In this correspondence, we introduce a maximum a posteriori probability (MAP) detector and show that it is identical to the heuristic and GLRT detectors. Consequently, neither GLRT nor MAP can offer any gain over the simple heuristic detector, which means that the latter should be the detector of choice.

画像処理技術 予測誤差に基づいたＭＡＰ受信機に関する検討

A MAP (Maximum A posteriori Probability) receiver is described that is designed for Markovian sources in a wireless environment. A MAP receiver, a well-known efficient receiver, uses the stochastic characteristics of the source in the decision procedure. However, it is very difficult to implement a MAP algorithm at the front of the receiver because of its calculation costs. To reduce these costs we introduce a source predictor in the receiver. With the aid of the predictor, the MAP detector can be operated with a small calculation cost. Experimental PCM (Pulse Coded Modulation) image transmission demonstrated the feasibility of the proposed receiver. Simulation of the receiver's performance showed it had better MSE (Mean Squared Error) performance in spite of its implementation simplicity.

Recursive decision directed estimation of reflection coefficients for seismic data deconvolution

This paper concerns the problem of estimation of the location and intensity of reflections of a seismic wavelet. A recursive maximum a posteriori probability (MAP) algorithm is derived as an alternative to the maximum likelihood (ML) algorithm of Mendel and Kormylo. The MAP approach proposed here yields a suboptimal detector which is substantially different in details from the corresponding approximate ML detector of Mendel and Kormylo. Simulation studies are presented to show that the MAP detector performs as well as the ML detector and can yield comparable results with much less computational effort. A comparative study of both the MAP and ML detectors has been made via simulations which show some interesting differences in structure as well as performance.

Map Detection and Estimation of Seismic Reflection Coefficients

The paper is concerned with the problem of estimation of the location and intensity of reflections of a seismic wavelet. A recursive maximum a posteriori probability (MAP) algorithm is derived as an alternative to the maximum likelihood (ML) algorithm of Mendel and Kormylo. The MAP approach proposed here yields a suboptimal detector which is substantially different in details from the corresponding approximate ML detector of Mendel and Kormylo. Simulation studies are presented to show that the MAP detector performs equally well as the ML detector and can yield comparable results with much less computational effort.

Simulation Results for the Decision-Directed MAP Receiver for M-ary Signals in Mulitiplicative and Additive Gaussian Noise

Simulation results are presented for the error-rate performance of the recursive digital maximum a posteriori probability (MAP) detector for known M -ary signals in multiplicative and additive Gaussian noise. The structure of the digital simulation of the optimum detector is generally described, with specific results obtained for a quaternary signal and 2500 digit per second transmission rate. The simulation is focused on the aeronautical multipath communication problem. Plots of detection error rate versus additive signal-to-noise ratio are given, with the power ratio of multiplicative process to desired signal as a parameter. Results are presented for the cases where the detector has perfect knowledge of the first- and second-order statistics of the multiplicative and additive processes and also where these statistics are estimated in near real time. For comparison, the error rates of conventional coherent and noncoherent digital MAP detectors are also obtained. It is shown that with nonzero multiplicative noise, the error rates of the conventional detectors saturate at a level that is irreducible for increasing additive signal-to-noise ratio. The error rate of the optimum detector having perfect statistical knowledge continues to decrease rapidly with increasing additive signal-to-noise ratio. In the absence of multiplicative noise, the conventional coherent detector and the optimum detector are shown to exhibit identical performance. Suboptimum detectors, having less than perfect statistical knowledge, yield error rates bounded below by the optimum detector rates and bounded above by the conventional detector rates.