Complexity Maximum Likelihood Research Articles

Low-Complexity Detection for Multidimensional Codebooks Over Fading Channels

Signal space diversity (SSD) introduced by Boutros and Viterbo tremendously improves the error performance over fading channels without any power or bandwidth sacrifice. Maximum benefit is obtained with full diversity (FD) multidimensional codebooks and the rather complex maximum likelihood (ML) detection. In the present work, we propose a generalized combinatorial representation and an associated low-complexity list-based detection algorithm that works for any non-full or full diversity multidimensional codebook. The algorithm includes three options of lists offering different complexity-performance trade-offs. One of the lists has random size and is guaranteed to contain the ML point, while the other two lists have fixed or limited size. Some analytical results are presented for the list sizes. The algorithm also includes a smart search to find the most probable codebook point in the list. Numerical results show that the proposed algorithm yields optimal or close-to-optimum performance with a noteworthy detection complexity reduction. Therefore, its adoption can be of practical interest, especially in applications where powerful error-correcting codes are not supported.

Optimal Low Complexity Detector for Signed-Quadrature Spatial Modulation MIMO System

Very recently, signed quadrature spatial modulation (sQSM) is developed as a competent technique that expands the spatial constellation diagram of QSM system by adding a bipolar dimension. Despite the enhanced spectral efficiency, the existing optimal maximum likelihood (ML) presents a serious computational challenge for large scale sQSM systems. Therefore, developing a reduced complexity detector for sQSM schemes is of significant importance to enable implementing and enjoying the inherent advantages of this promising system. Toward this end, a Tree Search (TS) optimal low complexity detector, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TSopt</i> , for sQSM Multiple Input Multiple Output (MIMO) system is proposed and analyzed in this paper. The proposed detector expands the computationally complex ML detector for sQSM into a tree-structure representation. The idea of the suggested algorithm is to employ an efficient searching strategy that can expeditiously find the branch corresponding to the minimum error without tracing the entire nodes as in the ML case. It is reported that the proposed TSopt algorithm achieves the exact error performance as ML detector but with substantial reduction in computational complexity. Besides, complexity analysis in terms of the number of visited nodes of the TSopt algorithm is analyzed and a closed-form expression for the expected complexity at high SNR values is derived. Reported results disclose agreement between simulation and expected analytical complexity with substantial gains of around 60–80% in complexity reduction for different system parameters.

Low Complexity Optimal and Suboptimal Detection at Spatial Modulation MIMO Receivers

This paper develops three low-complexity detection schemes for the spatial modulation (SM) Multiple Input Multiple Output (MIMO) systems. We first propose a reduced complexity maximum likelihood (RC-ML) detection scheme. For the practical values of the modulation index, the proposed RC-ML method is simpler than the existing hard-limiting-based ML schemes. The two other proposals are based on a suboptimal Maximum Ratio Combining (MRC) detection method. We present a new analysis of the MRC detector in the uncorrelated Rayleigh fading channel and identify the system operational scenarios for which the MRC performance is nearly identical to the ML performance. Our proposals — a hybrid MRC-ML method and an MRC scheme with rank reduction — are inspired by this analysis. The analytical and simulation results show that the proposed MRC-based schemes can attain a near-optimal performance while reducing the complexity of the ML-based SM receiver.

Low complexity maximum likelihood decoding for orthogonal space-time block codes using non-square and rotated quadrature amplitude modulation

ABSTRACT High diversity gain can be achieved for orthogonal space-time block codes (OSTBCs) using rotated QAM constellations at a cost of high Maximum Likelihood (ML) decoding complexity. Thus far, low complexity ML decoding algorithms were proposed only for OSTBCs with square QAM constellations. In this paper, an algorithm has been proposed to reduce the ML decoding complexity of OSTBCs with non-square and rotated QAM constellations. The ML formulation using real-valued lattice representations is modified in such a way that the complexity depends upon the number of real values required to construct the alphabet of any constellation. Arithmetic progression and symmetry are the two elementary characteristics observed in the real numbers of the alphabets. Based on these characteristics, a new approach called Add and accumulate method has been proposed which drastically reduces the complexity to and without sacrificing the performance.

Low Complexity Maximum Likelihood FBMC QAM for Improved Performance in Longer Delay Channels

Filter bank multi-carrier (FBMC) is an emerging 5G technology due to its finer spectral characteristics than its counterpart orthogonal frequency-division multiplexing (OFDM). In most cases, FBMC is united with an Offset Quadrature Amplitude modulation (OQAM) for individual sub-carrier to maximize the spectrum efficiency and Nyquist rate. But it is achieved at the cost of an inherent accumulative imaginary interference called intrinsic interference. When a channel is highly selective, the FBMC system undergoes inter-symbol-interference (ISI) and co-channel interference (CCI). In this research, we consider FBMC QAM as a solution to intrinsic interference and mitigates both ISI and CCI by incorporating ML equivalent signal detection. In this paper, some of the prominent issues related to the existing FBMC–OQAM are explored and its potential integrity constraints with existing MIMO and signal detection techniques are studied. In addition to that, a lightweight optimized ML which constitutes parallel sub-detectors with the least hardware complexity overhead is proposed. It also achieved a near-optimal performance that matches the CP-OFDM system. In this research, the experimental results proved that the proposed suboptimal ML detector offered significant complexity reduction with improved quality of services. Thus evidently shows the proposed system is attractive from both BER performance and hardware complexity reduction perspectives for 5G communications.

Maximum likelihood estimation with missing outcomes: From simplicity to complexity.

Many clinical or prevention studies involve missing or censored outcomes. Maximum likelihood (ML) methods provide a conceptually straightforward approach to estimation when the outcome is partially missing. Methods of implementing ML methods range from the simple to the complex, depending on the type of data and the missing-data mechanism. Simple ML methods for ignorable missing-data mechanisms (when data are missing at random) include complete-case analysis, complete-case analysis with covariate adjustment, survival analysis with covariate adjustment, and analysis via propensity-to-be-missing scores. More complex ML methods for ignorable missing-data mechanisms include the analysis of longitudinal dropouts via a marginal model for continuous data or a conditional model for categorical data. A moderately complex ML method for categorical data with a saturated model and either ignorable or nonignorable missing-data mechanisms is a perfect fit analysis, an algebraic method involving closed-form estimates and variances. A complex and flexible ML method with categorical data and either ignorable or nonignorable missing-data mechanisms is the method of composite linear models, a matrix method requiring specialized software. Except for the method of composite linear models, which can involve challenging matrix specifications, the implementation of these ML methods ranges in difficulty from easy to moderate.

An Accurate Substitution Method To Minimize Left Censoring Bias in Serum Steroid Measurements.

Hormone assay results below the assay detection limit (DL) can introduce bias into quantitative analysis. Although complex maximum likelihood estimation methods exist, they are not widely used, whereas simple substitution methods are often used ad hoc to replace the undetectable (UD) results with numeric values to facilitate data analysis with the full data set. However, the bias of substitution methods for steroid measurements is not reported. Using a large data set (n = 2896) of serum testosterone (T), DHT, estradiol (E2) concentrations from healthy men, we created modified data sets with increasing proportions of UD samples (≤40%) to which we applied five different substitution methods (deleting UD samples as missing and substituting UD sample with DL, DL/√2, DL/2, or 0) to calculate univariate descriptive statistics (mean, SD) or bivariate correlations. For all three steroids and for univariate as well as bivariate statistics, bias increased progressively with increasing proportion of UD samples. Bias was worst when UD samples were deleted or substituted with 0 and least when UD samples were substituted with DL/√2, whereas the other methods (DL or DL/2) displayed intermediate bias. Similar findings were replicated in randomly drawn small subsets of 25, 50, and 100. Hence, we propose that in steroid hormone data with ≤40% UD samples, substituting UD with DL/√2 is a simple, versatile, and reasonably accurate method to minimize left censoring bias, allowing for data analysis with the full data set.

BITFCM-OFDM scheme for power-line communication systems

Power-line communications (PLC) is viewed as a good potential solution for smart grid communications because of the established infrastructure around the world. However, power-line was not initially aimed to be used for continuous data communications. Hence, challenging problems may occur when the power-line channel is used as a communication channel. One of the major issues is the (bursty) impulsive noise in the power-line channel. This paper analyzes the system performance of the bit-interleaved time-frequency coded modulation (BITFCM) scheme with an optimal low complexity maximum likelihood (ML) decoding scheme in the orthogonal frequency-division multiplexing (OFDM)-based broadband PLC (BB-PLC) modems. The numerical results illustrate that this proposed scheme improves the system performance of the PLC modems under the bursty impulsive noise environment. Furthermore, the performance of the BITFCM-OFDM scheme can achieve up to 3 dB improvement at bit error rate (BER) of 10-4 in comparison with the bit-interleaved coded modulation (BICM)-OFDM and shows significant improvement compared with the coded OFDM (COFDM). Finally, a blanking nonlinear preprocessor is used at the receiver and further improvement of the BER performance is evaluated.

Censoring Outliers in Radar Data: An Approximate ML Approach and its Analysis

This paper deals with the problem of censoring outliers in a class of complex multivariate elliptically contoured distributed radar data, which is a vital issue in radar signal processing applications, such as adaptive radar detection and space-time adaptive processing. The maximum likelihood (ML) estimate of the outlier subset is derived resorting to the generalized likelihood function (GLF) criterion. Since the ML estimate involves the solution of a combinatorial problem, a reduced complexity but approximate ML (AML) procedure is also considered. At the analysis stage, the performance of the AML method is evaluated in the presence of both simulated and real radar data, also in comparison with the conventional generalized inner product (GIP) and the reiterative censored GIP (RCGIP) algorithms. The results highlight that the AML technique achieves a satisfactory performance level and can outperform both GIP and RCGIP in some situations.

Two-Layer LDPC Codes for Low Complexity ML Detection in GSM Systems

Although maximum-likelihood (ML) detection is able to achieve optimal performance in generalized spatial modulation (GSM) systems, its exhaustive search leads to an intractable computational complexity. In this letter, two-layer low-density parity-check (TL-LDPC) codes are proposed to reduce the combinations of transmission vectors in LDPC coded GSM systems. Simulation results show that the complexity of the ML detection in the TL-LDPC-coded GSM systems is much lower than that of the ML detection in conventional LDPC-coded GSM systems with a negligible performance loss.

Optical pulse width modulation based TDM-PON monitoring with asymmetric loop in ONUs

We propose a time division multiplexing passive optical network (TDM-PON) monitoring scheme based on the optical pulse width modulation (OPWM) by using a simple asymmetric loop (AL) located near the optical network unit (ONU). Various pulse widths can be easily obtained by configuring the appropriate length of the patchcord used to generate the path difference between two branches of a 1 × 2 splitter. Different wavelengths can be assigned to the same pulse width, which can further increase the network size. The optimized parameters of the AL are investigated and analysis models are established. The calculation results show that the proposed scheme has smaller correlation distance (CD) and lower multiple-customers interference probability (MCIP) than the periodic coding (PC) scheme. A simplified PON system with 8 ONUs is set up to experimentally demonstrate the feasibility of the proposed scheme. The network recognition processing used to identify the reflected monitoring signals in the proposed scheme is simple, especially compared with the reduced complexity maximum likelihood sequence estimation (RC-MLSE) used in the typical PC scheme.

Modified Multiple Feedback QR Aided Successive Interference Cancellation Algorithm for Large MIMO Detection

Multiple-input multiple-output (MIMO) systems have attracted increased interest due to their capability to achieve higher multiplexing and diversity gains. In MIMO systems, reliable symbol detection in one of the major challenges. Maximum likelihood (ML) detection is one such technique which achieves minimum error rate performance for MIMO systems, however due to its exponential complexity ML detection is practically infeasible for large number of antennas. Therefore, in this contribution, we propose a low-complexity modified multiple feedback QR aided successive interference cancellation (MMF-SIC) algorithm which is capable of achieving near optimal performance. The effect of error propagation in SIC can be reduced by using multiple constellation points in decision feedback loops based on the reliability criteria. In MMF-SIC, an enhanced detection diversity is achieved by considering the decision feedback loops in multiple layers of QR aided SIC algorithm. Furthermore, we employ two different ordering schemes in parallel for QR decomposition in MMF-SIC algorithm. Through simulations, it is observed that the MMF-SIC algorithm performs superior over the conventional SIC and other SIC based techniques for detection in MIMO systems, and approach near optimal performance.

Maximum Likelihood Detection With a Closed-Form Solution for the Square QAM Constellation

A low complexity maximum likelihood (ML) detection method is proposed for the square quadrature amplitude modulation (QAM) constellation. In order to reduce the implementation complexity of ML detection, set-partition, subset-selection, and subset-shift are recursively applied to the square QAM constellation. The estimated square QAM symbol is finally given in a closed form as a function of the received signal and the estimated channel. Complexity analysis and numerical simulation confirm that the proposed detection method reduces the implementation complexity substantially and achieves exactly the same performance as the conventional ML detection irrespective of the channel estimation error.

Investigation on Non-Orthogonal Multiple Access with Reduced Complexity Maximum Likelihood Receiver and Dynamic Resource Allocation

Investigation on Non-Orthogonal Multiple Access with Reduced Complexity Maximum Likelihood Receiver and Dynamic Resource Allocation

Life estimation using damage equalization method and step-stress breakdown tests

Conventional constant-stress accelerated ageing tests are time consuming, cumbersome and suffer from the disadvantage that some samples may not fail even after a long time. This necessitates censoring the data for life estimation, increasing the complexity of data analysis and leaving some amount of uncertainty due to censoring. Step-stress breakdown tests for life estimation were already proposed in the literature. Complex Weibull statistics were resorted to for life estimation. In this paper the authors present a different data analysis procedure i.e. damage equalization method for estimating the life of power equipment. Inverse power law model is used in conjunction with Miner's cumulative damage theory. Also, the procedure suggested is much simpler than the previous procedures, which involve solving a complex maximum likelihood function for which non-linear techniques like Newton-Raphson method is required. The approach is further compared with existing techniques of life estimation and found to be matching well. Life estimation of cables supplied by a local manufacturer for dc voltage applications has been performed. Several types of breakdown experiments were conducted for cables, with different step-size of step-stress accelerated ageing tests, in authors' laboratory, at two distinct temperatures. In addition, tests were also conducted on low density polyethylene samples.

The New Approach to the Synthesis of Single-Channel Consistent Estimates of the Time Signal Parameters

Based on the introduced modification of a maximum likelihood method we suggest the new technique for synthesis of single-channel quasi-optimal processing algorithms of signals with multiple unknown parameters. We illustrate the proposed approach by the estimation of the appearance time and duration of a rectangular video pulse. We show that unlike technically complex multichannel maximum likelihood estimates, the single-channel quasi-optimal estimates of time signal parameters are consistent for the implementation. We also find the analytical expressions for characteristics of passed estimates which allow us to assess the reasonableness of the application of this or that processing algorithm in each specific case.

A simplified hard output sphere decoder for large MIMO systems with the use of efficient search center and reduced domain neighborhood study

Multiple-input multiple-output (MIMO) with a spatial-multiplexing (SM) scheme is a topic of high interest for the next generation of wireless communications systems. At the receiver, neighborhood studies (NS) and lattice reduction (LR)-aided techniques are common solutions in the literature to approach the optimal and computationally complex maximum likelihood (ML) detection. However, the NS and LR solutions might not offer optimal performance for large dimensional systems, such as large number of antennas, and high-order constellations when they are considered separately. In this paper, we propose a novel equivalent metric dealing with the association of these solutions by introducing a reduced domain neighborhood study. We show that the proposed metric presents a relevant complexity reduction while maintaining near-ML performance. Moreover, the corresponding computational complexity is shown to be independent of the constellation size, but it is quadratic in the number of transmit antennas. For instance, for a 4 × 4 MIMO system with 16-QAM modulation on each layer, the proposed solution is simultaneously near-ML with perfect and real channel estimation and ten times less complex than the classical neighborhood-based K-best solution.

Efficient inference about the tail weight in multivariate Student [formula omitted] distributions

We propose a new testing procedure about the tail weight parameter of multivariate Student t distributions by having recourse to the Le Cam methodology. Our test is asymptotically as efficient as the classical likelihood ratio test, but outperforms the latter by its flexibility and simplicity: indeed, our approach allows to estimate the location and scatter nuisance parameters by any root-n consistent estimators, hereby avoiding numerically complex maximum likelihood estimation. The finite-sample properties of our test are analyzed in a Monte Carlo simulation study, and we apply our method on a financial data set. We conclude the paper by indicating how to use this framework for efficient point estimation.

A geometry based efficient decoder for underdetermined MIMO systems

In this paper, a geometry based decoder with low decoding complexity and exact maximum-likelihood (ML) performance is proposed for underdetermined multiple-input multiple-output (MIMO) systems. In the proposed decoder, an underdetermined MIMO system can be divided into a multiple-input single-output (MISO) sub-system and a regular MIMO sub-system in which numbers of transmit and receive antennas are equal. An efficient slab search algorithm (ESSA) is adopted to efficiently obtain valid candidate points in the MISO sub-system. By adopting ESSA in the MISO sub-system and sphere decoding algorithm (SDA) in the MIMO sub-system, ML solution of underdetermined MIMO system can be obtained with low computational complexity. To further reduce the computational complexity, a near-ML SDA is proposed to more efficiently find the candidate points in the MIMO sub-system. In addition, an optimal preprocessing technique is proposed from the geometrical perspective and the comprehensive analysis on the complexity reduction is also provided. Simulation results indicate that the proposed approach significantly reduces the complexity as compared to existing ML decoders, particularly for systems with large number of antennas and/or high-order constellations.

Time estimation with multichannel digital silicon photomultipliers

Accuracy in timemark estimation is crucial for time-of-flight positron emission tomography, in order to ensure high quality images after reconstruction. Since the introduction of multichannel digital silicon photomultipliers, it is possible to acquire several photoelectron timestamps for each individual gamma event.We study several timemark estimators based on multiple photoelectron timestamps by means of a comprehensive statistical model. In addition, we calculate the MSE of the estimators in comparison to the Cramér–Rao lower bound as a function of the system design parameters.We investigate the effect of skipping some of the photoelectron timestamps, which is a direct consequence of the limited number of time-to-digital converters and we propose a technique to compensate for this effect. In addition, we carry out an extensive analysis to evaluate the influence of dark counts on the detector timing performance.Moreover, we investigate the improvement of the timing performance that can be obtained with dark count filtering and we propose an appropriate filtering method based on measuring the time difference between sorted timestamps.Finally, we perform a full Monte Carlo simulation to compare different timemark estimators by exploring several system design parameters. It is demonstrated that a simple weighted-average estimator can achieve a comparable performance as the more complex maximum likelihood estimator.