Soft-decision equalization techniques for frequency selective MIMO channels

Multi-input multi-output (MIMO) technology is an emerging solution for high data rate wireless communications. We develop soft-decision based equalization techniques for frequency selective MIMO channels in the quest for low-complexity equalizers with BER performance competitive to that of ML sequence detection. We first propose soft decision equalization (SDE), and demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered, and linear in the signal constellation size. Building upon the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Motivated by the need for low-complexity receiver processing, we further present an alternative low-complexity soft-decision equalization approach for frequency selective MIMO communication systems. With the help of iterative processing, two detection and estimation schemes based on second-order statistics are harmoniously put together to yield a two-part receiver structure: local multiuser detection (MUD) using soft-decision Probabilistic Data Association (PDA) detection, and dynamic noise-interference tracking using Kalman filtering. The proposed Kalman-PDA detector performs local MUD within a sub-block of the received data instead of over the entire data set, to reduce the computational load. At the same time, all the inter-ference affecting the local sub-block, including both multiple access and inter-symbol interference, is properly modeled as the state vector of a linear system, and dynamically tracked by Kalman filtering. Two types of Kalman filters are designed, both of which are able to track an finite impulse response (FIR) MIMO channel of any memory length. The overall algorithms enjoy low complexity that is only polynomial in the number of information-bearing bits to be detected, regardless of the data block size. Furthermore, we introduce two optional performance-enhancing techniques: cross- layer automatic repeat request (ARQ) for uncoded systems and code-aided method for coded systems. We take Kalman-PDA as an example, and show via simulations that both techniques can render error performance that is better than Kalman-PDA alone and competitive to sphere decoding. At last, we consider the case that channel state information (CSI) is not perfectly known to the receiver, and present an iterative channel estimation algorithm. Simulations show that the performance of SDE with channel estimation approaches that of SDE with perfect CSI

Unified bit-based probabilistic data association aided MIMO detection for high-order QAM

A unified Bit-based Probabilistic Data Association (B-PDA) detection approach is proposed for Multiple-Input Multiple-Output (MIMO) systems employing high-order Quadrature Amplitude Modulation (QAM). The new approach transforms the symbol detection process of QAM to a bit-based process by introducing a Unified Matrix Representation (UMR) of QAM. Both linear natural and nonlinear Gray bit-to-symbol mapping schemes are considered. Our analytical and simulation results demonstrate that the linear natural mapping based B-PDA approach attains an improved detection performance, despite dramatically reducing the computational complexity in contrast to the conventional symbol-based PDA aided MIMO detector. Furthermore, it is shown that the linear natural mapping based B-PDA method is capable of approaching the lower bound performance provided by the nonlinear Gray mapping based B-PDA MIMO detector. Since the linear natural mapping based scheme is simpler and more applicable in practice than its nonlinear Gray mapping based counterpart, we conclude that in the context of the uncoded B-PDA MIMO detector it is preferable to use the linear natural bit-to-symbol mapping, rather than the nonlinear Gray mapping

Unified bit-based probabilistic data association aided MIMO detection for high-order QAM constellations

A unified Bit-based Probabilistic Data Association (B-PDA) detection approach is proposed for Multiple-Input Multiple-Output (MIMO) systems employing high-order rectangular Quadrature Amplitude Modulation (QAM). The new approach transforms the symbol detection process of QAM to a bit-based process by introducing a Unified Matrix Representation (UMR) of QAM. Both linear natural and nonlinear binary reflected Gray bit-to-symbol mappings are considered. With the aid of simulation results, we demonstrate that the linear natural mapping based B-PDA approach typically attained an improved detection performance (measured in terms of both Bit Error Ratio (BER) and Symbol Error Ratio (SER)) in comparison to the conventional symbol-based PDA aided MIMO detector, despite its dramatically reduced computational complexity. The only exception is that at low SNRs, the linear natural mapping based B-PDA is slightly inferior in terms of its BER to the conventional symbol-based PDA using binary reflected Gray mapping. Furthermore, the simulation results show that the linear natural mapping based B-PDA MIMO detector may approach the best-case performance provided by the nonlinear binary reflected Gray mapping based B-PDA MIMO detector under ideal conditions. Additionally, the implementation of the B-PDA MIMO detector is shown to be much simpler in the case of the linear natural mapping. Based on these two points, we conclude that in the context of the uncoded B-PDA MIMO detector it is preferable to use the linear natural bit-to-symbol mapping, rather than the nonlinear Gray mapping

Adaptive and Iterative Multi-Branch MMSE Decision Feedback Detection Algorithms for MIMO Systems

In this work, decision feedback (DF) detection algorithms based on multiple processing branches for multi-input multi-output (MIMO) spatial multiplexing systems are proposed. The proposed detector employs multiple cancellation branches with receive filters that are obtained from a common matrix inverse and achieves a performance close to the maximum likelihood detector (MLD). Constrained minimum mean-squared error (MMSE) receive filters designed with constraints on the shape and magnitude of the feedback filters for the multi-branch MMSE DF (MB-MMSE-DF) receivers are presented. An adaptive implementation of the proposed MB-MMSE-DF detector is developed along with a recursive least squares-type algorithm for estimating the parameters of the receive filters when the channel is time-varying. A soft-output version of the MB-MMSE-DF detector is also proposed as a component of an iterative detection and decoding receiver structure. A computational complexity analysis shows that the MB-MMSE-DF detector does not require a significant additional complexity over the conventional MMSE-DF detector, whereas a diversity analysis discusses the diversity order achieved by the MB-MMSE-DF detector. Simulation results show that the MB-MMSE-DF detector achieves a performance superior to existing suboptimal detectors and close to the MLD, while requiring significantly lower complexity.Comment: 10 figures, 3 tables; IEEE Transactions on Wireless Communications, 201

Multilane traffic density estimation with KDE and nonlinear LS and tracking with Scalar Kalman filtering

Tezin basılısı, İstanbul Şehir Üniversitesi Kütüphanesi'ndedir.With increasing population, the determination of traffic density becomes very critical in managing the urban city roads for safer driving and low carbon emission. In this study, Kernel Density Estimation is utilized in order to estimate the traffic density more accurately when the speeds of the vehicles are available for a given region. For the proposed approach, as a first step, the probability density function of the speed data is modeled by Kernel Density Estimation. Then, the speed centers from the density function are modeled as clusters. The cumulative distribution function of the speed data is then determined by Kolmogorov-Smirnov Test, whose complexity is less when compared to the other techniques and whose robustness is high when outliers exist. Then, the mean values of clusters are estimated from the smoothed density function of the distribution function, followed by a peak detection algorithm. The estimation of variance values and kernel weights, on the other hand, are found by a nonlinear Least Square approach. As the estimation problem has linear and non-linear components, the nonlinear Least Square with separation of parameters approach is adopted, instead of dealing with a high complexity nonlinear equation. Finally, the tracking of former and latter estimations of a road is calculated by using Scalar Kalman Filtering with scalar state - scalar observation generality level. Simulations are carried out in order to assess theperformanceoftheproposedapproach. Forallexampledatasets, theminimummean square error of kernel weights is found to be less than 0.002 while error of mean values is found to be less than 0.261. The proposed approach was also applied to real data from sample road traffic, and the speed center and the variance was accurately estimated. By using the proposed approach, accurate traffic density estimation is realized, providing extra information to the municipalities for better planning of their cities.Declaration of Authorship ii Abstract iii Öz iv Acknowledgments vi List of Figures ix List of Tables x Abbreviations xi 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Methods to Find Probability Density Function and Cumulative Distribution Function . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 1.3 Traffic Density Estimation with Kernel Density Estimation . . . . . . . . 4 1.4 The Approaches for Determination of Key Parameters of Traffic Density Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . .5 1.5 Tracking between Estimated Data and New Data . . . . . . . . . . . . . . 6 1.6 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Literature Review 7 2.1 Methodologies Used for Estimation of Traffic Density . . . . . . . . . . . . 7 2.2 An Example Study of Traffic Density Estimation with KDE and CvM . . 9 2.3 Three Complementary Studies for Traffic Density Estimation and Tracking 9 2.4 Comparison of Three Different Nonlinear Estimation Techniques on the Same Problem . . . . . . . . . . . . . . . . . . . . . . . . .10 2.4.1 A Maximum Likelihood Approach for Estimating DS-CDMA Multipath Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4.2 Channel Estimation for the Uplink of a DS-CDMA System . . . . 12 2.4.3 A Robust Method for Estimating Multipath Channel Parameters in the Uplink of a DS-CDMA System. . . . . . . . . . . . . . .13 3 The Model 16 3.1 Finding Density Distribution with KDE . . . . . . . . . . . . . . . . . . . 16 3.2 Finding Empirical CDF with KS Test . . . . . . . . . . . . . . . . . . . . 18 3.3 Determination of Speed Centers via PDA . . . . . . . . . . . . . . . . . . 20 3.4 Estimation of Variance and Kernel Weights with Nonlinear LS Method . . 21 3.5 Tracking of Traffic Density Estimation with Scalar Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4 Numerical Calculations for Traffic Density Estimation 26 4.1 An Example Traffic Scenario with Five Speed Centers . . . . . . . . . . . 26 4.2 The Estimation of A Real Time Data . . . . . . . . . . . . . . . . . . . . . 29 4.3 Traffic Density Estimation with Different Kernel Numbers . . . . . . . . . 29 5 Examples to Test Tracking Part of the Model 31 5.1 Tracking with the Change only in Mean Values . . . . . . . . . . . . . . . 32 5.2 Tracking with the Change only in Kernel Weights . . . . . . . . . . . . . . 35 5.3 Tracking with the Change in All Three Parameters . . . . . . . . . . . . . 36 6 Assesment 38 7 Conclusion 41 A Derivation of Newton-Raphson Method for the Estimation of Variance Values and Kernel Weights 43 Bibliography 4