On the variance of the Least Mean Square squared-error sample curve

Most studies of adaptive algorithm behavior consider performance measures based on mean values such as the mean-square error. The derived models are useful for understanding the algorithm behavior under different environments and can be used for design. Nevertheless, from a practical point of view, the adaptive filter user has only one realization of the algorithm to obtain the desired result. This letter derives a model for the variance of the squared-error sample curve of the least-mean-square (LMS) adaptive algorithm, so that the achievable cancellation level can be predicted based on the properties of the steady-state squared error. The derived results provide the user with useful design guidelines

Affine Projection Algorithm Based Decision Fusion for Cooperative Spectrum Sensing In Cognitive Radio Networks

Spectrum sensing is a main function in cognitive radio networks to detect the spectrum holes or unused spectrum. Cooperative spectrum sensing schemes are recently suggested and they provide fast and accurate results. In this paper, we suggested a new adaptive and cooperative spectrum sensing technique based on the affine projection algorithm (APA). In this method, each secondary user (SU) takes a binary decision by its local sensing of the spectrum using energy detector. Local decisions are then forward to the fusion center (FC), where definitive decision is taken on the status of the spectrum using adaptive filters. In our suggested technique, APA updates the weights of the adaptive filter by using the current and the 1 delayed input signal vectors. Simulation results indicate that the suggested approach provides faster convergence speed and less steady state mean square error than the existing methods that are based on the normalized least mean square (NLMS) or the so-called kernel least mean square (KLMS) algorithm

Performance Analysis of Shrinkage Linear Complex-Valued LMS Algorithm

The shrinkage linear complex-valued least mean squares (SL-CLMS) algorithm with a variable step size overcomes the conflicting issue between fast convergence and low steady-state misalignment. To the best of our knowledge, the theoretical performance analysis of the SL-CLMS algorithm has not been presented yet. This letter focuses on the theoretical analysis of the excess mean square error transient and steady-state performance of the SL-CLMS algorithm. Simulation results obtained for identification scenarios show a good match with the analytical results

Graphical model driven methods in adaptive system identification

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2016Identifying and tracking an unknown linear system from observations of its inputs and outputs is a problem at the heart of many different applications. Due to the complexity and rapid variability of modern systems, there is extensive interest in solving the problem with as little data and computation as possible. This thesis introduces the novel approach of reducing problem dimension by exploiting statistical structure on the input. By modeling the input to the system of interest as a graph-structured random process, it is shown that a large parameter identification problem can be reduced into several smaller pieces, making the overall problem considerably simpler. Algorithms that can leverage this property in order to either improve the performance or reduce the computational complexity of the estimation problem are developed. The first of these, termed the graphical expectation-maximization least squares (GEM-LS) algorithm, can utilize the reduced dimensional problems induced by the structure to improve the accuracy of the system identification problem in the low sample regime over conventional methods for linear learning with limited data, including regularized least squares methods. Next, a relaxation of the GEM-LS algorithm termed the relaxed approximate graph structured least squares (RAGS-LS) algorithm is obtained that exploits structure to perform highly efficient estimation. The RAGS-LS algorithm is then recast into a recursive framework termed the relaxed approximate graph structured recursive least squares (RAGSRLS) algorithm, which can be used to track time-varying linear systems with low complexity while achieving tracking performance comparable to much more computationally intensive methods. The performance of the algorithms developed in the thesis in applications such as channel identification, echo cancellation and adaptive equalization demonstrate that the gains admitted by the graph framework are realizable in practice. The methods have wide applicability, and in particular show promise as the estimation and adaptation algorithms for a new breed of fast, accurate underwater acoustic modems. The contributions of the thesis illustrate the power of graphical model structure in simplifying difficult learning problems, even when the target system is not directly structured.The work in this thesis was supported primarily by the Office of Naval Research through an ONR Special Research Award in Ocean Acoustics; and at various times by the National Science Foundation, the WHOI Academic Programs Office and the MIT Presidential Fellowship Program

On Minimal Second-order IIR Bandpass Filters with Constrained Poles and Zeros

In this paper, several forms of infinite impulse response (IIR) bandpass filters with constrained poles and zeros are presented and compared. The comparison includes the filter structure, the frequency ranges and a number of controlled parameters that affect computational efforts. Using the relationship between bandpass and notch filters, the two presented filters were originally developed for notch filters. This paper also proposes a second-order IIR bandpass filter structure that constrains poles and zeros and can be used as a  minimal parameter adaptive digital second-order filter. The proposed filter has a wider frequency range and more flexibility in the range values of the adaptation parameters

Blind adaptive near-far resistant receivers for DS/CDMA multi-user communication systems

Code-division multiple-access (CDMA) systems have multiple users that simultaneously share a common channel using pre-assigned signature waveforms. The conventional receiver suffers from the near-far problem when the received signal power of the desired user is weaker than those of the other users. Optimum and suboptimum multi-user detectors outperform the conventional receiver at the expense of a significant increase in complexity and need for side-information about interfering users. Complexity of these detectors may not be acceptable for many practical applications and communication security may restrict the distribution of all users\u27 signature waveforms to all the receivers;For a single-user receiver, the multi-user detection problem is viewed as an interference suppression problem. This dissertation presents a cost-constraint strategy to implement adaptive single-user receivers that suppress the multiple-access interference without using training sequences. A constrained LMS algorithm that converges to a near-optimum solution by using the received signal and some known properties of the desired signal is developed. The constrained LMS receiver is useful for static CDMA detection where the channel accessed by the desired user is time-invariant. The dissertation also develops an adaptive space-alternating generalized EM (SAGE) algorithm. This algorithm jointly updates estimates of filter weights and adaptive reference signal in a sequential manner. The SAGE receiver out-performs the existing: blind receiver that employ the constrained output-power-minimizing algorithm while using the same amount of information. The SAGE receiver is applicable to dynamic CDMA detection where the channel accessed by the desired user is time-varying. The dissertation further generalizes the adaptive SAGE algorithm to an adaptive space-alternating generalized projection (SAGP) algorithm that uses the same amount of information as in the conventional receiver;Proposed receivers are tested by simulations and compared with the existing receivers that use the same amount of information. Throughout the analytical analysis and simulations of the proposed receivers, the dissertation shows that, for realistic CDMA communications, achieving both the near-far resistance and the near-optimum performance is possible with the same or similar information required by the conventional receiver

Non-Gaussian Colored Noise Generation for Wireless Channel Simulation with Particle Swarm Optimizer

Random Variable (RV) with different Probability Density Function (PDF) and Power Spectral Density (PSD) is a critical component for simulation of different wireless channel fading profile. To get a specific PSD for simulation of different multi-path scenario, the usual method is to pass a white noise through a filter with the required shape. But the filtering process will cause the change of random variable’s PDF unless the input noise follows Gaussian Distribution. In this paper, a Particle Swarm optimization (PSO) based method to generate NonGaussian noise by a pre-distortion filter and Inverse Transform Sampling (ITS) that meets both the requirement of PSD and PDF is described. As the solution is based on filtering, after the filter weight is found using PSO, the simulation could be carried out in a real-time manner compared to block-based methods. The numerical simulation confirms that it can generate the required PDF and more than 90% similar to the required PSD

Post Conversion Correction of Non-Linear Mismatches for Time Interleaved Analog-to-Digital Converters

Time Interleaved Analog-to-Digital Converters (TI-ADCs) utilize an architecture which enables conversion rates well beyond the capabilities of a single converter while preserving most or all of the other performance characteristics of the converters on which said architecture is based. Most of the approaches discussed here are independent of architecture; some solutions take advantage of specific architectures. Chapter 1 provides the problem formulation and reviews the errors found in ADCs as well as a brief literature review of available TI-ADC error correction solutions. Chapter 2 presents the methods and materials used in implementation as well as extend the state of the art for post conversion correction. Chapter 3 presents the simulation results of this work and Chapter 4 concludes the work. The contribution of this research is three fold: A new behavioral model was developed in SimulinkTM and MATLABTM to model and test linear and nonlinear mismatch errors emulating the performance data of actual converters. The details of this model are presented as well as the results of cumulant statistical calculations of the mismatch errors which is followed by the detailed explanation and performance evaluation of the extension developed in this research effort. Leading post conversion correction methods are presented and an extension with derivations is presented. It is shown that the data converter subsystem architecture developed is capable of realizing better performance of those currently reported in the literature while having a more efficient implementation