On the Performance of Single-Threshold Detectors for Binary Communications in the Presence of Gaussian Mixture Noise

Cataloged from PDF version of article.In this paper, probability of error performance of single-threshold detectors is studied for binary communications systems in the presence of Gaussian mixture noise. First, suffi- cient conditions are proposed to specify when the sign detector is (not) an optimal detector among all the single-threshold detectors. Then, a monotonicity property of the error probability is derived for the optimal single-threshold detector. In addition, a theoretical limit is obtained on the maximum ratio between the average probabilities of error for the sign detector and the optimal single-threshold detector. Finally, numerical examples are presented to investigate the theoretical results

Distributed Nonparametric Sequential Spectrum Sensing under Electromagnetic Interference

A nonparametric distributed sequential algorithm for quick detection of spectral holes in a Cognitive Radio set up is proposed. Two or more local nodes make decisions and inform the fusion centre (FC) over a reporting Multiple Access Channel (MAC), which then makes the final decision. The local nodes use energy detection and the FC uses mean detection in the presence of fading, heavy-tailed electromagnetic interference (EMI) and outliers. The statistics of the primary signal, channel gain or the EMI is not known. Different nonparametric sequential algorithms are compared to choose appropriate algorithms to be used at the local nodes and the FC. Modification of a recently developed random walk test is selected for the local nodes for energy detection as well as at the fusion centre for mean detection. It is shown via simulations and analysis that the nonparametric distributed algorithm developed performs well in the presence of fading, EMI and is robust to outliers. The algorithm is iterative in nature making the computation and storage requirements minimal.Comment: 8 pages; 6 figures; Version 2 has the proofs for the theorems. Version 3 contains a new section on approximation analysi

Robust spectrum sensing techniques for cognitive radio networks

Cognitive radio is a promising technology that improves the spectral utilisation by allowing unlicensed secondary users to access underutilised frequency bands in an opportunistic manner. This task can be carried out through spectrum sensing: the secondary user monitors the presence of primary users over the radio spectrum periodically to avoid harmful interference to the licensed service. Traditional energy based sensing methods assume the value of noise power as prior knowledge. They suffer from the noise uncertainty problem as even a mild noise level mismatch will lead to significant performance loss. Hence, developing an efficient robust detection method is important. In this thesis, a novel sensing technique using the F-test is proposed. By assuming a multiple antenna assisted receiver, this detector uses the F-statistic as the test statistic which offers absolute robustness against the noise variance uncertainty. In addition, since the channel state information (CSI) is required to be known, the impact of CSI uncertainty is also discussed. Results show the F-test based sensing method performs better than the energy detector and has a constant false alarm probability, independent of the accuracy of the CSI estimate. Another main topic of this thesis is to address the sensing problem for non-Gaussian noise. Most of the current sensing techniques consider Gaussian noise as implied by the central limit theorem (CLT) and it offers mathematical tractability. However, it sometimes fails to model the noise in practical wireless communication systems, which often shows a non-Gaussian heavy-tailed behaviour. In this thesis, several sensing algorithms are proposed for non-Gaussian noise. Firstly, a non-parametric eigenvalue based detector is developed by exploiting the eigenstructure of the sample covariance matrix. This detector is blind as no information about the noise, signal and channel is required. In addition, the conventional energy detector and the aforementioned F-test based detector are generalised to non-Gaussian noise, which require the noise power and CSI to be known, respectively. A major concern of these detection methods is to control the false alarm probability. Although the test statistics are easy to evaluate, the corresponding null distributions are difficult to obtain as they depend on the noise type which may be unknown and non-Gaussian. In this thesis, we apply the powerful bootstrap technique to overcome this difficulty. The key idea is to reuse the data through resampling instead of repeating the experiment a large number of times. By using the nonparametric bootstrap approach to estimate the null distribution of the test statistic, the assumptions on the data model are minimised and no large sample assumption is invoked. In addition, for the F-statistic based method, we also propose a degrees-of-freedom modification approach for null distribution approximation. This method assumes a known noise kurtosis and yields closed form solutions. Simulation results show that in non-Gaussian noise, all the three detectors maintain the desired false alarm probability by using the proposed algorithms. The F-statistic based detector performs the best, e.g., to obtain a 90% detection probability in Laplacian noise, it provides a 2.5 dB and 4 dB signal-to-noise ratio (SNR) gain compared with the eigenvalue based detector and the energy based detector, respectively

On detection of OFDM signals for cognitive radio applications

As the requirement for wireless telecommunications services continues to grow, it has become increasingly important to ensure that the Radio Frequency (RF) spectrum is managed efficiently. As a result of the current spectrum allocation policy, it has been found that portions of RF spectrum belonging to licensed users are often severely underutilised, at particular times and geographical locations. Awareness of this problem has led to the development of Dynamic Spectrum Access (DSA) and Cognitive Radio (CR) as possible solutions. In one variation of the shared-use model for DSA, it is proposed that the inefficient use of licensed spectrum could be overcome by enabling unlicensed users to opportunistically access the spectrum when the licensed user is not transmitting. In order for an unlicensed device to make decisions, it must be aware of its own RF environment and, therefore, it has been proposed that DSA could been abled using CR. One approach that has be identified to allow the CR to gain information about its operating environment is spectrum sensing. An interesting solution that has been identified for spectrum sensing is cyclostationary detection. This property refers to the inherent periodic nature of the second order statistics of many communications signals. One of the most common modulation formats in use today is Orthogonal Frequency Division Multiplexing (OFDM), which exhibits cyclostationarity due to the addition of a Cyclic Prefix (CP). This thesis examines several statistical tests for cyclostationarity in OFDM signals that may be used for spectrum sensing in DSA and CR. In particular, focus is placed on statistical tests that rely on estimation of the Cyclic Autocorrelation Function (CAF). Based on splitting the CAF into two complex component functions, several new statistical tests are introduced and are shown to lead to an improvement in detection performance when compared to the existing algorithms. The performance of each new algorithm is assessed in Additive White Gaussian Noise (AWGN), impulsive noise and when subjected to impairments such as multipath fading and Carrier Frequency Offset (CFO). Finally, each algorithm is targeted for Field Programmable Gate Array (FPGA) implementation using a Xilinx 7 series device. In order to keep resource costs to a minimum, it is suggested that the new algorithms are implemented on the FPGA using hardware sharing, and a simple mathematical re-arrangement of certain tests statistics is proposed to circumvent a costly division operation.As the requirement for wireless telecommunications services continues to grow, it has become increasingly important to ensure that the Radio Frequency (RF) spectrum is managed efficiently. As a result of the current spectrum allocation policy, it has been found that portions of RF spectrum belonging to licensed users are often severely underutilised, at particular times and geographical locations. Awareness of this problem has led to the development of Dynamic Spectrum Access (DSA) and Cognitive Radio (CR) as possible solutions. In one variation of the shared-use model for DSA, it is proposed that the inefficient use of licensed spectrum could be overcome by enabling unlicensed users to opportunistically access the spectrum when the licensed user is not transmitting. In order for an unlicensed device to make decisions, it must be aware of its own RF environment and, therefore, it has been proposed that DSA could been abled using CR. One approach that has be identified to allow the CR to gain information about its operating environment is spectrum sensing. An interesting solution that has been identified for spectrum sensing is cyclostationary detection. This property refers to the inherent periodic nature of the second order statistics of many communications signals. One of the most common modulation formats in use today is Orthogonal Frequency Division Multiplexing (OFDM), which exhibits cyclostationarity due to the addition of a Cyclic Prefix (CP). This thesis examines several statistical tests for cyclostationarity in OFDM signals that may be used for spectrum sensing in DSA and CR. In particular, focus is placed on statistical tests that rely on estimation of the Cyclic Autocorrelation Function (CAF). Based on splitting the CAF into two complex component functions, several new statistical tests are introduced and are shown to lead to an improvement in detection performance when compared to the existing algorithms. The performance of each new algorithm is assessed in Additive White Gaussian Noise (AWGN), impulsive noise and when subjected to impairments such as multipath fading and Carrier Frequency Offset (CFO). Finally, each algorithm is targeted for Field Programmable Gate Array (FPGA) implementation using a Xilinx 7 series device. In order to keep resource costs to a minimum, it is suggested that the new algorithms are implemented on the FPGA using hardware sharing, and a simple mathematical re-arrangement of certain tests statistics is proposed to circumvent a costly division operation

A nonlinear M-estimation approach to robust asynchronous multiuser detection in Non-gaussian noise

A nonlinear M-estimation approach is proposed to solve the multiuser detection problem in asynchronous code-division multiple-access (CDMA) systems where the ambient noise is impulsive and the delays are not known. We treat the unknown delays as nuisance parameters and the transmitted symbols as parameters of interest. We also analyze the asymptotic performance of the proposed estimator and propose suboptimal but computationally efficient procedures for solving the nonlinear optimization function. Simulation results show considerable improvements over the conventional approaches

Robust Techniques for Signal Processing: A Survey

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryU.S. Army Research Office / DAAG29-81-K-0062U.S. Air Force Office of Scientific Research / AFOSR 82-0022Joint Services Electronics Program / N00014-84-C-0149National Science Foundation / ECS-82-12080U.S. Office of Naval Research / N00014-80-K-0945 and N00014-81-K-001

Novel channel sensing and access strategies in opportunistic spectrum access networks

textTraditionally radio spectrum was considered a commodity to be allocated in a fixed and centralized manner, but now the technical community and the regulators approach it as a shared resource that can be flexibly and intelligently shared between competing entities. In this thesis we focus on novel strategies to sense and access the radio spectrum within the framework of Opportunistic Spectrum Access via Cognitive Radio Networks (CRNs). In the first part we develop novel transmit opportunity detection methods that effectively exploit the gray space present in packet based networks. Our methods proactively detect the maximum safe transmit power that does not significantly affect the primary network nodes via an implicit feedback mechanism from the Primary network to the Secondary network. A novel use of packet interarrival duration is developed to robustly perform change detection in the primary network's Quality of Service. The methods are validated on real world IEEE 802.11 WLANs. In the second part we study the inferential use of Goodness-of-Fit tests for spectrum sensing applications. We provide the first comprehensive framework for decision fusion of an ensemble of goodness-of-fit tests through use of p-values. Also, we introduce a generalized Phi-divergence statistic to formulate goodness-of-fit tests that are tunable via a single parameter. We show that under uncertainty in the noise statistics or non-Gaussianity in the noise, the performance of such non-parametric tests is significantly superior to that of conventional spectrum sensing methods. Additionally, we describe a collaborative spatially separated version of the test for robust combining of tests in a distributed spectrum sensing setting. In the third part we develop the sequential energy detection problem for spectrum sensing and formulate a novel Sequential Energy Detector. Through extensive simulations we demonstrate that our doubly hierarchical sequential testing architecture delivers a significant throughput improvement of 2 to 6 times over the fixed sample size test while maintaining equivalent operating characteristics as measured by the Probabilities of Detection and False Alarm. We also demonstrate the throughput gains for a case study of sensing ATSC television signals in IEEE 802.22 systems.Electrical and Computer Engineerin

Collaborative Information Processing in Wireless Sensor Networks for Diffusive Source Estimation

In this dissertation, we address the issue of collaborative information processing for diffusive source parameter estimation using wireless sensor networks (WSNs) capable of sensing in dispersive medium/environment, from signal processing perspective. We begin the dissertation by focusing on the mathematical formulation of a special diffusion phenomenon, i.e., an underwater oil spill, along with statistical algorithms for meaningful analysis of sensor data leading to efficient estimation of desired parameters of interest. The objective is to obtain an analytical solution to the problem, rather than using non-model based sophisticated numerical techniques. We tried to make the physical diffusion model as much appropriate as possible, while maintaining some pragmatic and reasonable assumptions for the simplicity of exposition and analytical derivation. The dissertation studies both source localization and tracking for static and moving diffusive sources respectively. For static diffusive source localization, we investigate two parametric estimation techniques based on the maximum-likelihood (ML) and the best linear unbiased estimator (BLUE) for a special case of our obtained physical dispersion model. We prove the consistency and asymptotic normality of the obtained ML solution when the number of sensor nodes and samples approach infinity, and derive the Cramer-Rao lower bound (CRLB) on its performance. In case of a moving diffusive source, we propose a particle filter (PF) based target tracking scheme for moving diffusive source, and analytically derive the posterior Cramer-Rao lower bound (PCRLB) for the moving source state estimates as a theoretical performance bound. Further, we explore nonparametric, machine learning based estimation technique for diffusive source parameter estimation using Dirichlet process mixture model (DPMM). Since real data are often complicated, no parametric model is suitable. As an alternative, we exploit the rich tools of nonparametric Bayesian methods, in particular the DPMM, which provides us with a flexible and data-driven estimation process. We propose DPMM based static diffusive source localization algorithm and provide analytical proof of convergence. The proposed algorithm is also extended to the scenario when multiple diffusive sources of same kind are present in the diffusive field of interest. Efficient power allocation can play an important role in extending the lifetime of a resource constrained WSN. Resource-constrained WSNs rely on collaborative signal and information processing for efficient handling of large volumes of data collected by the sensor nodes. In this dissertation, the problem of collaborative information processing for sequential parameter estimation in a WSN is formulated in a cooperative game-theoretic framework, which addresses the issue of fair resource allocation for estimation task at the Fusion center (FC). The framework allows addressing either resource allocation or commitment for information processing as solutions of cooperative games with underlying theoretical justifications. Different solution concepts found in cooperative games, namely, the Shapley function and Nash bargaining are used to enforce certain kinds of fairness among the nodes in a WSN