Multiscale analysis of high frequency exchange rate time series

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Characterizing Cyclostationary Features of Digital Modulated Signals with Empirical Measurements Using Spectral Correlation Function

Signal detection is widely used in many applications. Some examples include Cognitive Radio (CR) and military intelligence. CRs use signal detection to sense spectral occupancy. Without guaranteed signal detection, a CR cannot reliably perform its role. Similarly, signal detection is the first step for garnering an opponent\u27s information. Wireless signal detection can be performed using many different techniques. Some of the most popular include matched filters, energy detectors (which use measurements such as the Power Spectral Density (PSD) of the signal), and Cyclostationary Feature Detectors (CFD). Among these techniques, CFD can be viewed as a compromise technique, in that it theoretically has better low Signal-to-Noise Ratio (SNR) detection performance than energy detectors and less strict requirements than matched filters. CFD uses the cyclostationarity of a signal to detect its presence. Signals that have cyclostationarity exhibit correlations between widely separated spectral components. Functions that describe this cyclostationarity include the Spectral Correlation Function (SCF). One advantage of cyclostationary approaches such as these is that Additive White Gaussian Noise (AWGN) is cancelled in these functions. This characteristic makes SCF outperform PSD under low SNR environments. However, whereas PSD has been well investigated through empirical experiments throughout many researches, SCF features under real world noise have not been investigated with empirical experiments. In this effort, firstly, the SCF features of modulated signals under real world channel noise are identified and characterized using the concept of path loss. Secondly, outperformance of SCF under low SNR environment with real world signals is verified with real world signals and noise

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

Time-frequency representations of generalized almost-cyclostationary signals

Nous proposons dans cet article une contribution à la théorie récemment introduite des signaux quasi-cyclostationnaires généralisés. Cette classe de signaux étend la classe des signaux quasi-cyclostationnaires au cas de signaux dont les fréquences cycliques dépendent du temps. Des représentations temps-fréquence de ces signaux sont données en fonction des statistiques cycliques généralisées. Notamment, la distribution de Wigner-Ville et la fonction d'ambiguïté sont examinées en détail. Le problème de l'extraction des caractéristiques des signaux quasi-cyclostationnaires généralisés, basée sur l'estimation d'un seul enregistrement, est également traité

Second-order cyclostationarity-based detection and classification of LTE SC-FDMA signals for cognitive radio

Cognitive radio (CR) was developed for utilizing the spectrum bands efficiently. Spectrum sensing and awareness represent main tasks of a CR, providing the possibility of exploiting the unused bands. In this thesis, we investigate the detection and classification of Long Term Evolution (LTE) single carrier-frequency division multiple access (SC-FDMA) signals, which are used in uplink LTE, with applications to cognitive radio. We explore the second-order cyclostationarity of the LTE SC-FDMA signals, and apply results obtained for the cyclic autocorrelation function to signal detection and classification (in other words, to spectrum sensing and awareness). The proposed detection and classification algorithms provide a very good performance under various channel conditions, with a short observation time and at low signal-to-noise ratios, with reduced complexity. The validity of the proposed algorithms is verified using signals generated and acquired by laboratory instrumentation, and the experimental results show a good match with computer simulation results

Statistical signal processing of nonstationary tensor-valued data

Real-world signals, such as the evolution of three-dimensional vector fields over time, can exhibit highly structured probabilistic interactions across their multiple constitutive dimensions. This calls for analysis tools capable of directly capturing the inherent multi-way couplings present in such data. Yet, current analyses typically employ multivariate matrix models and their associated linear algebras which are agnostic to the global data structure and can only describe local linear pairwise relationships between data entries. To address this issue, this thesis uses the property of linear separability -- a notion intrinsic to multi-dimensional data structures called tensors -- as a linchpin to consider the probabilistic, statistical and spectral separability under one umbrella. This helps to both enhance physical meaning in the analysis and reduce the dimensionality of tensor-valued problems. We first introduce a new identifiable probability distribution which appropriately models the interactions between random tensors, whereby linear relationships are considered between tensor fibres as opposed to between individual entries as in standard matrix analysis. Unlike existing models, the proposed tensor probability distribution formulation is shown to yield a unique maximum likelihood estimator which is demonstrated to be statistically efficient. Both matrices and vectors are lower-order tensors, and this gives us a unique opportunity to consider some matrix signal processing models under the more powerful framework of multilinear tensor algebra. By introducing a model for the joint distribution of multiple random tensors, it is also possible to treat random tensor regression analyses and subspace methods within a unified separability framework. Practical utility of the proposed analysis is demonstrated through case studies over synthetic and real-world tensor-valued data, including the evolution over time of global atmospheric temperatures and international interest rates. Another overarching theme in this thesis is the nonstationarity inherent to real-world signals, which typically consist of both deterministic and stochastic components. This thesis aims to help bridge the gap between formal probabilistic theory of stochastic processes and empirical signal processing methods for deterministic signals by providing a spectral model for a class of nonstationary signals, whereby the deterministic and stochastic time-domain signal properties are designated respectively by the first- and second-order moments of the signal in the frequency domain. By virtue of the assumed probabilistic model, novel tests for nonstationarity detection are devised and demonstrated to be effective in low-SNR environments. The proposed spectral analysis framework, which is intrinsically complex-valued, is facilitated by augmented complex algebra in order to fully capture the joint distribution of the real and imaginary parts of complex random variables, using a compact formulation. Finally, motivated by the need for signal processing algorithms which naturally cater for the nonstationarity inherent to real-world tensors, the above contributions are employed simultaneously to derive a general statistical signal processing framework for nonstationary tensors. This is achieved by introducing a new augmented complex multilinear algebra which allows for a concise description of the multilinear interactions between the real and imaginary parts of complex tensors. These contributions are further supported by new physically meaningful empirical results on the statistical analysis of nonstationary global atmospheric temperatures.Open Acces

Multi-stage Wireless Signal Identification for Blind Interception Receiver Design

Protection of critical wireless infrastructure from malicious attacks has become increasingly important in recent years, with the widespread deployment of various wireless technologies and dramatic growth in user populations. This brings substantial technical challenges to the interception receiver design to sense and identify various wireless signals using different transmission technologies. The key requirements for the receiver design include estimation of the signal parameters/features and classification of the modulation scheme. With the proper identification results, corresponding signal interception techniques can be developed, which can be further employed to enhance the network behaviour analysis and intrusion detection. In detail, the initial stage of the blind interception receiver design is to identify the signal parameters. In the thesis, two low-complexity approaches are provided to realize the parameter estimation, which are based on iterative cyclostationary analysis and envelope spectrum estimation, respectively. With the estimated signal parameters, automatic modulation classification (AMC) is performed to automatically identify the modulation schemes of the transmitted signals. A novel approach is presented based on Gaussian Mixture Models (GMM) in Chapter 4. The approach is capable of mitigating the negative effect from multipath fading channel. To validate the proposed design, the performance is evaluated under an experimental propagation environment. The results show that the proposed design is capable of adapting blind parameter estimation, realize timing and frequency synchronization and classifying the modulation schemes with improved performances