R-dimensional ESPRIT-type algorithms for strictly second-order non-circular sources and their performance analysis

High-resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second-order (SO) non-circular (NC) sources allow for a lower estimation error and can resolve twice as many sources. In this paper, we derive the R-D NC Standard ESPRIT and the R-D NC Unitary ESPRIT algorithms that provide a significantly better performance compared to their original versions for arbitrary source signals. They are applicable to shift-invariant R-D antenna arrays and do not require a centrosymmetric array structure. Moreover, we present a first-order asymptotic performance analysis of the proposed algorithms, which is based on the error in the signal subspace estimate arising from the noise perturbation. The derived expressions for the resulting parameter estimation error are explicit in the noise realizations and asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. We also provide mean squared error (MSE) expressions, where only the assumptions of a zero mean and finite SO moments of the noise are required, but no assumptions about its statistics are necessary. As a main result, we analytically prove that the asymptotic performance of both R-D NC ESPRIT-type algorithms is identical in the high effective SNR regime. Finally, a case study shows that no improvement from strictly non-circular sources can be achieved in the special case of a single source.Comment: accepted at IEEE Transactions on Signal Processing, 15 pages, 6 figure

Influence of model errors on some spatial analysis methods

The purpose of this article is ta study the influence of model errors on the performances of some spatial analysis methods. We present a unification of both the concerned methods and perturbations . This leads to a general expression of the estimation error on the sources bearings as a functon of both the perturbation and the method. This expression, calculated at the first order and in the non-asymptotic case, is then derived for each method and each perturbation .Nous étudions dans cet article l'influence d'erreurs de modèle sur le performances de certaines méthodes d'analyse spatiale. Une unification de methodes ainsi que des perturbations considérés nous permet de donner une formule générale pour l'erreur d'estimation des directions d'arrivées, en fonction de la perturbation et de la méthode utilisée. Cette formule, obtenue au premier ordre et dans le cas non-asymptotique, est ensuite dérivée pour chaque méthode et pour chaque perturbatio

Antenna array geometries and algorithms for direction of arrival estimation

Direction of arrival (DOA) estimation with the antenna array was a forever topic of scientist. In this dissertation, a detailed comparison of the direction of arrival (DOA) estimation algorithms, including three classic algorithms as MUSIC, Root-MUSIC and ESPRIT, was performed and an analysis of various array geometries’ (configurations) properties in DOA estimation was demonstrated. Cramer-Rao Bound (CRB) was used for theoretic analysis and Root Mean Square Error (RMSE), which determined the best performance for a given geometry, regardless the specific estimation algorithm used, was implemented in simulation comparison. In the first part, MUSIC, Root-MUSIC and ESPRIT were illustrated, where theoretic underlying of the algorithms were expressed by revisited, paseudo code algorithms, and compared in the aspects of accuracy and computational efficiency. Consequently, ESPRIT was found more efficient than the other two algorithms in computation. However, the accuracy of MUSIC was better than ESPRIT. In the second part, four particular array geometries, including Uniform Circular Array (UCA), L Shaped Array (LSA), Double L Shaped Array (DLSA) and Double Uniform Circular Array (DUCA), were analyzed in the area of directivity, accuracy and resolving ability. A simulation comparison of DOA estimation with these four array geometries by MUSIC algorithm in two dimensions was made then, since MUSIC had the best accuracy in these three algorithms. According to the analysis and comparison, it was found that L Shaped Array (LSA) and Double L Shaped Array (DLSA) were more accurate than others, considering both azimuth and elevation estimation. Also, in the case of two dimensional DOA estimation, the Double L Shaped Array (DLSA) was shown a theoretically relative isotropy to other array geometries. From the simulation, the detection ability of Double L Shaped Array (DLSA) was proved the best in the array geometries discussed in this dissertation. These findings had significant implications for the further study of the array geometry in DOA estimation

3-D Beamspace ML Based Bearing Estimator Incorporating Frequency Diversity and Interference Cancellation

The problem of low-angle radar tracking utilizing an array of antennas is considered. In the low-angle environment, echoes return from a low flying target via a specular path as well as a direct path. The problem is compounded by the fact that the two signals arrive within a beamwidth of each other and are usually fully correlated, or coherent. In addition, the SNR at each antenna element is typically low and only a small number of data samples, or snapshots, is available for processing due to the rapid movement of the target. Theoretical studies indicates that the Maximum Likelihood (ML) method is the only reliable estimation procedure in this type of scenario. However, the classical ML estimator involves a multi-dimensional search over a multi-modal surface and is consequently computationally burdensome. In order to facilitate real time processing, we here propose the idea of beamspace domain processing in which the element space snapshot vectors are first operated on by a reduced Butler matrix composed of three orthogonal beamforming weight vectors facilitating a simple, closed-form Beamspace Domain ML (BDML) estimator for the direct and specular path angles. The computational simplicity of the method arises from the fact that the respective beams associated with the three columns of the reduced Butler matrix have all but three nulls in common. The performance of the BDML estimator is enhanced by incorporating the estimation of the complex reflection coefficient and the bisector angle, respectively, for the symmetric and nonsymmetric multipath cases. To minimize the probability of track breaking, the use of frequency diversity is incorporated. The concept of coherent signal subspace processing is invoked as a means for retaining the computational simplicity of single frequency operation. With proper selection of the auxiliary frequencies, it is shown that perfect focusing may be achieved without iterating. In order to combat the effects of strong interfering sources, a novel scheme is presented for adaptively forming the three beams which retains the feature of common nulls

Antenna array geometries and algorithms for direction of arrival estimation

Direction of arrival (DOA) estimation with the antenna array was a forever topic of scientist. In this dissertation, a detailed comparison of the direction of arrival (DOA) estimation algorithms, including three classic algorithms as MUSIC, Root-MUSIC and ESPRIT, was performed and an analysis of various array geometries’ (configurations) properties in DOA estimation was demonstrated. Cramer-Rao Bound (CRB) was used for theoretic analysis and Root Mean Square Error (RMSE), which determined the best performance for a given geometry, regardless the specific estimation algorithm used, was implemented in simulation comparison. In the first part, MUSIC, Root-MUSIC and ESPRIT were illustrated, where theoretic underlying of the algorithms were expressed by revisited, paseudo code algorithms, and compared in the aspects of accuracy and computational efficiency. Consequently, ESPRIT was found more efficient than the other two algorithms in computation. However, the accuracy of MUSIC was better than ESPRIT. In the second part, four particular array geometries, including Uniform Circular Array (UCA), L Shaped Array (LSA), Double L Shaped Array (DLSA) and Double Uniform Circular Array (DUCA), were analyzed in the area of directivity, accuracy and resolving ability. A simulation comparison of DOA estimation with these four array geometries by MUSIC algorithm in two dimensions was made then, since MUSIC had the best accuracy in these three algorithms. According to the analysis and comparison, it was found that L Shaped Array (LSA) and Double L Shaped Array (DLSA) were more accurate than others, considering both azimuth and elevation estimation. Also, in the case of two dimensional DOA estimation, the Double L Shaped Array (DLSA) was shown a theoretically relative isotropy to other array geometries. From the simulation, the detection ability of Double L Shaped Array (DLSA) was proved the best in the array geometries discussed in this dissertation. These findings had significant implications for the further study of the array geometry in DOA estimation

Applications of Continuous Spatial Models in Multiple Antenna Signal Processing

This thesis covers the investigation and application of continuous spatial models for multiple antenna signal processing. The use of antenna arrays for advanced sensing and communications systems has been facilitated by the rapid increase in the capabilities of digital signal processing systems. The wireless communications channel will vary across space as different signal paths from the same source combine and interfere. This creates a level of spatial diversity that can be exploited to improve the robustness and overall capacity of the wireless channel. Conventional approaches to using spatial diversity have centered on smart, adaptive antennas and spatial beam forming. Recently, the more general theory of multiple input, multiple output (MIMO) systems has been developed to utilise the independent spatial communication modes offered in a scattering environment. ¶ ..

Estudio espectral del ritmo eléctrico básico del intestino delgado para la monitorización no invasiva del marcapasos intestinal

El aparato digestivo permite que los alimentos se conviertan en nutrientes y proporcionen al organismo las calorías y los elementos fundamentales para la vida, al mismo tiempo que se expulsan y eliminan los productos residuales de forma adecuada. La motilidad intestinal es muy importante para conseguir la segmentación del quimo y el tránsito intestinal y está determinada por la actividad mioeléctrica de las capas musculares intestinales. Dicha actividad también se le denomina electroenterograma (EEnG). La señal mioeléctrica es el resultado de una componente de baja frecuencia que en condiciones fisiológicas está siempre presente llamada onda lenta (OL) o ritmo eléctrico básico (BER) que constituye el marcapasos intestinal; y una componente de alta frecuencia llamada spike bursts o potenciales rápidos de acción que está asociada a las contracciones intestinales. El análisis del EEnG es un paso clave para monitorizar la actividad intestinal. El estudio del BER intestinal no sólo proporciona información acerca del ritmo básico de las contracciones del intestino, sino que puede ayudar a diagnosticar algunas patologías gastrointestinales. Para ofrecer esta herramienta como aplicación clínica, el registro de la señal del EEnG debe ser no invasivo. El objetivo de la presente Tesis Doctoral es detectar la actividad del marcapasos intestinal y caracterizar el ritmo eléctrico básico en el EEnG externo, comparándolo y estudiando su relación con el EEnG interno. Las señales analizadas fueron obtenidas simultáneamente en la superficie abdominal y en la serosa intestinal de perros Beagle en estado de ayuno. Los métodos de estimación autoregresivo (AR), autoregresivo de media móvil (ARMA), Prony y clasificación de señales múltiples (MUSIC), se emplearon para determinar la distribución espectral de potencia asociada a la actividad de la onda lenta, tanto en los registros internos como externos. Por otro lado, para estudiar la relación entre el espectro de la señal captada en superficie y las señales internas, se estimaron las funciones de coherencia utilizando los modelos autoregresivo multivariante (ARM) y MUSIC.Moreno Vázquez, JDJ. (2011). Estudio espectral del ritmo eléctrico básico del intestino delgado para la monitorización no invasiva del marcapasos intestinal [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/14276Palanci