Performance analysis of an improved MUSIC DoA estimator

This paper adresses the statistical performance of subspace DoA estimation using a sensor array, in the asymptotic regime where the number of samples and sensors both converge to infinity at the same rate. Improved subspace DoA estimators were derived (termed as G-MUSIC) in previous works, and were shown to be consistent and asymptotically Gaussian distributed in the case where the number of sources and their DoA remain fixed. In this case, which models widely spaced DoA scenarios, it is proved in the present paper that the traditional MUSIC method also provides DoA consistent estimates having the same asymptotic variances as the G-MUSIC estimates. The case of DoA that are spaced of the order of a beamwidth, which models closely spaced sources, is also considered. It is shown that G-MUSIC estimates are still able to consistently separate the sources, while it is no longer the case for the MUSIC ones. The asymptotic variances of G-MUSIC estimates are also evaluated.Comment: Revised versio

Signal Processing in Large Systems: a New Paradigm

For a long time, detection and parameter estimation methods for signal processing have relied on asymptotic statistics as the number $n$ of observations of a population grows large comparatively to the population size $N$, i.e. $n/N\to \infty$. Modern technological and societal advances now demand the study of sometimes extremely large populations and simultaneously require fast signal processing due to accelerated system dynamics. This results in not-so-large practical ratios $n/N$, sometimes even smaller than one. A disruptive change in classical signal processing methods has therefore been initiated in the past ten years, mostly spurred by the field of large dimensional random matrix theory. The early works in random matrix theory for signal processing applications are however scarce and highly technical. This tutorial provides an accessible methodological introduction to the modern tools of random matrix theory and to the signal processing methods derived from them, with an emphasis on simple illustrative examples

Design and theoretical analysis of advanced power based positioning in RF system

Accurate locating and tracking of people and resources has become a fundamental requirement for many applications. The global navigation satellite systems (GNSS) is widely used. But its accuracy suffers from signal obstruction by buildings, multipath fading, and disruption due to jamming and spoof. Hence, it is required to supplement GPS with inertial sensors and indoor localization schemes that make use of WiFi APs or beacon nodes. In the GPS-challenging or fault scenario, radio-frequency (RF) infrastructure based localization schemes can be a fallback solution for robust navigation. For the indoor/outdoor transition scenario, we propose hypothesis test based fusion method to integrate multi-modal localization sensors. In the first paper, a ubiquitous tracking using motion and location sensor (UTMLS) is proposed. As a fallback approach, power-based schemes are cost-effective when compared with the existing ToA or AoA schemes. However, traditional power-based positioning methods suffer from low accuracy and are vulnerable to environmental fading. Also, the expected accuracy of power-based localization is not well understood but is needed to derive the hypothesis test for the fusion scheme. Hence, in paper 2-5, we focus on developing more accurate power-based localization schemes. The second paper improves the power-based range estimation accuracy by estimating the LoS component. The ranging error model in fading channel is derived. The third paper introduces the LoS-based positioning method with corresponding theoretical limits and error models. In the fourth and fifth paper, a novel antenna radiation-pattern-aware power-based positioning (ARPAP) system and power contour circle fitting (PCCF) algorithm are proposed to address antenna directivity effect on power-based localization. Overall, a complete LoS signal power based positioning system has been developed that can be included in the fusion scheme --Abstract, page iv

On the Resolution Probability of Conditional and Unconditional Maximum Likelihood DoA Estimation

After decades of research in Direction of Arrival (DoA) estimation, today Maximum Likelihood (ML) algorithms still provide the best performance in terms of resolution capabilities. At the cost of a multidimensional search, ML algorithms achieve a significant reduction of the outlier production mechanism in the threshold region, where the number of snapshots per antenna and/or the signal to noise ratio (SNR) are low. The objective of this paper is to characterize the resolution capabilities of ML algorithms in the threshold region. Both conditional and unconditional versions of the ML algorithms are investigated in the asymptotic regime where both the number of antennas and the number of snapshots are large but comparable in magnitude. By using random matrix theory techniques, the finite dimensional distributions of both cost functions are shown to be Gaussian distributed in this asymptotic regime, and a closed form expression of the corresponding asymptotic covariance matrices is provided. These results allow to characterize the asymptotic behavior of the resolution probability, which is defined as the probability that the cost function evaluated at the true DoAs is smaller than the values that it takes at the positions of the other asymptotic local minima

Theoretical Performance of Low Rank Adaptive Filters in the Large Dimensional Regime

International audienceThis paper proposes a new approximation of the theoretical Signal to Interference plus Noise Ratio (SINR) loss of the Low-Rank (LR) adaptive filter built on the eigenvalue decomposition of the sample covariance matrix. This new result is based on an analysis in the large dimensional regime, i.e. when the size and the number of data tend to infinity at the same rate. Compared to previous works, this new derivation allows to measure the quality of the adaptive filter near the LR contribution. Moreover, we propose a new LR adaptive filter and we also derive its SINR loss approximation in a large dimensional regime. We validate these results on a jamming application and test their robustness in a Multiple Input Multiple Output Space Time Adaptive Processing (MIMO-STAP) application where the data size is larg

Channel Modeling and Direction-of-Arrival Estimation in Mobile Multiple-Antenna Communication Systems

Antennas that are able to adaptively direct the transmitted (and received) energy are of great interest in future wireless communication systems. The directivity implies reduced transmit power and interference, and also a potential for increased capacity. This thesis treats some modeling and estimation problems in mobile communication systems that employ multiple antennas, primarily at the base stations. With multiple antennas at the receive side, the spatial dimension is added, and processing is performed in both the temporal and spatial domains. The potential benefits are increased range, fading diversity and spatially selective transmission. Specifically, the problems dealt in this thesis are mainly related to the uplink transmission from mobile to the base station. Two main topics are studied, channel modeling and estimation of channel parameters. This thesis first describes the modeling of the reflected power distribution due to the scatterers close to the mobile stations, in terms of the received signal azimuth at the base station with multiple-antenna. As a more realistic channel modeling, a multipath fading deterministic channel model is proposed to generate properly correlated faded waveforms with appropriate power distribution through azimuth spread of received signal. The purpose of the proposed channel model is to model fading received signal waveforms with Laplacian distribution of power through received signal azimuth spread. This thesis is divided into two parts; in the first part multipath fading by local scattering are used to derive a channel model including the spatial dimension for non frequency-selective fading. This means that the mobile is not modeled as a point source but as a cluster of a large number of independent scatterers with small time delay spread to take into account angular spreading of the signal. Properly correlated fading waveforms are obtained by taking into account the angular spread of the scattered signals from a particular distribution of scatterers. By appropriate scaling of the array response vector (ARV) based on non-equal locations for various received signal components as a function of distance from the transmitter, the reflected power from a given scatterer is no longer constant but varies as a function of the distance from the transmitter. Our proposed channel model is able to produce fading signal waveform which agrees with the results of reflected angular power dispersions measured in the field, e.g. Laplacian distribution of power in azimuth. It is also shown that the channel response can be modeled as a complex Gaussian vector. Although the channel will be frequency selective in the case of multipath propagation with considerable time spread, this can be modeled as having more than one cluster of scatterers. By employing Walsh-Hadamard codewo VdLrs)l wideband multipath fading model is achieved. It is shown that the statistical properties of proposed model such as signal waveform's correlation, autocorrelation and crosscorrelation between generated paths, are in good agreement with the theory in space and time domain. The model can be applied to evaluate smart antenna systems and beamforming algorithms in the uplink by generating uncorrelated multipaths Rayleigh fading waveforms with certain spatio-temporal correlation and spatial coordinates relative to base stations to simulate received signals from mobiles and interferers. Bit-error-rate (BER) performance analysis of uniform linear array antenna (ULA) based on correlation - matrix is also presented as an application of our proposed model for multipleantenna evaluations. Our simulated results show 5% improvement than other published related works. One problem when modeling frequency selective fading is that each cluster has to be assigned spatial parameters. Since the joint spatial and temporal characteristics are unknown, non-parametric channel estimation approaches are required in this case in order to estimate the channel parameter, which is the subject of the second part. The second part of the thesis deals with channel parameter estimation of distributed scattering sources. Because of local scattering around the transmitter the signal waveforms appears spatially distributed at the receiver. The characterization of the spatial channel, in particular mean direction of arrival and spatial spread, is of prime interest for system optimization and performance prediction. Low-complexity spectral-based estimators are used for the estimation of direction and spatial spread of the distributed source by employing the proposed channel model for simulation. Estimated parameters from recent measurements ([PMFOO]) are compared with estimated parameters from model generated waveforms as well as theoretical distribution of received signal's angular spread. Good agreement between them is observed which shows the correctness of our proposed channel model for simulating spatio-temporally correlated received signal at an antenna array. The estimated parameter error improved by 5% over the other published related works

Detection Strategies and Intercept Metrics for Intra-Pulse Radar-Embedded Communications

This thesis presents various detection strategies and intercept metrics to evaluate and design an intra-pulse radar-embedded communication system. This system embeds covert communication symbols in masking interference provided by the reflections of a pulsed radar emission. This thesis considers the case where the communicating device is a transponder or tag present in an area that is illuminated by a radar. The radar is considered to be the communication receiver. As with any communication system, performance (as measured by reliability and data rate) should be maximized between the tag and radar. However, unlike conventional communication systems, the symbols here should also have a low-probability of intercept (LPI). This thesis examines the trade-offs associated with the design of a practical radar-embedded communication system. A diagonally-loaded decorrelating receiver is developed and enhanced with a second stage based on the Neyman-Pearson criterion. For a practical system, the communication symbols will likely encounter multipath. The tag may then use a pre-distortion strategy known as time-reversal to improve the signal-to-noise ratio at the radar receiver thereby enhancing communication performance. The development of several intercept metrics are shown and the logic behind the design evolutions are explained. A formal analysis of the processing gain by the desired receiver relative to the intercept receivers is given. Finally, simulations are shown for all cases, to validate the design metrics