Cramer-rao bound for time-delay estimation in the frequency domain

In this paper a measure of performance of time delay estimators arising from a frequency model of the received signal is presented. The aim is to derive theoretical analysis of the Cramer-Rao bound (CRB) for time delay estimation under realistic wireless channel propagation conditions. The derivation of the CRB is considered from the frequency domain signal model yielding a closed-form expression without imposing any constraints on the different propagation paths.Peer ReviewedPostprint (published version

Fundamental Limits of Wideband Localization - Part II: Cooperative Networks

The availability of positional information is of great importance in many commercial, governmental, and military applications. Localization is commonly accomplished through the use of radio communication between mobile devices (agents) and fixed infrastructure (anchors). However, precise determination of agent positions is a challenging task, especially in harsh environments due to radio blockage or limited anchor deployment. In these situations, cooperation among agents can significantly improve localization accuracy and reduce localization outage probabilities. A general framework of analyzing the fundamental limits of wideband localization has been developed in Part I of the paper. Here, we build on this framework and establish the fundamental limits of wideband cooperative location-aware networks. Our analysis is based on the waveforms received at the nodes, in conjunction with Fisher information inequality. We provide a geometrical interpretation of equivalent Fisher information for cooperative networks. This approach allows us to succinctly derive fundamental performance limits and their scaling behaviors, and to treat anchors and agents in a unified way from the perspective of localization accuracy. Our results yield important insights into how and when cooperation is beneficial.Comment: To appear in IEEE Transactions on Information Theor

Fundamental limits of wideband localization

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 107-112).Location-awareness is essential for many wireless network applications. However, determining nodes' positions precisely is a challenging task, especially in harsh multipath propagation environments. To address this problem, wide bandwidth signals are envisioned to be used in future localization systems, since such signals can provide accurate range measurements. In this paper, we investigate the localization performance of wideband networks and proposed a performance measure called the squared position error bound (SPEB) to characterize the localization accuracy. We derive the SPEB succinctly by applying the notion of equivalent Fisher information (EFI). The EFI provides insights into the essence of localization problem by unifying the localization information from individual anchors and that from a priori knowledge of the agent's position in a canonical form. We also investigate the use of wideband antenna arrays and the effect of clock asynchronism on the localization accuracy. Our analysis begins with the received waveforms themselves rather than utilizing only signal metrics, such as time-of-arrival and received signal strength, extracted from the waveforms. Our framework exploits all the information inherent in the received waveforms, and therefore the SPEB serves as a fundamental limit of localization accuracy.by Yuan Shen.S.M

Simultaneous Target and Multipath Positioning

<p>In this work, we present the Simultaneous Target and Multipath Positioning (STAMP) technique to jointly estimate the unknown target position and uncertain multipath channel parameters. We illustrate the applications of STAMP for target tracking/geolocation problems using single-station hybrid TOA/AOA system, monostatic MIMO radar and multistatic range-based/AOA based localization systems. The STAMP algorithm is derived using a recursive Bayesian framework by including the target state and multipath channel parameters as a single random vector, and the unknown correspondence between observations and signal propagation channels is solved using the multi-scan multi-hypothesis data association. In the presence of the unknown time-varying number of multipath propagation modes, the STAMP algorithm is modified based on the single-cluster PHD filtering by modeling the multipath parameter state as a random finite set. In this case, the target state is defined as the parent process, which is updated by using a particle filter or multi-hypothesis Kalman filter. The multipath channel parameter is defined as the daughter process and updated based on an explicit Gaussian mixture PHD filter. Moreover, the idenfiability analysis of the joint estimation problem is provided in terms of Cramér-Rao lower bound (CRLB). The Fisher information contributed by each propagation mode is investigated, and the effect of Fisher information loss caused by the measurement origin uncertainty is also studied. The proposed STAMP algorithms are evaluated based on a set of illustrative numeric simulations and real data experiments with an indoor multi-channel radar testbed. Substantial improvement in target localization accuracy is observed.</p>Dissertatio

Localization and cooperative communication methods for cognitive radio

We study localization of nearby nodes and cooperative communication for cognitive radios. Cognitive radios sensing their environment to estimate the channel gain between nodes can cooperate and adapt their transmission power to maximize the capacity of the communication between two nodes. We study the end-to-end capacity of a cooperative relaying scheme using orthogonal frequency-division modulation (OFDM) modulation, under power constraints for both the base station and the relay station. The relay uses amplify-and-forward and decodeand-forward cooperative relaying techniques to retransmit messages on a subset of the available subcarriers. The power used in the base station and the relay station transmitters is allocated to maximize the overall system capacity. The subcarrier selection and power allocation are obtained based on convex optimization formulations and an iterative algorithm. Additionally, decode-and-forward relaying schemes are allowed to pair source and relayed subcarriers to increase further the capacity of the system. The proposed techniques outperforms non-selective relaying schemes over a range of relay power budgets. Cognitive radios can be used for opportunistic access of the radio spectrum by detecting spectrum holes left unused by licensed primary users. We introduce a spectrum holes detection approach, which combines blind modulation classification, angle of arrival estimation and number of sources detection. We perform eigenspace analysis to determine the number of sources, and estimate their angles of arrival (AOA). In addition, we classify detected sources as primary or secondary users with their distinct second-orde one-conjugate cyclostationarity features. Extensive simulations carried out indicate that the proposed system identifies and locates individual sources correctly, even at -4 dB signal-to-noise ratios (SNR). In environments with a high density of scatterers, several wireless channels experience non-line-of-sight (NLOS) condition, increasing the localization error, even when the AOA estimate is accurate. We present a real-time localization solver (RTLS) for time-of-arrival (TOA) estimates using ray-tracing methods on the map of the geometry of walls and compare its performance with classical TOA trilateration localization methods. Extensive simulations and field trials for indoor environments show that our method increases the coverage area from 1.9% of the floor to 82.3 % and the accuracy by a 10-fold factor when compared with trilateration. We implemented our ray tracing model in C++ using the CGAL computational geometry algorithm library. We illustrate the real-time property of our RTLS that performs most ray tracing tasks in a preprocessing phase with time and space complexity analyses and profiling of our software