Exact Conditional and Unconditional Cram\`er-Rao Bounds for Near Field Localization

This paper considers the Cram\`er-Rao lower Bound (CRB) for the source localization problem in the near field. More specifically, we use the exact expression of the delay parameter for the CRB derivation and show how this exact CRB can be significantly different from the one given in the literature and based on an approximate time delay expression (usually considered in the Fresnel region). This CRB derivation is then generalized by considering the exact expression of the received power profile (i.e., variable gain case) which, to our best knowledge, has been ignored in the literature. Finally, we exploit the CRB expression to introduce the new concept of Near Field Localization (NFL) region for a target localization performance associated to the application at hand. We illustrate the usefulness of the proposed CRB derivation and its developments as well as the NFL region concept through numerical simulations in different scenarios

The Cramer-Rao Bound for channel estimation in block fading amplify-and-forward relaying networks

In this paper, we express the Cramer-Rao Bound (CRB) for channel coefficient and noise variance estimation at the destination of an Amplify-and- Forward (AF) based cooperative system, in terms of the a posteriori expectation of the codewords. An algorithm based on factor graphs can be applied in order to calculate this expectation. As the computation of the CRB is rather intensive, the modified CRB (MCRB), which is a looser bound, is derived in closed form. It can be shown that the MCRB coincides with the CRB in the high signal-to-noise ratio (SNR) limit and to that end the CRB/MCRB ratio is simulated in case of uncoded and convolutional encoded transmission

Deterministic Cramer-Rao bound for strictly non-circular sources and analytical analysis of the achievable gains

Recently, several high-resolution parameter estimation algorithms have been developed to exploit the structure of strictly second-order (SO) non-circular (NC) signals. They achieve a higher estimation accuracy and can resolve up to twice as many signal sources compared to the traditional methods for arbitrary signals. In this paper, as a benchmark for these NC methods, we derive the closed-form deterministic R-D NC Cramer-Rao bound (NC CRB) for the multi-dimensional parameter estimation of strictly non-circular (rectilinear) signal sources. Assuming a separable centro-symmetric R-D array, we show that in some special cases, the deterministic R-D NC CRB reduces to the existing deterministic R-D CRB for arbitrary signals. This suggests that no gain from strictly non-circular sources (NC gain) can be achieved in these cases. For more general scenarios, finding an analytical expression of the NC gain for an arbitrary number of sources is very challenging. Thus, in this paper, we simplify the derived NC CRB and the existing CRB for the special case of two closely-spaced strictly non-circular sources captured by a uniform linear array (ULA). Subsequently, we use these simplified CRB expressions to analytically compute the maximum achievable asymptotic NC gain for the considered two source case. The resulting expression only depends on the various physical parameters and we find the conditions that provide the largest NC gain for two sources. Our analysis is supported by extensive simulation results.Comment: submitted to IEEE Transactions on Signal Processing, 13 pages, 4 figure

Cramer-Rao Bounds for Joint RSS/DoA-Based Primary-User Localization in Cognitive Radio Networks

Knowledge about the location of licensed primary-users (PU) could enable several key features in cognitive radio (CR) networks including improved spatio-temporal sensing, intelligent location-aware routing, as well as aiding spectrum policy enforcement. In this paper we consider the achievable accuracy of PU localization algorithms that jointly utilize received-signal-strength (RSS) and direction-of-arrival (DoA) measurements by evaluating the Cramer-Rao Bound (CRB). Previous works evaluate the CRB for RSS-only and DoA-only localization algorithms separately and assume DoA estimation error variance is a fixed constant or rather independent of RSS. We derive the CRB for joint RSS/DoA-based PU localization algorithms based on the mathematical model of DoA estimation error variance as a function of RSS, for a given CR placement. The bound is compared with practical localization algorithms and the impact of several key parameters, such as number of nodes, number of antennas and samples, channel shadowing variance and correlation distance, on the achievable accuracy are thoroughly analyzed and discussed. We also derive the closed-form asymptotic CRB for uniform random CR placement, and perform theoretical and numerical studies on the required number of CRs such that the asymptotic CRB tightly approximates the numerical integration of the CRB for a given placement.Comment: 20 pages, 11 figures, 1 table, submitted to IEEE Transactions on Wireless Communication

Contemporary Seismicity in and Around the Yakima Fold-and-Thrust Belt in Eastern Washington

We examined characteristics of routinely cataloged seismicity from 1970 to the present in and around the Yakima fold-and-thrust belt (YFTB) in eastern Washington to determine if the characteristics of contemporary seismicity provide clues about regional-scale active tectonics or about more localized, near-surface processes. We employed new structural and hydrologic models of the Columbia River basalts (CRB) and found that one-third to one-half of the cataloged earthquakes occur within the CRB and that these CRB earthquakes exhibit significantly more clustered, and swarmlike, behavior than those outside. These results and inferences from published studies led us to hypothesize that clustered seismicity is likely associated with hydrologic changes in the CRB, which hosts the regional aquifer system. While some general features of the regional groundwater system support this hypothesis, seismicity patterns and mapped long-term changes in groundwater levels and present-day irrigation neither support nor refute it. Regional tectonic processes and crustal-scale structures likely influence the distribution of earthquakes both outside and within the CRB as well. We based this inference on qualitatively assessed alignments between the dominant northwest trends in the geologic structure and the seismicity generally and between specific faults and characteristics of the 2009 Wooded Island swarm and aseismic slip, which is the only cluster studied in detail and the most vigorous since regional monitoring began.USGS-NAGTGeological Science