Signal Strength Based Localization and Path-loss Exponent Self-Estimation in Wireless Networks

Wireless communications and networking are gradually permeating our life and substantially influencing every corner of this world. Wireless devices, particularly those of small size, will take part in this trend more widely, efficiently, seamlessly and smartly. Techniques requiring only limited resources, especially in terms of hardware, are becoming more important and urgently needed. That is why we focus this thesis around analyzing wireless communications and networking based on signal strength (SS) measurements, since these are easy and convenient to gather. SS-based techniques can be incorporated into any device that is equipped with a wireless chip. More specifically, this thesis studies \textbf{SS-based localization} and \textbf{path-loss exponent (PLE) self-estimation}. Although these two research lines might seem unrelated, they are actually marching towards the same goal. The former can easily enable a very simple wireless chip to infer its location. But to solve that localization problem, the PLE is required, which is one of the key parameters in wireless propagation channels that decides the SS level. This makes the PLE very crucial to SS-based localization, although it is often unknown. Therefore, we need to develop accurate and robust PLE self-estimation approaches, which will eventually contribute to the improvement of the localization performance. Additionally, our work also provides very useful links to possible applications in other related fields. In this thesis, we start with the first research line, where we try to cope with all possible issues that we encounter in solving the localization problem. To eliminate the unknown transmit power issue, we adopt differential received signal strength (DRSS) measurements. Colored noise, non-linearity and non-convexity are the next three major issues. To deal with the first two, we introduce a whitened linear data model for DRSS-based localization. Based on that and assuming the PLE is known, three different approaches are respectively proposed to tackle the non-convexity issue: an advanced best linear unbiased estimator (A-BLUE a Lagrangian estimator (LE) and a robust semi-definite programming (SDP)-based estimator (RSDPE). Note that the RSDPE is particularly designed to be robust against the model uncertainties (imperfect PLE and inaccurate anchor location information) while the A-BLUE and the LE are based on an exact data model. We thoroughly compare them from different perspectives and conclude they have their own advantages: the A-BLUE has the lowest computational complexity; the LE holds the best accuracy for a small measurement noise; and the RSDPE yields the best performance under a large measurement noise and possesses a very good robustness against model uncertainties. Moreover, to cope with an unknown PLE, we propose a robust SDP-based block coordinate descent estimator (RSDP-BCDE) that jointly estimates the PLE and the target location. Its performance iteratively converges to that of the RSDPE with a known PLE. As mentioned earlier, while generating DRSS measurements, we eliminate the unknown transmit power. This is very similar to the way time-difference-of-arrival (TDOA) methods cope with an unknown transmit time. Both of them use a differencing process to cope with an unknown linear nuisance parameter. Our DRSS study shows the differencing process does not cause any information loss and hence the selection of the reference is not important. However, this apparently contradicts what is commonly known in TDOA-based localization, where selecting a good reference is very crucial. To resolve this conflict, we introduce a unified framework for linear nuisance parameters such that all our conclusions apply to any kind of problem that can be written into this form. Three methods that can cope with linear nuisance parameters are considered by investigating their best linear unbiased estimators (BLUEs): joint estimation, orthogonal subspace projection (OSP) method and differential method. The results coincide with those obtained in our DRSS study. For TDOA-based localization, it is actually the modelling process that causes a reference-dependent information loss, not the differencing process. Many other interesting conclusions are also drawn here. Next, we turn our attention to the second research line. Undoubtedly, knowledge of the PLE is decisive to SS-based localization and hence accurately estimating the PLE will lead to a better localization performance. However, estimating the PLE also has benefits for other applications. If each node can self-estimate the PLE in a distributed fashion without any external assistance or information, it might be very helpful for efficiently designing some wireless communication and networking systems, since the PLE yields a multi-faceted influence therein. Driven by this idea, we propose two closed-form (weighted) total least squares (TLS) methods for self-estimating the PLE, which are merely based on the locally collected SS measurements. To solve the unknown nodal distance issue, we particularly extract information from the random placement of neighbours in order to facilitate the derivations. We also elaborate on many possible applications thereafter, since this kind of PLE self-estimation has never been introduced before. Although the previous two methods estimate the PLE by minimizing some residue, we also want to introduce Bayesian methods, such as maximizing the likelihood. Some obstacles related to such approaches are the totally unknown distribution for the SS measurements and the mathematical difficulties of computing it, since the SS is subject to not only the wireless channel effects but also the geometric dynamics (the random node placement). To deal with that, we start with a simple case that only considers the geometric path-loss for wireless channels. We are the first to discover that in this case the SS measurements in random networks are \emph{Pareto} distributed. Based on that, we derive the CRLB and introduce two maximum likelihood (ML) estimators for PLE self-estimation. Although we considered a simplified setting, finding the general SS distribution would still be very useful for studying wireless communications and networking. Finally, we wrap up this thesis by summarizing our research results and providing suggestions for future work.