On reducing the Cramer-Rao lower bound of localization by selecting base stations based on convex relaxation

In wireless network systems, time of arrival (TOA) scheme is always needed to implement the self-localization of the user manual. If multiple positions of interest exist, the Cramer-Rao lower bounds (CRLBs) of TOA localization in these positions are determined by the deployment of the base stations. The design of base station placement is addressed in this paper; and rather than the exhaustive method (EXM) we propose to optimize over a selection vector. Under a certain condition, this non-convex optimization problem can be relaxed into a convex one; and improvements are also made to avoid the limitation from the condition. What's more, a fusion strategy is designed by combining these convex algorithms together, which further reduces the maximum CRLB of the interested positions. Complexity analysis and numerical results certify the efficiency of the proposed methods in different scenes.