Semidefinite Relaxation for Moving Target Localization in Asynchronous MIMO Systems
Xiaoping Wu, Xiaoting Mao, Hengnian Qi
Abstract
Considering an asynchronous multiple input multiple output (MIMO) system, we propose to obtain the position and velocity of a moving target by applying differential time delay (DTD) and differential frequency shift (DFS) measurements. The asynchronous MIMO systems are generally divided into quasi-synchronous (QS) and fully-asynchronous (FA) systems. Applying the semidefinite relaxation (SDR), we further design two semidefinite programming (SDP) solutions: QS-SDP for quasi-synchronous systems and FA-SDP for fully-asynchronous systems. We give the conditions under which the QS-SDP and FA-SDP forms are shown to be sufficiently tight so that their solutions perform to the Cramér-Rao Lower Bound (CRLB) precision. The results from the simulations demonstrate that the QS-SDP and FA-SDP solutions require few transmitters and receivers to uniquely determine the unknown parameters of the moving target. Besides, the QS-SDP and FA-SDP solutions provide the equivalent performance to the CRLB even at high noise levels.