Abstract
Thanks to massive antenna arrays in millimeter wave communications, a much higher resolution can be achieved for the estimation of angle of arrival. By taking full advantage of beamforming capability and high angular resolution in millimeter wave systems, a single anchor is sufficient to obtain a good position estimation for agents by combining angle of arrival and time of arrival. In this paper, a single-anchor based cooperative localization is proposed for millimeter wave systems. Fundamental limits of cooperative localization with a single anchor is investigated, where all nodes are equipped with massive antenna arrays. Bounds of time-based range and position estimation are derived by Crámer-Rao bound in general multipath channels. For the single-anchor based cooperative localization, the structure of the fisher information matrix is investigated and the relationship between ranging accuracy and positioning accuracy is theoretically clarified. Numerical results demonstrate a consistency with theory behind the proposed millimeter wave’s cooperative localization network.
Highlights
As is well known, millimeter wave communication operates with the wide spectrum from 30 GHz to 300 GHz [1]
In addition to offering a large available bandwidth and massive antenna arrays, Millimeter wave (mmWave) transmissions have a higher transmit power that leads to a higher signal noise ratio (SNR) compared with another probing signal with a large band named ultra wideband (UWB) ([4, 5]) in the frequency range of 3.1 ∼ 10.6 GHz
In the proposed model associated with mmWave transmission and massive antenna arrays, we analyze the fisher information matrix (FIM) structure and derive the Crámer-Rao bound (CRB) for position estimation in single anchor-based cooperative localization;
Summary
Millimeter wave (mmWave) communication operates with the wide spectrum from 30 GHz to 300 GHz [1]. This paper proposes single-anchor based cooperative localization and investigates the fundamental limits on ranging and positioning in mmWave-based cooperative localization. In the proposed model associated with mmWave transmission and massive antenna arrays, we derive the CRB for range and orientation estimations for a single anchor and range estimation for agents;. In the proposed model associated with mmWave transmission and massive antenna arrays, we analyze the FIM structure and derive the CRB for position estimation in single anchor-based cooperative localization;. The close relationship between the bound for range estimation and that for position estimation is theoretically disclosed in single-anchor based cooperative localization. Notations: The superscripts [ ·]∗ , |·|, [ ·]T , [ ·]−1 and [ ·] denote the conjugate, the modulus, the transpose, the inverse, and the first derivation of the argument, respectively; A B means that matrix A − B is positive semidefinite; [ ·]i,j denotes the element at the ith row and jth column of its argument; [ ·]r1:r2,c1:c2 denotes a submatrix composed of the rows r1 to r2 and the columns c1 to c2 of its argument; [ ·]n×n,k denotes the kth n × n submatrix beginning from the element 2n(k − 1) + 1 on the diagonal of its argument; In denotes a n × n identity matrix, 1m×n denotes a m × n matrix with all elements of 1 and 0m×n denotes a m × n matrix with all elements of 0; A ⊗ B denotes the Kronecker product of A and B and A ◦ B denotes the Hadamard product of A and B; Ev{·} is the expectation operator with respect to the random vector v; tr(·) denotes the trace of a matrix
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