1. How are deterministic measurement matrices designed?
Deterministic measurement matrices are designed by researchers, where the elements are intentionally designed. Various approaches have been proposed in recent years. For example, [15] uses specific codes and optimal codebooks to generate a deterministic CS matrix. [16] constructs the matrix through Bose balanced incomplete blocks, enhancing embedding flexibility. [17] applies a sparse fast Fourier transform in the matrix. [18] proposes a bipolar measurement matrix based on binary sequence families. Additionally, [19] uses singular value decomposition to improve the sensing matrix, ensuring sparsity and restricted isometry property (RIP), though with high computational costs. [20] optimizes the sensing matrix by multiplying its orthogonal form with its pseudo-inverse. [21] employs equiangular noncoherent cell norm compact frame sensing matrices, using a random matrix as an initial preconditioning matrix, and iteratively relaxes the Gram matrix to achieve an optimal Frobinius norm compact frame. However, the effectiveness of these methods may decrease with measurement noise, as SNR decreases when multiplied by the transformation matrix, leading to a higher misestimation probability.
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2. How does the virtual sensor node model work?
The virtual sensor node model utilizes the localization signal reflected from the intelligent reflective surface (IRS) to reduce the loss of the received signal strength indicator (RSS) value and ensure accurate localization. In this model, the reflected signals from multiple paths are modeled as signals from a mirror sensor behind the IRS. The physical and virtual sensors are placed inside the rectangle formed by the IRS. The deployment pattern of real and virtual sensors is specified using a symmetric orthogonal matrix and an offset. The normal vector of the IRS is represented by homogeneous coordinates. Through reverse ray tracing, the number of communication links increases without increasing hardware consumption. Overall, the virtual sensor node model enhances localization accuracy and communication efficiency.
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3. How are virtual sensor nodes formed?
Virtual sensor nodes are formed when signals from several mirror sensors converge at a position between two real sensors. This convergence creates a virtual sensor node, which plays a crucial role in estimating the positions of targets in a rectangular localization region with intelligent reflecting surfaces. The signals received by real and virtual sensors on the communication link are used to calculate the difference in received signal strengths, aiding in the localization process. This innovative approach increases the number of communication links without increasing hardware consumption, enhancing the efficiency of the system model.
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4. What is the significance of mesh in device-free location localization using compressed sensing theory?
Mesh plays a crucial role in device-free location localization using compressed sensing theory. The localization area is divided into N grids of the same size and numbered in order, namely, 1, 2, 3, . . ., n, . . ., N. An n-dimensional vector th Nx1 is used to represent the position distribution of K targets (K << N) to be located. If a grid contains targets, the coordinate position of the center point of the grid in the rectangular coordinate system is regarded as the target position, and the value of the corresponding position in the th Nx1 vector is set to 1, while the other positions without targets are set to 0. The mesh helps in transforming the position estimation problem into a sparse signal recovery problem, which involves solving a norm 0 minimization problem with a known sensing matrix and vector th. This approach allows for the recovery of a sparse signal th by solving the equation th = arg min th 0 s.t. y = Phth + e (5), where y is the signal strength difference vector, Ph is the sensing matrix, and e is the noise vector. The mesh ensures that the sensing matrix used in this scenario is optimized to achieve higher localization accuracy, as it helps in reducing the degree of coherence between the columns in the sensing matrix, which can severely confuse any recovery algorithm and lead to poor localization results. Therefore, the mesh is essential in device-free location localization using compressed sensing theory as it enables the accurate estimation of target positions and improves the overall performance of the localization system.
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