A linear minimum mean square error estimation method and system based on reconfigurable microwave network

Abstract

This invention discloses a linear minimum mean square error estimation method and system based on a reconfigurable microwave network. Addressing the computational bottleneck of high-dimensional matrix inversion in the traditional digital domain, this invention configures a reconfigurable microwave network with P ports. A target matrix is ​​constructed based on the system matrix, noise covariance, and prior covariance, and mapped to set values ​​for the interconnect admittance between network ports and the port-to-ground admittance. After loading the observation vector onto the input ports, the network reaches a steady state, and the estimated result is obtained by directly reading the output port voltage vector. This method transforms complex mathematical operations into a linear steady-state solution of the physical network, avoiding digital matrix inversion. It offers advantages such as strong parallelism, low latency, low power consumption, and dynamic reconfigurability. Combined with online calibration and error statistics functions, it is suitable for high-speed real-time signal processing scenarios.

Description

Technical Field

[0001] This invention relates to the fields of analog computing and microwave network signal processing technology, and in particular to a linear minimum mean square error estimation method and system based on reconfigurable microwave networks. Background Technology

[0002] In many cutting-edge electronic information and signal processing fields such as modern wireless communication, radar detection, high-precision positioning, automatic control, and artificial intelligence machine learning, signal parameter estimation, state filtering, and data reconstruction are core foundational technologies supporting the normal operation of systems. The signal acquisition and observation processes in various practical engineering scenarios can be modeled and represented using a classic linear observation model. This model accurately depicts the mapping relationship between the system's estimated parameters, the observed output, the system's transmission characteristics, and random noise, serving as the core modeling foundation for algorithms such as Linear Minimum Mean Square Error (LMMSE) estimation, optimal filtering, and signal restoration.

[0003] Specifically, the expression for the general linear observation model is as follows: The physical definitions and dimensional characteristics of each parameter in the formula are explained in detail below: This is the system observation vector, used to characterize the observation data actually acquired by the equipment; For the random vector to be estimated, the corresponding target parameters, state variables or original signals that the system needs to solve, reconstruct or track. The system transmission matrix is ​​used to characterize the linear transmission characteristics, channel response, or state mapping of the observation system. It is an additive random noise vector that encompasses various random disturbance factors such as system thermal noise, channel interference, and measurement errors.

[0004] In typical engineering applications, the covariance matrix of the random vector to be estimated can usually be obtained in advance through methods such as channel measurement, noise statistical modeling, and sample training. and the covariance matrix of the observation noise vector In this context, the superscript H represents the matrix conjugate transpose operation. This represents the expected value in mathematical calculations. Furthermore, in most practical operating conditions, the covariance matrix... and All of them satisfy the positive definite invertibility condition. Based on this prior condition, the LMMSE estimation algorithm can derive the closed-form analytical solution of the optimal estimator without needing to converge through iterative calculations. It has the theoretically optimal estimation accuracy and is therefore widely used in various high-precision signal estimation scenarios.

[0005] Currently, all existing engineering implementations of LMMSE estimation involve offline / online computation in the digital domain, meaning that all linear algebra operations are performed using digital hardware platforms such as digital chips, processors, and FPGAs. The core computational process of traditional digital implementations requires multiple high-precision matrix multiplications and high-dimensional matrix inversions, and the core solution formulas require... or It performs inversion on high-dimensional composite matrices and simultaneously completes complex operations such as matrix multiplication, matrix addition, and subtraction.

[0006] As modern electronic systems rapidly develop towards larger dimensions, larger scale, and higher density, the observation dimension Y and the dimension of the parameters to be estimated X continue to increase, and the dimensionality of matrix operations grows exponentially. This has led to many unavoidable technical defects exposed in traditional digital domain LMMSE implementation schemes, which seriously restrict the overall system performance and engineering implementation capabilities. The specific defects are reflected in the following three aspects: First, the algorithm has high computational complexity and large processing latency. The computational complexity of inverting and multiplying high-dimensional matrices increases quadratically or even cubically with the increase of matrix dimension. Massive floating-point operations will consume a lot of computing resources of digital processors, resulting in a significant increase in the estimation and processing latency of a single frame signal, which cannot meet the basic requirements of high-speed signal processing.

[0007] Second, storage access overhead and system power consumption are high. High-dimensional matrix operations require frequent reading, caching, and updating of large-scale matrix data, which places extremely high demands on the read / write bandwidth and cache capacity of hardware storage units. Frequent storage interaction operations not only increase hardware resource utilization but also significantly increase system dynamic power consumption, which is not conducive to the engineering design requirements of device miniaturization and low power consumption.

[0008] Third, it is difficult to adapt to high-end application scenarios with real-time and high throughput requirements. In scenarios with stringent requirements for real-time data processing and throughput, such as 5G / 6G high-speed communication, real-time radar imaging, dynamic UAV positioning, and high-speed machine learning inference, the high latency and low efficiency of traditional digital LMMSE solutions will become the performance bottleneck of the entire signal processing link, limiting the system's real-time response capability and data processing throughput, and greatly restricting the application scope of LMMSE estimation algorithms in high-end real-time systems.

[0009] In summary, current LMMSE estimation implementations based on pure digital computation are constrained by high-complexity linear algebraic operations such as matrix inversion and matrix multiplication. In high-dimensional scenarios, they suffer from multiple technical shortcomings in terms of complexity, latency, power consumption, and throughput, failing to meet the demands of modern large-scale, real-time, and low-power signal processing. Therefore, there is an urgent need to develop a novel implementation scheme that physically maps and hardware-enabled the core linear algebraic operations upon which the LMMSE algorithm relies. This scheme abandons the traditional successive digital computation mode, enabling the optimal estimation result to be directly output through the steady-state response of the physical network, fundamentally solving the technical bottlenecks of traditional digital implementation schemes. Summary of the Invention

[0010] This invention provides a linear minimum mean square error estimation method based on reconfigurable microwave networks. By incorporating the system matrix and statistical matrix in the LMMSE estimation problem into the equivalent matrix parameters of the microwave network, the output port voltage of the network in steady state directly gives the LMMSE estimation result, thereby reducing or avoiding digital domain matrix inversion and matrix multiplication operations.

[0011] This invention provides a linear minimum mean square error estimation method based on reconfigurable microwave networks, comprising: Configure a reconfigurable microwave network with P ports, setting the total number of ports P to be equal to the sum of the number of input ports N and the number of output ports M, and letting the number of input ports N be equal to the dimension Y of the observation vector y, and the number of output ports M be equal to the dimension X of the vector x to be estimated; A reference admittance Y0 is connected in series at all P ports to construct a uniform port boundary condition, and the observation vector is loaded to the first N input ports through a controlled voltage source, and the last M output ports are connected to a matching terminal. Adjusting the tunable admittance units within the reconfigurable microwave network allows the network's equivalent matrix to be adjusted. The target matrix is ​​mapped to the linear minimum mean square error estimate. ; After reading the output port block voltage vectors of the M output ports, output the output port block voltage vectors as the linear minimum mean square error estimation result.

[0012] In one embodiment of the present invention, the target matrix It is a P×P dimensional block matrix, which is divided into four sub-blocks according to the input and output ports: = ; in For noise covariance, For the system matrix, The conjugate transpose of the system matrix. It is the inverse of the prior covariance; The port voltage vector is divided into input / output blocks as follows: v= ; Where v1∈ Y×1 , is the input port block voltage vector; v2∈ X×1 , is the output port block voltage vector; The network equivalent matrix satisfies the port voltage vector. With external excitation vector linear equations ,in The network equivalent matrix is: = in: P 11 ∈ Y×Y ;P 22 ∈ X×X ;P 12 ∈ Y×X ;P 21 ∈ X×Y ; External excitation vector = , =y; The derivation yields v2=(P) 21 P 11 -1 P 12 -P 22 ) -1 P 21 P 11 -1 u1.

[0013] In one embodiment of the present invention, it further includes: A known test vector is periodically loaded onto the first N input ports; Read the amplitude and phase responses of the last M output ports; Based on the deviation between the amplitude and phase response and the theoretically expected output, the set value of the adjustable admittance unit or the reading of the output port block voltage vector is corrected.

[0014] In one embodiment of the present invention, it further includes: Construct the network objective matrix for error statistics; The unit vector is loaded column by column into the first N input ports; Read the output port block voltage vectors of the last M output ports, and output the output port block voltage vectors as column vectors of the linear minimum mean square error estimation error covariance matrix.

[0015] In one embodiment of the present invention, when the system matrix H, the noise covariance matrix Cn, and the prior covariance matrix Cx are updated inversely, a new admittance parameter value is calculated according to a preset mapping formula, and the new admittance parameter value is written into the adjustable admittance unit.

[0016] In one embodiment of the present invention, adjusting the adjustable admittance unit includes: adjusting the port interconnect admittance unit to set the off-diagonal elements of the target matrix; and adjusting the port-to-reference node admittance unit to set the diagonal elements of the target matrix.

[0017] In one embodiment of the present invention, the network equivalent matrix P is mapped to the target matrix of the linear minimum mean square error estimation. So that: v2=x`=(H H C n -1 H+C x -1 ) -1 H H C n -1 y; or v2=x`=C x H H (HC x H H +C n ) -1 y; Where x' is the target matrix The equivalent closed-form solution.

[0018] The present invention also provides a linear minimum mean square error estimation system based on a reconfigurable microwave network, comprising: A reconfigurable microwave network has P ports, wherein the total number of ports P is equal to the sum of the number of input ports N and the number of output ports M, and the number of input ports N is equal to the dimension Y of the observation vector y and the number of output ports M is equal to the dimension X of the vector x to be estimated. A reference admittance unit, connected in series at the P ports, is used to construct a unified port boundary condition; An input loading module, connected to the first N input ports, is used to load the observation vector to the first N input ports through a controlled voltage source; An output measurement module is connected to the last M output ports and is used to read the output port block voltage vector of the last M output ports; The admittance parameter configuration module, connected to the reconfigurable microwave network, is used to adjust the adjustable admittance units within the network, so that the equivalent matrix of the reconfigurable microwave network is mapped to the target matrix of the linear minimum mean square error estimation. .

[0019] In one embodiment of the present invention, the reconfigurable microwave network is internally composed of port interconnection admittance units and port-to-reference node admittance units. The port interconnection admittance units connect different ports to realize off-diagonal elements of the target matrix, and the port-to-reference node admittance units connect ports and reference nodes to realize diagonal elements of the target matrix.

[0020] In one embodiment of the present invention, it further includes: An online calibration module, connected to the input loading module and the output measurement module, is used to periodically send known test vectors to the input loading module, and generate correction instructions based on the deviation between the amplitude and phase response read by the output measurement module and the theoretically expected output, and send them to the admittance parameter configuration module or the output measurement module. An error statistics module, connected to the admittance parameter configuration module, is used to construct a network target matrix for error statistics and send it to the admittance parameter configuration module, so that when the reconfigurable microwave network receives unit vector column-by-column excitation at the input port, it outputs the column vector of the linear minimum mean square error estimation error covariance matrix through the output measurement module.

[0021] The present invention has the following beneficial effects: (1) By configuring the P-port reconfigurable microwave network (P=N+M, N=Y, M=X), the reference admittance Y0 is connected in series at all ports and the observation vector is loaded onto the first N input ports. The internal adjustable admittance unit is adjusted so that the network equivalent matrix strictly maps the LMMSE target matrix, thereby realizing that the output port voltage directly corresponds to the linear minimum mean square error estimation result.

[0022] (2) Introduce an online calibration and drift compensation mechanism. During system operation, periodically input known test vectors or known statistical conditions to identify the amplitude and phase deviation of the output port in real time and correct the admittance set value or voltage reading.

[0023] (3) Construct a joint output error statistical network target matrix. Without changing the core estimation output path, when the network is given a unit vector column-by-column excitation at the input port, the output port directly provides the column vector of the LMMSE error covariance matrix. This technique provides directly usable statistical features for subsequent confidence assessment, adaptive filtering algorithm iteration, or system health status monitoring, enhancing the adaptability and robustness of the end-to-end signal processing system.

[0024] (4) By adopting a dynamic admittance reconfiguration strategy, when the system matrix H, noise covariance matrix Cn and prior covariance matrix Cx inverse are updated, the parameter settings of the adjustable admittance unit can be updated according to the preset mapping formula to quickly switch to the new estimation task.

[0025] This invention does not simply describe the LMMSE algorithm or mathematical logic, but rather explicitly defines the construction of a hardware carrier using the physical structure of a reconfigurable microwave network (port allocation, reference admittance series connection, and adjustable admittance unit connection relationship). By adjusting the parameters of the physical admittance devices, the abstract target mathematical matrix is ​​written into the equivalent parameters of the physical network. The port voltage signal is directly output using the electromagnetic wave propagation and physical steady-state establishment process, forming a complete hardware and software linkage implementation step of "mathematical model mapping—hardware parameter configuration—physical layer steady-state solution—voltage signal reading." The algorithm only serves as the underlying data processing step for hardware parameter configuration and is not divorced from the specific engineering implementation method. The specific technical field to which this application belongs is microwave analog computing and signal processing hardware design. The technical problem this patent aims to solve is that high-dimensional matrix inversion in traditional digital domain LMMSE estimation leads to large computational delays, high power consumption, and throughput bottlenecks. The technical approach adopted is to construct a P-port reconfigurable microwave network, configure reference admittance and adjustable admittance units to map the LMMSE target matrix, and replace digital matrix operations with the steady-state response of physical port voltage. The achieved technical effects are to avoid the bottleneck of digital inversion, directly output the estimated voltage, and achieve low-latency parallel processing and low power consumption, which meets the requirements of "technical solutions that utilize natural laws to solve technical problems" as stipulated in Article 2, Paragraph 2 of the Patent Law. Attached Figure Description

[0026] Figure 1 A schematic diagram of a linear minimum mean square error estimation system based on a reconfigurable microwave network is shown in one embodiment of the present invention. Figure 2 (a) shows a circuit diagram of the port-to-reference node admittance unit in one embodiment of the present invention; Figure 2 (b) shows a schematic diagram of the inter-port interconnect admittance unit and multi-port topology connection in one embodiment of the present invention. Detailed Implementation

[0027] In the following description, the invention is described with reference to various embodiments. However, those skilled in the art will recognize that the embodiments may be practiced without one or more specific details or with other alternatives and / or additional methods, materials, or components. In other instances, well-known structures, materials, or operations are not shown or described in detail so as not to obscure the inventive points of the invention. Similarly, for illustrative purposes, specific quantities, materials, and configurations are set forth to provide a comprehensive understanding of embodiments of the invention. However, the invention is not limited to these specific details.

[0028] In this invention, the various embodiments are merely intended to illustrate the solutions of the invention and should not be construed as limiting.

[0029] In this specification, references to "an embodiment" or "this embodiment" mean that a particular feature, structure, or characteristic described in connection with that embodiment is included in at least one embodiment of the invention. The phrase "in one embodiment" appearing throughout this specification does not necessarily refer to the same embodiment in all instances.

[0030] Furthermore, the numbering of the steps in the methods of the present invention does not limit the execution order of the method steps. Unless otherwise specified, the method steps may be executed in different orders.

[0031] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0032] In applications such as communication, radar, positioning, control, and machine learning, a common linear observation model is: y = Hx + n, where: y∈ Y×1 For observation vectors; x∈ X×1 Let the random vector be to be estimated; H∈ Y×X For the system matrix; n∈ Y×1 This is the noise vector.

[0033] When the covariance C of x is known x =E[xx H [With noise covariance C] n =E[nn H When (the two are usually invertible), the LMMSE estimate has a closed-form solution.

[0034] This invention uses a P-port reconfigurable microwave network as the core of analog computing.

[0035] P: Total number of ports in the microwave network. The voltage and current vectors at the network ports are both P-dimensional; the network can be described by an equivalent matrix of P×P.

[0036] N: Number of input ports (number of ports for loading input stimuli).

[0037] M: Number of output ports (the number of ports used to read results without loading input).

[0038] The relationship is: P = N + M, N <P。

[0039] To achieve LMMSE: Let N=Y (the input port dimension is equal to the observation dimension); Let M=X (the output port dimension is equal to the unknown variable dimension); Thus: P=X+Y.

[0040] Partition the port voltage vector by input / output blocks: = ,v1∈ Y×1 ,v2∈ X×1 The objective of the present invention is to make v2=x' at steady state. That is, the output port block voltage is directly equal to the LMMSE estimation value.

[0041] The reconfigurable microwave network is a linear multi-port network. Its port variables satisfy a "linear equation" structure: under given port boundary conditions (for example, uniform reference admittance / impedance termination and controlled excitation), the network steady-state port voltage vector v is the solution of a certain system of linear equations. For the convenience of engineering implementation, the present invention adopts a unified port connection mode: the input port is connected to a controlled voltage source (to form an input vector); all ports realize consistent port boundary conditions through the reference admittance Y0 (or equivalent reference impedance). Under this boundary condition, the network steady state can be written as: where: ∈ P×1 is the steady-state port voltage; ∈ P×1 is the excitation vector (extended input) externally loaded to the port; ∈ P×P is the equivalent matrix jointly determined by the network admittance configuration and the reference admittance.

[0042] When N<P, the present invention loads input excitation only to the first N ports, and does not load input to the last M ports (only performs matched termination and reads the output). At this time, the matrix P is also partitioned in the same manner: = , where: P 11 ∈ Y×Y ; P 22 ∈ X×X ; P 12 ∈ Y×X ; P 21 ∈ X×Y ; The input vector is divided into ports as follows: u= ; That is, the output port does not load input.

[0043] Under this structure, the steady-state output block v2 can be obtained in a fixed form by block matrix elimination: As long as P 11 If it is reversible, then v2 can be written as: v2=(P 21 P 11 -1 P 12 -P 22 ) -1 P 21 P 11 -1 u1 (another equivalent form in P) 22 (This also applies when it is reversible).

[0044] LMMSE has two equivalent closed-ended solutions under the above model: x`=(H H C n -1 H+C x -1 ) -1 H H C n -1 y; And the equivalent form: x`=C x H H (HC x H H +C n ) -1 y.

[0045] This invention constructs a specific P×P target matrix (where P=X+Y): = ; The top left block represents the noise covariance (with a sign); The top right and bottom left blocks are H and H. H ; The bottom right block is the inverse of the prior covariance (with the opposite sign).

[0046] The “± / ∓± / ∓” appear in pairs, corresponding to different derivation paths of the two equivalent expressions of LMMSE; theoretically, they will both lead to the same x`, but in engineering, one can be chosen based on implementation convenience or numerical stability.

[0047] Simultaneously, the input is set to u1=y, meaning the observation vector is used as the input port excitation and applied to the first Y ports. Under this construction, the general expression of v2 in the previous section is strictly reduced to an LMMSE closed-form solution, so x` can be obtained by reading the output port block in steady state.

[0048] The system employs an array of adjustable admittance elements to implement a reconfigurable network, and provides formulas for determining element parameters from matrices. The network comprises: 1) Interconnection of ports with adjustable admittance units (achieving off-diagonal coupling); 2) Adjustable admittance unit for port to reference node (implementing diagonal and summary terms).

[0049] Let the reference admittance be Y0. For a given target matrix... Set each admittance element as follows: If i ≠ k: Let the interconnect admittance between port i and port k be Y. i,k =-Y0[P] i,k ; If i=k: the admittance of port k to ground is set to Y. k,k =Y0 -Y0.

[0050] One embodiment of the present invention discloses a linear minimum mean square error estimation system and method based on a reconfigurable microwave network. Given the computational bottleneck and latency accumulation issues inherent in traditional digital domain processing for high-dimensional matrix inversion, this invention employs an analog microwave network as the core of physical computation. By constructing specific network topology and admittance parameters, the mathematical operations of linear minimum mean square error estimation are transformed into the steady-state voltage response of the microwave port.

[0051] like Figure 1As shown, the overall system layout of this embodiment consists of a left input side, a central computing core, and a right output side. The central area houses a reconfigurable microwave network 1 with P ports. This network integrates numerous controllable impedance components to simulate the linear relationship of the target mathematical model. To unify port boundary conditions and reduce reflection loss, a reference admittance Y0 is connected in series at all P ports. This reference admittance serves as a reference impedance matching network, ensuring a consistent electrical environment during signal transmission at the ports. The left input side is equipped with an input loading module 2, which connects sequentially to the first N input ports. It integrates a multi-channel controlled voltage source array to convert the external observation vector y into a microwave voltage excitation signal channel by channel and apply it to the corresponding port. The right output side is equipped with an output measurement module 3, directly coupled to the last M output ports. It contains a high-sensitivity microwave detector circuit and an amplitude-phase measurement circuit for real-time acquisition of the port steady-state voltage. Furthermore, the admittance parameter configuration module communicates with the control interface within the reconfigurable microwave network via a control bus. It receives matrix parameters from the host computer and parses them into specific admittance settings to drive the internal adjustable components. In terms of workflow, the system first determines the port allocation relationship based on the observation dimension Y and the dimension to be estimated X, that is, the number of input ports N equals Y, and the number of output ports M equals X, thus satisfying the condition that the total number of ports P equals the sum of N and M. Subsequently, the admittance parameter configuration module reads the preset mapping relationship and initializes the admittance within the network. When the input loading module applies the observation vector y to the first N ports, the controlled voltage source immediately establishes a stable microwave excitation field, and the signal is coupled into the reconfigurable microwave network 1 via the reference admittance Y0. Since the network equivalent matrix has been pre-mapped to the target matrix, microwave energy undergoes linear superposition and coupling between multi-port nodes within the network, ultimately establishing a steady-state distribution at the last M output ports. At this time, the output measurement module reads the voltage amplitude and phase of the last M ports, and the resulting output port block voltage vector directly corresponds to the linear minimum mean square error estimation result. Thanks to this physical mapping mechanism, the system avoids iterative solutions in the digital domain, achieving not only high-throughput data processing but also significantly reducing overall power consumption.

[0052] To accurately reproduce the closed-form solution of the linear minimum mean square error estimation, a rigorous block design is required for the structure of the network equivalent matrix. Specifically, the target matrix... The network is constructed as a P×P dimensional block matrix and divided into four sub-regions according to the physical locations of the input and output ports: the upper left sub-block corresponds to the noise covariance term, the upper right sub-block corresponds to the conjugate transpose of the system matrix, the lower left sub-block corresponds to the system matrix, and the lower right sub-block corresponds to the negative value of the inverse of the prior covariance. Since the port voltage vectors are divided into input port block voltage vector v1 and output port block voltage vector v2, the steady-state behavior of the network under the unified reference admittance boundary can be expressed as a linear equation. Pv equals the external excitation vector u. The first N dimensions of the external excitation vector u are provided by the observation values ​​y from the input loading module, while the last M dimensions are zero vectors because no excitation is applied to the output port. Based on block matrix elimination theory, when the upper left submatrix P11 is invertible, the output port block voltage vector v2 can be directly solved through a specific algebraic transformation. Its mathematical expression is strictly equivalent to the two classical closed-form solutions with linear minimum mean square error. Therefore, as long as the network equivalent matrix... P Exactly match the target matrix The steady-state voltage at the output port will automatically converge to the optimal estimated value x`.

[0053] At the physical implementation level, to achieve accurate mapping of the aforementioned target matrix, the reconfigurable microwave network consists of two types of independently controllable admittance units. The port-to-interconnect admittance unit connects any two different ports and is used to set the off-diagonal elements of the target matrix, reflecting the coupling strength and phase relationship between signal channels. The port-to-reference node admittance unit connects each port to the system ground and is used to set the diagonal elements of the target matrix, controlling the self-impedance and energy dissipation characteristics of each port. The admittance parameter configuration module calculates the set values ​​of the interconnect admittance and ground admittance based on the value of the target matrix, and drives internal varactor diodes, adjustable resistors, or microelectromechanical switch arrays for dynamic adjustment. When the system matrix H, noise covariance matrix Cn, and prior covariance matrix Cx are updated inversely, the admittance parameter configuration module immediately recalculates the admittance parameter values ​​according to the preset mapping formula and writes the new parameters into the corresponding adjustable admittance unit, thereby achieving seamless switching of the estimation task.

[0054] Given the unavoidable amplitude and phase drift in microwave networks under actual operating conditions, this embodiment introduces an online calibration module. This module is electrically connected to the input loading module and the output measurement module to perform periodic self-tests. During operation, the online calibration module periodically loads known test vectors onto the first N input ports. These test vectors can be unit pulses or calibration signals with a specific spectrum. Subsequently, the output measurement module reads the amplitude and phase responses of the last M output ports and compares them with the theoretically expected output. Since the deviation between the amplitude and phase response and the theoretically expected output directly reflects the degree of network admittance drift, the online calibration module generates correction commands accordingly. These commands are sent to the admittance parameter configuration module to fine-tune the setpoint of the adjustable admittance unit, or to the output measurement module to compensate for reading deviations. Through this closed-loop feedback mechanism, the system can continuously maintain estimation accuracy, ensuring the reliability of the output results even under long-term operation or drastic environmental changes.

[0055] Furthermore, to support subsequent filtering algorithms or system health monitoring, this embodiment further integrates an error statistics module. This module, connected to the admittance parameter configuration module, is used to construct a network target matrix specifically for error statistics. Once the target matrix is ​​configured, the system loads unit vectors column by column onto the first N input ports, and the reconfigurable microwave network transforms the steady-state response of each single-channel excitation into a column vector of the error covariance matrix. After the output measurement module reads all column vectors sequentially, it can completely reconstruct the linear minimum mean square error estimation error covariance matrix. This mechanism provides additional confidence assessment data without changing the core estimation output architecture, facilitating uncertainty quantification in upper-layer applications. In summary, this embodiment significantly improves the system's engineering practicality and environmental adaptability through hardware and software collaborative calibration and statistical design.

[0056] Figure 2 (a) is a detailed circuit diagram of the port-to-reference node admittance unit. This diagram focuses on the electrical connection details between a single port and the system reference ground. The node on the left in the diagram is Port k, representing the k-th port of the microwave network; this node is connected downwards to an adjustable admittance element Yk,k, the other end of which is directly grounded and used to set the (k,k)-th parameter at the diagonal position of the target matrix. The branch extending to the right of Port k is used to connect to external circuits or other nodes within the network. In the diagram, vk is marked as the steady-state voltage of this node to ground, and ik is the net current flowing into this node. This structure precisely controls the self-impedance characteristics of port k by independently adjusting the conductance and susceptance components of Yk,k, thereby affecting the diagonal element distribution of the network's equivalent matrix. In actual hardware implementation, Yk,k is usually constructed by connecting a voltage-controlled varactor diode in parallel with a microelectromechanical system switch. The admittance parameter configuration module can achieve continuous or step adjustment by sending a DC control voltage. This unit design is not only simple in structure and easy to integrate on a large scale, but also maintains low insertion loss over a wide bandwidth, thereby ensuring rapid reconfiguration and high-precision mapping of the diagonal parameters.

[0057] Figure 2(b) is a schematic diagram of the inter-port interconnect admittance unit and multi-port topology connection. This diagram illustrates the mutual coupling mechanism between multiple ports through a distributed admittance network. From top to bottom on the left side of the diagram, Port P to Port 1 represent all port nodes of the network; each port node is interconnected through multiple lateral branches, each branch containing an adjustable interconnect admittance element, such as Yp,k representing the coupling admittance between Port p and Port k. The dashed arrows in the diagram indicate the adjustment direction of the interconnect admittance and the signal coupling path, and Y1,k in the lower right corner represents the specific coupling element between Port 1 and Port k. Each port node is simultaneously connected downwards to the reference ground, forming a complete loop topology. This structure, by independently adjusting each Yp,k parameter, precisely sets the off-diagonal elements of the target matrix, thereby physically reproducing the mathematical relationship between the system matrix H and its conjugate transpose. In practical microwave circuits, interconnect admittance is typically implemented through directional couplers, microstrip line cross-coupling structures, or variable attenuators, and dynamically updated in conjunction with a digital control interface. This topology ensures the accuracy of linear superposition between multiple ports and is a key hardware foundation for realizing high-dimensional matrix physical mapping and low crosstalk transmission.

[0058] Although various embodiments of the invention have been described above, it should be understood that they are presented by way of example only and not as limitations. It will be apparent to those skilled in the art that various combinations, modifications, and alterations can be made without departing from the spirit and scope of the invention. Therefore, the breadth and scope of the invention disclosed herein should not be limited by the exemplary embodiments disclosed above, but should be defined solely by the appended claims and their equivalents.

Claims

1. A linear minimum mean square error estimation method based on reconfigurable microwave networks, characterized in that, include: Configure a reconfigurable microwave network with P ports, setting the total number of ports P to be equal to the sum of the number of input ports N and the number of output ports M, and letting the number of input ports N be equal to the dimension Y of the observation vector y, and the number of output ports M be equal to the dimension X of the vector x to be estimated; A reference admittance Y0 is connected in series at all P ports to construct a uniform port boundary condition, and the observation vector is loaded to the first N input ports through a controlled voltage source, and the last M output ports are connected to a matching terminal. Adjusting the tunable admittance units within the reconfigurable microwave network allows the network's equivalent matrix to be adjusted. The target matrix is ​​mapped to the linear minimum mean square error estimate. ; After reading the output port block voltage vectors of the M output ports, output the output port block voltage vectors as the linear minimum mean square error estimation result.

2. The method according to claim 1, characterized in that, in, The target matrix It is a P×P dimensional block matrix, which is divided into four sub-blocks according to the input and output ports: = ； in For noise covariance, For the system matrix, The conjugate transpose of the system matrix. It is the inverse of the prior covariance; The port voltage vector is divided into input / output blocks as follows: v= ； Where v1∈ Y×1 , is the input port block voltage vector; v2∈ X×1 , is the output port block voltage vector; The network equivalent matrix satisfies the port voltage vector. With external excitation vector linear equations ,in Network equivalent matrix: = in: P 11 ∈ Y×Y ;P 22 ∈ X×X ;P 12 ∈ Y×X ;P 21 ∈ X×Y ; External excitation vector = , =y; The derivation yields v2=(P) 21 P 11 -1 P 12 -P 22 ) -1 P 21 P 11 -1 u1.

3. The method according to claim 1, characterized in that, Also includes: A known test vector is periodically loaded onto the first N input ports; Read the amplitude and phase responses of the last M output ports; Based on the deviation between the amplitude and phase response and the theoretically expected output, the set value of the adjustable admittance unit or the reading of the output port block voltage vector is corrected.

4. The method according to claim 1, characterized in that, Also includes: Construct the network objective matrix for error statistics; The unit vector is loaded column by column into the first N input ports; Read the output port block voltage vectors of the last M output ports, and output the output port block voltage vectors as column vectors of the linear minimum mean square error estimation error covariance matrix.

5. The method according to claim 1, characterized in that, When the system matrix H, noise covariance matrix Cn, and prior covariance matrix Cx are updated in reverse, new admittance parameter values ​​are calculated according to a preset mapping formula, and the new admittance parameter values ​​are written into the adjustable admittance unit.

6. The method according to claim 1, characterized in that, The adjustment of the adjustable admittance unit includes: adjusting the port interconnect admittance unit to set the off-diagonal elements of the target matrix; and adjusting the port-to-reference node admittance unit to set the diagonal elements of the target matrix.

7. The method according to claim 1, characterized in that, in, The network equivalent matrix P is mapped to the target matrix of the linear minimum mean square error estimation. So that: v2=x`=(H H C n -1 H+C x -1 ) -1 H H C n -1 y; or v2=x`=C x H H (HC x H H +C n ) -1 y; Where x' is the target matrix The equivalent closed-form solution.

8. A linear minimum mean square error estimation system based on a reconfigurable microwave network, characterized in that, include: A reconfigurable microwave network has P ports, wherein the total number of ports P is equal to the sum of the number of input ports N and the number of output ports M, and the number of input ports N is equal to the dimension Y of the observation vector y and the number of output ports M is equal to the dimension X of the vector x to be estimated. A reference admittance unit, connected in series at the P ports, is used to construct a unified port boundary condition; An input loading module, connected to the first N input ports, is used to load the observation vector to the first N input ports through a controlled voltage source; An output measurement module is connected to the last M output ports and is used to read the output port block voltage vector of the last M output ports; The admittance parameter configuration module, connected to the reconfigurable microwave network, is used to adjust the adjustable admittance units within the network, so that the equivalent matrix of the reconfigurable microwave network is mapped to the target matrix of the linear minimum mean square error estimation. .

9. The system according to claim 8, characterized in that, The reconfigurable microwave network is internally composed of port interconnection admittance units and port-to-reference node admittance units. The port interconnection admittance units connect different ports to realize the off-diagonal elements of the target matrix, and the port-to-reference node admittance units connect ports and reference nodes to realize the diagonal elements of the target matrix.

10. The system according to claim 8, characterized in that, Also includes: An online calibration module, connected to the input loading module and the output measurement module, is used to periodically send known test vectors to the input loading module, and generate correction instructions based on the deviation between the amplitude and phase response read by the output measurement module and the theoretically expected output, and send them to the admittance parameter configuration module or the output measurement module. An error statistics module, connected to the admittance parameter configuration module, is used to construct a network target matrix for error statistics and send it to the admittance parameter configuration module, so that when the reconfigurable microwave network receives unit vector column-by-column excitation at the input port, it outputs the column vector of the linear minimum mean square error estimation error covariance matrix through the output measurement module.

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