PCRB analysis and power optimization method and system for OTFS multi-satellite channel estimation

Abstract

The application discloses a PCRB analysis and power optimization method and system for OTFS multi-satellite channel estimation, comprising the following steps: constructing a pilot and data superposition transmission model based on an OTFS signal; constructing a pilot observation covariance matrix based on multi-satellite LoS path correlation and data interference; constructing an observation Fisher information matrix based on PCRB; using a spread pilot derivative subspace to scalarize an inverse matrix of the pilot observation covariance matrix in the observation Fisher information matrix based on PCRB; based on the scalarization processing result, constructing an equivalent observation Fisher information matrix for PCRB calculation and power optimization; calculating PCRB according to the equivalent observation Fisher information matrix; constructing a power optimization problem for throughput maximization based on PCRB; solving the power optimization problem for throughput maximization to obtain an optimal power optimization scheme. The application can achieve a better balance between channel estimation accuracy and data transmission rate, and avoid the problem that simply increasing data power leads to increased channel estimation error and decreased actual throughput.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a PCRB analysis and power optimization method and system for OTFS multi-satellite channel estimation. Background Technology

[0002] With the development of low-Earth orbit (LEO) satellite communication, integrated space-ground networks, and multi-satellite cooperative transmission technologies, satellite communication systems are gradually evolving from independent single-satellite transmission to multi-satellite joint transmission. Multiple satellites working together to provide services to the same user or area can improve coverage, link reliability, and system throughput, representing a significant future development direction for broadband satellite communication. However, LEO satellites exhibit high-speed motion characteristics, and the channel between the satellite and ground terminals typically displays significant Doppler shift, time-varying fading, and delay spread. Traditional time-frequency domain modulation and channel estimation methods are ill-suited to this high-speed, dynamic channel environment.

[0003] Orthogonal time-frequency spatial modulation (OTFS) modulation, by modeling and processing the wireless channel in the delay-Doppler domain, can effectively address the Doppler spread problem in high-speed mobile scenarios, and is therefore considered an important candidate technology for both low-Earth orbit satellite communication and high-speed mobile communication. In OTFS systems, the accuracy of channel estimation directly affects the receiver's data detection, equalization, combining, and subsequent throughput performance. Especially in multi-satellite joint transmission scenarios, the receiver needs to simultaneously estimate multiple delay-Doppler paths from multiple satellites, increasing the number of channel parameters and making the channel structure more complex, thus placing higher demands on pilot design and channel estimation methods.

[0004] To improve spectral efficiency, pilot-data overlay transmission has become an attractive scheme. This scheme allows pilot and data signals to be transmitted simultaneously within the same OTFS resource block, thus avoiding the resource overhead of traditional orthogonal pilot-data allocation. However, pilot-data overlay transmission also introduces new problems: the data signal can become interference with pilot observations during channel estimation, and both pilot power and data power are constrained by the total transmit power of each satellite. Therefore, while increasing data power helps improve the instantaneous transmission rate, it compresses pilot power and enhances data interference, leading to a decrease in channel estimation accuracy; conversely, while increasing pilot power can improve channel estimation accuracy, it reduces the power available for data transmission, affecting system throughput. Thus, a clear trade-off exists between pilot power and data power in pilot-data overlay transmission systems.

[0005] On the other hand, in multi-satellite cooperative transmission systems, there are usually distinct line-of-sight propagation paths between different satellites and the receiver. The LoS paths of multiple satellites may have non-zero means or statistical correlations. This cross-satellite LoS path correlation will form a non-whitened interference term in pilot observations. Existing methods often simply approximate data interference as independent white noise, or assume that different satellite channels are independent of each other, failing to fully characterize the impact of multi-satellite LoS path correlation on channel estimation accuracy. When this correlation is coupled with data power, the pilot observation covariance becomes more complex, making it difficult to express the channel estimation error in a simple closed-form expression.

[0006] The posterior Cramér-Rao lower bound, or PCRB, is an important tool for characterizing the lower bound of channel parameter estimation errors. It can be used to quantitatively analyze the impact of pilot power, data power, channel statistical characteristics, and interference terms on channel estimation accuracy. However, in multi-satellite OTFS systems with pilot data overlay transmission, the original PCRB calculation typically involves inverting a high-dimensional Fisher information matrix and a covariance matrix containing data interference and cross-satellite correlation terms, resulting in high computational complexity. Furthermore, pilot power and data power are highly coupled in the matrix inversion, making it difficult to directly apply to throughput maximization and power allocation optimization.

[0007] Therefore, it is necessary to propose a PCRB analysis and power optimization method for OTFS multi-satellite channel estimation, which can simultaneously consider data interference and multi-satellite Loss path correlation in pilot data superposition transmission scenarios, establish a computable, interpretable and easily optimized PCRB expression, and further optimize pilot power and data power jointly under the single satellite total power constraint based on the PCRB, thereby improving the effective throughput of the system while ensuring the channel estimation accuracy. Summary of the Invention

[0008] To address the aforementioned shortcomings in existing technologies, the present invention provides a PCRB analysis and power optimization method and system for OTFS multi-satellite channel estimation. This method solves the problems of existing technologies failing to accurately characterize the interference of data power on pilot channel estimation in pilot data superposition transmission scenarios, failing to explicitly model the impact of multi-satellite Loss path correlation on pilot observation covariance, and having complex coupling between pilot power and data power, making it difficult to directly use for throughput maximization power optimization.

[0009] To achieve the above-mentioned objectives, this invention provides a PCRB analysis and power optimization method for OTFS multi-satellite channel estimation, comprising: Construct a pilot and data superposition transmission model based on OTFS signals; Based on the pilot and data superposition transmission model based on OTFS signals, the pilot observation covariance matrix is ​​constructed based on multi-satellite LosS path correlation and data interference; Construct an observation Fisher information matrix based on PCRB; The inverse matrix of the pilot observation covariance matrix is ​​scalarized in the PCRB-based observation Fisher information matrix using the spread spectrum pilot derivative subspace. Based on the scalarization results, an equivalent observation Fisher information matrix is ​​constructed for PCRB calculation and power optimization. Calculate PCRB based on the equivalent observation Fisher information matrix; A power optimization problem oriented towards maximizing throughput is constructed based on PCRB; Solve the power optimization problem aimed at maximizing throughput to obtain the optimal power optimization scheme.

[0010] Secondly, the present invention also provides a system for implementing a PCRB analysis and power optimization method for OTFS multi-satellite channel estimation, comprising: The channel modeling module is used to construct a pilot and data superposition transmission model based on OTFS signals; The covariance construction module is used to construct the pilot observation covariance matrix based on the multi-satellite LosS path correlation and data interference, according to the pilot and data superposition transmission model based on OTFS signals. The scaling processing module is used to construct the observation Fisher information matrix based on PCRB; the inverse matrix of the pilot observation covariance matrix is ​​scaled in the observation Fisher information matrix based on PCRB using the spread spectrum pilot derivative subspace. The PCRB calculation module is used to construct an equivalent observation Fisher information matrix for PCRB calculation and power optimization based on the scalarization processing results; and to calculate PCRB based on the equivalent observation Fisher information matrix. The power optimization module is used to construct a power optimization problem oriented towards maximizing throughput based on PCRB; solve the power optimization problem oriented towards maximizing throughput, and obtain the optimal power optimization scheme.

[0011] The beneficial effects of this invention include: 1. Improve the throughput of pilot and data overlay transmission systems. This invention aims to maximize system throughput by jointly optimizing pilot power and data power under the constraint of total power of a single satellite. This achieves a better balance between channel estimation accuracy and data transmission rate, avoiding the problem of increased channel estimation error and decreased actual throughput caused by simply increasing data power.

[0012] 2. Effectively characterizes the coupling relationship between pilot power and data power. This invention, by deriving PCRB under pilot-data superposition transmission conditions, unifies the improvement of channel estimation accuracy by pilot power and the impact of data power on pilot observation interference into the same analytical framework, so that power allocation no longer depends on empirical parameters, but has a clear theoretical basis.

[0013] 3. Solving the problem of data interference modeling under pilot data superposition transmission. This invention explicitly incorporates the interference generated by the data signal in pilot observation into the equivalent noise model, so that the impact of data power on channel estimation error can be quantitatively calculated. Compared with the method of simply treating data interference as fixed noise or ignoring it, it can more accurately reflect the actual performance of the superposition transmission system.

[0014] 4. Addressing the impact of multi-satellite LosS path correlation on channel estimation. This invention explicitly considers the correlation between LosS paths in multi-satellite channels, incorporates cross-satellite LosS correlation terms into the pilot observation covariance matrix, and quantifies its impact through a supporting overlap factor, thereby avoiding the problem of underestimating multi-satellite correlation interference in the traditional independent channel assumption.

[0015] 5. Reduces the computational complexity of PCRB, facilitating engineering implementation. This invention utilizes the orthogonality of the delay-Doppler domain of the spread-pilot to scalarize the Fisher information matrix in the derivative subspace, transforming the original PCRB calculation involving the inversion of a high-dimensional covariance matrix into equivalent noise and equivalent Fisher information matrix forms, significantly reducing computational complexity.

[0016] 6. Ensure the power optimization model has good computability and stability. This invention constructs an equivalent noise power and an equivalent Fisher information matrix, so that pilot power mainly affects PCRB through the pilot power matrix, and data power mainly affects PCRB through the equivalent noise. This forms a power optimization problem with a clear structure that is easy to solve, and avoids the problem that the Fisher information matrix may be non-positive semidefinite if low-order matrix expansion is directly used.

[0017] 7. Suitable for high-dynamic multi-satellite transmission scenarios in OTFS. This invention performs channel modeling, PCRB analysis, and power optimization in the delay-Doppler domain, which can adapt to the Doppler spread and time-varying channel characteristics caused by the high-speed motion of low-Earth orbit satellites. It is suitable for multi-satellite collaborative OTFS transmission, pilot data superposition transmission, and high-dynamic satellite communication scenarios.

[0018] 8. Strong scalability. This invention can be used not only for channel gain estimation error analysis, but also for calculating PCRB for various channel parameters such as delay and Doppler; it can be used not only to maximize throughput, but also to meet channel estimation accuracy constraints, minimize PCRB, or perform pilot / data power trade-off optimization, making it suitable for deployment in satellite communication baseband processing platforms or multi-satellite resource management systems. Attached Figure Description

[0019] Figure 1 A flowchart of a PCRB analysis and power optimization method for OTFS multi-satellite channel estimation is provided for an example. Figure 2 This is a comparison chart of the system throughput of the present invention with other methods; Figure 3 This is a comparison diagram of the PCRB method of the present invention with other methods. Detailed Implementation

[0020] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0021] like Figure 1 As shown, in one embodiment of the present invention, a PCRB analysis and power optimization method for OTFS multi-satellite channel estimation includes the following steps: S1. Construct a pilot and data superposition transmission model based on OTFS signals.

[0022] Based on the pilot and data superposition transmission model of OTFS signals, for the first... The satellite transmits signals consisting of a superposition of pilot and data signals, expressed as follows:

[0023] Each satellite is subject to a single satellite's total power constraint:

[0024] This constraint directly leads to a trade-off between pilot power and data power: increasing... It can improve the strength of the data transmission signal, but it will reduce the power that can be allocated to the pilot. This reduces the accuracy of channel estimation and increases the need for further adjustments. It can reduce channel estimation error, but it will reduce data transmission power and affect throughput.

[0025] In the formula, For the first The transmission signals of the satellite; Indicates the first The power allocated to the pilot signal for each satellite; Indicates the first The power allocated to data by each satellite; This represents the spread-pilot vector. Indicates the first Data vectors of each satellite; Indicates the first The maximum transmit power of the satellite. Spread-pilots are extended across the entire OTFS resource block to enhance the distinguishability and anti-jamming capability of the pilots in the delay-Doppler domain.

[0026] No. The channel between the satellite and the receiver includes The first path, The complex gain, delay index, and Doppler index of each path are denoted as: .

[0027] Among them, complex gain It can be written as:

[0028] In the formula, Let represent the real part of the complex channel gain of the p-th path for the q-th satellite; Let represent the imaginary part of the complex channel gain for the p-th path of the q-th satellite; It is the imaginary unit.

[0029] Define the delay-Doppler shift matrix as follows: Then the first The average pilot observation value corresponding to each satellite can be expressed as:

[0030] In the formula, For the first The average pilot observation value corresponding to each satellite; This represents the delay-Doppler shift matrix corresponding to the p-th path of the q-th satellite; When multiple satellites transmit together, the average value of the total pilot observations is:

[0031] In the formula, This represents the average of all pilot signal observations. When the receiver performs pilot observations, in addition to thermal noise, it is also subject to interference from superimposed data symbols. Therefore, the received signal on the pilot side can be written as:

[0032] in, For receiving signals on the pilot side; This represents the equivalent data interference introduced by the superimposed transmission of data signals. This indicates additive noise.

[0033] S2. Construct the pilot observation covariance matrix based on multi-satellite LoS path correlation and data interference.

[0034] In multi-satellite cooperative transmission, the Loss-of-Sight (LoS) paths from different satellites to the same receiver may exhibit statistical correlation. Directly assuming that the LoS paths of different satellites are independent would underestimate the impact of cross-satellite correlation interference on channel estimation accuracy. To address this issue, this invention explicitly introduces a correlation term between the LoS paths of multiple satellites.

[0035] Specifically, define the first The mean Loss path of each satellite is expressed as:

[0036] In the formula, For the first The mean of the Loss paths of the satellites; For the first The complex gain of the first path between the satellite and the receiver; The power coupling term corresponding to the LoS path correlation between different satellites is defined as follows:

[0037] In the formula, and All are satellite indexes; For the first The power allocated to data by each satellite; For the first The power allocated to data by each satellite; For the first The mean of the Loss paths of the satellites; For the first The mean of the Loss paths of the satellites; It can be seen that, Data power of the two satellites and Directly related. Therefore, the path correlation of multiple satellites' Loss of Sight (LoS) means that the pilot observation noise covariance is related not only to the data power of a single satellite, but also to the product term between the data powers of different satellites.

[0038] Definition of the first The effective support set of the satellites in the delay-Doppler domain is expressed as:

[0039] In the formula, For the first The effective support set of the satellites in the delay-Doppler domain; This is the minimum delay index in the effective DD support of the q-th satellite; The maximum delay index in the effective DD support of the q-th satellite; The minimum Doppler index in the effective DD support of the q-th satellite; The maximum Doppler index in the effective DD support of the q-th satellite; Define the average delay-Doppler shift matrix, its expression is:

[0040] in,

[0041] In the formula, Let be the average delay-Doppler shift matrix of the q-th satellite; Let be the delayed-Doppler twisted-shift matrix, representing the two-dimensional shift operator in the DD field corresponding to the delayed index a and the Doppler index b; Let be the size of the effective DD support set for the q-th satellite; The number of delay indices in the effective delay support of the q-th satellite; The number of Doppler indices in the effective Doppler support of the q-th satellite; The cross-satellite covariance term caused by the multi-satellite LosS path correlation is constructed, and its expression is as follows:

[0042] In the formula, The cross-satellite covariance term is caused by the correlation of multiple satellite LoS paths; For the first m The average delay-Doppler shift matrix of the satellite; For the first n The conjugate transpose of the average delay-Doppler shift matrix of the satellites; The pilot observation covariance matrix is ​​constructed, and its expression is as follows:

[0043] in,

[0044] In the formula, The pilot observation covariance matrix; It is the identity matrix. This represents the whitening equivalent noise term resulting from data interference and thermal noise. Indicates thermal noise power. Indicates the first Average power statistics for each satellite channel.

[0045] The above formula shows that, It also includes the correlation between the mean LosS values ​​of different satellites. Coupling terms between different satellite data powers Furthermore, it describes the overlapping structure between different satellite delay-Doppler supports. Therefore, compared to traditional methods that treat data interference as independent white noise, this invention can explicitly describe the impact of multi-satellite Loss path correlation on pilot channel estimation.

[0046] S3. Construct the observation Fisher information matrix based on PCRB.

[0047] To characterize the impact of pilot power and data power on channel estimation error, this invention constructs a vector of parameters to be estimated: .

[0048] For any parameter and The elements of its observed Fisher information matrix are: .

[0049] Due to pilot mean With pilot power This can be further defined:

[0050] in: .

[0051] For the real and imaginary parts of the channel parameters, we have:

[0052] ; For delayed indexes and Doppler indexes, finite difference forms can be used:

[0053] .

[0054] Therefore, the Fisher information matrix based on PCRB observations is as follows:

[0055] In the formula, The Fisher information matrix based on PCRB observations; For the first The transmission power allocated to the pilot signal by each satellite; For the first The transmission power allocated to the pilot signal by each satellite; This indicates the expectation of the variable θ. Indicates taking the real part; Indicates parameters The corresponding derivative vector; This represents the inverse matrix of the pilot observation covariance matrix; parameter The corresponding derivative vector; for The i-th variable in; for The j-th variable in; The vector of channel parameters to be estimated contains the real and imaginary parts of the channel gain, the delay index, and the Doppler index for all paths of all satellites.

[0056] This formula reveals the key difficulty of the problem: Includes data power Related items for cross-satellite Loss This leads to pilot power and data power The complex coupling caused by high-dimensional matrix inversion makes it difficult to directly apply to power optimization. To reduce the computational complexity introduced by the high-dimensional matrix inversion, this invention utilizes the approximate orthogonality of spread-pilot in the delay-Doppler domain to... Scalarization is performed on the derivative subspace.

[0057] S4. Use the spread spectrum pilot derivative subspace to standardize the inverse matrix of the pilot observation covariance matrix in the observation Fisher information matrix based on PCRB.

[0058] Specifically, it includes: Define the derivative subspace, its expression is:

[0059] In the formula, Represent the derivative subspace; This indicates that Zhang Cheng is operating; ; Within this subspace, the spread-pilot shift responses satisfy approximately orthogonality:

[0060] In the formula, This represents the Kronecker delta function, when... The value is 1 if it is true, and 0 otherwise. This represents the Kronecker delta function, when... The value is 1 if it is true, and 0 otherwise. Therefore, for any ,have:

[0061] In the formula, Furthermore, due to the presence of thermal noise, we have:

[0062] Let be a constant related to the derivative form of the parameters. For the channel gain parameter, we have: For the delay and Doppler finite difference parameters, since each derivative contains two adjacent shift terms, we can take... This inequality shows that, within the spread-pilot derivative subspace, It can be approximated as a scalar matrix: .

[0063] Meanwhile, the approximation error is caused by Control, and Furthermore, it is jointly determined by the multi-satellite LoS correlation, data power, and the degree of delay-Doppler support overlap. Therefore, this invention not only reduces the complexity of matrix inversion but also retains a quantifiable description of the multi-satellite LoS path correlation.

[0064] S5. Based on the scalarization results, construct the equivalent observation Fisher information matrix for PCRB calculation and power optimization.

[0065] Based on the above scalarization process, define the geometric matrix. , its first The elements are: ; The Fisher information matrix can then be approximated as: .

[0066] To further ensure the semi-positive definiteness of the Fisher information matrix used for optimization, and to incorporate cross-satellite LoS correlation terms as conservative interference, this invention defines the equivalent noise power, expressed as follows:

[0067] In the formula, Indicates equivalent noise power; Represents a constant related to the parametric derivative form; Interference intensity for cross-satellite LoS related terms; Based on the equivalent noise power, the equivalent observation Fisher information matrix is ​​constructed, and its expression is as follows:

[0068] in,

[0069] In the formula, To obtain an equivalent observation Fisher information matrix; For geometric matrices, The first in the geometric matrix One element; This represents the pilot power of the satellite to which the 4th parameter (PQ) in the parameter vector to be estimated belongs, where Q represents the total number of satellites and P represents the total number of satellite paths.

[0070] The specific methods for quantifying the interference intensity of cross-satellite LoS related terms include: Definition of the first satellite and the first Differential support overlap number between satellites:

[0071] In the formula, For the first satellite and the first Differential support overlap number between satellites; For the first The effective support set of the satellites in the delay-Doppler domain; For the first The effective support set of the satellites in the delay-Doppler domain; This is a delayed-Doppler index point in the support set of the m-th satellite; Let n be a delayed-Doppler index point in the support set of the nth satellite; This represents the difference in cyclic delay index between two DD support points; This represents the cyclic Doppler index difference between two DD support points; Based on the satellite and the first The differential support overlap number between satellites is defined by the normalized support overlap factor, which is expressed as follows:

[0072] In the formula, This is the normalized support overlap factor; this factor characterizes the correlation between the delay-Doppler supports of different satellites under spread-pilot conditions. When the support region is large and the delay-Doppler supports between different satellites are highly distinguishable, we have: .

[0073] therefore, It can serve as a quantifiable indicator of the strength of the impact of cross-satellite LoS correlation on pilot estimation.

[0074] The cross-satellite LoS correlation term interference intensity is defined based on the normalized support overlap factor, and its expression is as follows: .

[0075] S6. Calculate PCRB based on the equivalent observation Fisher information matrix.

[0076] The specific expression for PCRB is as follows:

[0077] in,

[0078] In the formula, Represents the trace of a matrix; This is the equivalent posterior Fisher information matrix; This is the prior information matrix of the channel parameters.

[0079] For example, the complex channel gain parameter can be defined as follows: ; The delay parameter and the Doppler parameter can be defined separately: , .

[0080] When the spread-pilot shift responses of different paths do not overlap, the geometric matrix It can be approximated as a diagonal matrix. Definition:

[0081] in, Indicates the Loss of Path (LoS) path. This indicates a non-LoS path. In this case:

[0082]

[0083] Therefore, the Fisher information corresponding to the real and imaginary parts of the channel gain is: ; Fisher information corresponding to the delay and Doppler parameters is as follows: ; This allows us to obtain closed-form PCRB expression. For example, channel-gain PCRB can be written as: ; The PCRB for delayed indexing can be written as: ; The PCRB for Doppler indexing can be written as: .

[0084] The closed-form expression above clearly demonstrates the coupling relationship between pilot power and data power: increasing It can improve Fisher information and reduce PCRB; increase It will increase This reduces Fisher information and increases PCRB. This relationship is the core trade-off that must be considered for throughput optimization in pilot data overlay transmission systems.

[0085] S7. Construct a power optimization problem oriented towards maximizing throughput based on PCRB.

[0086] Based on the aforementioned PCRB expression, a power optimization problem aimed at maximizing throughput is constructed. Let the system throughput be expressed as... ,in, , This represents the lower bound of the channel estimation error characterized by the PCRB. Since the channel estimation error reduces the effective signal-to-noise ratio, the PCRB can be introduced into the throughput expression as a channel uncertainty.

[0087] Specifically, it includes: The effective signal-to-interference-plus-noise ratio (SIN / N) is expressed as follows:

[0088] In the formula, For an effective signal-to-interference-plus-noise ratio; Let be the estimated equivalent channel for the q-th satellite; This represents the residual interference term, indicating interference that was not completely eliminated, excluding noise and channel estimation errors. For the first given by PCRB The error metric for satellite channel estimation is expressed as follows:

[0089] In the formula, Indicates parameters The corresponding equivalent PCRB diagonal element; Indicates parameters The corresponding equivalent PCRB diagonal element; The throughput is defined as:

[0090] In the formula, Indicates throughput; Constructing power optimization problems specifically includes: Objective function:

[0091] Constraints:

[0092] .

[0093] In another feasible embodiment of the present invention, PCRB can be used as a constraint condition, specifically:

[0094] In the formula, Indicates the channel gain PCRB constraint threshold; Indicates the delayed index PCRB constraint threshold; Indicates the PCRB constraint threshold for the Doppler index; S8. Solve the power optimization problem for maximizing throughput to obtain the optimal power optimization scheme.

[0095] To verify the beneficial effects and effectiveness of the method provided by this invention, the system throughput was compared with that of schemes using a fixed pilot / data power ratio, optimized data power only, traditional PCRB, and pilot / data power allocation under unified simulation experimental conditions. The comparison results are as follows: Figure 2 As shown. Simultaneously, the method provided by this invention is compared with a scheme considering data interference and line-of-sight correlation, a traditional PCRB scheme, a scheme considering only data interference, and a PCRB scheme with fixed noise using channel gain PCRB. The comparison results are as follows. Figure 3As shown in the figure. The comparison results show that as the signal-to-noise ratio increases, the present invention demonstrates significantly better performance than other schemes in terms of both throughput and PCRB.

[0096] In summary, the beneficial effects of the present invention include: This invention aims to improve the throughput of pilot and data overlay transmission systems. With the goal of maximizing system throughput, it jointly optimizes pilot power and data power under the constraint of total power of a single satellite. This achieves a better balance between channel estimation accuracy and data transmission rate, avoiding the problems of increased channel estimation error and decreased actual throughput caused by simply increasing data power.

[0097] This invention effectively characterizes the coupling relationship between pilot power and data power. By deriving PCRB under pilot-data superposition transmission conditions, it unifies the improvement of channel estimation accuracy by pilot power and the impact of data power on pilot observation interference into the same analytical framework, so that power allocation no longer depends on empirical parameters, but has a clear theoretical basis.

[0098] This invention addresses the problem of data interference modeling in pilot data superposition transmission. It explicitly incorporates the interference generated by the data signal during pilot observation into the equivalent noise model, enabling quantitative calculation of the impact of data power on channel estimation error. Compared to methods that simply treat data interference as fixed noise or ignore it, this approach more accurately reflects the actual performance of the superposition transmission system.

[0099] This invention addresses the impact of multi-satellite Loss-of-Sight (LoS) path correlation on channel estimation. It explicitly considers the correlation between LoS paths in multi-satellite channels, incorporating cross-satellite LoS correlation terms into the pilot observation covariance matrix and quantifying their impact through a support overlap factor. This avoids the problem of underestimating multi-satellite correlation interference as assumed in traditional independent channel models.

[0100] This invention reduces the computational complexity of PCRB and facilitates engineering implementation. It utilizes the orthogonality of the delay-Doppler domain in spread-pilot to scalarize the Fisher information matrix in the derivative subspace, transforming the original PCRB calculation involving the inversion of a high-dimensional covariance matrix into equivalent noise and equivalent Fisher information matrix forms, significantly reducing computational complexity.

[0101] To ensure the power optimization model has good computability and stability, this invention constructs an equivalent noise power and an equivalent Fisher information matrix. This allows pilot power to primarily affect the PCRB through the pilot power matrix, and data power to primarily affect the PCRB through the equivalent noise. This results in a power optimization problem with a clear structure that is easy to solve, and avoids the problem that directly using low-order matrix expansion may lead to a non-positive semidefinite Fisher information matrix.

[0102] Suitable for high-dynamic multi-satellite transmission scenarios in OTFS. This invention performs channel modeling, PCRB analysis, and power optimization in the delay-Doppler domain, which can adapt to the Doppler spread and time-varying channel characteristics caused by the high-speed motion of low-Earth orbit satellites. It is suitable for multi-satellite collaborative OTFS transmission, pilot data superposition transmission, and high-dynamic satellite communication scenarios.

[0103] It has strong scalability. This invention can be used not only for channel gain estimation error analysis, but also for calculating PCRB for various channel parameters such as delay and Doppler; it can be used not only to maximize throughput, but also to meet channel estimation accuracy constraints, minimize PCRB, or perform pilot / data power trade-off optimization, and is suitable for deployment in satellite communication baseband processing platforms or multi-satellite resource management systems.

Claims

1. A PCRB analysis and power optimization method for multi-satellite channel estimation in OTFS, characterized in that, include: Construct a pilot and data superposition transmission model based on OTFS signals; Based on the pilot and data superposition transmission model based on OTFS signals, the pilot observation covariance matrix is ​​constructed based on multi-satellite LosS path correlation and data interference; Construct an observation Fisher information matrix based on PCRB; The inverse matrix of the pilot observation covariance matrix is ​​scalarized in the PCRB-based observation Fisher information matrix using the spread spectrum pilot derivative subspace. Based on the scalarization results, an equivalent observation Fisher information matrix is ​​constructed for PCRB calculation and power optimization. Calculate PCRB based on the equivalent observation Fisher information matrix; A power optimization problem oriented towards maximizing throughput is constructed based on PCRB; Solve the power optimization problem aimed at maximizing throughput to obtain the optimal power optimization scheme.

2. The method according to claim 1, characterized in that, The pilot and data superposition transmission model based on OTFS signals is expressed as follows: In the formula, For the first The transmission signals of the satellite; Indicates the first The power allocated to the pilot signal for each satellite; Indicates the first The power allocated to data by each satellite; Represents the spreading pilot vector; Indicates the first Data vectors of each satellite; Indicates the first The maximum launch power of each satellite.

3. The method according to claim 2, characterized in that, The pilot observation covariance matrix is ​​constructed based on multi-satellite LoS path correlation and data interference, including: Definition of the first The mean Loss path of each satellite is expressed as: In the formula, For the first The average Loss path of each satellite; For the first The complex gain of the first path between the satellite and the receiver; Indicates the expectation; The power coupling term corresponding to the LoS path correlation between different satellites is defined as follows: In the formula, and All are satellite indexes; For the first The power allocated to data by each satellite; For the first The power allocated to data by each satellite; For the first The average Loss path of each satellite; For the first The average Loss path of each satellite; Definition of the first The effective support set of the satellites in the delay-Doppler domain is expressed as: In the formula, For the first The effective support set of the satellites in the delay-Doppler domain; Let be the minimum delay index of the effective support set of the q-th satellite in the delay-Doppler domain; The maximum delay index of the effective support set of the q-th satellite in the delay-Doppler domain; The minimum Doppler index in the effective DD support of the q-th satellite; The maximum Doppler index of the effective support set of the q-th satellite in the delay-Doppler domain; Define the average delay-Doppler shift matrix, its expression is: in, In the formula, Let be the average delay-Doppler shift matrix of the q-th satellite; The delay-Doppler twisted-shift matrix represents the delay index in the delay-Doppler domain. The two-dimensional shift operator corresponding to the Doppler index b; Let be the size of the effective support set of the q-th satellite in the delay-Doppler domain; The number of delay indices in the effective delay support of the q-th satellite; The number of Doppler indices in the effective Doppler support of the q-th satellite; The cross-satellite covariance term caused by the multi-satellite LosS path correlation is constructed, and its expression is as follows: In the formula, The cross-satellite covariance term is caused by the correlation of multiple satellite LoS paths; For the first m The average delay-Doppler shift matrix of the satellite; For the first n The conjugate transpose of the average delay-Doppler shift matrix of the satellites; The pilot observation covariance matrix is ​​constructed, and its expression is as follows: in, In the formula, The pilot observation covariance matrix; It is the identity matrix. This represents the whitening equivalent noise term resulting from data interference and thermal noise. Indicates thermal noise power. Indicates the first Average power statistics for each satellite channel.

4. The method according to claim 3, characterized in that, The Fisher information matrix based on PCRB observations is as follows: In the formula, The Fisher information matrix based on PCRB observations; For the first The transmission power allocated to the pilot signal by each satellite; For the first The transmission power allocated to the pilot signal by each satellite; This indicates the expectation of the variable θ. Indicates taking the real part; Indicates parameters The corresponding derivative vector; This represents the inverse matrix of the pilot observation covariance matrix; parameter The corresponding derivative vector; for The i-th variable in; for The j-th variable in; The vector of channel parameters to be estimated contains the real and imaginary parts of the channel gain, the delay index, and the Doppler index for all paths of all satellites.

5. The method according to claim 4, characterized in that, The inverse matrix of the pilot observation covariance matrix is ​​standardized in the PCRB-based observation Fisher information matrix using the spread spectrum pilot derivative subspace, including: Define the derivative subspace, its expression is: In the formula, Represent the derivative subspace; This indicates that Zhang Cheng is operating; ; The inverse of the pilot observation covariance matrix can be approximated as a scalar matrix in the derivative subspace, and its expression is as follows: 。 6. The method according to claim 5, characterized in that, Based on the scalarization results, an equivalent observation Fisher information matrix for PCRB calculation and power optimization is constructed, including: The equivalent noise power is defined as follows: In the formula, Indicates equivalent noise power; Represents a constant related to the parametric derivative form; Interference intensity for cross-satellite LoS related terms; Based on the equivalent noise power, the equivalent observation Fisher information matrix is ​​constructed, and its expression is as follows: in, In the formula, To obtain an equivalent observation Fisher information matrix; For geometric matrices, The first in the geometric matrix One element; This represents the pilot power of the satellite to which the 4th parameter (PQ) in the parameter vector to be estimated belongs, where Q represents the total number of satellites and P represents the total number of satellite paths.

7. The method according to claim 6, characterized in that, The specific methods for quantifying the interference intensity of cross-satellite LoS correlation terms include: Definition of the first satellite and the first Differential support overlap number between satellites: In the formula, For the first satellite and the first Differential support overlap number between satellites; For the first The effective support set of the satellites in the delay-Doppler domain; For the first The effective support set of the satellites in the delay-Doppler domain; This is a delayed-Doppler index point in the support set of the m-th satellite; Let n be a delayed-Doppler index point in the support set of the nth satellite; This represents the difference in cyclic delay index between two DD support points; This represents the cyclic Doppler index difference between two delay-Doppler support points; Based on the satellite and the first The differential support overlap number between satellites is defined by the normalized support overlap factor, which is expressed as follows: In the formula, This is a normalized support overlap factor; The cross-satellite LoS correlation term interference intensity is defined based on the normalized support overlap factor, and its expression is as follows: 。 8. The method according to claim 7, characterized in that, The specific expression for PCRB is as follows: in, In the formula, Represents the trace of a matrix; This is the equivalent posterior Fisher information matrix; This is the prior information matrix of the channel parameters.

9. The method according to claim 8, characterized in that, Construct power optimization problems oriented towards maximizing throughput, including: The effective signal-to-interference-plus-noise ratio (SIN / N) is expressed as follows: In the formula, For an effective signal-to-interference-plus-noise ratio; Let be the estimated equivalent channel for the q-th satellite; This represents residual interference, indicating interference that was not completely eliminated, excluding noise and channel estimation errors. For the first given by PCRB The satellite channel estimation error metric is expressed as follows: In the formula, Indicates parameters The corresponding equivalent PCRB diagonal element; Indicates parameters Corresponding equivalent PCRB diagonal elements; parameters Let be the real part of the complex channel gain of the p-th path of the q-th satellite; Let represent the imaginary part of the complex channel gain for the p-th path of the q-th satellite; The throughput is defined as: In the formula, Indicates throughput; Constructing power optimization problems specifically includes: Objective function: Constraints: 。 10. A system for implementing the PCRB analysis and power optimization method for OTFS multi-satellite channel estimation as described in any one of claims 1 to 9, characterized in that, include: The channel modeling module is used to construct a pilot and data superposition transmission model based on OTFS signals; The covariance construction module is used to construct the pilot observation covariance matrix based on the multi-satellite LosS path correlation and data interference, according to the pilot and data superposition transmission model based on OTFS signals. The scalarization processing module is used to construct the observation Fisher information matrix based on PCRB; The inverse matrix of the pilot observation covariance matrix is ​​scalarized in the PCRB-based observation Fisher information matrix using the spread spectrum pilot derivative subspace. The PCRB calculation module is used to construct an equivalent observation Fisher information matrix for PCRB calculation and power optimization based on the scalarization processing results. Calculate PCRB based on the equivalent observation Fisher information matrix; The power optimization module is used to construct a power optimization problem oriented towards maximizing throughput based on PCRB; solve the power optimization problem oriented towards maximizing throughput, and obtain the optimal power optimization scheme.

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