NOMA-ALOHA protocol method and system based on circular polarization modulation under imperfect CSI

Abstract

The invention belongs to the technical field of satellite communication, discloses a circular polarization modulation-based NOMA-ALOHA protocol method under imperfect CSI (Channel State Information), and provides a binary circular polarization modulation-based NOMA-SA scheme for solving the problem of insufficient utilization of polarization dimensions of an existing NOMA-SA system. According to the modulation scheme, the orthogonal characteristics of the LHCP and the RHCP are utilized, so that user signals with the same power level can be decoded through polarization diversity, and the system capacity is remarkably improved. In order to solve the influence of channel estimation errors on performance in an actual system, CRLBs of channel estimation are deduced in TDD and FDD modes respectively. By establishing an equivalent noise model, the influence of the channel estimation error on the system performance is quantified. In order to accurately evaluate the performance of the system, the upper bound of the throughput of the system is deduced by considering two favorable scenes of monopolization of a single user and coexistence of orthogonal polarization users. The analysis model reveals the cooperative gain of polarization diversity and power domain multiplexing, and provides a theoretical basis for system parameter optimization.

Description

Technical Field

[0001] This invention belongs to the field of satellite communication technology, and in particular relates to a NOMA-ALOHA protocol method and system based on circular polarization modulation under imperfect CSI. Background Technology

[0002] With the rapid development of IoT technology, the demand for massive device access in smart cities, industrial automation, and other application scenarios is increasing daily, posing a severe challenge to the capacity and efficiency of wireless communication systems. In large-scale machine-type communication scenarios, traditional orthogonal multiple access (OMA) technologies are inefficient in resource allocation and struggle to meet high-density connection requirements, while contention-based random access schemes have emerged as a potential solution due to their low signaling overhead. However, existing ALOHA-type protocols experience a sharp drop in throughput under high loads, severely limiting system performance.

[0003] Power-domain non-orthogonal multiple access (NOMA-ALOHA) technology offers new possibilities for improving random access performance through power domain multiplexing and continuous interference cancellation mechanisms. The earliest proposed NOMA-ALOHA protocol improved the throughput of collision slots by 40% through power domain multiplexing. This study investigates the random access performance of large-scale IoT systems with sparse active users by deriving the upper and lower bounds of NOMA-ALOHA throughput and analyzing optimal load conditions. Some studies have given an upper bound on the throughput of multi-channel NOMA-ALOHA systems and proposed a practical user constraint algorithm for adaptive load adjustment. Based on this, a new lower bound is derived as a closed-form expression. Other studies have proposed a multi-beam NOMA random access scheme based on deep reinforcement learning, which significantly improves the throughput performance of low-Earth orbit satellite IoT systems through beam region partitioning, inter-slot SIC joint decoding, and heterogeneous device power allocation. However, these studies have significant limitations: firstly, they only utilize power domain degrees of freedom, neglecting the polarization characteristics of satellite channels; secondly, most studies assume ideal channel state information and fail to consider estimation errors in real-world systems. Therefore, existing research needs to be improved to increase the throughput of the NOMA-ALOHA protocol under high load conditions under imperfect CSI.

[0004] A similar published patent is US20230216599A1—Polarization Division Multiple Access (PDMA series methods and systems). In this patent, the system transmits different polarization signals to different users through a polarized antenna array, and in conjunction with OFDMA technology, allows two users to receive signals simultaneously at the same frequency but with different polarization directions, thereby increasing the system throughput.

[0005] Although the patent attempts to reuse spectrum and improve spectrum efficiency in the polarization dimension, it still has several technical problems: (1) The scheme mainly assumes that the orthogonality between polarized signals is ideal or approximately orthogonal, and lacks theoretical boundary analysis on the impact of channel estimation error, polarization cross-interference and demodulation misjudgment; (2) The technology does not consider how to handle collision, multi-user overlap and successive interference cancellation (SIC) mechanism in random access (ALOHA) scenarios. Whether it can effectively guarantee multi-user simultaneous access, signal separation and throughput optimization under imperfect CSI conditions is still unproven. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI.

[0007] This invention is implemented as follows: A NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI includes:

[0008] Step 1: Design BCPM polarization coding rules to achieve separate decoding of two polarization signals at the same power level;

[0009] Step 2: Construct imperfect CSI transmission models for TDD and FDD modes respectively;

[0010] Step 3: Derive the Cramer-Rao lower bound of the channel estimation error in TDD / FDD mode to determine the minimum variance of the error; construct an equivalent noise model;

[0011] Step 4: Define two successful decoding scenarios, calculate the probability and the average number of users successfully decoded at each power level; perform SIC decoding, and accumulate the number of users to derive the upper bound of throughput.

[0012] Furthermore, the specific implementation of step 1 is as follows: utilizing the orthogonality of left-hand circular polarization and right-hand circular polarization, define in-phase / quadrature components and positive / negative polarization basis functions; binary "0" corresponds to generating RHCP wave, and "1" corresponds to generating LHCP wave, ensuring that the two polarization signals can be separated and decoded under the same power level.

[0013] Furthermore, the specific steps for constructing the imperfect CSI transmission model in step 2 are as follows: In TDD mode, the user estimates the channel coefficients through satellite pilots to clarify the deviation between the actual and estimated channel coefficients; in FDD mode, by utilizing the consistency of uplink and downlink channel path parameters, the path attenuation and distance are estimated through least squares optimization to obtain the uplink channel estimation result.

[0014] Furthermore, the specific steps in step 3 are as follows: For TDD mode, the Cramer-Rao lower bound of the channel estimation error is derived by combining the beacon signal length and signal-to-noise ratio, and the minimum variance of the error is determined; For FDD mode, the uplink and downlink wavelength differences are additionally considered, and the CRLB of the uplink channel estimation error is derived; The channel estimation errors in the two modes are equivalent to system noise, and the impact of imperfect CSI on protocol performance is quantified.

[0015] Furthermore, the specific implementation of step 4 is as follows: assuming that the number of active users follows a Poisson distribution, users uniformly select power levels and randomly select polarization directions; define two successful decoding scenarios: "single user exclusive power level" and "two orthogonal polarization users coexisting", calculate the probability and the average number of successfully decoded users at each power level, the satellite performs SIC decoding from high to low power, and the upper bound of throughput is derived by accumulating the number of users at each power level.

[0016] Furthermore, the circular polarization basis function is based on a sinusoidal signal, with a 90-degree phase difference between the in-phase and quadrature components, and the positive and negative polarity basis functions have opposite amplitudes, ensuring that LHCP and RHCP signals are transmitted without interference and can be decoded independently upon reception;

[0017] In TDD mode, the channel estimation error follows a complex Gaussian distribution. In FDD mode, the path attenuation and distance are estimated by least squares optimization using the consistency of uplink and downlink channel path parameters.

[0018] The CRLB of TDD mode is determined by the beacon signal length and signal-to-noise ratio, while the CRLB of FDD mode is additionally affected by the uplink-to-downlink wavelength ratio; the equivalent noise power is the sum of background noise and error variance.

[0019] The predefined power level must meet the SIC decoding signal-to-interference-plus-noise ratio requirement. It is assumed that the number of active users follows a Poisson distribution, and users uniformly select power levels and randomly select polarization directions. Two successful decoding scenarios are defined: "single user exclusive power level" and "two orthogonal polarization users coexist".

[0020] Another objective of this invention is to provide a NOMA-ALOHA protocol system based on circular polarization modulation under imperfect CSI, comprising:

[0021] The coding rule design module is used to design BCPM polarization coding rules to achieve separate decoding of two polarization signals at the same power level.

[0022] The transmission model construction module is used to construct imperfect CSI transmission models under TDD and FDD modes, respectively.

[0023] The derivation module is used to derive the Cramer-Rao lower bound of the channel estimation error in TDD / FDD mode to determine the minimum variance of the error; and to construct an equivalent noise model.

[0024] The calculation module is used to define two successful decoding scenarios, calculate the probability and the average number of users successfully decoded at each power level; perform SIC decoding, and accumulate the number of users to derive the upper bound of throughput.

[0025] Another object of the present invention is to provide a computer device comprising a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI.

[0026] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI.

[0027] Another objective of this invention is to provide an information data processing terminal for implementing the NOMA-ALOHA protocol system based on circular polarization modulation under imperfect CSI.

[0028] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0029] To address the issue of insufficient polarization dimension utilization in existing NOMA-SA systems, a NOMA-SA scheme based on binary circular polarization modulation is proposed. This modulation scheme utilizes the orthogonality of LHCP and RHCP, enabling user signals of the same power level to be decoded through polarization diversity, significantly improving system capacity.

[0030] To address the impact of channel estimation errors on performance in practical systems, the CRLB of channel estimation was derived in both TDD and FDD modes. An equivalent noise model was established to quantify the impact of channel estimation errors on system performance.

[0031] To accurately evaluate system performance, an upper bound on system throughput was derived by considering two favorable scenarios: single-user exclusive access and coexistence of orthogonally polarized users. This analytical model reveals the synergistic gain of polarization diversity and power domain multiplexing, providing a theoretical basis for system parameter optimization.

[0032] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0033] ① Reduced operating costs and increased revenue: Protocol throughput increases by 20%-35%, and packet loss rate decreases by 0.2-0.27, reducing satellite link retransmission overhead. The number of concurrent terminals supported by a single satellite increases by 20%-35%, allowing operators to expand their user base and directly increase revenue.

[0034] Application scenarios and cost optimization: Adaptable to both TDD / FDD modes and imperfect CSI, it can support scenarios such as polar monitoring and marine communication. For example, the effective data transmission rate of polar monitoring terminals can be increased to 80%-85%. Moreover, no new hardware is required, and it can be achieved only through software upgrades, resulting in low modification costs for terminal manufacturers and accelerating the commercialization of the technology.

[0035] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally:

[0036] Polarization dimension reuse gap: The current satellite NOMA-ALOHA protocol only focuses on power domain reuse. This protocol is the first to integrate BCPM polarization modulation with the protocol and utilize the orthogonality of LHCP / RHCP to enable two users to access a single power level, filling the technical gap in polarization dimension reuse in the satellite NOMA-ALOHA protocol.

[0037] The gap in quantification of imperfect CSI in dual-mode: Existing solutions do not distinguish between channel estimation errors in TDD / FDD modes. This protocol derives the CRLB of channel estimation errors in both modes, establishes an equivalent noise model, and accurately quantifies the impact of imperfect CSI on performance, filling the gap in the quantification analysis of imperfect CSI in dual-mode satellite NOMA protocols.

[0038] (3) Whether the technical solution of the present invention solves the technical problem that people have long wanted to solve but have never been able to solve successfully:

[0039] In satellite IoT mMTC scenarios, the challenge of balancing capacity and robustness against imperfect CSI in the NOMA-ALOHA protocol has long been unresolved. Traditional protocols rely solely on power domain multiplexing, resulting in limited capacity; under imperfect CSI, the lack of a quantization error model leads to a throughput reduction of over 10%. This protocol addresses this challenge by doubling the number of users per power class through BCPM polarization multiplexing; and by deriving CRLB and establishing an equivalent noise model, the throughput reduction under imperfect CSI is reduced to 4%, successfully resolving the problem.

[0040] (4) Does the technical solution of the present invention overcome technical bias?

[0041] Overcoming the prejudice that "NOMA can only reuse the power domain": The industry believes that satellite channel polarization characteristics are unstable, and NOMA protocols can only rely on power domain multiplexing. This protocol, under high K-factor Ricean channels, ensures polarization orthogonality through BCPM coding, achieving polarization multiplexing, increasing capacity without increasing decoding complexity, thus breaking this prejudice.

[0042] Overcoming the bias of "imperfect CSI analysis ignoring dual-mode differences": Due to the inertia of terrestrial communication, the industry ignores the CSI error differences between satellite TDD / FDD modes. This protocol derives dual-mode CRLB, proving that the differences are significant (e.g., the CRLB of FDD mode may be 1.5 times that of TDD). After targeted compensation, the throughput of FDD mode is increased by 10%, overcoming this bias. Attached Figure Description

[0043] Figure 1 This is a flowchart of the NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI provided in an embodiment of the present invention.

[0044] Figure 2 This is a system structure block diagram of the NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI provided in an embodiment of the present invention.

[0045] Figure 3 This is a system diagram of PDNOMA-ALOHA based on circular polarization modulation provided in an embodiment of the present invention.

[0046] Figure 4 This is a diagram of the PD-NOMA-assisted MS-ALOHA system provided in an embodiment of the present invention.

[0047] Figure 5 This is a diagram of TDD and FDD modes provided in an embodiment of the present invention.

[0048] Figure 6 This is the MSE and CRLB diagram under TDD and FDD modes provided in the embodiments of the present invention.

[0049] Figure 7 This is a throughput characteristic diagram of the BCPM-NOMA-SA system provided in an embodiment of the present invention.

[0050] Figure 8 This is a packet loss rate characteristic diagram of the BCPM-NOMA-SA system provided in an embodiment of the present invention.

[0051] Figure 9 This is the upper bound diagram of the throughput of the BCPM-NOMA-SA system provided in the embodiments of the present invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0053] This invention proposes a novel NOMA-ALOHA protocol method based on circular polarization modulation (BCPM) for multi-user non-orthogonal multiple access (ALOHA) systems under imperfect channel state information (CSI) environments. This addresses the limitations of existing random access systems in terms of throughput and the difficulty in effectively separating interference between users under channel estimation errors. The technical principles and industrialization process can be described in the following six stages.

[0054] First, addressing the issue of signal superposition interference in traditional NOMA systems at the same power level, this invention designs a Binary Circular Polarization Modulation (BCPM) coding rule. This introduces a complex phase rotation mapping in the polarization dimension, enabling signal differentiation and mapping in the polarization angle space. Through the orthogonality caused by the difference in polarization angles, signals from different users within the same power domain can be decoupled at the receiver via a polarization correlation coefficient matrix, improving the separation of users at the same level and thus overcoming the limitations of traditional power grading.

[0055] Second, imperfect CSI channel transmission models were established under both Time Division Duplex (TDD) and Frequency Division Duplex (FDD) modes. This model represents the channel estimation error as a complex Gaussian perturbation term related to the actual channel, and constructs a joint estimation bias matrix based on the pilot signal length and signal-to-noise ratio. In the TDD scenario, uplink estimation and downlink compensation are achieved using the channel reciprocity approximation; in the FDD scenario, phase distortion caused by uplink and downlink frequency offsets and feedback delays is considered, forming an independent channel uncertainty model, providing a theoretical basis for subsequent system performance derivation.

[0056] Third, based on the aforementioned channel model, the Cramer-Rao Lower Bound (CRLB) for channel estimation errors in TDD and FDD modes is derived. By differentiating the statistical expectation of the signal reception equation, a closed-form solution for the minimum mean square error (MMSE) estimator is obtained, and the variance of the estimation error is constrained within the CRLB limit, thereby constructing an equivalent noise model. This model incorporates the CSI imperfection as additional Gaussian noise into the receiver signal expression, achieving an analytical characterization of system error propagation.

[0057] Fourth, two successful decoding scenarios are defined: successful single-user polarization differentiation and successful serial interference cancellation (SIC) under multi-user power superposition. For each scenario, the success decoding probability distribution is calculated by analyzing the polarization correlation matrix and power allocation ratio of the received signal. This step couples the polarization angle difference and channel estimation error into the SIC algorithm, enabling the system to adaptively adjust the user decision order and reduce the impact of misjudgments and residual interference on subsequent users.

[0058] Fifth, an improved SIC (Successive Interference Cancellation) strategy is introduced at the decoding level. This strategy employs an iterative decision criterion based on polarization weights to perform weighted reconstruction and interference cancellation on the decoded signal. By accumulating statistics on the number of successful users, a functional relationship is established between system throughput and the average number of successfully decoded users, thereby deriving the theoretical upper bound of throughput. This upper bound serves as a metric for the system's performance limits under imperfect CSI conditions, providing a reference for protocol design and parameter optimization.

[0059] Sixth, from an industrial application perspective, this method can be applied to large-scale access scenarios such as next-generation low-power wide-area networks (LPWAN), drone communications, and satellite IoT. Its core advantage lies in improving user separation capabilities and reducing pilot resource consumption without additional power grading overhead, while maintaining high system capacity and robustness even in non-ideal CSI environments. Through the joint design of polarization domain signal modulation and error compensation, a three-dimensional expansion of physical layer resources is achieved, providing a feasible path for the future spatial expansion of non-orthogonal access protocols.

[0060] like Figure 1 As shown, an embodiment of the present invention provides a NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI, comprising the following steps:

[0061] S101, design BCPM polarization coding rules to achieve separate decoding of two polarization signals at the same power level;

[0062] S102, construct imperfect CSI transmission models under TDD and FDD modes respectively;

[0063] S103, Derive the Cramer-Rao lower bound of the channel estimation error in TDD / FDD mode to determine the minimum variance of the error; construct an equivalent noise model;

[0064] S104 defines two successful decoding scenarios, calculates the probability and the average number of users successfully decoded at each power level; performs SIC decoding, and accumulates the number of users to derive the upper bound of throughput.

[0065] The specific implementation in S101 provided in this embodiment of the invention is as follows: by utilizing the orthogonality of left-hand circular polarization and right-hand circular polarization, in-phase / quadrature components and positive / negative polarization basis functions are defined; binary "0" corresponds to generating RHCP wave and "1" corresponds to generating LHCP wave, ensuring that the two polarization signals can be separated and decoded under the same power level.

[0066] The specific steps for constructing the imperfect CSI transmission model in S102 provided in this embodiment of the invention are as follows: In TDD mode, the user estimates the channel coefficients through satellite pilots to clarify the deviation between the actual and estimated channel coefficients; in FDD mode, the uplink and downlink channel path parameters are optimized by least squares to estimate the path attenuation and distance, thereby obtaining the uplink channel estimation result.

[0067] The specific implementation in S103 of this embodiment is as follows: For TDD mode, the Cramer-Rao lower bound of the channel estimation error is derived by combining the beacon signal length and the signal-to-noise ratio, and the minimum variance of the error is determined; For FDD mode, the difference between uplink and downlink wavelengths is considered in addition, and the CRLB of the uplink channel estimation error is derived; The channel estimation error in both modes is equivalent to system noise, and the impact of imperfect CSI on protocol performance is quantified.

[0068] The specific implementation in S104 provided in this embodiment of the invention is as follows: assuming that the number of active users follows a Poisson distribution, users uniformly select power levels and randomly select polarization directions; defining two successful decoding scenarios, "single user exclusive power level" and "two orthogonal polarization users coexisting", calculating the probability and the average number of successfully decoded users at each power level, the satellite performs SIC decoding from high to low power, and derives the upper bound of throughput by accumulating the number of users at each power level.

[0069] The circular polarization basis function provided in this embodiment of the invention is based on a sinusoidal signal, with a 90-degree phase difference between the in-phase and quadrature components, and opposite amplitudes for the positive and negative polarity basis functions, ensuring that LHCP and RHCP signals are transmitted without interference and can be independently decoded upon reception;

[0070] In TDD mode, the channel estimation error follows a complex Gaussian distribution. In FDD mode, the path attenuation and distance are estimated by least squares optimization using the consistency of uplink and downlink channel path parameters.

[0071] The CRLB of TDD mode is determined by the beacon signal length and signal-to-noise ratio, while the CRLB of FDD mode is additionally affected by the uplink-to-downlink wavelength ratio; the equivalent noise power is the sum of background noise and error variance.

[0072] The predefined power level must meet the SIC decoding signal-to-interference-plus-noise ratio requirement. It is assumed that the number of active users follows a Poisson distribution, and users uniformly select power levels and randomly select polarization directions. Two successful decoding scenarios are defined: "single user exclusive power level" and "two orthogonal polarization users coexist".

[0073] like Figure 2 As shown, an embodiment of the present invention provides a NOMA-ALOHA protocol system based on circular polarization modulation under imperfect CSI, comprising:

[0074] The coding rule design module is used to design BCPM polarization coding rules to achieve separate decoding of two polarization signals at the same power level.

[0075] The transmission model construction module is used to construct imperfect CSI transmission models under TDD and FDD modes, respectively.

[0076] The derivation module is used to derive the Cramer-Rao lower bound of the channel estimation error in TDD / FDD mode to determine the minimum variance of the error; and to construct an equivalent noise model.

[0077] The calculation module is used to define two successful decoding scenarios, calculate the probability and the average number of users successfully decoded at each power level; perform SIC decoding, and accumulate the number of users to derive the upper bound of throughput.

[0078] Another object of the present invention is to provide a computer device comprising a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI.

[0079] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI.

[0080] Another objective of this invention is to provide an information data processing terminal for implementing the NOMA-ALOHA protocol system based on circular polarization modulation under imperfect CSI.

[0081] Specific implementation of the present invention:

[0082] like Figure 3 Step 1: Design BCPM polarization coding rules

[0083] Circular polarization modulation (CPM) is an innovative digital communication technology that utilizes the circular polarization characteristics of electromagnetic waves as an information carrier. Unlike traditional amplitude, frequency, or phase modulation, CPM encodes information by controlling the rotation direction (left-hand or right-hand) of the electromagnetic waves.

[0084] The basis functions of circular polarization can be represented by four sinusoidal signals:

[0085] E IP (t)=E0cos(2πf c t),

[0086] E IN (t)=-E0cos(2πf c t),

[0087] E QP(t)=E0cos(2πf c t-π / 2),

[0088] E QN (t)=-E0cos(2πf c t-π / 2),

[0089] Where E0 represents the signal amplitude, f c This represents the carrier frequency. The subscripts I and Q indicate in-phase and quadrature-phase components, while P and N indicate positive or negative polarity.

[0090] In this paper, we employ a binary circular polarization modulation scheme, encoding binary data through the orthogonality of left-hand and right-hand circular polarization states. During modulation, for bit "0", the antenna input E... IP (t) and -E QP (t) Generates the RHCP wave; for bit "1", the input E IP (t) and E QP (t) generates an LHCP wave. Therefore, the complete BCPM signal can be represented as:

[0091]

[0092] At the receiving end, the demodulation process first extracts the horizontal component (E) of the received signal. H ) and vertical component (E) V These components are then correlated with a reference signal. The output of the correlation operation is fed into a maximum likelihood (ML) detector to recover the transmitted bit information.

[0093] Step 2: Constructing a protocol transmission model under imperfect CSI

[0094] Signal transmission models under imperfect CSI are constructed based on both time-division duplex and frequency-division duplex modes.

[0095] In time-division duplex mode, assuming the channel remains essentially constant within a frame, each user can estimate its own channel state information based on the received pilot signals, such as... Figure 4 As shown.

[0096] In a non-orthogonal multiple access slotted ALOHA system, L receive power levels are predefined, and these power levels are arranged in descending order as v1 > v2 > ... > v L >0. Within a data packet transmission slot, each active user randomly selects a power level to send data packets and initiate uplink access, such as... Figure 3 As shown. Therefore, the signal received at the satellite can be represented as:

[0097]

[0098] Where K represents the number of active users who have selected this channel; h k and p k Let z represent the channel coefficient and transmit power corresponding to user k, respectively; z ~ CN(0,N0) represents the background noise with variance N0. This paper assumes that the background noise power has been normalized, i.e., N0 = 1.

[0099] Suppose user k estimates its channel coefficients based on the received pilot signal as follows: In practical systems, due to estimation errors, With the real channel h k The relationship between them can be represented as:

[0100]

[0101] Among them, e k The variance represents the channel estimation error. Determined by the Cramero lower bound. The system performs pre-equalization based on the estimated channel to compensate for channel fading. The signal received at the satellite can be expressed as:

[0102]

[0103] In frequency division duplex mode, it is assumed that the uplink and downlink channels remain unchanged within a frame. Due to the invariance of the physical propagation path, each user can estimate the uplink channel based on the received downlink pilot signal, such as... Figure 5 As shown.

[0104] For a narrowband signal transmitted through a single propagation path, its channel response can be expressed as:

[0105]

[0106] in, Indicates wavelength; a represents path attenuation; d represents path distance; This represents the phase, which is independent of frequency. For a direct path, Therefore, the downlink channel and the uplink channel can be represented as follows:

[0107]

[0108] Although the channel varies with frequency, the fundamental parameters of the physical propagation path (path attenuation *a* and path distance *d*) remain constant. Assuming the base station sends pilot signals s1 and s2 to the user, the signals received by the user can be expressed as follows:

[0109] y1 = h D s1+n1,y2=h D s² + n².

[0110] The channel estimation problem can be transformed into a least-squares optimization problem, the core idea of ​​which is to minimize the difference between the observed received signal and its model-based prediction (dependent on unknown parameters). This optimization problem can be expressed as:

[0111] min a,d (|y1-h D s1| 2 +|y2-h D s2| 2 ).

[0112] By solving the above optimization problem, the estimated path decay can be obtained. and path distance And use them to estimate the uplink channel.

[0113] At the satellite end, sequential interference cancellation technology is used to decode overlapping data packets sequentially. Specifically, first, the signals from other users are treated as noise, and the data packet with the highest power level is decoded; then, the interference from this highest power level data packet is completely eliminated, and the data packet with the second highest power level is decoded next. Therefore, for user k with power level l, assuming that the first k-1 data packets have been successfully decoded and eliminated, its signal-to-interference-plus-noise ratio (SIR) can be expressed as:

[0114]

[0115] in, This represents the total interference from users with lower power levels (from l+1 to L) to user k. According to Shannon's capacity formula, to successfully transmit data packets in each time slot, the data rate R must satisfy:

[0116]

[0117] Therefore, based on the principle of power-domain non-orthogonal multiple access, user k's data packets can be successfully decoded when the following conditions are met:

[0118] SINR k ≥γ,

[0119] Where γ represents the signal-to-interference-plus-noise ratio (SINR) threshold required for successful decoding, i.e., the target SINR. Using the power level specified in the formula, the satellite can ensure that the SINR requirement in the formula is met when there is no power conflict. Received power level v l Defined as:

[0120] v l =γ(1+γ)L-l N0, l∈{1,2,...,L}.

[0121] Step 3: Derive the CRLB of the channel estimation error and construct an equivalent noise model.

[0122] Assume the downlink channel can be represented as The received signal can then be represented as y1 = h D ·s1+n1 and y2=h D ·s²+n², where s₁ and s₂ represent signal sources; h D The channel gain includes path loss *a* and distance *d*; *n1* and *n2* represent independent and identically distributed additive white Gaussian noise with variance σ. 2 To evaluate the uplink channel estimation performance, this paper considers the mean squared error (MSE) of the estimator and uses the Cramer-Rao lower bound to optimize the estimation performance.

[0123] Taking the logarithm of the likelihood function and differentiating it with respect to the parameters yields the Fisher information matrix:

[0124]

[0125] The Fisher information matrix is ​​defined as follows:

[0126]

[0127] The Fisher information matrix is ​​calculated by taking partial derivatives with respect to parameters a and d:

[0128]

[0129] The uplink channel can be represented as Where h U It is a function of parameters a and d. This is achieved by calculating h. U For the parameter vector θ = [a, d] T The partial derivatives are used to obtain the Jacobian matrix J:

[0130]

[0131] Based on the definition of Cramero's lower bound, and combining Fisher's information matrix transformation and parameter transformation, the uplink channel h is obtained. U Clamero's Lower Realm:

[0132]

[0133] Let the estimated channel be Channel estimation error can be modeled as equivalent additional noise in the system. The channel estimation error manifests as equivalent noise in the received signal, and its expression is:

[0134]

[0135] in, This represents the minimum estimation error variance. The resulting effective signal-to-interference-plus-noise ratio is:

[0136]

[0137] Theoretical analysis shows that when At this point, the system performance should converge to the performance when the channel state information is ideal. Fourth step: Derive the upper bound of throughput based on the successful decoding conditions.

[0138] We analyze the throughput performance of the BCPM-NOMA-SA system by deriving an upper bound. Throughput is defined as the average number of data packets successfully decoded by the base station per timeslot. To establish the theoretical framework, we first give the basic assumptions of the system model.

[0139] This system operates based on the following assumptions:

[0140] A1) Each active user independently and uniformly selects one of L predefined power levels, with the power levels ordered as v1 > v2 > ... > v L >0, and at the same time, left-hand circular polarization or right-hand circular polarization (RHCP) is randomly selected with equal probability.

[0141] A2) The number of active users K follows a Poisson distribution with a mean of λ. Due to the uniform selection characteristic, the number of users who select power level l follows a Poisson distribution with a mean of λ / L.

[0142] Under these assumptions, the base station employs a successive interference cancellation decoding scheme from high to low power levels. For successful decoding at a specific power level, we consider two favorable scenarios:

[0143] B1) This power stage has only one user (polarization direction is not limited);

[0144] B1) This power level has two users with opposite polarization states. The probability that power level l has exactly one user is P1 = (λ / L)e -λ / L The probability of having two orthogonally polarized users is P2 = (λ 2 / (4L 2 ))e -λ / L .

[0145] The average number of users successfully decoded per power level can be expressed as:

[0146]

[0147] Considering the characteristic that high-power stages must be successfully decoded first during SIC decoding, by summing all power stages and considering the probability that the preceding high-power stage meets the decoding condition, we obtain the upper bound expression for the total throughput:

[0148]

[0149] The reason this expression is an upper bound is because it optimistically assumes that any two orthogonally polarized users at the same power level can always be successfully decoded, while the actual decoding capability depends on the specific signal-to-interference-plus-noise ratio (SNR) conditions. For example, when there are multiple users at the low power level, their cumulative interference may hinder the successful decoding of orthogonally polarized users at the high power level, which makes our derived value an upper bound on the achievable throughput.

[0150] Simulation results

[0151] The performance of this invention is analyzed below using simulation. In the simulation, the number of time slots N in one frame is 200, the flow model is a Poisson model, the channel coding and modulation model is BCPM, the channel model is a Ricean channel with a Ricean factor of 10dB, and the number of power levels L is 3.

[0152] Figure 6 The relationship between the mean square error (MSE) of channel estimation and the signal-to-noise ratio (SNR) is shown for different signal lengths, and the consistency between the simulated MSE and the theoretical Cramer-Rao lower bound is verified. The results show that the MSE decreases significantly with increasing SNR, indicating that a higher SNR is effective in suppressing estimation errors. Furthermore, the figure shows that the MSE gradually decreases with increasing signal length. This improvement is attributed to the fact that longer signals provide more observation samples, thus improving the accuracy of channel estimation. Finally, the figure compares the system performance under TDD and FDD modes. It can be seen that the theoretical and simulated performance of the TDD system is superior to that of the FDD system, thanks to the channel reciprocity of the TDD system, which reduces estimation errors.

[0153] Figure 7The throughput characteristics of the BCPM-NOMA-SA system are demonstrated. First, the curves show three typical stages: in the low-load stage, NOMA's SIC mechanism effectively resolves collisions, resulting in near-linear throughput growth, peaking at 0.75 packets / slot at a load of 1.8, after which throughput begins to decline. Second, a comparison with other systems shows that BCPM-NOMA-SA outperforms both BCPM-SA and NOMA-SA systems by 20-35% under all loads. This advantage stems from synergistic effects: BCPM's polarization orthogonality reduces inter-user interference by 3dB compared to traditional SA; NOMA's power domain multiplexing nearly doubles the number of decorable users. Finally, it can be seen that due to channel estimation errors, the throughput of the non-ideal CSI scheme is 4% lower than that of the ideal CSI. Simulation results demonstrate that this system has a significant throughput gain compared to traditional schemes or schemes using only a single technology.

[0154] Figure 8 Simulation analysis shows that the packet loss rate of the BCPM-NOMA-SA system is close to zero under low load. When the packet loss rate is 0.1, the system load is 0.3. The packet loss rate gradually increases with increasing load. Compared with the BCPM-SA and NOMA-SA systems, the BCPM-NOMA-SA system has a lower packet loss rate. Taking a load of 0.5 as an example, the packet loss rate of the BCPM-NOMA-SA system is approximately 0.23, which is 0.20 lower than the BCPM-SA system and 0.27 lower than the NOMA-SA system. This is due to the dual gain brought by the power domain multiplexing of NOMA and the polarization orthogonality of BCPM. Furthermore, in actual systems, due to the influence of channel estimation errors, the packet loss rate is about 0.01-0.1 higher than the ideal CSI scenario, and this difference is more significant at low SNR.

[0155] Figure 9 This paper presents the upper bound of the system throughput of BCPM-NOMA-SA and the throughput based on the CRLB equivalent noise model. The theoretical upper bound is almost identical to the actual simulation at low loads. However, as the load increases, the gap between the theoretical upper bound and the actual simulation widens. This is because the theoretical upper bound assumes that all users satisfying the B1 / B2 conditions can successfully decode, ignoring actual SINR constraints. Under high loads, the cumulative interference of low-power levels significantly deteriorates the SINR of high-power users, leading to actual decoding failures. The throughput curve predicted by the equivalent noise model constructed based on the channel estimation error (CRLB) is almost identical to the simulation results, indicating that this model can effectively quantify the impact of non-ideal CSI on system performance.

[0156] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0157] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI, characterized in that, Includes the following steps: Step 1: Design BCPM polarization coding rules to achieve separate decoding of two polarization signals at the same power level; Step 2: Construct imperfect CSI transmission models for TDD and FDD modes respectively; Step 3: Derive the Cramer-Rao lower bound of the channel estimation error in TDD / FDD mode to determine the minimum variance of the error; Construct an equivalent noise model; Step 4: Define two successful decoding scenarios, calculate the probability and the average number of users successfully decoded at each power level; perform SIC decoding, and accumulate the number of users to derive the upper bound of throughput.

2. The NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI as described in claim 1, characterized in that, The specific steps in step 1 are as follows: Utilizing the orthogonality of left-hand circular polarization and right-hand circular polarization, define in-phase / quadrature components and positive / negative polarization basis functions; binary "0" corresponds to generating RHCP waves, and "1" corresponds to generating LHCP waves, ensuring that the two polarization signals can be separated and decoded at the same power level.

3. The NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI as described in claim 1, characterized in that, The specific steps for constructing the imperfect CSI transmission model in step 2 are as follows: In TDD mode, the user estimates the channel coefficients through satellite pilots to clarify the deviation between the actual and estimated channel coefficients; in FDD mode, the uplink channel estimation results are obtained by optimizing the path attenuation and distance through least squares by utilizing the consistency of uplink and downlink channel path parameters.

4. The NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI as described in claim 1, characterized in that, The specific steps in step 3 are as follows: For TDD mode, the Cramer-Rao lower bound of the channel estimation error is derived by combining the beacon signal length and signal-to-noise ratio, and the minimum variance of the error is determined; For FDD mode, the difference between uplink and downlink wavelengths is considered in addition, and the CRLB of the uplink channel estimation error is derived; The channel estimation error in both modes is equivalent to system noise, and the impact of imperfect CSI on protocol performance is quantified.

5. The NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI as described in claim 1, characterized in that, The specific steps in step 4 are as follows: Assuming that the number of active users follows a Poisson distribution, users uniformly select power levels and randomly select polarization directions; defining two successful decoding scenarios, "single user exclusive power level" and "two orthogonal polarization users coexisting", calculating the probability and the average number of successfully decoded users at each power level, the satellite performs SIC decoding from high to low power, and derives the upper bound of throughput by accumulating the number of users at each power level.

6. The NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI as described in claim 1, characterized in that, The circular polarization basis function is based on a sinusoidal signal. The phase difference between the in-phase and quadrature components is 90 degrees, and the amplitudes of the positive and negative polarity basis functions are opposite, ensuring that LHCP and RHCP signals are transmitted without interference and can be decoded independently upon reception. In TDD mode, the channel estimation error follows a complex Gaussian distribution. In FDD mode, the path attenuation and distance are estimated by least squares optimization using the consistency of uplink and downlink channel path parameters. The CRLB of TDD mode is determined by the beacon signal length and signal-to-noise ratio, while the CRLB of FDD mode is additionally affected by the uplink-to-downlink wavelength ratio. The equivalent noise power is the sum of the background noise and the error variance; The predefined power level must meet the SIC decoding signal-to-interference-plus-noise ratio requirements. It is assumed that the number of active users follows a Poisson distribution, and users uniformly select power levels and randomly select polarization directions. Two successful decoding scenarios are defined: "single user exclusive power level" and "coexistence of two orthogonal polarization users".

7. A NOMA-ALOHA protocol system based on circular polarization modulation under imperfect CSI, implementing the NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI as described in any one of claims 1-6, characterized in that, The NOMA-ALOHA protocol system based on circular polarization modulation under imperfect CSI includes: The coding rule design module is used to design BCPM polarization coding rules to achieve separate decoding of two polarization signals at the same power level. The transmission model construction module is used to construct imperfect CSI transmission models under TDD and FDD modes, respectively. The derivation module is used to derive the Cramer-Rao lower bound of the channel estimation error in TDD / FDD mode to determine the minimum variance of the error; and to construct an equivalent noise model. The calculation module is used to define two successful decoding scenarios, calculate the probability and the average number of users successfully decoded at each power level; perform SIC decoding, and accumulate the number of users to derive the upper bound of throughput.

8. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program that, when executed by the processor, causes the processor to perform the steps of the NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the NOMA-ALOHA protocol method based on circular polarization modulation under imperfect CSI as described in any one of claims 1-6.

10. An information data processing terminal, characterized in that, The information data processing terminal is used to implement the NOMA-ALOHA protocol system based on circular polarization modulation under imperfect CSI as described in claim 7.

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