A Multi-Carrier Channel Characteristic Estimation Method for 5G NTN Low-Earth Orbit Satellite Communication Systems

Abstract

This invention discloses a multi-carrier channel characteristic estimation method for 5G NTN low-Earth orbit satellite communication systems. The method includes a three-stage cascaded architecture: Integer frequency offset estimation uses FFT transformation after conjugate correlation between the received DMRS and the local DMRS to locate the spectral peak index and estimate the frequency offset of integer multiple subcarrier intervals; Coarse frequency offset estimation utilizes the conjugate correlation between the CP and the symbol tail and the CP length sliding integral to suppress noise, extracts the sample phase of the middle region of the CP through multi-symbol averaging, and calculates the residual fractional frequency offset; Fine frequency offset estimation utilizes inter-symbol conjugate multiplication after DMRS frequency domain LS channel estimation to eliminate the influence of channel frequency selective fading, and combines weighted linear regression to fit the phase slope, achieving high-precision frequency offset back-calculation. The three-stage cascaded architecture achieves progressively accurate estimation from a large frequency offset of 50kHz to Hz-level precision, balancing wide range and high accuracy. This invention effectively solves the problems of low estimation accuracy and difficulty in real-time adaptive correction of IQ imbalance in large frequency offset scenarios.

Description

Technical Field

[0001] This invention relates to a multi-carrier channel characteristic estimation method for 5G NTN low-Earth orbit satellite communication systems, belonging to the fields of digital signal processing and 5G NTN satellite communication technology. Background Technology

[0002] 5G NTN, short for Non-Terrestrial Network, serves as a supplement and extension to terrestrial communication. It achieves wide-area coverage through Low Earth Orbit (LEO) satellites, Medium Earth Orbit (MEO) satellites, and high-altitude platforms, and is a core technology for realizing integrated air-space-ground communication. 3GPP Release 17 officially incorporated LEO satellites into the NTN architecture, clarifying their application requirements in scenarios such as remote area access and emergency communication. OFDM, a representative multi-carrier technology, has been identified as the core modulation scheme for 5G NTN due to its strong resistance to multipath interference and high spectral efficiency. However, the Doppler frequency offset (up to ±50kHz) caused by the high-speed movement of LEO satellites (approximately 7.8 km / s) can disrupt the orthogonality of OFDM subcarriers, leading to severe inter-carrier interference (ICI). Simultaneously, the long latency, rapid time-varying characteristics, and deep fading of satellite channels render traditional terrestrial communication channel estimation methods ineffective. Therefore, frequency offset compensation and channel estimation have become key technologies for ensuring the performance of 5G NTN (Non-Terrestrial Network) satellite communication systems, and related research has become a hot topic in the field of communications. 5G NTN, short for Non-Terrestrial Network, serves as a supplement and extension to terrestrial communication. It achieves wide-area coverage through Low Earth Orbit (LEO) satellites, Medium Earth Orbit (MEO) satellites, and high-altitude platforms, and is a core technology for realizing integrated air-space-ground communication. 3GPP Release 17 officially incorporated LEO satellites into the NTN system, clarifying their application requirements in scenarios such as remote area access and emergency communication. Multi-carrier technology, represented by OFDM, has been identified as the core modulation scheme for 5G NTN due to its strong anti-multipath interference capability and high spectral efficiency. However, the high-speed movement of LEO satellites (approximately 7.8 km / s) causes Doppler frequency offsets (up to ±50 kHz), which can disrupt OFDM subcarrier orthogonality and lead to severe inter-carrier interference (ICI). Simultaneously, the long latency, rapid time-varying characteristics, and deep fading of satellite channels render traditional terrestrial communication channel estimation methods ineffective. Therefore, frequency offset compensation and channel estimation have become key technologies for ensuring the performance of 5G NTN LEO satellite communication systems, and related research has become a hot topic in the field of communications.

[0003] Despite its inherent advantages, OFDM technology still faces challenges in complex 5G NTN scenarios, such as Doppler frequency offset leading to subcarrier orthogonality disruption, synchronization difficulties caused by large latency, and complex resource scheduling under dynamic topology. These issues have become the core direction of current 5G NTN OFDM technology research, providing clear research entry points and practical value for related research projects.

[0004] 5G non-terrestrial networks integrate satellite and terrestrial communications, becoming a key technology for achieving seamless global coverage and high reliability. Channel estimation, as a core component of NTN systems, directly impacts system capacity, reliability, and anti-interference capabilities. In recent years, significant progress has been made both domestically and internationally in the field of 5G NTN channel estimation, primarily in algorithm innovation, AI-enabled technologies, and adaptation to highly dynamic environments. Currently, major technological advancements and methods include model-driven approaches, pilot and reference signal design, data-assisted and semi-blind estimation, and AI and deep learning methods.

[0005] In terms of model-driven methods, researchers have constructed more accurate channel fading models. For example, they have optimized the adaptability of classic algorithms such as Kalman filtering and minimum mean square error (MMSE) to address the unique characteristics of satellite communication, such as large time delay and Doppler frequency offset, effectively reducing estimation errors in complex channel environments. Regarding pilot and reference signal design, in addition to traditional time-division and frequency-division pilots, new space-division pilot and compressed sensing pilot schemes are gradually emerging. The former improves pilot resource utilization through multi-antenna beamforming technology, while the latter reduces pilot overhead while ensuring estimation accuracy through sparse signal reconstruction principles, making it particularly suitable for narrowband satellite communication scenarios.

[0006] Data-assisted and semi-blind estimation methods cleverly combine the statistical characteristics of known training sequences and received data. Under conditions of limited pilot resources, they continuously refine the estimation results through iterative optimization algorithms, balancing estimation performance with system spectral efficiency. AI and deep learning methods, with their powerful data fitting and feature extraction capabilities, exhibit unique advantages: channel estimation models based on convolutional neural networks (CNNs) can directly learn feature patterns from massive amounts of channel data without relying on complex mathematical modeling; recurrent neural networks (RNNs) and their variants can effectively capture the time-varying characteristics of the channel, significantly improving the real-time performance and stability of estimation results in highly dynamic low-Earth orbit (LEO) satellite communication scenarios. However, these technologies still face some challenges. For example, AI models are highly dependent on training data, have insufficient generalization ability when channel scenarios change abruptly, and complex models have high computational complexity, making lightweight deployment on terminal devices difficult. These are key areas for future research.

[0007] Channel estimation in 5G NTN scenarios has developed rapidly in China, with significant achievements in related industries and technologies. For example, a team from Beijing University of Posts and Telecommunications proposed a channel estimation method based on pilot clusters and BEM (Browser Estimation Model). By optimizing the pilot insertion density, the algorithm complexity was reduced by more than 30% while maintaining estimation accuracy. This method, combined with the sparsity characteristics of satellite channels, can control the delay estimation error to within 0.1μs in high-frequency (e.g., Ka-band) scenarios. In a patent application filed in 2024, Huawei reduced the bit error rate (BER) of joint channel estimation to 10% by defining a precise channel estimation window to avoid uplink and downlink transmission conflicts. -5 The following is a summary of the key points. This technology has been included as a candidate solution in 3GPP Release 18 and is suitable for high-speed mobile scenarios of low Earth orbit (LEO) satellites. Besides technological research and algorithmic innovation, there are also examples of 3GPP protocol standardization applications, such as the parameter optimization of the NTN channel model in 3GPP Release 17 / 18 led by the Telecommunication Research Institute of the Ministry of Industry and Information Technology, proposing a dynamic pilot configuration scheme that reduces pilot overhead from 15% to 8%. Furthermore, in terms of hardware implementation and lightweighting, the Nanjing University of Aeronautics and Astronautics team reduced the number of parameters by 65% ​​and the FPGA resource utilization rate to 22% through knowledge distillation compression of deep learning models, making it suitable for the low-power requirements of satellite payloads. The lightweight CNN model developed by the 38th Research Institute of China Electronics Technology Group Corporation is implemented on an FPGA with a resource utilization rate of only 30% and a processing latency of <1ms.

[0008] On the other hand, 5G NTN channel estimation has also made some progress abroad. For example, Telesat, in its "Lightspeed" constellation, achieves seamless integration with terrestrial networks by pre-compensating for Doppler frequency shift through satellite orbit parameters and combining it with the MEF standard, achieving link latency <20ms and frame error rate (FER) <1%. In field tests in remote areas of northern Canada, this scheme achieved downlink speeds of 100Mbps. Another example is the GraphNet model proposed by a US research team, which captures channel time-frequency correlations through a lightweight GNN. In high-dynamic scenarios (Doppler shift >10kHz), the block error rate (BLER) is 5dB lower than the traditional MMSE algorithm. This model has been incorporated into OneWeb's second-generation constellation design. Furthermore, there are cutting-edge explorations and interdisciplinary applications: an MIT team is researching terahertz-visible light fusion channel estimation, utilizing the high bandwidth of terahertz and the anti-interference characteristics of visible light to increase channel capacity to 10Gbps in non-line-of-sight (NLOS) scenarios.

[0009] In summary, there are key gaps in the current estimation of 5G NTN channel characteristics. One issue is the "triangular contradiction" in frequency offset estimation, where existing algorithms struggle to balance "wide range, high accuracy, and low latency." Blind estimation algorithms have a narrow estimation range (only ±½ subcarrier spacing) and large errors at low signal-to-noise ratios. Correlation estimation algorithms based on CP (Yih, IEEE TVT 2009, etc.) extract phase differences using the replication relationship between the OFDM symbol cyclic prefix and tail, but the correlation between CP and the symbol tail completely fails in scenarios with large frequency offsets, resulting in an estimation range of only ±Δf / 2. Methods combining DMRS and CP show a sharp increase in error to ±120Hz at ±45kHz frequency offsets. Integer multiple frequency offset estimation methods based on FFT frequency domain search suffer from computation delays exceeding frame length under broadband transmission, and peak detection is easily interfered with in noisy instrument environments. On the other hand, regarding DC offset (carrier leakage) estimation, Yih (IEEE TVT 2009) proposed a receiver DCO estimator using -1 / 1 subcarriers, which is only applicable to scenarios with small residual frequency offset. Xia et al. (2011) proposed a coarse + fine two-stage estimation scheme, but based on the WLAN preamble structure, it cannot be adapted to 5G NTN PUSCH channels. The digital baseband calibration scheme proposed by Zhou et al. (Chinese Academy of Sciences 2014) requires additional hardware loops. Existing DCO methods rely on specific pilot structures or additional hardware, and cannot achieve low-complexity real-time tracking in 5G NTN PUSCH continuous transmission mode. In terms of IQ imbalance estimation and correction, existing statistical methods require long-term accumulation, resulting in large parameter fluctuations in time-varying channels, and the correction matrix design does not consider moving geometric mean smoothing, leading to parameter instability and a decrease in EVM performance. Summary of the Invention

[0010] The purpose of this invention is to address the shortcomings and deficiencies of existing technologies by proposing a multi-carrier channel characteristic estimation method for 5G NTN low-Earth orbit satellite communication systems. This method comprises two parallel modules: frequency offset estimation and IQ imbalance estimation. Channel estimation and EVM calculation follow the 3GPP 38521 protocol specification. This invention effectively solves the problems of low estimation accuracy and difficulty in real-time adaptive correction of IQ imbalance in scenarios with large frequency offset.

[0011] The technical solution adopted by this invention to solve its technical problem is: a multi-carrier channel characteristic estimation method for 5G NTN low-Earth orbit satellite communication systems, which includes the following steps: Step 1: Slot-by-slot frequency offset estimation and correction. Frequency offset for different time slots is estimated using a three-tiered cascade method: integer multiple frequency offset estimation, coarse frequency offset estimation, and fine frequency offset estimation. The core of integer multiple frequency offset estimation is frequency domain correlation peak detection, based on the logic of "time domain correlation between the received signal and the known reference signal → frequency domain peak position mapping to integer frequency offset". Coarse frequency offset estimation is used to eliminate residual frequency offset within ±0.5 times the subcarrier spacing. Its core principle is to utilize the inherent correlation between the cyclic prefix (CP) and the tail of the useful symbol in OFDM symbols. First, the CP and tail are extracted and multiplied conjugately to extract the phase difference. Then, a sliding integral over the CP length is performed to suppress noise. After integration, the noise term is suppressed by average, leaving only the phase term. Subsequently, multi-symbol averaging is performed to improve robustness. Then, peak detection is used to locate the optimal correlation position, specifically including extracting the correlation amplitude sequence of the current time slot, finding the index of the sampling point with the strongest correlation, performing boundary correction to avoid the index falling in the invalid tail region, calculating candidate offsets relative to the symbol start point and selecting the optimal symbol with the smallest absolute offset value, and determining the final cyclic shift. Finally, samples from the middle region of the CP (to avoid CP edge noise) are extracted from the original correlation sequence. This region is least affected by multipath interference. After averaging multiple symbols, the phase is taken, and the residual fractional frequency offset is calculated. This step fills the large gap between the integer frequency offset granularity and the final Hz-level accuracy. The fine frequency offset estimation uses the DMRS frequency domain signal to achieve high-precision Hz-level frequency offset back-calculation, which is completed in four steps: frequency domain LS channel estimation, inter-symbol conjugate differential (to eliminate channel frequency selective fading), frequency domain aggregation, and weighted linear regression. First, LS channel estimation is performed on the frequency domain DMRS signal to obtain the channel frequency response H. Then, the first DMRS reference symbol (i.e., the third symbol) is selected as the reference, and the channel estimation of subsequent symbols is multiplied by the reference symbol conjugate. Based on the slow-varying channel assumption, the masking of phase information by channel frequency selective fading is automatically eliminated. Then, the differential phase of all subcarriers is averaged to obtain the average phase of each symbol. At this time, the phase and symbol index have a strict linear relationship. Finally, using the actual DMRS symbol index as the independent variable x (instead of the continuous index used in traditional methods, eliminating the 4.5-fold systematic bias), and the number of effective subcarriers per symbol as the weight, a weighted linear regression is used to fit the phase slope. Combined with the OFDM symbol period and subcarrier spacing, the final frequency offset result is obtained, achieving high-precision reverse estimation from large frequency offsets to Hz-level accuracy. The above frequency offset estimation process is as follows: Figure 1-4 As shown. Finally, the integer multiples of the frequency offset, coarse frequency offset, and fine frequency offset are added together to obtain the total frequency offset, which is then compensated.

[0012] Step 2: Estimate and compensate for IQ imbalance. IQ imbalance estimation and correction mainly includes five steps: DC offset removal, imbalance characterization, correction matrix construction, and parameter smoothing. First, the exponential averaging method is used to track the DC offset in real time, with the weighting factor λ fixed at 2. -10After reaching steady state, the mean of the last 1000 converged points is directly subtracted from the DC components of both the I and Q paths to avoid low-pass filter variance contaminating the statistics. Subsequently, the signal after removing the DC offset is characterized for IQ imbalance. By accumulating the statistics piecewise, amplitude imbalance and phase imbalance estimates are derived. A lower triangular correction matrix is ​​constructed based on the above parameters. To maintain the I-path amplitude constant and avoid signal power degradation, the matrix is ​​scaled by dividing by A to obtain the final correction matrix. Since the finite segment length L causes fluctuations in the X / Y / Z statistics, unstable correction parameters will worsen the EVM. Therefore, a moving geometric mean (α=0.1) is introduced to iteratively and smoothly update the correction parameters calculated for each segment, achieving a balance between tracking speed and stability. The specific implementation process can be found in [link to implementation details]. Figure 5 Finally, the IQ imbalance estimation result is obtained, and the original signal is then multiplied by the final calibration matrix after DC correction to obtain the signal after IQ imbalance correction.

[0013] Step 3: Channel estimation. After performing FFT transform on the signal, channel estimation is performed. Based on the DMRS reference signal and the received frequency domain signal, the channel frequency response of the OFDM system is estimated through LS estimation, CIR time-domain denoising, and frequency-domain averaging interpolation. The channel frequency response is then applied to Step 1 and subsequent EVM calculations.

[0014] Beneficial effects: 1. The present invention designs a three-stage cascaded architecture of "integer frequency offset estimation -> coarse frequency offset estimation -> fine frequency offset estimation". Integer frequency offset estimation uses FFT transformation after conjugate correlation between the received DMRS and the local DMRS to locate the spectral peak index and estimate the frequency offset of integer multiple subcarrier intervals. Coarse frequency offset estimation uses the conjugate correlation between CP and symbol tail and CP length sliding integral to suppress noise. It extracts the sample phase of the middle region of CP by averaging multiple symbols and calculates the residual fractional frequency offset. Fine frequency offset estimation uses the conjugate multiplication between symbols after DMRS frequency domain LS channel estimation to eliminate the influence of channel frequency selective fading. Combined with weighted linear regression to fit the phase slope, it realizes high-precision frequency offset back-calculation. The three-stage cascaded architecture realizes progressively accurate estimation from a large frequency offset of ±50kHz to ±Hz level, taking into account both wide range and high accuracy.

[0015] 2. This invention utilizes the actual DMRS symbol index [3,8,12] as the independent variable x, instead of the continuous index [1,2,3] used in traditional methods, thus eliminating the 4.5-fold systematic bias caused by symbol index mapping errors. The number of effective subcarriers per symbol is used as the weight w, and weighted linear regression is applied (…). Suppress the impact of noise on phase estimation fluctuations. Inter-symbol conjugate multiplication (Z(k,m)=H(k,m)*conj(H(k,fc))) automatically eliminates the influence of channel frequency-selective fading, improving estimation accuracy under low signal-to-noise ratio.

[0016] 3. This invention uses exponential averaging (... This method tracks DC offset changes in real time, replacing multiplication with binary shift operations. It achieves high efficiency in hardware implementation on 5G terminal integrated testing instruments. The steady-state DC offset is directly subtracted from the mean of the last 1000 points after convergence, avoiding low-pass filter variance contamination of the statistics. This is achieved through segmented (L=1024) statistics. , Z = sum(I*Q) is used to represent the degree of imbalance between I and Q through piecewise summation. The amplitude imbalance estimate K_est = sqrt(X / Y) and the phase imbalance estimate P_est = Z / Y are calculated. The lower triangular correction matrix (parameters) is designed. After scaling (A1=1, B1=B / A, C1=C / A), adaptive real-time tracking is achieved by smoothing the update segment by segment using the moving geometric mean (alpha=0.1), reducing the EVM from over 4% without correction to below 3%. Attached Figure Description

[0017] Figure 1 This is a flowchart of the three-stage cascaded architecture for frequency offset estimation in this invention.

[0018] Figure 2 This is a schematic diagram illustrating the principle of integer multiple frequency offset estimation in this invention.

[0019] Figure 3 This is a schematic diagram illustrating the principle of coarse frequency offset estimation for CP in this invention.

[0020] Figure 4 This is a flowchart of the weighted linear regression precise frequency partial estimation of the present invention.

[0021] Figure 5 This is a flowchart of the IQ imbalance estimation and correction process of the present invention.

[0022] Figure 6 This is an example diagram of the simulation results of the present invention. Detailed Implementation

[0023] The invention will now be described in further detail with reference to the accompanying drawings.

[0024] The system model of this invention specifically includes: Based on a 5G NTN OFDM multi-carrier system, the PUSCH channel signal is generated according to the 3GPP TS 38.211 protocol. Let the transmitted time-domain signal be... The received signal after passing through the channel is: Equation (1) Where f_offset is the frequency offset. For channel impulse response, It is additive white Gaussian noise.

[0025] For IQ imbalance, the received signal model with distortion adopts a general symmetric model, which considers the IQ path gain and the IQ path DC offset.

[0026] System parameters: bandwidth 20MHz, subcarrier spacing 30kHz, FFT points 1024, modulation scheme QPSK / 16QAM / 64QAM.

[0027] The frequency offset estimation of this invention specifically includes: The core of this invention's integer frequency offset estimation is frequency domain correlation peak detection, based on the logic of "time domain correlation between the received signal and a known reference signal → mapping the frequency domain peak position to the integer frequency offset," as follows: Figure 2 As shown below, the specific process will be explained.

[0028] 1. Signal Model Definition Send signal The time-domain sample of the m-th DMRS symbol (m=1,2,3 corresponding to the 3rd, 8th, and 12th symbols) in the received DMRS time-domain signal (after CP removal) is as follows: Equation (2) in, It is an integer multiple of the frequency offset, where n is the sequence number and f is the frequency offset. s The sampling frequency.

[0029] 2. Pretreatment Received signal extraction (retain only DMRS symbols) The 3rd, 8th, and 12th columns (DMRS symbols) are extracted from the 1024×14 de-CP signal and reconstructed into a 3072×1 time-domain sequence. The reference signal is a known 1024×3 DMRS (after de-CP), which is also reconstructed into a 3072×1 sequence and its conjugate is taken.

[0030] 3. Time-domain correlation and frequency-domain peak detection, specifically including: Step 1: Time-domain correlation to highlight the phase characteristics of integer frequency offset Calculate the product of the received signal and the conjugate of the reference signal: Equation (3) Physical meaning: When the received signal matches the reference signal (DMRS symbol alignment). Equation (4) in, , is a constant, at this time It is simplified to a single-frequency signal.

[0031] Step 2: FFT transform, converting the single-frequency signal into a frequency domain peak value. For the relevant results Perform FFT to extract amplitude and single-frequency signal. The FFT is: Equation (5) in, This represents the frequency of a single-frequency signal, i.e., an integer multiple of the frequency offset. ; , indicating the peak index.

[0032] Step 3: Peak location, find the index corresponding to the frequency offset. Accumulate the amplitudes of multiple antennas / multi-ports and locate the peak index loc.

[0033] Combined parameters ( , The peak index loc satisfies: Equation (6) Step 4: Negative frequency offset correction (FFT periodic processing) The frequency domain of FFT is periodic (range). ),when When the frequency is actually negative, it is corrected to an equivalent negative index loc - 3072 (for example, loc=1537 corresponds to -1535).

[0034] Step 5: Subcarrier offset number (scIdx) calculation Calculate the integer offset scIdx using loc: Normally, if both the reference signal and the input signal occupy 14 OFDM symbols, the integer offsets are as follows: Equation (7) Where nSlots is the number of time slots, N symbslot This represents the number of OFDM symbols in a single time slot, set to 14.

[0035] However, we only consider the DMRS case, that is, only the 3 symbols in one time slot. Therefore, the formula for integer offset is rewritten as: Equation (8) Where loc is the peak index in equation (6).

[0036] Step 6: Final Integer Frequency Offset Output Equation (9) Among them, f sc The subcarrier spacing is 30kHz, and the test is conducted at this frequency.

[0037] Note: The algorithm will output a non-zero result only when the frequency offset is an integer multiple of 30kHz (such as 30kHz, 60kHz, -30kHz).

[0038] The coarse frequency offset estimation (coarseF mode) of this invention is used in OFDM systems to eliminate ±0.5 times the subcarrier spacing (Δf). sc The key step in the coarse frequency offset estimation within the range is to utilize the inherent correlation between the cyclic prefix (CP) in OFDM symbols and the tail of useful symbols. The coarse frequency offset estimation process is as follows: Figure 3 As shown, the specific implementation logic is as follows.

[0039] Let the transmitted time-domain signal be OFDM symbols at the transmitting end are frequency offset After the effect, the globally discrete received signal (including frequency offset and noise, after sampling) is as follows: Equation (10) in, For coarse frequency offset, T s Let w(n) be the symbol period and w(n) be the noise.

[0040] By utilizing the replication relationship between the CP and the tail of the useful symbol in OFDM symbols, the phase difference is extracted by conjugate multiplication of two sets of related signals. Equation (11) Where, r cp (n) represents the CP part of the signal, r tail (n) represents the useful symbol tail portion. For coarse frequency offset, T s For the symbol period, N FFT The number of FFT points.

[0041] Noise suppression is achieved by performing a moving integral with a CP length (short CP = 72 sampling points) on the conjugate multiplication result: Equation (12) in, Let be the sum of CP energy (real, non-negative) within the m-th sliding window. Most of the symbols are short CP, which have stronger statistical significance; after integration, the noise term is suppressed by average, leaving only Sum frequency offset phase term.

[0042] Perform multi-symbol averaging to improve robustness: Equation (13) Where M is the number of symbols participating in the averaging (number of symbols within a subframe, 30KSCS, one subframe contains two time slots). Record The average energy (real, non-negative) ensures that the phase after averaging is still determined solely by the frequency offset.

[0043] Without averaging cpcorravg, directly calculating the phase using a single-symbol cpcorr will cause noise to lead to phase estimation bias (especially in low signal-to-noise ratio scenarios).

[0044] Next, the optimal correlation position is located by peak detection, the timing deviation is corrected, and the phase of the sample in the middle region of the CP is extracted. The derivation process is as follows: 1. Extract the correlation amplitude sequence of the current time slot (cpcorrmagSlot) Total number of samples in time slots: Equation (14) Where, N CPlong N represents the number of long CP points. CPshort For the short CP point, these two parameters are specified by the signal generation protocol. For a 20MHz bandwidth, 30kHz subcarrier spacing PUSCH channel signal, they are defined as 88 and 72 respectively.

[0045] Correlation magnitude sequence Definition: Equation (15) in, This represents the correlation strength of the k-th sampling point (the larger the value, the better the CP matches the tail).

[0046] 2. Find the index of the sampling points with the strongest correlation (tmpCycshift) Equation (16) in, For the correlation amplitude sequence of equation (15), It is a 1-based index.

[0047] Physical meaning: The sampling point with the strongest correlation between CP and tail within the current time slot, that is, the phase difference at this point is least affected by multipath interference and is closest to the ideal CP replication characteristics.

[0048] 3. Boundary correction (to prevent indexes from falling into invalid tail regions) The 0-based starting point for each symbol is symbolStarts0, denoted as... (p=1,...,14), (e.g., the first symbol starts at 0, the second symbol starts at...) (etc.), then Equation (17) in, Let tail (0-based) be the number of invalid samples from the start of the last symbol to the end of the time slot. .

[0049] Correction logic: If (1-based) Beyond the starting point of the last symbol (0-based, corresponding to 1-based) This indicates that the text falls at the end of an invalid section and needs to be corrected. If the offset exceeds the midpoint of the tail: Then, the index is "looped" to the valid region of the previous symbol through modulo operation, ensuring that the index falls within the valid symbol range and avoiding the introduction of noise when extracting samples later. Equation (18) in, This is used to calculate the corrected maximum value index.

[0050] 4. Calculate the candidate offsets relative to the starting point of the symbol. Definition of candidate offset: Calculate the index of the corrected maximum value. (1-based) relative to the starting point of each symbol (0-based) offset d(p): Equation (19) Optimal sign selection: Find the sign with the smallest absolute offset. ,Right now: Equation (20) Where d(p) is the candidate offset defined by equation (19); p * Physical meaning: Closest to The starting point of a symbol indicates that the CP of that symbol matches the tail best (minimizing interference between symbols).

[0051] 5. Determine the final cyclic shift (cycshift) Equation (21) Among them, record The unit is sampling points, and its physical meaning is "the offset of the point with the strongest correlation relative to the starting point of the optimal symbol". This is the core output of peak detection.

[0052] Note: If you input a timing offset, use `toffset` to override `cycshift`. Finally, the frequency offset is calculated using the average phase, as follows: (1) Collect the relevant values ​​of multiple symbols: Equation (22) The parameters are defined as follows: : The starting sampling point for all symbols (frequency domain, calculated via cumsum).

[0053] : CP middle region offset ( This ensures that the most stable part of the CP is extracted.

[0054] : Correcting timing bias. Without Δ, the extracted samples may fall on the edge of CP or in the invalid region, resulting in phase noise.

[0055] Note: Extract "CP middle region samples" from the original correlation sequence (cpCorrRaw) (avoid CP edge noise).

[0056] (2) Calculate the average of the correlation values ​​and take the phase: Equation (23) (3) Calculate the frequency offset: Equation (24) The precise frequency offset estimation process of this invention is as follows: Figure 4 As shown, the specific implementation logic is as follows: In an OFDM system, the signal is modulated onto multiple subcarriers, forming a two-dimensional frequency domain grid of "subcarrier-symbol". The signal model is as follows: Horizontal axis: Symbol index (time dimension, t = m·T_sym, where m is the symbol number and T_sym is the OFDM symbol period). Vertical axis: Subcarrier index (frequency dimension, f = k·Δf_sc, where k is the subcarrier number and Δf_sc is the subcarrier spacing).

[0057] Frequency offset (f) offset The effect in the frequency domain is different from that in the time domain: it causes the phase of each subcarrier to rotate linearly with time (symbol) and frequency (subcarrier), which is the core feature of frequency domain processing.

[0058] The mathematical model for frequency shift in the frequency domain is as follows: First, define the frequency domain signals of a single subcarrier k and a single OFDM symbol m (multiple antennas are not considered for now). Reference signal (known): X(k, m) (e.g., pilot signal, known beforehand). True channel gain: H(k, m) (time-varying, but under slow variation H(k, m) ≈ H(k, m-1)).

[0059] Received signal (including CFO and noise): Y(k, m) Equation (25) Where w(k, m) represents frequency domain noise; key terms It is the phase rotation of frequency offset in the frequency domain: As the symbol m (time) changes: (Linear phase in the time dimension); As the subcarrier k (frequency) changes: (Linear phase in the frequency dimension, Δt_sc = 1 / (N·Δf_sc) is the time interval between subcarriers, and N is the number of FFT points).

[0060] The algorithm achieves precise frequency offset estimation through four steps: "channel estimation → phase difference → linear regression → frequency offset calculation". The derivation process is as follows: Step 1: Perform LS channel estimation on the frequency domain DMRS signal In the time domain, the least squares (LS) channel estimation formula is: Equation (26) Correspondingly, in the frequency domain: Equation (27) Key observation at this point: The phase consists of two parts: Equation (28) Step 2: Frequency domain phase differential (eliminating channel frequency selectivity) The true channel H(k, m) exhibits frequency selectivity (varying with k), and its phase arg(H(k, m)) masks the phase information of the frequency offset. This needs to be eliminated through differential operations: 1. Selecting the first valid symbol (firstColumn = fc) as the reference, its channel estimation phase is: Equation (29) Among them, f c This is the index of the first valid symbol.

[0061] 2. For subsequent symbols (m>fc), calculate the conjugate product of the channel estimate and the reference symbol (ignoring noise terms): Equation (30) Based on the "slowly varying channel" assumption, we have arg(H(k, m)) ≈ arg(H(k, fc)), therefore: Equation (31) Therefore, the result of conjugate multiplication can be simplified to: Equation (32) Now calculate the phase of Z(k,m): Equation (33) Note: After frequency domain differential, the effect of subcarrier index k is eliminated because the k·Δt_sc terms cancel each other out in the differential (the coefficients of k in φ(k, m) - φ(k, fc) are the same), leaving only the phase change in the time dimension (sign difference), which is independent of the subcarrier.

[0062] 3. Frequency domain aggregation and linear regression (extracting the phase slope in the time dimension) Averaging the differential phases of all subcarriers k (to eliminate frequency-selective interference) yields the average phase θ(m) for each symbol m: Equation (34) Where K is the number of subcarriers. The average phase of symbol m can be seen. It has a strictly linear relationship with the symbol index m, and the slope .

[0063] Step 3: Weighted linear regression to estimate the rate of change of phase with sign index Slope estimation using weighted linear regression: Equation (35) in, The weight is the number of effective subcarriers for each symbol. Based on the above derivation, the parameter we can obtain during frequency offset estimation is the average phase corresponding to symbol m. We can obtain the desired slope by estimating its slope based on its linear relationship. .

[0064] The process of deriving the slope in the weighted linear regression algorithm will be explained in detail below.

[0065] First, the linear model we need to fit is the "linear relationship between the phase value y and the sign index x", that is: Equation (36) The parameter correspondences are as follows: x: The independent variable, corresponding to the "symbol index"; y: Dependent variable, corresponding to "mean phase difference"; slope: The slope to be determined (a core parameter that reflects the rate of change of phase with sign index, ultimately used to calculate frequency offset); b: Intercept (a constant term that has no effect on frequency offset estimation and can be eliminated in the derivation).

[0066] The goal of weighted linear regression is to find the optimal slope and b that minimizes the weighted sum of squared residuals. Here, "weights" refers to the number of valid reference signals per symbol; the more valid reference signals, the more reliable the phase measurement of that symbol, and the greater the weight. The specific steps are as follows: 1) Define the weighted sum of squared residuals (objective function) For each symbol index (Corresponding to the i-th symbol in x), its phase measurement value is The weight is .

[0067] Model prediction value Weighted residuals Defined as: Equation (37) in, For the i-th symbol, its phase measurement value is The weight is This applies to all subsequent formulas.

[0068] Note: Multiplied by This is to incorporate weights into the residuals, giving greater weight to the residuals of reliable data.

[0069] The objective of weighted linear regression is to minimize the weighted sum of squared residuals: Equation (38) in, (Total number of symbols, i.e., the lengths of x and y).

[0070] 2) Take the partial derivative of the objective function and set it to 0 (find the extrema) To find To find the minimum slope and b, we need to take the partial derivatives of each and then set the partial derivatives to 0.

[0071] Take the partial derivative of b in the equation and set it to 0: Equation (39) We obtain the intercept b (which will be used later to eliminate the intercept and retain only the slope): Equation (40) Take the partial derivative of slope in the equation and set it to 0: Equation (41) After simplification, we get: Equation (42) 3) Substitute the intercept b, eliminate the constant term, and solve for the slope. Equation (43) 4) Final result of formula simplification Total weight S Equation (44) The weighted mean of x, X Equation (45) The weighted mean of y, Y Equation (46) x 2 weighted mean X2 Equation (47) The weighted mean XY of x·y Equation (48) Substitute Calculation formula:

[0072]

[0073] The final slope is obtained as follows: Equation (49) Where X, Y, XY, X2 are defined by equations (44-48).

[0074] Step 4: Frequency Offset Calculation As can be seen from step 2, the slope Combining the slope of the weighted linear regression fit, we can obtain the formula for calculating the frequency offset: Equation (50) in, The OFDM symbol period consists of two parts: Useful symbol time (FFT processing time): T_u = N / f_s, where f_s is the sampling rate and N is the number of FFT points; Cyclic prefix (CP) time: T_CP = N_g / f_s, where N_g is the number of sampling points for CP.

[0075] This definition is used in all subsequent formulas.

[0076] Therefore, the complete OFDM symbol period formula is: Equation (51) Combining the subcarrier spacing Δf_sc = f_s / N, we can obtain: Equation (52) Substitute The formula yields the final frequency offset result: Equation (53) The IQ imbalance estimation process of this invention is as follows: Figure 5 As shown, the specific implementation logic is as follows: IQ signal model with distortion: Equation (54) in, For IQ path signals containing distortion, For ideal IQ path signals, Let be the distortion matrix, where and For IQ channel amplitude distortion parameters, and This is the phase distortion offset parameter.

[0077] (a) DC offset estimation and removal DC offset is estimated in real time using the "exponential average": Equation (55) The parameters are explained below: - Current input signal ( or ); - : Real-time estimated DC offset value; - (Fixed value): Weighting factor is ; - Advantage: Replaces multiplication with binary shift ( (Equivalent to right shift by k bits), efficient hardware implementation.

[0078] Directly subtract the DC mean to remove DC offset: Equation (56) Equation (57) in, and These are the DC offsets for the I-path and Q-path, respectively. and These are the signals after removing the DC offset from the I and Q paths, respectively.

[0079] The IQ imbalance calculation and calibration of this invention specifically includes: The correction matrix of this invention is a lower triangular matrix: Equation (58) in, Defined as a calibration matrix, it is used to remove amplitude and phase imbalances.

[0080] Reasons for choosing this structure: - Keep the I-channel signal unchanged ( Adjust the amplitude only by scaling A; - The Q-channel signal is jointly corrected by the I-channel and the Q-channel ( This cancels out I / Q crosstalk caused by phase imbalance.

[0081] To keep the amplitude of the I-path completely unchanged ( Therefore, we need to set A=1, so we divide the correction matrix by A to obtain the final correction matrix:

[0082] Step 1: Imbalance Characterization (Calculate X / Y / Z Parameters) The degree of I / Q imbalance is characterized by summing the statistics from L sampling points: Equation (59) Equation (60) Equation (61) The parameters are explained below: - L: Accumulation length (configurable, typically a power of 2 such as 1024, 2048, 4096, etc.); - Accumulation must be performed continuously. After accumulating L samples, update X / Y / Z and reset the delay line. Step 2: Calculate the correction parameters and Derive estimates of amplitude and phase imbalances from X / Y / Z: 1. Amplitude Imbalance Estimation: Equation (62) Derivation logic: In an ideal situation ,but If the Q-path amplitude is too small (e.g.) ),but It is used to compensate for the Q-path amplitude.

[0083] 2. Phase imbalance estimation: Equation (63) Derivation logic: Ideal orthogonal time and Unrelated If a phase shift exists, , It reflects the degree of crosstalk.

[0084] Step 3: Calculate the correction matrix parameters A / B / C Will and Substitute the correction matrix: Equation (64) The meanings of each parameter are as follows: - : I-channel amplitude correction coefficient (to compensate for the deviation of K_I); - Q-path amplitude correction coefficient (to compensate for the deviation of K_Q); - I / Q crosstalk cancellation factor (compensates for crosstalk caused by phase imbalance).

[0085] Step 4: Parameter scaling (to avoid signal power degradation) To keep the signal power constant, divide B / C by A: Equation (65) Equation (66) The final correction matrix is:

[0086] Step 5: Parameter Stabilization (Moving Geometric Mean) Since L is of finite length, the statistics of X / Y / Z fluctuate, leading to... Instability, which in turn affects the EVM. A moving geometric mean is used to smooth the parameters: Equation (67) Equation (68) The meanings of each parameter are as follows: - : The smoothed parameters of the nth iteration; - The original parameters calculated from the current L samples; - (Weighting factor): Range 0.004~0.9, determines the parameter update speed. The larger the value, the faster the update and the shorter the convergence time, but the worse the stability; conversely, the smaller the value, the slower the convergence and the better the stability. - Initial value: (Corresponding to the identity matrix, no correction effect).

[0087] Step 6: Apply the correction matrix For no DC offset signal By applying the correction matrix, the ideal signal is obtained: Equation (69) Equation (70) The simulation verification of this invention specifically includes: 5G NTN PUSCH signals were generated according to the 3GPP TS 38.211 protocol. Simulation parameters: bandwidth 20MHz, subcarrier spacing 30kHz, FFT points 1024, modulation scheme QPSK / 16QAM / 64QAM, signal-to-noise ratio range -10~30dB.

[0088] The following tests were conducted using a 20MHz bandwidth, 30kHz subcarrier bandwidth, and 64QAM modulation scheme. During the tests, frequency offset and IQ imbalance were manually introduced to verify the algorithm. Simulation results are as follows: Figure 6 As shown in the example, the specific results are listed in Table 1-5 below.

[0089] (1) Comparison of estimation accuracy under different SNRs. The results are averaged after multiple measurements, specifically including: Frequency offset setting: 32567Hz; IQ Imbalance Settings: Amplitude Imbalance = 1.2 dB; Phase Error = 3°; I-channel DC Offset = 4; Q-channel DC Offset = 7 Table 1 Comparison of estimation accuracy under different SNRs

[0090] Note: When SNR is too low, EVM will be very poor, but it will not affect the frequency offset and IQ estimation algorithms. (2) The impact of different frequency offsets on the frequency offset estimation results for the same SNR SNR setting: 25dB; Modulation method: QPSK Table 2. Impact of different frequency offsets on frequency offset estimation results

[0091] (3) The impact of different IQ shifts on IQ estimation results for the same SNR Note: DC offset measurement and IQ are independent and do not affect each other; frequency offset is not added by default. SNR setting: 25dB; Modulation method: QPSK Table 3 IQ estimation results

[0092] (4) The effect of iteration length L on the results The IQ imbalance setting uses a set of highly accurate data: DCI: 5, DCQ: 8, amplitude: 1.2dB, phase: 3° Table 4. Impact of Iteration Length L on IQ Estimation Results

[0093] The results are visible. Figure 6 .

[0094] Note: The optimal length L is the number of FFT points. The test used 1024-point FFT, so the test results for 1024 and 2048 iteration lengths were better.

[0095] (5) Iteration factor α The IQ imbalance setting uses a set of highly accurate data: DCI: 5, DCQ: 8, amplitude: 1.2dB, phase: 3°, L=1024. Table 5. The influence of iteration factor α on IQ estimation results

[0096] Where α↑: more trust in the current segment, faster tracking of IQ mismatch changes, but larger estimation jitter and poor noise resistance; α↓: more trust in historical average, smoother and more stable estimation and stronger noise suppression, but slower tracking of time-varying mismatch.

[0097] L=1024 (multiple segments, high noise per segment), can be paired with: α=0.05 ~ 0.15, small segments have large statistical fluctuations, large α cannot be used, otherwise the correction coefficient will oscillate violently; L=2048 (balanced segmentation), can be paired with: α=0.1 ~ 0.2, a universal combination, most 5G uplink demodulation directly use 0.15; L=4096 (few segments, clean statistics per segment), can be paired with: α=0.2 ~ 0.4, when the number of segments is small and the number of iteration steps is insufficient, appropriately increase α to improve the tracking speed, and do not worry about noise jitter.

[0098] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for estimating the multi-carrier channel characteristics of a 5G NTN low-Earth orbit satellite communication system, characterized in that, The method includes the following steps: Step 1: Time-slot frequency offset estimation and correction; frequency offset is estimated for different time slots through a three-stage cascade method of integer multiple frequency offset estimation, coarse frequency offset estimation, and fine frequency offset estimation. The core of integer multiple frequency offset estimation is frequency domain correlation peak detection, based on the logic of "time domain correlation between the received signal and the known reference signal → frequency domain peak position mapping to integer frequency offset". Coarse frequency offset estimation is used to eliminate residual frequency offset within ±0.5 times the subcarrier spacing. Its core principle is to utilize the inherent correlation between the cyclic prefix (CP) and the tail of the useful symbol in OFDM symbols. First, the two sets of correlated signals of CP and tail are extracted and multiplied by conjugate to extract the phase difference. Then, the sliding integral of the CP length is used to suppress the phase difference. Noise is suppressed by integration, and the noise term is averaged and suppressed, leaving only the phase term. Then, multi-symbol averaging is performed to improve robustness. After that, the optimal correlation position is located by peak detection. Specifically, this includes extracting the correlation amplitude sequence of the current time slot, finding the index of the sampling point with the strongest correlation, performing boundary correction to avoid the index falling in the invalid tail region, calculating the candidate offset relative to the symbol start point and selecting the optimal symbol with the smallest absolute value of the offset, determining the final cyclic shift, and finally extracting the CP middle region sample from the original correlation sequence (to avoid CP edge noise). This region is least affected by multipath interference. After multi-symbol averaging, the phase is taken, and the residual fractional octave frequency offset is calculated. Step 2: Estimate and compensate for IQ imbalance; IQ imbalance estimation and correction includes five steps: DC offset removal, imbalance characterization, correction matrix construction, and parameter smoothing. First, the exponential averaging method is used to track the DC offset in real time, with the weighting factor λ fixed at 2. -10 After reaching steady state, the mean of the last 1000 points of convergence is taken and the DC components of the I and Q paths are directly subtracted to avoid low-pass filter variance contaminating the statistics. Then, the IQ imbalance is characterized on the signal after removing DC offset. The amplitude imbalance estimate and phase imbalance estimate are derived from the segmented accumulation of statistics. Based on the above parameters, a lower triangular correction matrix is ​​constructed. Step 3: Channel estimation. After performing FFT transformation on the signal, channel estimation is performed. Based on the DMRS reference signal and the received frequency domain signal, the channel frequency response of the OFDM system is estimated through LS estimation, CIR time-domain denoising, and frequency-domain averaging interpolation. The channel frequency domain response is obtained and applied to Step 1 and subsequent EVM calculations. This step lays the groundwork for frequency offset estimation and subsequent EVM-related calculations.

2. The method for estimating the multi-carrier channel characteristics of a 5G NTN low-Earth orbit satellite communication system according to claim 1, characterized in that, Step 1 includes: the method fills the large gap between integer frequency offset granularity and final Hz-level accuracy; fine frequency offset estimation uses the DMRS frequency domain signal to achieve Hz-level high-precision frequency offset back-calculation, which is completed in four steps: frequency domain LS channel estimation, inter-symbol conjugate difference (to eliminate channel frequency-selective fading), frequency domain aggregation, and weighted linear regression. First, LS channel estimation is performed on the frequency domain DMRS signal to obtain the channel frequency domain response H; then, the first DMRS reference symbol, i.e., the third symbol, is selected as the reference, and the channel estimation of subsequent symbols is multiplied by the reference symbol using conjugate multiplication, based on the slow-varying channel hypothesis. Assume that the phase information is automatically masked by the channel frequency selective fading; then, the differential phase of all subcarriers is averaged to obtain the average phase of each symbol. At this time, the phase and the symbol index have a strict linear relationship. Finally, the actual DMRS symbol index is used as the independent variable x, and the number of effective subcarriers per symbol is used as the weight. The phase slope is fitted by weighted linear regression. Combined with the OFDM symbol period and the subcarrier spacing, the final frequency offset result is obtained, realizing high-precision back-calculation from large frequency offset to Hz level accuracy. Finally, the integer multiple frequency offset, coarse frequency offset and fine frequency offset results are added to obtain the total frequency offset and compensation is performed.

3. The multi-carrier channel characteristic estimation method for a 5G NTN low-Earth orbit satellite communication system according to claim 1, characterized in that, Step 2 includes: to keep the I-channel amplitude constant and avoid signal power degradation, the matrix is ​​divided by A for scaling to obtain the final calibration matrix. Since the finite segment length L causes fluctuations in the X / Y / Z statistics, the unstable calibration parameters will worsen the EVM. Therefore, a moving geometric mean (α=0.1) is introduced to iteratively and smoothly update the calibration parameters calculated for each segment, achieving a balance between tracking speed and stability. Finally, the IQ imbalance estimation result is obtained. The original signal is then de-DC and multiplied by the final calibration matrix to obtain the signal after IQ imbalance is removed.

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