Efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood correction SAGE algorithm

Abstract

The invention discloses an efficient channel measurement method based on sparse non-uniform frequency sampling and a likelihood correction SAGE algorithm, and belongs to the field of wireless communication and channel measurement. According to the method, through non-uniform parabola frequency sampling, on the premise of ensuring no time delay fuzzy, the number of measurement frequency points is remarkably reduced, the measurement efficiency is improved, and the data volume and the post-processing complexity are reduced; by constructing a frequency-time delay related likelihood correction factor, the influence of molecular absorption and non-uniform frequency stepping is compensated, so that a likelihood main lobe shape under a non-uniform sampling condition is equivalent to dense and uniform sampling, and the time delay resolution is kept; and the likelihood correction factor is embedded into M steps of an SAGE algorithm, an LR-SAGE algorithm is constructed, and high-precision estimation of multipath time delay and gain is realized. Verification is carried out on an actual 280-300GHz terahertz channel measurement platform, and a large-scale communication-inductance integrated channel data set of which the acquisition scale is increased by dozens of times when the measurement duration is basically unchanged is realized.

Description

An efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood-corrected SAGE algorithm Technical Field

[0001] This invention belongs to the field of wireless communication and channel measurement technology, specifically relating to an efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood correction SAGE (Space-Alternating Generalized Expectation-Maximization) algorithm. It is applicable to frequency domain measurement and multipath parameter extraction of broadband wireless channels such as millimeter wave and terahertz, and can be used for large-scale channel data acquisition in 6G AI-native and ISAC scenarios. Background Technology

[0002] To support ultra-high bandwidth and high-resolution environmental sensing, future B5G / 6G communication systems will typically operate in millimeter wave, terahertz, or even higher frequency bands, employing measurement bandwidths of several GHz or even tens of GHz. To construct a comprehensive sensing-communication channel dataset that accurately reflects the complexity of the propagation environment, long-term, wide-area broadband channel measurements need to be conducted in real-world scenarios, and parameters such as multipath delay, gain, and angle need to be accurately extracted.

[0003] Existing broadband channel measurements often employ devices such as Vector Network Analyzers (VNAs) or Universal Software Radio Peripherals (USRPs), achieving frequency sweep measurements in the frequency domain through uniform frequency sampling, and then recovering the time-delay domain channel impulse response using Discrete Fourier Transform. To avoid time delay ambiguity, the frequency step of uniform frequency sampling needs to satisfy the following: ,in For frequency intervals, The desired maximum unambiguous time delay is achieved by scanning tens of thousands or even more frequency points within a typical terahertz measurement bandwidth. This results in long measurement times, large data volumes, and extremely high post-processing computational complexity, severely limiting the acquisition efficiency of large-scale channel datasets.

[0004] For example, Chinese patent CN106850099B proposes a frequency-domain sequence correlation channel measurement method based on hypersonic scenarios. It utilizes CAZAC sequences and frequency-domain sliding correlation to improve measurement accuracy, but it still relies on regular frequency-domain sampling and does not design a delay-free sampling structure for broadband non-uniform frequency sampling, nor does it consider the molecular absorption effect unique to the millimeter-wave / terahertz bands. Similarly, Chinese patent CN116582200A proposes a wireless channel measurement method based on a general-purpose software radio peripheral. It obtains the power delay spectrum through pseudo-random sequences and correlation processing, focusing on hardware system construction and sequence design, but insufficiently considering the frequency sampling method and frequency-selective attenuation caused by terahertz molecular absorption. The delay-Doppler domain channel measurement method proposed in Chinese patent CN119030641A is mainly for CSF extraction in OTFS modulation scenarios and is not suitable for broadband frequency-domain sweep measurements based on VNA.

[0005] On the other hand, in terms of multipath parameter extraction, the SAGE algorithm is widely used in broadband channel measurements due to its path-by-path iterative estimation structure. However, in the millimeter-wave / terahertz band, due to the significant frequency-selective attenuation caused by molecular absorption such as water vapor, the measured frequency domain channel gain exhibits strong fluctuations in the frequency dimension. Directly applying the traditional SAGE algorithm will distort the main lobe shape of the single-path likelihood function, causing the estimation results to deviate from the true time delay and gain. This problem is particularly prominent when combined with sparse and non-uniform frequency sampling.

[0006] In summary, the existing technology has at least the following shortcomings:

[0007] (1) In order to avoid time delay ambiguity, uniform frequency sampling requires a very small frequency step, resulting in a huge number of frequency sampling points. The measurement duration and data volume are difficult to meet the requirements of large-scale 6G channel dataset construction.

[0008] (2) Existing non-uniform frequency sampling methods are mostly derived from radar or antenna array fields, and there is still a lack of systematic frequency sampling design methods that can guarantee no time delay ambiguity for 6G broadband channel measurement.

[0009] (3) Traditional multipath extraction algorithms such as SAGE do not explicitly model the frequency-dependent gain caused by molecular absorption and the weight difference introduced by non-uniform frequency sampling, resulting in obvious model mismatch and estimation error in the millimeter wave / terahertz band.

[0010] (4) There is still a lack of an efficient channel measurement method that integrates delay-free fuzzy sparse frequency sampling with the likelihood-corrected SAGE algorithm for molecular absorption and non-uniform sampling for unified design and experimental verification. Summary of the Invention

[0011] The purpose of this invention is to overcome the shortcomings of the prior art and propose an efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood-corrected SAGE algorithm, achieving the following objectives: In millimeter-wave / terahertz broadband scenarios, non-uniform parabolic frequency sampling significantly reduces the number of measurement frequency points while ensuring no time delay ambiguity, thereby improving measurement efficiency, reducing data volume, and reducing post-processing complexity; by constructing a frequency-delay-related likelihood correction factor, the influence of molecular absorption and non-uniform frequency stepping is compensated, making the likelihood main lobe shape in non-uniform sampling equivalent to dense uniform sampling, thus maintaining time delay resolution; this likelihood correction factor is embedded into the M-step of the SAGE algorithm to construct the likelihood-corrected SAGE (LR-SAGE) algorithm, achieving high-precision estimation of multipath delay and gain; the proposed method is verified on a practical 280~300GHz terahertz channel measurement platform, realizing a large-scale integrated sensing channel dataset with a data acquisition scale increased by tens of times while maintaining a basically unchanged measurement duration.

[0012] The objective of this invention is achieved through the following technical solution:

[0013] An efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood-corrected SAGE algorithm includes:

[0014] S1: Based on the terahertz molecular absorption model, establish a broadband channel model containing molecular absorption;

[0015] S2: Based on the design principle of no-delay fuzziness, design a local frequency stepping for parabolic frequency sampling;

[0016] S3: Generate a set of parabolic frequency sampling points based on local frequency stepping of parabolic frequency sampling;

[0017] S4: Measure the frequency domain channel response at each frequency point based on the parabolic frequency sampling point set;

[0018] S5: Construct a frequency-delay-related likelihood correction factor to correct the likelihood function, and obtain the corrected likelihood function;

[0019] S6: Introduce a likelihood correction factor into the SAGE algorithm to form a likelihood-corrected SAGE algorithm, and use the likelihood-corrected SAGE algorithm to iteratively estimate the multipath delay and gain to obtain the final multipath delay and gain.

[0020] Furthermore, the establishment of the broadband channel model containing molecular absorption in step S1 specifically includes:

[0021] Based on the target measurement scenario and test equipment, obtain the following system parameters: center frequency. Total measurement bandwidth and the number of frequency sampling points etc., among which: Indicates the center frequency of the channel measurement; This represents the total bandwidth of the frequency domain sweep. This indicates the total number of frequency sampling points to be designed;

[0022] Based on the terahertz molecular absorption model, the frequency domain channel response function of the measurement channel is established as a broadband channel model:

[0023] (1)

[0024] in, The sampling frequency; Number of multipaths; and They represent the first Complex gain and time delay of the stripe; It is additive noise; The frequency-dependent gain factor, which takes into account the effects of molecular absorption, can be calculated using the following expression:

[0025]

[0026] in, It is the molecular absorption gain factor under reference time delay. This is a pre-agreed reference time delay.

[0027] Furthermore, in step S2, the local frequency stepping design process for parabolic frequency sampling is as follows:

[0028] make Define the frequency distribution function for the frequency sampling index. The derivative at the frequency sampling index is:

[0029] (2)

[0030] in, Indicates local frequency stepping;

[0031] According to the design principle of time-delay-free fuzziness, namely: (1) Select a nonlinear frequency distribution function (2) Within the valid range The minimum value in the range is not less than half of its maximum value. A local step size in the form of a quadratic parabola is selected.

[0032] (3)

[0033] in, For the curvature of the parabola, Minimum frequency step;

[0034] From equation (3), we can obtain:

[0035] (4)

[0036] (5)

[0037] in, and These represent the maximum frequency step and the minimum frequency step, respectively.

[0038] To avoid enhancement caused by the superposition of adjacent side lobes, the minimum frequency step must satisfy the following constraints:

[0039] (6)

[0040] Therefore, we get:

[0041] (7)

[0042] Meanwhile, the integral of the local frequency step should satisfy the total bandwidth constraint:

[0043] (8)

[0044] Substituting equations (3) and (7) into equation (8), we can obtain:

[0045] (9)

[0046] (10)

[0047] parameters and Substituting into equation (3), we obtain the local frequency step of the parabolic frequency sampling. .

[0048] Furthermore, in step S3, the specific process of generating the parabolic frequency sampling point set is as follows:

[0049] Local frequency stepping for parabolic frequency sampling Integrating yields the parabolic frequency distribution function. :

[0050] (11)

[0051] in, The starting frequency for the frequency sweep is preferably set to [value]. This causes the frequency sampling points to be concentrated in the area of Centered bandwidth Inside;

[0052] right In discrete index By sampling at a certain point, a set of parabolic frequency sampling points is obtained:

[0053]

[0054] in, Indicates the first Each frequency point.

[0055] Furthermore, in step S4, measuring the frequency domain channel response specifically includes:

[0056] S4.1: Set the start frequency and end frequency of the frequency domain sweep channel detection device to be respectively... and ;

[0057] S4.2: Load the parabolic frequency sampling point set into the internal or external control software of the frequency domain sweep channel detection equipment. ,according to Non-equal interval frequency sweep control is performed on the frequency domain sweep channel detection equipment;

[0058] S4.3: At each frequency point Record multiples Parameters (such as) ( ), as the measured frequency domain channel response ;

[0059] S4.4: Measured frequency domain channel response Amplitude and phase calibration and noise removal are performed to obtain the calibrated frequency domain channel response sample sequence. .

[0060] Furthermore, the frequency domain sweep channel detection device includes a VNA.

[0061] Furthermore, in step S5, a frequency-delay related likelihood correction factor is constructed to correct the likelihood function, specifically including:

[0062] Under the single-path assumption, the frequency domain channel response It can be written as:

[0063] (12)

[0064] in, For this path complex gain, This is the path delay;

[0065] The main lobe shape of the traditional likelihood function in the time delay domain will be affected and The distortion is caused by the combined effects of molecular absorption and non-uniform frequency sampling; to correct the influence of molecular absorption and non-uniform frequency sampling on the main lobe shape of the single-path likelihood function, this invention constructs a frequency-time delay-related likelihood correction factor. :

[0066] (13)

[0067] in, For index The local frequency step at a given point can be calculated using equation (3); The actual time delay of the path to be estimated;

[0068] By applying to the measurement sample Weights, construct the corrected single-path likelihood function:

[0069] (14)

[0070] Make the main lobe shape of the modified likelihood function approximate the same bandwidth The ideal shape of the dense, uniform frequency sampling system is obtained, thereby maintaining the original time delay resolution.

[0071] Furthermore, in step S6, the likelihood-corrected SAGE algorithm iteratively estimates the multipath delay and gain, specifically including:

[0072] In multipath scenarios, let there be a common... Effective multipath; definition of the first The parameter for strip diameter is All multipath parameters are ;

[0073] Initialization: based on the modified likelihood function A coarse search for the main peak location yields an initial multipath delay estimate. The initial gain is estimated using weighted least squares. , forming the initial multipath parameters ;

[0074] Step E: In the first In the nth iteration, for the th Strip path, calculate the residual channel after removing contributions from other paths:

[0075] (15)

[0076] M-step: Based on residual channel With correction factor Update # Stripe delay and gain estimation:

[0077] First, maximize the modified likelihood function within the preset time delay search interval:

[0078] (16)

[0079] Then, in the fixed Under the given conditions, the gain is updated using weighted least squares:

[0080] (17)

[0081] Iteration Termination: Repeat E-step and M-step for all paths until the number of iterations reaches the preset upper limit or the parameters converge;

[0082] After the iteration, the multipath parameter estimates are obtained. Furthermore, the sparse delay domain channel impulse response and power delay spectrum are constructed.

[0083] The beneficial effects of this invention are:

[0084] 1) Achieve sparse frequency sampling with no time delay or ambiguity. This is achieved through design that satisfies… The parabolic frequency step function effectively disperses the sidelobe positions while keeping the total bandwidth constant, avoiding the time delay ambiguity of fixed period in traditional uniform frequency sampling, and realizing theoretically time delay-free ambiguity sparse sampling.

[0085] 2) Significantly reduces the number of measurement frequency points and measurement overhead. Under typical 10~20GHz bandwidth, this invention can reduce the number of frequency sampling points from tens of thousands of points in traditional uniform sampling to the order of hundreds of points, improve measurement time by about 50 times, and reduce data storage by about 98%, making it possible to rapidly acquire large-scale experimental datasets;

[0086] 3) Effectively compensates for the dual effects of molecular absorption and non-uniform sampling. By constructing a frequency-delay-related likelihood correction factor, molecular absorption loss and local frequency stepping are incorporated into a unified weight, making the corrected likelihood main lobe shape consistent with the ideal uniform sampling system, thus avoiding the decrease in time delay estimation accuracy caused by main lobe broadening;

[0087] 4) Improve the accuracy and robustness of multipath parameter extraction. By embedding the correction factor into the M-step of the SAGE algorithm to form the LR-SAGE algorithm, high-precision estimation of multipath delay and gain can still be achieved under conditions of strong molecular absorption and non-uniform sampling. Compared with the traditional SAGE algorithm, it has a lower root mean square error of delay.

[0088] 5) Significantly reduces post-processing computational complexity. Thanks to the order-of-magnitude reduction in the number of frequency sampling points and the efficient iterative structure in the LR-SAGE algorithm, this invention can reduce the post-processing computational load by approximately 99.96% while maintaining estimation accuracy, significantly alleviating the burden on the computing platform;

[0089] 6) Ensuring the fidelity of channel statistical characteristics. Experimental results show that, while significantly reducing the number of frequency sampling points, the path loss distribution and RMS delay spread distribution extracted by this invention remain highly consistent with the results of traditional dense uniform frequency sweeping, and can be used for accurate channel modeling and AI training data generation. Attached Figure Description

[0090] Figure 1 is an overall block diagram of the efficient channel measurement method based on parabolic frequency sampling and LR-SAGE algorithm of the present invention.

[0091] Figure 2 shows the local frequency stepping of the parabolic frequency sampling in this invention. and frequency distribution A schematic diagram; where (a) represents the local frequency step. (b) shows the frequency distribution. .

[0092] Figure 3 is a flowchart of the likelihood-corrected SAGE algorithm (LR-SAGE) of this invention.

[0093] Figure 4 shows the measured channel impulse response results of the present invention.

[0094] Figure 5 shows the measured channel power angle delay spectrum results of the present invention.

[0095] Figure 6 shows the measured channel path loss and delay spread results of the present invention; where (a) is the path loss and (b) is the RMS delay spread. Detailed Implementation

[0096] To enable those skilled in the art to better understand the present invention, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. The following description of exemplary embodiments is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0097] Example 1: General Channel Measurement Procedure Based on Sparse Non-Uniform Frequency Sampling and LR-SAGE Algorithm

[0098] As shown in Figure 1, the specific implementation process of this embodiment corresponds to steps S1 to S6 above, mainly illustrating the application of the present invention in general broadband channel measurement scenarios.

[0099] First, select the center frequency based on the scenario to be tested. With total measurement bandwidth ,For example GHz GHz, expected latency-free fuzzy maximum latency ns, and select the number of frequency sampling points. The curvature of the parabola is calculated using equations (9) and (10) respectively. With minimum frequency step This leads to the generation of the parabolic frequency distribution function. and parabolic frequency sampling point set .

[0100] Then, the parabolic frequency sampling point set Import VNA control software to control the VNA at each frequency point. Perform a frequency sweep measurement and record the measured complex numbers. Parameters as frequency domain channel response After completing the measurement, the frequency domain channel response was analyzed. Perform system calibration of amplitude and phase to obtain the calibrated frequency domain channel response sample sequence. .

[0101] Subsequently, according to With ambient temperature Water vapor density Calculate molecular absorption gain And construct the likelihood correction factor according to equation (13). The corrected single-path likelihood function is calculated using equation (14). Referring to Figure 3, the initial time delay estimate of the multipath is obtained by searching for the main peak position of the likelihood function, and then the multipath parameters are iteratively estimated using the LR-SAGE algorithm.

[0102] Finally, based on the multipath parameter set output by the LR-SAGE algorithm, channel statistics such as power delay spectrum, path loss, and root mean square delay spread (RMS delay spread) are calculated for subsequent design and simulation of the integrated communication and sensing system.

[0103] Example 2: Application of a 280~300 GHz Terahertz Integrated Sensing Channel Measurement Platform

[0104] This embodiment illustrates the specific application of the present invention on a 280~300 GHz terahertz integrated sensing (ISAC) channel measurement platform.

[0105] The measurement platform uses an external terahertz extension module connected to a VNA to form the transmitting and receiving front end, operating in the 280~300 GHz frequency band, with a total bandwidth of GHz. To cover typical scenarios such as indoor corridors and conference rooms, the measurement path length is set to approximately 10-40 m, with the desired maximum delay without ambiguity. µs. In traditional uniform frequency sampling schemes, to meet the requirement of no ambiguity in this time delay, the frequency step needs to be less than 1 MHz, corresponding to the number of frequency sampling points. The measurement time is long and the data storage pressure is enormous.

[0106] Using the parabolic frequency sampling scheme of the present invention, select Using Equation (11), a parabolic local frequency step and frequency distribution are designed to make the frequency samples non-uniformly distributed in the range of 280~300 GHz, and more densely distributed near the center of the bandwidth. Under this setting, the number of frequency sampling points is reduced by about 80 times compared with traditional uniform sampling, while still satisfying the principle of delay-free fuzzy design.

[0107] In actual measurements, the VNA is controlled at various frequency points. After collecting multiple sets of averages The measurements were repeated for different transmit and receive angle combinations to form angle-delay combined channel data. After the measurements were completed, the LR-SAGE algorithm of this invention was used to extract multipath from the channel data at each angle to obtain multipath delay, gain, and angle information.

[0108] Experimental results show that the present invention is effective in use. Given a parabolic frequency sampling point, the extracted channel power delay angle spectrum is similar to that of traditional methods. The results of uniform frequency sampling points + IDFT / SAGE are highly consistent (as shown in Figure 5), and the cumulative distribution function curves of path loss and RMS delay spread almost overlap (see Figure 6). Furthermore, under the same measurement duration, this invention can obtain a much larger combination of measurement positions and angles, enabling the efficient construction of large-scale terahertz sensing integrated channel datasets.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. An efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood-corrected SAGE algorithm, characterized in that, include: Based on the terahertz molecular absorption model, a broadband channel model containing molecular absorption is established; Based on the design principle of delay-free fuzziness, a local frequency stepping mechanism for parabolic frequency sampling is designed. A set of parabolic frequency sampling points is generated based on this local frequency stepping mechanism. The frequency domain channel response is measured at each frequency point according to the parabolic frequency sampling point set. A frequency-delay correlated likelihood correction factor is constructed to correct the likelihood function, resulting in a corrected likelihood function. The likelihood correction factor is introduced into the SAGE algorithm to form a likelihood-corrected SAGE algorithm. This algorithm is then used to iteratively estimate the multipath delay and gain, yielding the final multipath delay and gain.

2. The efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood-corrected SAGE algorithm according to claim 1, characterized in that, The establishment of the broadband channel model containing molecular absorption specifically includes: obtaining the center frequency based on the target measurement scenario and test equipment. Total measurement bandwidth and the number of frequency sampling points Based on the terahertz molecular absorption model, the frequency domain channel response function of the measurement channel is established as a broadband channel model: (1) Among them, The sampling frequency; Number of multipaths; and They represent the first Complex gain and time delay of the stripe; It is additive noise; A frequency-dependent gain factor to account for the effects of molecular absorption.

3. The efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood-corrected SAGE algorithm according to claim 2, characterized in that, The local frequency stepping design for the parabolic frequency sampling is as follows: Let Define the frequency distribution function for the frequency sampling index. The derivative at the frequency sampling index is: (2) Among them, This represents the local frequency step; based on the design principle of no-delay ambiguity, a quadratic parabolic form of local step is selected: (3) Among them, For the curvature of the parabola, ； For minimum frequency step, ; parameters and Substituting into equation (3), we obtain the local frequency step of the parabolic frequency sampling. 。 4. The efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood-corrected SAGE algorithm according to claim 3, characterized in that, The specific process for generating the parabolic frequency sampling point set is as follows: local frequency stepping of parabolic frequency sampling. Integrating yields the parabolic frequency distribution function. ： (4) Among them, The sweep start frequency is preferably set to [value]. This causes the frequency sampling points to be concentrated in the area of Centered bandwidth Inside; To In discrete index By sampling at a certain point, a set of parabolic frequency sampling points is obtained: in, Indicates the first Each frequency point.

5. The efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood-corrected SAGE algorithm according to claim 4, characterized in that, Measuring the frequency domain channel response at each frequency point specifically includes: setting the start and end frequencies of the frequency domain sweep channel probing device to be respectively... and Load the parabolic frequency sampling point set into the internal or external control software of the frequency domain sweep channel detection equipment. ,according to Non-equal interval frequency sweep control is performed on the frequency domain sweep channel detection equipment; at each frequency point Record multiples Parameters, as measured frequency domain channel response ; Measured frequency domain channel response Amplitude and phase calibration and noise removal are performed to obtain the calibrated frequency domain channel response sample sequence. 。 6. The efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood-corrected SAGE algorithm according to claim 5, characterized in that, The frequency domain sweep channel detection device includes a VNA.

7. The efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood-corrected SAGE algorithm according to claim 5 or 6, characterized in that, The modified likelihood function is constructed as follows: Under the single-path assumption, the frequency domain channel response... for: (5) Among them, For this path complex gain, Given the path delay; construct a frequency-delay related likelihood correction factor. ： (6) Among them, For index Local frequency stepping at the location; The true time delay of the path to be estimated; by applying a pressure to the measurement sample Weights, construct the corrected single-path likelihood function: （7）。 8. The efficient channel measurement method based on sparse non-uniform frequency sampling and likelihood-corrected SAGE algorithm according to claim 7, characterized in that, The likelihood-corrected SAGE algorithm iteratively estimates multipath delay and gain, specifically including: in a multipath scenario, assuming a total of Effective multipath; definition of the first The parameter for strip diameter is All multipath parameters are Initialization: based on the modified likelihood function A coarse search for the main peak location yields an initial multipath delay estimate. The initial gain is estimated using weighted least squares. , forming the initial multipath parameters Step E: In the first step In the nth iteration, for the th Strip path, calculate the residual channel after removing contributions from other paths: (8) M-step: Based on residual channel With correction factor Update # Stripe delay and gain estimation: First, maximize the modified likelihood function within the preset delay search interval: (9) Then, in the fixed Under the given conditions, the gain is updated using weighted least squares: (10) Iteration Termination: Repeat the E-step and M-step for all paths until the number of iterations reaches the preset upper limit or the parameters converge; after the iteration ends, the multipath parameter estimates are obtained. Furthermore, the sparse delay domain channel impulse response and power delay spectrum are constructed.

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