Iterative channel estimation and signal decoding method for windowing OFDM (Orthogonal Frequency Division Multiplexing) system in time-varying frequency selective fading channel

Abstract

The invention relates to the field of wireless communication, and provides an iterative channel estimation and signal decoding method of a windowing OFDM (Orthogonal Frequency Division Multiplexing) system in a time-varying frequency selective fading channel. The windowing OFDM system comprises a transmitting end and a receiving end, wherein the transmitting end is used for generating and converting an OFDM symbol into a transmitting signal; performing windowing processing on the transmitted signal by using a time domain window function, and adding a cyclic prefix to obtain a final transmitted signal; transmitting the final transmitting signal to a receiving end through a time-varying frequency selective fading channel; the receiving end is used for removing the cyclic prefix of the transmitting signal transmitted by the transmitting end and demodulating to obtain a frequency domain receiving signal; converting a frequency domain receiving signal into a simplified form based on windowing operation of a time domain window function; obtaining an input and output relation of pilot frequency subcarriers based on the simplified form of the frequency domain receiving signal; and performing channel estimation and signal decoding based on the input and output relationship of the pilot frequency subcarriers. By adopting the method, the inter-carrier interference generated by improving the spectrum efficiency can be effectively inhibited.

Description

Technical Field

[0001] This application relates to the field of wireless communication technology, and in particular to an iterative channel estimation and signal decoding method for windowed OFDM systems in time-varying frequency-selective fading channels. Background Technology

[0002] In high-mobility scenarios such as high-speed rail, vehicle-to-everything (V2X) communication, and low-Earth orbit satellite communication, wireless channels exhibit time-varying frequency-selective fading characteristics. This time-selective fading in such channels can lead to severe inter-carrier interference (ICI) in traditional orthogonal frequency division multiplexing (OFDM) systems.

[0003] In recent years, existing technologies have proposed orthogonal time-frequency-space (OTFS) modulation techniques, which combat time- and frequency-selective fading by modulating the signal in the time-delay-Doppler domain. However, OTFS modulation is only suitable for channels with integer time delays and normalized Doppler shifts less than 0.5. When the channel has large fractional Doppler shifts and fractional time delays, the performance of OTFS deteriorates significantly.

[0004] To address the fractional Doppler shift and fractional delay (ICI) issues in time-varying frequency-selective fading (TFCFS) channels, existing technologies propose OFDM systems based on raised cosine roll-off windows or Slepian function windowing, combined with a surround-type frequency-varying Viterbi detection scheme for decoding. This scheme can suppress the widespread ICI in traditional OFDM to affect only a few adjacent subcarriers, remaining effective even at normalized Doppler frequencies as high as 1.333. Through surround-type frequency-varying Viterbi detection, ICI is significantly suppressed.

[0005] The aforementioned windowed OFDM system assumes perfect channel state information. To verify the feasibility of this system, existing technologies propose an interpolation-based channel estimation scheme: employing a comb-shaped pilot structure, interference from data subcarriers (carrying data signals) is completely eliminated by inserting empty subcarriers (not transmitting data or pilot signals) on both sides of the pilot subcarriers (carrying pilot signals), ensuring that the pilots are only affected by additive white Gaussian noise. First, channel estimates on the pilot subcarriers are obtained, and then the full-band channel characteristics are reconstructed through channel interpolation.

[0006] This interpolation method suffers from reduced spectral efficiency—although pilot subcarriers are essential, spectral efficiency can be improved by reducing the number of empty subcarriers. However, reducing empty subcarriers introduces ICI interference during channel estimation. Summary of the Invention

[0007] Therefore, it is necessary to provide an iterative channel estimation and signal decoding method for windowed OFDM systems in time-varying frequency-selective fading channels that can suppress ICI interference caused by the reduction of empty subcarriers, in order to address the above-mentioned technical problems.

[0008] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: A windowed OFDM system in a time-varying frequency-selective fading channel includes: a transmitter and a receiver; The transmitter is used for: Inserting the pilot sequence into the quadrature amplitude modulation data sequence constitutes a sequence consisting of... OFDM symbols composed of frequency domain signals; Make OFDM symbols pass through The point-based discrete Fourier inverse transform converts the signal into a transmitted signal. The transmitted signal is windowed using a time-domain window function; A cyclic prefix is ​​added to the processed transmit signal to obtain the final transmit signal; The final transmitted signal is transmitted to the receiving end through a time-varying frequency-selective fading channel; The receiving end is used for: Receive the transmitted signal from the transmitter; Remove the cyclic prefix from the received signal, and through The frequency domain received signal is obtained by demodulating the point-discrete Fourier transform. The channel matrix parameters at the pilot position are obtained by using pilot subcarriers, and then the complete channel matrix is ​​obtained by interpolation. Windowing operations based on time-domain window functions transform the frequency-domain received signal into a form that limits inter-carrier interference. The simplified form within the subcarrier range, where, It is a positive integer; The input-output relationship of the pilot subcarrier is obtained based on the simplified form of the frequency domain received signal; Channel estimation and signal decoding are performed based on the input-output relationship of pilot subcarriers.

[0009] This invention also proposes an iterative channel estimation and signal decoding method for windowed OFDM systems in time-varying frequency-selective fading channels. The steps of channel estimation and signal decoding at the receiver based on the input-output relationship of pilot subcarriers include: S1: Cyclic shift of the subcarriers in the transmitted signal from the transmitter; S2: For the subcarriers after cyclic shift, calculate the estimated values ​​of the elements on the first preset diagonal of the channel matrix based on the minimum mean square error estimation and interpolation method; S3: Obtain the initial estimate of the transmitted signal by Viterbi decoding based on the estimated values ​​of the elements on the first preset diagonal of the channel matrix; based on the initial estimate of the transmitted signal, obtain the estimated values ​​of the elements on the second preset diagonal of the channel matrix using the minimum mean square error estimation and interpolation method; combine the estimated values ​​of the elements obtained in this step with the estimated values ​​of the elements obtained in step S2 to obtain the estimated value of the initial channel matrix. S4: Perform Viterbi decoding using the estimated value of the initial channel matrix to update the estimated value of the signal transmitted by the transmitter; S5: Based on the estimated value of the transmitted signal obtained in step S4, the estimated value of the channel matrix is ​​updated using the residual to perform minimum mean square error estimation. S6: Iterate and repeat steps S4 and S5 until the transmitted signal estimate obtained in the current iteration is equal to the transmitted signal estimate obtained in the previous iteration. Stop the iteration, obtain the final estimate of the channel matrix and the final transmitted signal estimate, and complete the iterative channel estimation.

[0010] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: This invention performs channel estimation and signal decoding based on the input-output relationship of pilot subcarriers, thereby reducing the number of empty subcarriers while suppressing inter-subcarrier interference, and making full use of the characteristics of the window function to reduce decoding errors through the transmission of repeating codes. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the overall structure of the windowed DFOM system proposed in Example 1; Figure 2 This is an example diagram of the pilot arrangement proposed in Example 2; Figure 3 This is a flowchart illustrating Algorithm 1 proposed in Example 2; Figure 4 This is an example diagram of the comb-shaped pilot arrangement proposed in Example 2; Figure 5 This is a structural block diagram proposed in Example 2; Figure 6 This is a flowchart illustrating Algorithm 2 proposed in Example 2; Figure 7 This is a schematic diagram comparing the performance of the first frame error rate proposed in Example 3; Figure 8 The convergence graph of the first iterative scheme proposed in Example 3. Figure 9 This is a schematic diagram comparing the performance of the second frame error rate proposed in Example 3; Figure 10 The convergence graph of the second iterative scheme proposed in Example 3 is shown. Figure 11 This is a schematic diagram comparing the performance of the third frame error rate proposed in Example 3. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0013] Example 1 This embodiment proposes a windowed OFDM system in a time-varying frequency selective fading channel.

[0014] like Figure 1 As shown, the windowed OFDM system in the time-varying frequency selective fading channel includes: a transmitter and a receiver; The transmitter is used for: Inserting the pilot sequence into the quadrature amplitude modulation data sequence constitutes a sequence consisting of... OFDM symbols composed of frequency domain signals; Make OFDM symbols pass through The point-based discrete Fourier inverse transform converts the signal into a transmitted signal. The transmitted signal is windowed using a time-domain window function; A cyclic prefix is ​​added to the processed transmit signal to obtain the final transmit signal; The final transmitted signal is transmitted to the receiving end through a time-varying frequency-selective fading channel; The receiving end is used for: Receive the transmitted signal from the transmitter; Remove the cyclic prefix from the received signal and pass through The frequency domain received signal is obtained by demodulating the point-discrete Fourier transform. The channel matrix parameters at the pilot position are obtained by using pilot subcarriers, and then the complete channel matrix is ​​obtained by interpolation. Windowing operations based on time-domain window functions transform the frequency-domain received signal into a form that limits inter-carrier interference. The simplified form within the subcarrier range, where, It is a positive integer; The input-output relationship of the pilot subcarrier is obtained based on the simplified form of the frequency domain received signal; Channel estimation and signal decoding are performed based on the input-output relationship of pilot subcarriers.

[0015] In an optional embodiment, the OFDM symbol includes pilot subcarriers and data subcarriers; Let the pilot subcarrier and the data subcarrier be collectively referred to as subcarriers; To eliminate interference from the data subcarriers, the transmitting end inserts a preset number of empty subcarriers between the data subcarriers and the pilot subcarriers based on the input-output relationship between the transmitted and received signals at the pilot. This preset number is adjusted according to the magnitude of the Doppler frequency shift and is an even number. Half of the preset number of empty subcarriers are on the left side of the pilot subcarriers, and the remaining empty subcarriers are on the right side of the pilot subcarriers.

[0016] In an optional embodiment, the simplified form of the frequency domain received signal includes:

[0017]

[0018] In the formula, This indicates that inter-carrier interference is limited to Frequency domain received signal within the subcarrier range Indicates the number of the subcarrier of the received signal in the frequency domain; Indicates the first The first subcarrier Individual frequency domain channel response; Indicates the first The frequency domain signal corresponding to each subcarrier; This indicates that the mean is zero and the power spectral density is Gaussian noise in the frequency domain; Indicates the total number of scattering path components; , and They represent the first The complex channel coefficients, Doppler frequency shift, and time delay corresponding to each path component; Represents the time-domain window function Point-based discrete Fourier transform; Indicates the subcarrier spacing; Represents the natural constant; It represents the imaginary unit.

[0019] This application also proposes an iterative channel estimation and signal decoding method for a windowed OFDM system in a time-varying frequency-selective fading channel. The steps of the receiver performing channel estimation and signal decoding based on the input-output relationship of pilot subcarriers include: S1: Cyclic shift of the subcarriers in the transmitted signal from the transmitter; S2: For the subcarriers after cyclic shift, calculate the estimated values ​​of the elements on the first preset diagonal of the channel matrix based on the minimum mean square error estimation and interpolation method; S3: Obtain the initial estimate of the transmitted signal by Viterbi decoding based on the estimated values ​​of the elements on the first preset diagonal of the channel matrix; based on the initial estimate of the transmitted signal, obtain the estimated values ​​of the elements on the second preset diagonal of the channel matrix using the minimum mean square error estimation and interpolation method; combine the estimated values ​​of the elements obtained in this step with the estimated values ​​of the elements obtained in step S2 to obtain the estimated value of the initial channel matrix. S4: Perform Viterbi decoding using the estimated value of the initial channel matrix to update the estimated value of the signal transmitted by the transmitter; S5: Based on the estimated value of the transmitted signal obtained in step S4, the estimated value of the channel matrix is ​​updated using the residual to perform minimum mean square error estimation. S6: Iterate and repeat steps S4 and S5 until the transmitted signal estimate obtained in the current iteration is equal to the transmitted signal estimate obtained in the previous iteration. Stop the iteration, obtain the final estimate of the channel matrix and the final transmitted signal estimate, and complete the iterative channel estimation.

[0020] As an example, at the receiving end, the subcarriers need to be cyclically shifted to counteract the problem of additional interpolation errors caused by the fractional delay disrupting the inter-channel correlation.

[0021] In an optional embodiment, step S1 includes: Considering that fractional delay sampling can destroy the high correlation between channels, leading to additional channel estimation errors during interpolation, cyclic shifting of subcarriers can avoid estimation errors during interpolation. The expressions for the cyclically shifted subcarriers include:

[0022] In the formula, This represents the modulo operation. This indicates the subcarrier number after the cyclic shift. This indicates the number of the first subcarrier. This indicates the number of the last subcarrier.

[0023] In an optional embodiment, the first preset diagonal of the channel matrix includes: the main diagonal of the channel matrix, a first upper diagonal, and a first lower diagonal; In step S2, for the subcarriers after cyclic shift, the minimum mean square error estimation is used to calculate the initial estimates of the three diagonal elements of the channel matrix at the pilot point: the main diagonal, the first upper diagonal, and the lower diagonal. Then, interpolation is performed to obtain all the initial estimates of these three diagonal elements in the channel matrix. The steps include: Let the subcarriers after the cyclic shift be numbered as The pilot subcarriers after cyclic displacement are numbered as follows: , Wherein, let the number of pilots in the OFDM symbol be... The spacing between pilots is , Can be Divisible , Represents the division symbol; Channel estimation is performed at all pilot points. The channel elements at each pilot point are estimated using a small mean square error method with the pilot subcarriers to obtain all channel estimation results. The estimated value of the channel element at that location and Then, all of them are obtained through spline interpolation. The estimated value of the channel element and ; The expression for the channel element at that location includes:

[0024]

[0025] In the formula, The channel matrix represents the first... Line 1, Page Estimated values ​​of channel elements in column 1. The channel matrix represents the first... Line number Estimated values ​​of channel elements in column 1. Indicates the conjugate of the pilot symbol. Represents the mathematical expectation. Represents the square of the absolute value. Indicates pilot symbol, Indicates noise power. Indicates the first One received symbol, Indicates the first One received symbol; all The estimated value of the channel element and This refers to the initial estimates of the main diagonal, the first upper diagonal, and the first lower diagonal of the channel matrix.

[0026] In an optional embodiment, the second preset diagonal of the channel matrix includes: a second upper diagonal and a second lower diagonal of the channel matrix; In step S3, Viterbi decoding is performed based on the estimated values ​​of the elements on the first preset diagonal of the channel matrix to obtain the initial estimated value of the transmitted signal. Then, using the input-output relationship of the pilot subcarriers, the interference of data signals near the pilot point on the received signal near the pilot point is subtracted. Based on the initial estimated value of the transmitted signal, the estimated values ​​of the elements on the second upper diagonal and the second lower diagonal at the pilot point are obtained using minimum mean square error estimation. After interpolation, these values ​​are merged with the channel elements obtained in S2 to obtain the estimated value of the initial channel matrix, completing the initial coarse channel estimation step. The steps of this process include: Based on the estimated values ​​of the elements on the first preset diagonal of the channel matrix and the input-output relationship of the pilot subcarriers, the initial estimated value of the transmitted signal is obtained using a surround-type time-varying Viterbi decoding algorithm. ,in, And the initial transmitted signal The estimated value of the nth subcarrier corresponds to the nth subcarrier in the channel matrix. The non-zero elements of the column; Based on the initial estimate ,for The channel matrix of the first Line number Channel elements of the column Perform minimum mean square error estimation to obtain The estimated value :

[0027] All are obtained through spline interpolation. The estimated value ; Corresponding estimated value That is, the estimated values ​​of the elements of the second upper diagonal and the second lower diagonal at the pilot point; The corresponding estimated values ​​of channel parameters , The channel matrix formed is the estimated value of the initial channel matrix.

[0028] In an optional embodiment, let the first In the iteration, based on the first The channel matrix estimate obtained in the second iteration is denoted as . , This represents the estimated value of the initial channel matrix; Step S4 includes: Using the encircling time-varying Viterbi decoding algorithm, the solution is obtained for the first... The estimated value of the transmitted signal in the next iteration ;in, And the first iteration of the transmitted signal The estimated value of the nth subcarrier corresponds to the nth subcarrier in the channel matrix. The non-zero elements of the column.

[0029] In an optional embodiment, step S5 includes: Let the pilot subcarriers after cyclic displacement be numbered as follows: , ,definition For the channel matrix The column vector consisting of the non-zero elements of the column, the th The residual of the next iteration Expressions, including: , , In the formula, This represents the column vector formed by the received signals near the pilot point. Indicates the first Distraction terms in the next iteration; in, The expressions include: , , In the formula, For the first Channel matrix estimate obtained in the next iteration For the first Channel matrix estimation obtained in the next iteration; The minimum mean square error estimate includes:

[0030] In the formula, for The autocorrelation matrix, for and The cross-correlation matrix; Representation matrix The Line number The elements of the column, where The expressions include:

[0031] In the formula, , Indicates the power of the pilot signal. Indicates noise power; Representation matrix The Line number The elements of the column, where ; The expressions include:

[0032] in Indicates the pilot transmit power. This represents the average power across all paths of the wireless channel. express and The cross-correlation function, whose expression includes:

[0033]

[0034] In the formula, For the maximum Doppler frequency shift, For the transmission subcarrier spacing, Indicates that the independent variable is The cosine function; Get , and ( After that, all can be obtained through spline interpolation. The estimated value of the corresponding channel is then combined to form the first... The next iteration yields an updated channel matrix estimate. .

[0035] In an alternative embodiment, when When, the simplified steps corresponding to steps S2~S5 include: In step S2, for the subcarriers after cyclic shift, channel estimation is performed at all pilot points. The minimum mean square error estimation of the channel elements at the pilot points is performed on the pilot subcarriers to obtain all... Channel elements at the location Then, all of them are obtained through spline interpolation. The estimated value of the main diagonal of the channel element Then use approximate conditions

[0036] Obtain the estimated values ​​of the first upper and lower diagonals. ,Will and The estimated value of the merged initial channel matrix Complete the initial coarse channel estimation step; when When, step S3 is omitted. In step S4, the estimated value based on the initial channel matrix is... The solution is obtained by using the encircling time-varying Viterbi decoding algorithm. Decoding signals in the initial stage of the next iteration , ,all The estimated value of the channel element The initial stage decoded signal That is, the first The estimated value of the signal transmitted by the transmitter in the next iteration; In step S5, the decoded signal is obtained. Afterwards, for According to the incremental model:

[0037]

[0038] Using the minimum variance unbiased estimation criterion, we obtain and , :

[0039]

[0040] in and Defined as

[0041]

[0042] get and The estimated values ​​of the first and second diagonals of the channel matrix are obtained by interpolation. The next iteration The estimated value of the main diagonal of the channel element Combining the results, we finally obtain the first... Estimation of the channel matrix of the order of magnitude

[0043] In an alternative embodiment, as proposed in Embodiment 2 and The specific implementation examples do not represent Other values ​​cannot be taken. However, since a beta of 2 can handle a Doppler frequency shift of 20,000 Hz, which is already quite large, we will not propose a larger Doppler frequency shift. The specific solution process for the case is as follows, but... The same applies to the situation. The solution steps, and Applicable The solution steps are also applicable. Simplified steps.

[0044] Example 2 This embodiment proposes a specific implementation example based on the windowed OFDM system in the time-varying frequency-selective fading channel and its iterative channel estimation and signal decoding method in Embodiment 1.

[0045] 1) The windowed OFDM system model is as follows: Consider an OFDM system with a cyclic prefix (CP). The time-varying frequency-selective fading channel is represented as follows: (1) This multipath channel model includes There are scattering path components, where the u-th path component corresponds to the complex channel coefficients. Doppler frequency shift and latency .

[0046] After inserting the pilot sequence into the quadrature amplitude modulation (QAM) data sequence, a structure is formed by... OFDM symbols composed of frequency domain signals can be represented as vectors. .

[0047] The input-output channel model is as follows: (2) The matrix form of the input-output relation (2) is as follows: (3) in: (4) (5) (6) matrix The The elements are .

[0048] 2.1) Pilot arrangement ( ): In this paper, subcarriers with inserted pilot signals are denoted as pilot subcarriers, and subcarriers with inserted data are denoted as data subcarriers. To reduce interference from data subcarriers to pilot subcarriers, subcarriers without data or pilot transmission are denoted as empty subcarriers.

[0049] when At that time, At that time, for The In pilot-based channel estimation, we should estimate the following: Parameters (7) In this paper, we recommend inserting only between the data and pilot subcarriers. Empty subcarriers. An iterative channel estimation and signal decoding scheme is employed to reduce interference on data subcarriers.

[0050] Since this paper considers that fractional delay will destroy the channel coefficient... and The high correlation between them, for This results in additional channel estimation errors during interpolation.

[0051] To solve this problem, we perform cyclic shifting of the subcarriers.

[0052] In an optional embodiment, a comb-shaped pilot arrangement is used. Let the number of pilots be... (in Can be Divisible The n'th symbol of the transmitted OFDM vector is: (8) in , Pilot symbol, This is QAM modulated data. Figure 1 Showing , , Example of pilot arrangement at time, such as Figure 2 As shown.

[0053] Initial coarse channel estimation ( ): 2.2) This section proposes an initial coarse channel estimation method. Due to the insertion of empty subcarriers, the input-output relationship at the pilot subcarrier can be expressed as: (9) in .

[0054] The input-output relationship at the empty subcarrier adjacent to the pilot subcarrier is as follows: (10) in According to the properties of the window function, when Time assumption Therefore, there is .

[0055] Based on this, an approximate expression is proposed: (11) Used for initial coarse channel estimation.

[0056] Based on input-output relationship: (12) The initial stage decoded signal is obtained by employing a surround-type time-varying Viterbi decoding algorithm. .

[0057] Assumption The decoding was correct, and the result was obtained. The minimum mean square error estimate can be obtained through spline interpolation. ( ).

[0058] 2.3) Iterative Channel Estimation and Signal Detection ( ): After completing the initial coarse channel estimation, it is noted that due to the existence of approximations, the channel estimation... and It contains interference terms. To obtain accurate estimates, this paper proposes an iterative channel estimation and signal decoding scheme.

[0059] In the In the next iteration ( The time-varying Viterbi decoding algorithm is used to obtain... ( ).

[0060] According to (2), we can obtain: (13) Assume the first Channel estimation obtained in the next iteration and the Sub-iteration decoding signal If correct, then: (14) get Minimum mean square error estimation .

[0061] The autocorrelation matrix is ​​derived below. and cross-correlation matrix The expression. The The item is: (15) in , express and Covariance function: (16) Pilot transmit power: (17) Substituting the expression for the channel element into (16), we get: (18) Assuming Doppler frequency shift It follows the Jakes spectral model: (19) in For the maximum Doppler frequency shift, for A uniformly distributed random variable on [a, b]. At this time: (20) This integral can be calculated using numerical methods.

[0062] Similarly, matrix The The item is: (twenty one) in .

[0063] Get , and ( After that, all can be obtained through spline interpolation. The corresponding estimated value.

[0064] Figure 3 A complete iterative channel estimation and signal decoding scheme is summarized.

[0065] 2.4) Iterative scheme when the normalized Doppler frequency shift exceeds 0.5 When the normalized Doppler frequency exceeds 0.5, the data subcarrier adjacent to the empty subcarrier will... or The estimation introduces strong interference. To obtain... and To achieve accurate estimation, this paper proposes inserting three empty subcarriers between the data and pilot subcarriers. Therefore, in the initial coarse channel estimation stage, an improved estimation formula is adopted: .(twenty two) 3) When Iterative channel estimation and signal detection schemes for different time periods: Under normal circumstances, when The design of the pilot arrangement, iterative channel estimation, and signal decoding scheme is similar to that in the previous section. However, we will demonstrate that using a raised cosine roll-off window function can further improve spectral efficiency.

[0066] The raised cosine roll-off window function with a roll-off factor of 1 is expressed as: (twenty three) in ,coefficient Used to ensure power normalization of the window function.

[0067] . (twenty four) Proposition 1: When At that time, the following conditions are met: (25) Where the approximation error and Proportional. And there is (26) The proof is in Appendix A.

[0068] 3.1) Pilot arrangement ( ): when If a pilot arrangement scheme similar to that in Section 4.2.1 is adopted, an empty subcarrier needs to be inserted on both the left and right sides of each pilot subcarrier.

[0069] For pilot subcarriers ( For adjacent subcarriers, we insert a repeating code. and ,in: (27) Therefore, two adjacent subcarriers carry only one data symbol. Furthermore, in the... Transmission on each pilot subcarrier: (28) Its power distribution satisfies: (29) (30) in This represents the transmit power of the data symbol. The input-output relationship at the pilot subcarrier can be simplified to: (31) At this point, the interference between adjacent subcarriers is completely canceled out.

[0070] therefore, In the pilot arrangement scheme of time, the first OFDM vector to be transmitted... The symbols are: (32) in . Figure 4 Showing , And Example of a comb-shaped pilot arrangement.

[0071] 3.2) Initial rough estimate ( ): Based on the pilot configuration scheme in the previous section, we propose an initial coarse channel estimation method. For the index... Channel parameters, channel matrix The minimum mean square error estimate for all diagonal elements is consistent with the previous description. The channel matrix can be obtained using spline interpolation. The estimated values ​​of all diagonal elements, i.e. ( ).

[0072] When using approximate conditions In this case, all can be obtained corresponding Estimated value.

[0073] 3.3) Iterative Channel Estimation and Signal Detection ): Because of the existence of channel relationships: (33) when At that time, the accuracy of channel estimation mainly depends on and The correctness of decoding, these signals It is estimated that strong interference will occur. Incorrect decoding will significantly degrade the performance. The estimated performance. Considering Use duplicate code protection. The iterative scheme for this time requires special design.

[0074] for Scenario, statistics show and The probability of simultaneous errors is much lower than that of a single error event. To limit the impact of decoding errors on channel estimation, a method is adopted... , and The separation estimation strategy.

[0075] In the In the next iteration ( The frequency-varying Viterbi decoding algorithm based on cyclic shift is used to obtain... ,in .

[0076] In terms of channel estimation, diagonal elements The estimate does not contain any interference terms, so it directly inherits the previous result: (34) Next, we will derive and Channel estimation methods. For subcarrier indexing , No. and The input-output relationship of the subcarrier can be expressed as: (35) In the In this iteration, we establish the following incremental model: (36) (37) According to the minimum variance unbiased estimation criterion, we obtain and The smallest unbiased estimator.

[0077] Depend on Available and The estimated values ​​were obtained, and all subcarrier positions were obtained through spline interpolation. of .based on Computable and And a complete channel estimate is obtained through spline interpolation. To reduce... or The impact of decoding errors, ultimately using the obtained ( The average of ) is used as the first The channel estimation results of the next iteration.

[0078] Figure 5 A complete iterative channel estimation and signal decoding scheme is summarized.

[0079] Appendix A: From equation (24), we can obtain (38) in (39) because (40) Therefore, we can obtain (41) and (42) Therefore, we obtain (43) Similarly, we can obtain (44) By combining equations (43) and (44), we can obtain (45) when Sometimes, (46) when At that time, the following approximate relationships also exist: (47) At this time, the approximation error and It is directly proportional, from which we can obtain equation (26).

[0080] Example 3 This embodiment presents the following specific implementation examples based on Embodiment 1 and Embodiment 2.

[0081] In this patent, we propose an iterative channel estimation and signal decoding joint scheme for windowed OFDM systems in time-varying frequency-selective fading channels, considering fractional Doppler shift and fractional time delay. The proposed iterative method aims to effectively suppress inter-carrier interference (ICI) caused by improved spectral efficiency. Simulation analysis shows that the improvement in spectral efficiency will lead to a moderate decrease in system performance within an acceptable range.

[0082] This section verifies the performance of the proposed iterative channel estimation and signal decoding scheme through simulation. The simulation uses the 3GPP standard TDL-A channel model, which defines the normalized delay and power of each scattering component. The time delay of each scattering component is generated by the following formula: (48) in ns represents the delay spread. Channel coefficients The power follows the definition, and the phase is in Uniform distribution. Fractional Doppler frequency. Calculated by equation (19). To demonstrate the fractional delay effect, an upsampling rate of 8 is used. The windowed OFDM system uses a raised cosine window with a roll-off factor of 1, and the modulation method is four-phase phase shift keying (i.e., 4-QAM), so the power transmitted per bit is... The remaining parameters are shown in Table I.

[0083]

[0084] Figure 6 and Figure 7 The maximum Doppler frequencies are shown respectively. Hz and Hz (at this time) Normalized Doppler frequency When the value is greater than 0.5, the convergence characteristics and frame error rate (FER) performance of the proposed iterative scheme (labeled as "iterative estimation scheme" in the figure) are analyzed. According to the design in Section 4.3, three empty subcarriers are inserted between the data and pilot subcarriers, using a total of... pilot and With empty subcarriers, the spectral efficiency is approximately: (49) Figure 6 The average channel estimate (MSE) after each iteration is given, and the calculation formula is as follows: (50) In contrast, the insertion between data and pilot signals is also given. The lower bound of MSE when there are empty subcarriers (completely eliminating data interference) is shown in the figure (labeled as "lower bound of channel estimation"). It can be seen that the proposed scheme converges after about 4 iterations, and the MSE after convergence is close to the theoretical lower bound.

[0085] Figure 7 The frame error rate performance of the proposed iterative scheme is compared with that of the "sufficiently spaced channel estimation" scheme. Based on a non-iterative decoding scheme (labeled as "sufficiently spaced channel estimation" in the figure), additional information is provided. Comparison of FER at Hz. The results show that the proposed scheme is comparable to the benchmark performance, and with increasing... Increasing the value can yield greater diversity gain.

[0086] Figure 8 and Figure 9 Show each Hz and 4 000 Hz (at this time) Normalized Doppler frequency Performance when <0.5). At this point, only two empty subcarriers need to be inserted, and the spectral efficiency is improved to: (51) Figure 8 Convergence graph of the proposed iterative scheme ( ),from Figure 8 As can be seen, our proposed scheme converges after approximately four iterations. The MSE performance achieved after convergence is close to the corresponding lower bound of channel estimation.

[0087] Figure 9 The frame error rate performance of the proposed iterative scheme is compared with that of the "sufficiently spaced channel estimation" scheme. ), Figure 9 Additional displays in The FER performance at Hz is shown for a more comprehensive explanation. It can be seen that the FER achieved by the proposed scheme is almost identical to the baseline scheme of "sufficiently spaced channel estimation".

[0088] Figure 10 and Figure 11 They were shown respectively Hz, 1 500 Hz and 1 000 Hz (at this time) The convergence characteristics and FER performance of the scheme are analyzed. Based on the design in Section IV, we insert a repeating code subcarrier between the data and pilot subcarriers. The spectral efficiency is then approximately: (52) Figure 10 The convergence graph of the proposed iterative scheme is shown. ), Figure 10 This indicates that, with As the MSE of the proposed scheme decreases, the gap between the MSE and the lower bound of the channel estimation gradually narrows.

[0089] Figure 11 Comparison of frame error rate performance between the proposed iterative scheme and the "sufficiently spaced channel estimation" scheme. ) Figure 11 This shows that due to interference introduced by the repetitive data subcarrier, when FER is... At that time, the proposed scheme performed about 1-2 dB worse than the "sufficiently spaced channel estimation" scheme. It should be noted that the "sufficiently spaced channel estimation" scheme requires inserting data between the data and pilot signals. With empty subcarriers to completely eliminate interference, the spectral efficiency is: (53) The proposed solution trades 1-2 dB of performance loss for improved performance. Improved spectral efficiency.

Claims

1. A windowed OFDM system for time-varying frequency-selective fading channels, characterized in that, include: Transmitter and receiver; The transmitter is used for: Inserting the pilot sequence into the quadrature amplitude modulation data sequence constitutes a sequence consisting of... OFDM symbols composed of frequency domain signals; Make OFDM symbols pass through The point-based discrete Fourier inverse transform converts the signal into a transmitted signal. The transmitted signal is windowed using a time-domain window function; Add a cyclic prefix to obtain the final transmitted signal; The final transmitted signal is transmitted to the receiving end through a time-varying frequency-selective fading channel; The receiving end is used for: Receive the transmitted signal from the transmitter; Remove the cyclic prefix from the received signal, and through The frequency domain received signal is obtained by point-discrete Fourier transform demodulation; Windowing operations based on time-domain window functions transform the frequency-domain received signal into a process that limits inter-carrier interference. The simplified form within the subcarrier range, where, It is a positive integer; The input-output relationship of the pilot subcarrier is obtained based on the simplified form of the frequency domain received signal; Channel estimation and signal decoding are performed based on the input-output relationship of pilot subcarriers.

2. The windowed OFDM system in a time-varying frequency-selective fading channel according to claim 1, characterized in that, The OFDM symbol includes pilot subcarriers and data subcarriers; Let the pilot subcarrier and the data subcarrier be collectively referred to as subcarriers; To eliminate interference from the data subcarriers, the transmitting end inserts a preset number of empty subcarriers between the data subcarriers and the pilot subcarriers based on the input-output relationship between the transmitted and received signals at the pilot. This preset number is adjusted according to the magnitude of the Doppler frequency shift and is an even number. Half of the preset number of empty subcarriers are on the left side of the pilot subcarriers, and the remaining empty subcarriers are on the right side of the pilot subcarriers.

3. The windowed OFDM system in a time-varying frequency-selective fading channel according to claim 1 or 2, characterized in that, The simplified form of the frequency domain received signal includes: In the formula, This indicates that inter-carrier interference is limited to Frequency domain received signal within the subcarrier range Indicates the number of the subcarrier of the received signal in the frequency domain; Indicates the first The first subcarrier Individual frequency domain channel response; Indicates the first The frequency domain signal corresponding to each subcarrier; This indicates that the mean is zero and the power spectral density is Gaussian noise in the frequency domain; Indicates the total number of scattering path components; , and They represent the first The complex channel coefficients, Doppler frequency shift, and time delay corresponding to each path component; Represents the time-domain window function Point-based discrete Fourier transform; Indicates the subcarrier spacing; Represents the natural constant; It represents the imaginary unit.

4. An iterative channel estimation and signal decoding method for a windowed OFDM system in a time-varying frequency-selective fading channel, characterized in that, The steps of channel estimation and signal decoding at the receiving end based on the input-output relationship of pilot subcarriers include: S1: Cyclic shift of the subcarriers in the transmitted signal from the transmitter; S2: For the subcarriers after cyclic shift, calculate the estimated values ​​of the elements on the first preset diagonal of the channel matrix based on the minimum mean square error estimation and interpolation method; S3: Obtain the initial estimate of the transmitted signal by Viterbi decoding based on the estimated values ​​of the elements on the first preset diagonal of the channel matrix; based on the initial estimate of the transmitted signal, obtain the estimated values ​​of the elements on the second preset diagonal of the channel matrix using the minimum mean square error estimation and interpolation method; combine the estimated values ​​of the elements obtained in this step with the estimated values ​​of the elements obtained in step S2 to obtain the estimated value of the initial channel matrix. S4: Perform Viterbi decoding using the estimated value of the initial channel matrix to update the estimated value of the signal transmitted by the transmitter; S5: Based on the estimated value of the transmitted signal obtained in step S4, the estimated value of the channel matrix is ​​updated using the residual to perform minimum mean square error estimation. S6: Iterate and repeat steps S4 and S5 until the transmitted signal estimate obtained in the current iteration is equal to the transmitted signal estimate obtained in the previous iteration. Stop the iteration, obtain the final estimate of the channel matrix and the final transmitted signal estimate, and complete the iterative channel estimation.

5. The iterative channel estimation and signal decoding method for a windowed OFDM system in a time-varying frequency-selective fading channel according to claim 4, characterized in that, Step S1 includes: Considering that fractional delays disrupt the high correlation between channels, leading to additional channel estimation errors during interpolation, cyclic shifting of subcarriers can avoid estimation errors during interpolation. The expressions for the cyclically shifted subcarriers include: In the formula, This represents the modulo operation. This indicates the subcarrier number after the cyclic shift. This indicates the number of the first subcarrier. This indicates the number of the last subcarrier.

6. The iterative channel estimation and signal decoding method for a windowed OFDM system in a time-varying frequency-selective fading channel according to claim 4, characterized in that, The first preset diagonal of the channel matrix includes: the main diagonal of the channel matrix, the first upper diagonal, and the first lower diagonal; In step S2, for the subcarriers after cyclic shift, the minimum mean square error estimation is used to calculate the initial estimates of the three diagonal elements of the channel matrix at the pilot point: the main diagonal, the first upper diagonal, and the lower diagonal. Then, interpolation is performed to obtain all the initial estimates of these three diagonal elements in the channel matrix. The steps include: Let the subcarriers after the cyclic shift be numbered as The pilot subcarriers after cyclic displacement are numbered as follows: , Wherein, let the number of pilots in the OFDM symbol be... The spacing between pilots is , Can be Divisible , Represents the division symbol; Channel estimation is performed at all pilot points. The channel elements at each pilot point are estimated using a small mean square error method with the pilot subcarriers to obtain all channel estimation results. The estimated value of the channel element at that location and Then, all of them are obtained through spline interpolation. The estimated value of the channel element and ; The expression for the channel element at that location includes: In the formula, The channel matrix represents the first... Line 1, Page Estimated values ​​of channel elements in column 1. The channel matrix represents the first... Line 1 Estimated values ​​of channel elements in column 1. Indicates the conjugate of pilot symbols, Represents the mathematical expectation. Represents the square of the absolute value. Indicates pilot symbol, Indicates noise power. Indicates the first One received symbol, Indicates the first One received symbol; all The estimated value of the channel element and This refers to the initial estimates of the main diagonal, the first upper diagonal, and the first lower diagonal of the channel matrix.

7. The iterative channel estimation and signal decoding method for a windowed OFDM system in a time-varying frequency-selective fading channel according to claim 4, characterized in that, The second preset diagonal of the channel matrix includes: the second upper diagonal and the second lower diagonal of the channel matrix; In step S3, Viterbi decoding is performed based on the estimated values ​​of the elements on the first preset diagonal of the channel matrix to obtain the initial estimated value of the transmitted signal. Then, using the input-output relationship of the pilot subcarriers, the interference of data signals near the pilot point on the received signal near the pilot point is subtracted. Based on the initial estimated value of the transmitted signal, the estimated values ​​of the elements on the second upper diagonal and the second lower diagonal at the pilot point are obtained using minimum mean square error estimation. After interpolation, these values ​​are merged with the channel elements obtained in S2 to obtain the estimated value of the initial channel matrix, completing the initial coarse channel estimation step. The steps of this process include: Based on the estimated values ​​of the elements on the first preset diagonal of the channel matrix and the input-output relationship of the pilot subcarriers, the initial estimated value of the transmitted signal is obtained using a surround-type time-varying Viterbi decoding algorithm. ,in, And the initial transmitted signal The estimated value of the nth subcarrier corresponds to the nth subcarrier in the channel matrix. The non-zero elements of the column; Based on the initial estimate ,for The channel matrix of the first Line 1 Channel elements of the column Perform minimum mean square error estimation to obtain The estimated value : All are obtained through spline interpolation. The estimated value ; Corresponding estimated value That is, the estimated values ​​of the elements of the second upper diagonal and the second lower diagonal at the pilot point; The corresponding estimated values ​​of channel parameters , The channel matrix formed is the estimated value of the initial channel matrix.

8. The iterative channel estimation and signal decoding method for a windowed OFDM system in a time-varying frequency-selective fading channel according to claim 4, characterized in that, Let the first In the iteration, based on the first The channel matrix estimate obtained in the second iteration is denoted as . , This represents the estimated value of the initial channel matrix; Step S4 includes: Using the encircling time-varying Viterbi decoding algorithm, the solution is obtained for the first... The estimated value of the transmitted signal in the next iteration ;in, And the first iteration of the transmitted signal The estimated value of the nth subcarrier corresponds to the nth subcarrier in the channel matrix. The non-zero elements of the column.

9. The iterative channel estimation and signal decoding method for a windowed OFDM system in a time-varying frequency-selective fading channel according to claim 4, characterized in that, The S5 steps include: Let the pilot subcarriers after cyclic displacement be numbered as follows: , ,definition For the channel matrix The column vector consisting of the non-zero elements of the column, the th The residual of the next iteration Expressions, including: ， ， In the formula, This represents the column vector formed by the received signals near the pilot point. Indicates the first Distraction terms in the next iteration; in, The expressions include: ， ， In the formula, For the first Channel matrix estimate obtained in the next iteration For the first Channel matrix estimation obtained in the next iteration; The minimum mean square error estimate includes: In the formula, for The autocorrelation matrix, for and The cross-correlation matrix; Representation matrix The Line 1 The elements of the column, where The expressions include: In the formula, , Indicates the power of the pilot signal. Indicates noise power; Representation matrix The Line 1 The elements of the column, where ; The expressions include: in Indicates the pilot transmit power. This represents the average power across all paths of the wireless channel. express and The cross-correlation function, whose expression includes: In the formula, For the maximum Doppler frequency shift, For the transmission subcarrier spacing, Indicates that the independent variable is The cosine function; Get , and ( After that, all can be obtained through spline interpolation. The estimated value of the corresponding channel is then combined to form the first... The next iteration yields an updated channel matrix estimate. .

10. The iterative channel estimation and signal decoding method for a windowed OFDM system in a time-varying frequency-selective fading channel according to any one of claims 4 to 9, characterized in that, when When, the simplified steps corresponding to steps S2~S5 include: In step S2, for the cyclically shifted subcarriers, channel estimation is performed at all pilot points. The minimum mean square error estimation of the channel elements at the pilot points is performed on the pilot subcarriers to obtain all... Channel elements at the location Then, all of them are obtained through spline interpolation. The estimated value of the main diagonal of the channel element Then use approximate conditions Obtain the estimated values ​​of the first upper and lower diagonals. ,Will and The estimated value of the merged initial channel matrix Complete the initial coarse channel estimation step; when When, step S3 is omitted. In step S4, the estimated value based on the initial channel matrix is... The solution is obtained by using the encircling time-varying Viterbi decoding algorithm. Decoding signals in the initial stage of the next iteration , ,all The estimated value of the channel element The initial stage decoded signal That is, the first The estimated value of the signal transmitted by the transmitter in the next iteration; In step S5, the decoded signal is obtained. Afterwards, for According to the incremental model: Using the minimum variance unbiased estimation criterion, we obtain and , : in and Defined as get and The estimated values ​​of the first and second diagonals of the channel matrix are obtained by interpolation. The next iteration The estimated value of the main diagonal of the channel element Combining the results, we finally obtain the first... Estimation of the channel matrix of the order of magnitude .

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