A peak-to-average ratio suppression method for precoded DFT spread spectrum OTFS system

Abstract

The invention discloses a method for suppressing peak-to-average ratio of a precoded DFT spread spectrum OTFS system, and relates to the technical field of wireless communication. The method comprises the following steps: step 1, performing precoding matrix processing on modulated input data, and obtaining precoded data by using the coefficients of the corresponding precoding matrix as the least square solution; step 2, performing DFT spread spectrum processing on the precoded data to obtain spread spectrum data; step 3, performing subcarrier mapping on the spread spectrum data, and distributing the subcarrier mapped data to a two-dimensional grid to obtain DD domain data; step 4, performing inverse discrete Zak transform on the DD domain data to obtain a time domain signal. The invention effectively reduces the peak-to-average power ratio of the system through corresponding design, thereby reducing system complexity and cost.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a peak-to-average ratio suppression method for a precoded DFT spread spectrum OTFS system. Background Art

[0002] Low Earth Orbit (LEO) satellites and their communication systems have become key components in building the sixth generation mobile communication (6G) network due to their advantages such as low launch cost, short communication delay, low transmission loss, and global coverage after networking. However, this system also faces many challenges, among which the high speed of satellites relative to the ground leads to large Doppler shift and fast changes in channel characteristics. In 2017, the orthogonal time-frequency-space (OTFS) modulation technology proposed by Hadani et al. brought hope to solving these problems. By introducing the concept of delay-Doppler domain, OTFS converts the time-frequency dual-selective channel in high dynamic scenarios into a sparse slowly varying channel in the delay-Doppler domain, significantly enhancing the robustness of the system and making it an ideal choice for low earth orbit satellite communication scenarios.

[0003] Compared with traditional orthogonal frequency division multiplexing (OFDM) modulation, OTFS modulation performs better in peak-to-average power ratio (PAPR) performance. However, in practical applications, when the number of OTFS symbols is large, the high PAPR problem still exists. Especially in low-orbit satellite communication systems, the battery capacity of mobile terminals is limited, and improving the efficiency of power amplifiers becomes the key, so the sensitivity to the PAPR problem is extremely high. At present, one of the research focuses of industry and academia is the OTFS system PAPR suppression technology (DZT-OTFS) based on discrete Zak transform (DZT) in one step, in order to break through the limitations of existing technologies.

[0004] The existing peak-to-average ratio suppression methods for OTFS systems based on two-step conversion have many shortcomings. First, although traditional methods such as limiting method, selective mapping method (SLM), partial transmission sequence method (PTS) and coding methods can reduce the peak-to-average ratio to a certain extent, they all have their own disadvantages. The limiting method is prone to cause signal distortion and affect system performance; the SLM and PTS methods will increase system overhead and computational complexity. Secondly, for the linear segmented compression and expansion scheme of the OTFS system implemented by the traditional two-step conversion, although the medium-amplitude signal is not compressed and expanded when compressing the large-amplitude signal to reduce the distortion effect, it still cannot completely avoid signal distortion, and this method relies on the statistical characteristics of the modulated signal and has poor adaptability. Furthermore, although the selective mapping method based on the particle swarm optimization algorithm does not introduce signal distortion, the computational complexity is extremely high, which is not conducive to practical engineering applications. Finally, although the peak-to-average ratio suppression method using discrete Fourier transform (DFT) spread spectrum technology has low computational complexity and does not introduce signal distortion, its suppression ability is limited and can only achieve a suppression amount of 1~2dB.

[0005] Low-orbit satellite communication systems play an important role in the construction of 6G networks. OTFS modulation technology provides strong support for its development, but it still faces many challenges in peak-to-average ratio suppression. The existing OTFS system peak-to-average ratio suppression methods based on two-step conversion have their own advantages and disadvantages, but all have problems to varying degrees, and it is difficult to meet the needs of low-orbit satellite communication systems for high-efficiency, low-complexity, and low-distortion peak-to-average ratio suppression technology. Therefore, exploring the OTFS system peak-to-average ratio suppression technology based on DZT one-step implementation is of great significance to promote the development of low-orbit satellite communication technology. Summary of the invention

[0006] The object of the present invention is to provide a method for suppressing peak-to-average ratio of a precoded DFT spread spectrum OTFS system to solve at least one of the above problems.

[0007] The present invention is achieved through the following technical solutions:

[0008] A method for suppressing peak-to-average ratio of a precoded DFT spread spectrum OTFS system is implemented by the following steps:

[0009] Step 1, performing precoding matrix processing on the modulated input data, and obtaining precoded data through the least square solution of the corresponding precoding matrix;

[0010] Step 2: Perform DFT spread spectrum processing on the precoded data to obtain spread spectrum data; spread the precoded data through discrete Fourier transform (DFT) to increase the signal's anti-interference ability and spectrum utilization rate;

[0011] Step 3: Perform subcarrier mapping on the spread spectrum data and assign the subcarrier mapped data to The DD domain data is obtained in the two-dimensional grid of FIG. 1 ; the spread spectrum data is mapped to a specific subcarrier for transmission in the frequency domain;

[0012] Step 4: Perform inverse discrete Zak transform on the DD domain data to obtain the time domain signal; obtain DD domain (time-frequency domain) data to prepare for subsequent operations.

[0013] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0014] 1. The present invention significantly reduces the peak-to-average power ratio (PAPR) of the system by introducing precoding technology, combining DFT spread spectrum and DZT-OTFS modulation. The traditional OTFS system uses inverse symplectic finite Fourier transform (ISFFT) and Heisenberg transform (HT) in the modulation process. Although it can realize modulation in the delay-Doppler domain, its PAPR value is relatively high, resulting in extremely high linearity requirements for the power amplifier in the system, which increases the complexity and cost of hardware implementation. The present invention adds special precoding processing on the basis of DFT spread spectrum, so that the OTFS modulation output is approximately a repetition of the modulation input data, thereby giving the modulated signal the characteristics of single carrier modulation. This characteristic significantly reduces the peak power of the signal while maintaining the integrity of the signal, avoiding the signal distortion problem caused by excessive PAPR in traditional methods. In addition, the present invention uses inverse discrete Zak transform (IDZT) to replace traditional ISFFT and HT, which further simplifies the modulation process and reduces the computational complexity. Experimental results show that this method can effectively suppress PAPR under different modulation modes (such as 4-QAM, 16-QAM and 64-QAM), especially under high-order modulation (such as 64-QAM), the improvement effect of PAPR is more significant. This low PAPR characteristic makes the present invention particularly suitable for application in the mobile phone direct connection low-orbit satellite OTFS communication system, which can significantly improve the power efficiency and transmission reliability of the system;

[0015] 2. The present invention not only reduces the PAPR but also significantly simplifies the implementation complexity of the system by combining precoding and centralized DFT spread spectrum. The traditional OTFS system adopts ISFFT and HT implemented in two steps, which has high computational complexity. Especially in large-scale multi-user scenarios, the real-time performance and resource consumption of the system become bottlenecks. The present invention simplifies the complex modulation process into linear matrix operations and discrete transformations by introducing precoding matrix and IDZT transformation, which greatly reduces the computational complexity. Specifically, the precoding matrix is ​​solved by the least squares method, which can optimize the modulation output without introducing additional complexity. In addition, compared with the distributed DFT spread spectrum, the centralized DFT spread spectrum method has stronger anti-frequency deviation capability, avoids the problem of inter-subcarrier interference caused by frequency offset, thereby reducing the demand for protection bandwidth, and further reducing the difficulty of system implementation and resource consumption. In the uplink of low-orbit satellite communication, the present invention efficiently maps the signals of multiple users into the delay-Doppler domain grid through frequency division multiple access (FDMA) technology, and completes the modulation through IDZT transformation. This design not only simplifies the signal processing process, but also improves the flexibility and scalability of the system, and is suitable for complex communication scenarios with multiple users and multiple carriers. Experimental results show that the present invention significantly reduces the implementation complexity of the system while ensuring the PAPR suppression effect, and has high engineering practicality and promotion value. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0017] Figure 1 The overall schematic diagram of the precoded DFT spread spectrum OTFS system;

[0018] Figure 2 Schematic diagram of the peak-to-average ratio suppression method of the precoded DFT spread spectrum OTFS system in this embodiment;

[0019] Figure 3 This is a schematic diagram of centralized DFT spread spectrum OTFS modulation based on precoding in this embodiment;

[0020] Figure 4 This is a block diagram of the DFT spread spectrum OTFS implementation of uplink precoding in this embodiment;

[0021] Figure 5 This is a schematic diagram of PAPR performance analysis using the Pre-DFT-S-OTFS method to simulate 4-QAM in this embodiment;

[0022] Figure 6 This is a schematic diagram of PAPR performance analysis using the Pre-DFT-S-OTFS method to simulate 16-QAM in this embodiment;

[0023] Figure 7 This is a schematic diagram of PAPR performance analysis of 64-QAM simulated by the Pre-DFT-S-OTFS method in this embodiment. DETAILED DESCRIPTION

[0024] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0025] This embodiment relates to a method for suppressing the peak-to-average ratio of a precoded DFT spread spectrum OTFS system. The method aims to solve the problem that the centralized DFT spread spectrum improves the PAPR of the OTFS system in two steps and has high complexity. According to the present invention, a method for suppressing the peak-to-average ratio of a precoded DFT spread spectrum OTFS (more specifically, DZT-OTFS) system is proposed (see Figure 1). The method for suppressing the peak-to-average power ratio (PAPR) of the precoded DFT spread spectrum OTFS system described in the embodiment has significant advantages in design and implementation. First, the method effectively solves the problem of excessively high PAPR in the traditional OTFS system by introducing precoding technology, combining DFT spread spectrum and inverse discrete Zak transform (IDZT). The traditional OTFS system uses inverse symplectic finite Fourier transform (ISFFT) and Heisenberg transform (HT) in the modulation process. Although it can realize modulation in the delay-Doppler domain, its PAPR value is relatively high, resulting in extremely high linearity requirements for the power amplifier in the system, which increases the complexity and cost of hardware implementation. The method described in the embodiment adds specific precoding processing on the basis of DFT spread spectrum, so that the OTFS modulation output is approximately a repetition of the modulation input data, thereby giving the modulated signal the characteristics of single carrier modulation. This characteristic significantly reduces the peak power of the signal while maintaining the integrity of the signal, avoiding the signal distortion problem caused by excessively high PAPR in the traditional method. In addition, the method described in the embodiment uses IDZT to replace the traditional ISFFT and HT, further simplifying the modulation process and reducing the computational complexity. Experimental results show that this method can effectively suppress PAPR under different modulation modes (such as 4-QAM, 16-QAM and 64-QAM), especially under high-order modulation (such as 64-QAM), the improvement effect of PAPR is more significant. This low PAPR characteristic makes the present invention particularly suitable for application in the mobile phone direct connection low-orbit satellite OTFS communication system, which can significantly improve the power efficiency and transmission reliability of the system.

[0026] In addition, the method described in this embodiment not only reduces the PAPR but also significantly simplifies the implementation complexity of the system by combining precoding and centralized DFT spread spectrum. The traditional OTFS system uses ISFFT and HT implemented in two steps, which has high computational complexity, especially in large-scale multi-user scenarios, the real-time performance and resource consumption of the system become bottlenecks. The present invention simplifies the complex modulation process into linear matrix operations and discrete transformations by introducing precoding matrix and IDZT transformation, which greatly reduces the computational complexity. Specifically, the precoding matrix is ​​solved by the least squares method, which can optimize the modulation output without introducing additional complexity. In addition, compared with the distributed DFT spread spectrum, the centralized DFT spread spectrum method has stronger anti-frequency deviation capability, avoids the problem of inter-subcarrier interference caused by frequency offset, thereby reducing the demand for protection bandwidth, and further reducing the difficulty of system implementation and resource consumption. In the uplink of low-orbit satellite communication, the present invention efficiently maps the signals of multiple users into the delay-Doppler domain grid through frequency division multiple access (FDMA) technology, and completes the modulation through IDZT transformation. This design not only simplifies the signal processing process, but also improves the flexibility and scalability of the system, and is suitable for complex communication scenarios with multiple users and multiple carriers. Experimental results show that the present invention significantly reduces the implementation complexity of the system while ensuring the PAPR suppression effect. This embodiment not only effectively suppresses the PAPR of the OTFS system through the combination of precoding and centralized DFT spread spectrum, but also significantly reduces the implementation complexity of the system, and has high engineering practicality and promotion value. This method is particularly suitable for low-orbit satellite communication systems, and can significantly improve the power efficiency and transmission reliability of the system, providing strong support for the development of the network.

[0027] Specifically, the signal processing flow of the peak-to-average ratio suppression method of the precoded DFT spread spectrum DZT-OTFS system (see Figure 2 )as follows:

[0028] (1) The following is expressed in matrix form, and the modulated input data input is recorded as , , for The modulation alphabet set matrix, For modulation letters, and Represents the number of rows and columns of the matrix respectively (in other matrices later, if similar to this is used The expression is different, but the symbols are different, which also indicates the corresponding number of rows and columns, which will not be repeated in the following text).

[0029] (2) The calculation process of precoding is as follows. The precoding modulation matrix set for the modulated input data is recorded as , its general form can be expressed as formula A1:

[0030] (A1)

[0031] In formula A1, for A two-dimensional matrix with each row having 1 consecutive "1", the rest of the data is "0", is a positive integer greater than or equal to 2. If the precoding matrix is ​​used express, , since it is aimed at the centralized subcarrier mapping method, the actual modulation matrix It can be expressed as formula A2:

[0032] (A2)

[0033] in, for The matrix of the point DFT transform, is the subcarrier mapping matrix in precoding, for The Hermitian matrix of the point IDFT transform, is a general modulation matrix;

[0034] make , which is the modulation matrix when centralized subcarrier mapping is adopted, , then we have formula A3:

[0035] (A3)

[0036] Establish the matrix equation, let , we can get formula A4:

[0037] (A4)

[0038] In formula A4, and are matrices with known coefficients. Therefore, the matrix can be calculated by solving the equation The coefficient of . Through calculation, we know that the matrix is a full row rank matrix, so there exists a right inverse matrix , , so that , where Further analysis shows that the matrix equation shown in Formula A4 does not have an exact solution, but there is a least squares solution, which can be expressed as Formula A5:

[0039] (A5)

[0040] The least squares solution As the coefficients of the precoding matrix, the input data is precoded so that the modulated output is approximately a repetition of the modulated input data.

[0041] (3) The pre-coded data is , and then perform Point DFT processing, get , , we have formula A6:

[0042] (A6)

[0043] In formula A6, for The matrix of the point DFT transform.

[0044] (4) Check again Perform subcarrier mapping. The subcarrier mapping method is as follows: Figure 3 Mapping in a centralized manner. The data in is mapped to The mapped DD domain data is obtained in the two-dimensional matrix , , we get formula A7:

[0045] (A7)

[0046] In formula A7: is the subcarrier mapping matrix after precoding, .

[0047] (5) Allocate the data after the centralized subcarrier mapping to In the two-dimensional grid of Indicates; each column in the grid is an OTFS sub-symbol, and the data in the grid is represented by Indicates. Among them, is the number of grids in the delay domain; is the number of Doppler domain grids, and also the number of OTFS sub-symbols; is the delay domain grid index, ; is the Doppler domain grid index, Then Perform IDZT transformation to obtain the time domain signal , , we get formula A8:

[0048] (A8)

[0049] In formula A8: for The Hermitian matrix of the point IDFT transform. Formula A9:

[0050] (A9)

[0051] In formula A9: The modulated output It can be expressed as formula A10:

[0052] (A10)

[0053] From formula A10, we can see that the PAPR suppression method of DFT spread spectrum DZT-OTFS system based on precoding is equivalent to converting the input data Through a modulation matrix Modulation, by introducing specific precoding, makes the output of the inverse discrete Fourier transform (IDFT) For input data Repetition (such as Figure 3 The schematic diagram of each row data processing in the centralized DFT spread spectrum DZT-OTFS modulation based on precoding is given, where ).

[0054] It should be noted that in discrete Fourier transform (DFT) spread spectrum, there are two subcarrier mapping methods: distributed (Distributed FDMA, DFDMA) and centralized (Localized FDMA, LFDMA). DFDMA is to map the frequency domain data output by DFT to distributed subcarriers, and the commonly used method is uniform distribution. LFDMA is to map the frequency domain data output by DFT to continuous subcarriers. In distributed subcarrier mapping, the subcarriers of the same user are arranged at intervals; while in centralized subcarrier mapping, the subcarriers of the same user are arranged continuously. Although precoded distributed DFT spread spectrum has obvious effects on improving PAPR, once the subcarriers are offset in the frequency domain, interference will be formed between the subcarriers of different users, so additional protection bandwidth is required. Precoded centralized DFT spread spectrum is not easily affected by frequency offset and is easy to implement in engineering. Therefore, it is used in the uplink of the low-orbit satellite DZT-OTFS system. The scheme proposed in the present invention mainly uses centralized DFT spread spectrum based on precoding. When performing subcarrier mapping, the subcarrier mapping method is centralized mapping.

[0055] It has a strong ability to resist frequency deviation, can effectively avoid the problem of inter-subcarrier interference caused by frequency offset, and reduce the demand for protection bandwidth, thereby reducing the difficulty of system implementation and resource consumption. In addition, centralized DFT spread spectrum is easier to implement in engineering, simplifies the signal processing process, and improves the flexibility and scalability of the system. In addition, the introduction of precoding technology further reduces the peak-to-average power ratio (PAPR) of the system, reduces signal distortion, and improves the power efficiency and transmission reliability of the system. Therefore, precoded centralized DFT spread spectrum is particularly suitable for low-orbit satellite communication systems.

[0056] In the uplink of the OTFS system of low-orbit satellite communication, Users use frequency division multiplexing to multiplex the wireless channel, and the number of subcarriers allocated to each user is The total number of subcarriers is , Each user can send This is an information symbol. Information symbols are placed in M×Q In the two-dimensional grid, then for each row The data is pre-coded and Click DFT, the data after DFT is placed continuously in rows Finally, the data of the delay-Doppler grid is IDZTed to complete the OTFS modulation (see Figure 4 ). In the figure, grids of the same format are grouped together and are processed in the same way; the light-colored grids are the remaining subcarriers that do not transmit data, which are filled with zeros; by using frequency division multiple access (FDMA) technology in the uplink of the low-orbit satellite communication OTFS system, the signals of multiple users are efficiently mapped to the delay-Doppler domain grid, and the modulation is completed through the IDZT transformation, which has significant advantages and benefits. First, through precoding and DFT spread spectrum processing, the peak-to-average power ratio (PAPR) of the signal is effectively suppressed, which reduces the linearity requirements of the system on the power amplifier and reduces the complexity and cost of hardware implementation. Secondly, the centralized DFT spread spectrum method has a strong ability to resist frequency deviation, avoids the problem of inter-subcarrier interference caused by frequency offset, reduces the demand for protection bandwidth, and further reduces the difficulty of system implementation and resource consumption. In addition, the data of multiple users are continuously placed in the delay-Doppler grid by row, and the modulation is completed through the IDZT transformation, which simplifies the signal processing process, improves the flexibility and scalability of the system, and is suitable for complex communication scenarios with multiple users and multiple carriers. This design not only significantly improves the system's power efficiency and transmission reliability, but also reduces computational complexity.

[0057] In wireless communication systems, the complementary cumulative distribution function (CCDF) is usually used to represent the statistical characteristics of the system PAPR. The present invention also uses CCDF to evaluate the improvement of the DFT spread spectrum on the PAPR of the DZT-OTFS system. In order to study the influence of the modulation mode on the PAPR, the present invention simulates the PAPR suppression performance of the three modulation modes of 4-QAM, 16-QAM and 64-QAM by the Pre-DFT-S-OTFS method (see Figures 5 to 7 ), experimental results show that the present invention can effectively suppress PAPR under different modulation modes (such as 4-QAM, 16-QAM and 64-QAM), especially under high-order modulation (such as 64-QAM), the improvement effect of PAPR is more significant. This low PAPR characteristic makes the present invention particularly suitable for application in low-orbit satellite communication systems, which can significantly improve the power efficiency and transmission reliability of the system, while reducing the complexity and cost of hardware implementation.

[0058] In addition, the symbols in the drawings are explained as follows:

[0059] exist Figure 1 middle, is the input modulation signal, i.e. the modulated input data. is the modulated signal after precoding, is the modulated signal after Q-point DFT spreading, is the modulation data after centralized subcarrier mapping, is the time domain signal matrix obtained after IDZT transformation, is the received signal after passing through the channel, is the DD domain demodulated signal after DZT transformation, is the demodulated signal after subcarrier mapping, The demodulated signal after Q point IDFT is: is the demodulated signal after inverse precoding processing; Figure 4 middle, Users ( arrive )and( arrive ) is a one-to-one mapping relationship. Figure 5 In the middle, the horizontal axis is Uplink PAPR 0 [dB] for 4-QAM represents the peak-to-average power ratio of the uplink under 4QAM modulation mode, and the vertical axis Pr (PAPR>PAPR 0) represents the complementary cumulative distribution function, that is, the probability that the PAPR value exceeds the threshold value; OTFS represents orthogonal time-frequency-space modulation, DFT-S-OTFS represents discrete Fourier transform extended OTFS, and Pre-DFT-S-OTFS represents pre-processed DFT extended OTFS; Figure 6 and Figure 7 The horizontal axis and Figure 5 Similar, no further description is given here.

[0060] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for suppressing peak-to-average ratio of a precoded DFT spread spectrum OTFS system, characterized in that: The following steps are involved: Step 1, performing precoding matrix processing on the modulated input data, and obtaining precoded data through the least square solution of the corresponding precoding matrix; Step 2: Perform DFT spread spectrum processing on the precoded data to obtain spread spectrum data; Step 3: Subcarrier map the spread spectrum data and assign the subcarrier mapped data to In the two-dimensional grid, DD domain data is obtained; Step 4: Perform inverse discrete Zak transform on the DD domain data to obtain the time domain signal; Among them, in step 1, the corresponding precoding matrix is ​​recorded as , , express The modulation letter set matrix, the least squares solution of the corresponding precoding matrix is ​​recorded as , then the least squares solution It is obtained by solving the following matrix equation: ； In the formula, The precoding modulation matrix set for modulating input data has each row 1 consecutive "1", the rest of the data is "0", is a positive integer greater than or equal to 2, and its general form is: ； matrix is the modulation matrix when centralized subcarrier mapping is adopted, which satisfies: ,in, for The matrix of the point DFT transform, is the subcarrier mapping matrix in precoding, for The Hermitian matrix of the point IDFT transform; The least squares solution Can be expressed as: ， Among them, the matrix For the matrix The right inverse matrix of , which satisfies: , for The identity matrix of order; In step 3, when subcarrier mapping is performed on the spread spectrum data, a centralized mapping is adopted, so that when the subcarrier mapped data is allocated to the two-dimensional grid, the entire grid is an OTFS symbol, and each column in the grid is an OTFS sub-symbol; the data in the two-dimensional grid is used Indicates; among them, is the number of grids in the delay domain; is the number of Doppler domain grids, and also the number of OTFS sub-symbols; is the delay domain grid index, ; is the Doppler domain grid index, .

2. A method for suppressing peak-to-average ratio of a precoded DFT spread spectrum OTFS system as claimed in claim 1, characterized in that: In step one, the least square solution is used as the coefficient of the precoding matrix to perform precoding processing on the modulated input data so that the modulated output is approximately a repetition of the modulated input data.

3. The method for suppressing peak-to-average ratio of a precoded DFT spread spectrum OTFS system according to claim 1, characterized in that: The modulated input data is recorded as , the pre-coded data is recorded as , the data after spread spectrum is recorded as , then it satisfies: , .

4. The method for suppressing peak-to-average ratio of a precoded DFT spread spectrum OTFS system according to claim 3, characterized in that: In step 3, subcarrier mapping is performed on the spread data, and the data in the spread data is mapped to The mapped DD domain data is obtained in the two-dimensional grid , , for The modulation letter set matrix is ,in, is the subcarrier mapping matrix after precoding, .

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