Joint structured ofdm modulation and precoding design method for massive mimo systems

Abstract

The application provides a joint structured OFDM modulation and precoding design method of a large-scale MIMO system, and relates to the technical field of MIMO communication.In the application, a point-to-point large-scale MIMO structured OFDM (mMIMO-SOFDM) system is constructed by using a structured OFDM modulation method; and based on a joint spatial precoding and structured frequency domain equalization scheme, a closed-form solution of each subcarrier frequency domain equalizer, transmission precoding and reception precoding of the mMIMO-SOFDM system is solved.By proposing the structured OFDM scheme, the excessive cyclic prefix overhead caused by the double wideband effect of the large-scale MIMO system is reduced.In addition, the proposed joint spatial precoding and structured frequency domain equalization scheme further improves the spectral efficiency of the system and reduces the peak-to-average ratio.

Description

Technical Field

[0001] This invention relates to the field of MIMO communication technology, and more specifically to a joint structured OFDM modulation and precoding design method for large-scale MIMO systems. Background Technology

[0002] To meet the exponentially growing demand for high data traffic in current mobile communication systems, Massive Multiple Input Multiple Output (mMIMO) is considered one of the key physical layer technologies for improving the spectrum and energy efficiency of wireless systems.

[0003] Orthogonal Frequency Division Multiplexing (OFDM) is a widely used modulation technique that transforms a frequency-selective channel into a set of parallel frequency-flat channels to eliminate inter-symbol interference (ISI) caused by channel delay spread and improve spectral efficiency.

[0004] As antenna sizes evolve from small arrays to large-scale arrays and even very large-scale arrays, a non-negligible delay exists between different array elements for the same signal; this phenomenon is known as the spatial broadband effect. Large-scale MIMO exhibits both spatial selectivity and frequency selectivity, i.e., a dual broadband effect, leading to even more severe delay spread. Therefore, using traditional OFDM schemes, communication systems must expend more cyclic prefix (CP) overhead to combat the delay spread in large-scale MIMO systems; this additional CP overhead may offset the improvement in spectral efficiency. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] To address the shortcomings of existing technologies, this invention provides a joint structured OFDM modulation and precoding design method for large-scale MIMO systems. This method solves the technical problem that, when using previous OFDM schemes, communication systems must incur more CP overhead to combat delay spread in large-scale MIMO systems, and the additional cyclic prefix overhead may offset the improvement in spectral efficiency.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A joint structured OFDM modulation and precoding design method for large-scale MIMO systems includes:

[0010] A point-to-point mMIMO-SOFDM system is constructed using a structured OFDM modulation method.

[0011] Based on the joint spatial precoding and structured frequency domain equalization scheme, the closed-form solution of each subcarrier frequency domain equalizer, transmit precoding and receive precoding of the mMIMO-SOFDM system is obtained.

[0012] Preferably, the structured OFDM modulation method refers to:

[0013] All symbols transmitted from the transmitter to the receiver are divided into block structures to obtain multiple subcarriers. Multiple sub-time slots are divided in the wave of any subcarrier. Multiple symbols transmitted on a single subcarrier are inserted into each sub-time slot. A subcarrier frequency domain equalization algorithm is designed at the receiver end to overcome inter-symbol interference within the carrier.

[0014] Preferably, in the mMIMO-SOFDM system:

[0015] The transmitter Tx and receiver Rx are equipped with I antennas and J antennas, respectively; for the time-domain wireless channel, a delayed MIMO channel model is adopted;

[0016] Suppose Tx emits N symbols to Rx, denoted as Based on the structured OFDM modulation method, multiple subcarriers corresponding to the symbol vector s are obtained, and M symbols are allocated in each subcarrier. Then, the transmitted symbol vector s is rewritten in matrix form.

[0017] S = [s0, ..., s k ,…,s K-1 ]

[0018] in, K represents the number of subcarriers, and M represents the length of the modulated symbol in each subcarrier, i.e., N = MK;

[0019] make Let represent the transmission precoding vector of the k-th subcarrier. Then, the permutation precoding matrix transmitted at subcarrier k is defined as:

[0020]

[0021] Represents an identity matrix of dimension M×M;

[0022] Transmitted signal on the k-th subcarrier Represented as:

[0023]

[0024] in, Let Tx represent the pre-equalization matrix for subcarrier k at position Tx;

[0025] By using the inverse discrete Fourier transform (IDFT), the transmitted signal in the time domain... It is given by the following formula:

[0026]

[0027] Based on time-domain channels and block-structured transmission signals Received signal in the time domain Represented as:

[0028]

[0029] in, Represents a noise vector;

[0030] Received signal with block structure at subcarrier k in the frequency domain

[0031]

[0032] in, This represents the received permutation precoding matrix; It is the received precoding vector of subcarrier k; The channel matrix η represents the block structure of subcarrier k. k It is an additive Gaussian noise vector;

[0033] Will Defined as the equalization matrix of subcarrier k at position Rx, the signal received by the equalizer Written as:

[0034]

[0035] The spectral efficiency on subcarrier k is given by the following equation:

[0036]

[0037] in, This represents the noise covariance matrix at subcarrier k after receiving precoding and frequency domain equalization.

[0038] Preferably, before proposing the joint spatial precoding and structured frequency domain equalization scheme, the following is also performed:

[0039] By designing transmit / receive precoders and frequency domain equalizers to maximize the overall spectral efficiency of the system, and considering the total power constraint, the optimization problem is formulated as follows:

[0040]

[0041]

[0042] Where P is the total transmit power.

[0043] Preferably, the step of solving the closed-form solution for each subcarrier frequency domain equalizer, transmit precoder, and receive precoder of the mMIMO-SOFDM system based on the joint spatial precoding and structured frequency domain equalization scheme includes:

[0044] Based on the block structure channel matrix H k , By utilizing the characteristics of [the system / mechanism], the equalizer and pre-encoder are decoupled, and the frequency domain equalizer {U} is obtained by solving the problem. t,k U r,k};

[0045] According to the frequency domain equalizer {U t,k U r,k}, solve sequentially to obtain the transmit precoding {w k} and receive pre-encoded {v k The closed-form solution of}.

[0046] Preferably, the block-structured channel matrix H k , By utilizing the characteristics of [the system / mechanism], the equalizer and pre-encoder are decoupled, and the frequency domain equalizer {U} is obtained by solving the problem. t,k U r,k},include:

[0047] The block structure channel matrix H k , Decompose into block diagonal form:

[0048]

[0049]

[0050] in, Λ is the DFT matrix; k =diag(1,…,e -j2π(M-1)k / N ) indicates frequency shift The corresponding diagonal matrix; H k This represents the channel of subcarrier k obtained by multiplying the time-domain channel H(τ) by the DFT matrix;

[0051] By applying variables The change in , the received signal is rewritten as:

[0052]

[0053] The frequency domain equalizer is then designed as follows:

[0054]

[0055] And the remaining spectral efficiency of subcarrier k is:

[0056]

[0057] And abbreviated as:

[0058]

[0059] Using the equilibrium matrix {U t,k U r,k The transmit and receive precoders are designed to maximize the overall spectral efficiency of the system by addressing the following issues:

[0060]

[0061] Preferably, the step of using the frequency domain equalizer {U} t,k U r,k}, solve sequentially to obtain the transmit precoding {w k} and receive pre-encoded {v k The closed-form solutions to} include:

[0062] The upper limit of the spectral efficiency for each subcarrier is given by the following formula:

[0063]

[0064] in, Represents set {H k ,…,H k+MK The channel matrix corresponding to the maximum spectral norm in}, where i is the block index corresponding to the maximum spectral norm; (a) indicates the use of Jensen's inequality, and (b) indicates that Tx transmits single-stream data within a symbol period;

[0065] The optimization problem is then further transformed into designing the transmit and receive precoders to maximize the upper bound of the system's overall spectral efficiency:

[0066]

[0067]

[0068] Among them, through channel H k+iK The singular value decomposition (SVD) is used to obtain the optimal solution for the receiver precoder;

[0069] The channel SVD decomposition at subcarrier k is defined as... The optimal receive and transmit precoders are then expressed as follows:

[0070]

[0071] Among them, F k , Σ k , H respectively k+iK The left singular matrix, singular value matrix, and right singular matrix of F; k (1,:) and Q k (1,:) represent matrix F respectively. k and Q k The first column represents the left and right eigenvectors corresponding to the maximum singular value; p k It is the power control factor of subcarrier k using the water-filling power allocation strategy, that is:

[0072]

[0073] And μ satisfies:

[0074]

[0075] (III) Beneficial Effects

[0076] This invention provides a joint structured OFDM modulation and precoding design method for large-scale MIMO systems. Compared with existing technologies, it has the following advantages:

[0077] This invention employs a structured OFDM modulation method to construct a point-to-point mMIMO-SOFDM system. Based on a joint spatial precoding and structured frequency domain equalization scheme, closed-form solutions for the frequency domain equalizer, transmit precoding, and receive precoding of each subcarrier in the mMIMO-SOFDM system are obtained. By proposing a structured OFDM scheme, the excessive cyclic prefix overhead caused by the double-wideband effect in large-scale MIMO systems is reduced. Furthermore, the proposed joint spatial precoding and structured frequency domain equalization scheme further improves the system's spectral efficiency and reduces the peak-to-average power ratio (PAPR). Attached Figure Description

[0078] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0079] Figure 1 A flowchart illustrating a structured OFDM design for a large-scale MIMO system, provided as an embodiment of the present invention;

[0080] Figure 2A diagram of a broadband MIMO system with structured OFDM modulation provided in an embodiment of the present invention;

[0081] Figure 3 A schematic diagram of spatial broadband effect provided for an embodiment of the present invention;

[0082] Figure 4 A graph showing the relationship between spectral efficiency and SNR is provided for an embodiment of the present invention;

[0083] Figure 5 A graph showing the relationship between complementary cumulative distribution function (CCDF) and peak-to-average ratio (PAPR) is provided for an embodiment of the present invention. Detailed Implementation

[0084] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0085] This application provides a joint structured OFDM modulation and precoding design method for large-scale MIMO systems, which solves the technical problem that when using conventional OFDM schemes, the communication system must spend more CP overhead to combat delay spread in large-scale MIMO systems, and the additional cyclic prefix overhead may offset the improvement in spectral efficiency.

[0086] The technical solution in this application is to solve the above-mentioned technical problems, and the general idea is as follows:

[0087] First, in the context of a point-to-point large-scale MIMO system with dual broadband effects, this invention proposes a structured OFDM modulation scheme, which effectively improves the spectral efficiency of the system and reduces the peak-to-average power ratio.

[0088] As mentioned in the background section, in large-scale MIMO systems, due to the large antenna array, the channel typically exhibits dual broadband effects: frequency broadband (frequency selectivity) and spatial broadband (spatial selectivity). When the channel is simultaneously affected by both spatial and frequency selectivity, the channel delay spread becomes even greater. In this case, traditional OFDM requires a longer cyclic prefix to suppress inter-symbol interference. Therefore, this invention proposes a Structured OFDM (SOFDM) modulation scheme to relatively reduce the overhead of the cyclic prefix. By transmitting a vector block on a subcarrier, the total amount of data transmitted by the system is increased, thereby relatively reducing the overhead of the cyclic prefix.

[0089] Secondly, this invention addresses the spectral efficiency problem of MIMO-SOFDM systems with dual broadband effects. Specifically, it designs transmit / receive precoders and frequency domain equalizers to maximize the overall spectral efficiency of the system, while the system is constrained by total power. The challenge lies in the fact that the precoder and equalizer operate in the spatial and frequency domains respectively, and cannot be designed as a whole. Furthermore, the coupling of variables and the non-convexity of the objective function make the problem difficult to solve directly. To address this issue, this invention proposes a low-complexity algorithm that utilizes the factor cyclic property of the channel matrix to decouple the equalizer and precoder, allowing for their separate design.

[0090] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0091] Example:

[0092] like Figure 1 As shown, this embodiment of the invention provides a joint structured OFDM modulation and precoding design method for a large-scale MIMO system, including:

[0093] Step 1: Construct a point-to-point mMIMO-SOFDM system using the structured OFDM modulation method;

[0094] Step 2: Based on the joint spatial precoding and structured frequency domain equalization scheme, solve the closed-form solutions for the frequency domain equalizer, transmit precoding, and receive precoding of each subcarrier of the mMIMO-SOFDM system.

[0095] This invention proposes a structured OFDM scheme to reduce excessive cyclic prefix overhead caused by the double-wideband effect in large-scale MIMO systems. Furthermore, the proposed joint spatial precoding and structured frequency domain equalization scheme further improves the system's spectral efficiency and reduces the peak-to-average power ratio (PAPR).

[0096] The specific details of the above plan will be introduced in the following sections:

[0097] First, it should be noted that in this embodiment of the invention, uppercase and lowercase bold text represent matrices and vectors, respectively; these are represented using (·). T 、(·) * 、(·) H These represent the transpose, conjugate transpose, and Hermitian transpose, respectively. Diag(X) is the diagonal matrix of vector X along its diagonal. ⊙ denotes the Kronecker product, convolution, and Hadamard product operations, respectively. λ(X) represents the largest singular value of the matrix |X|, and ||X||2 represent the absolute value of the complex number X and the spectral norm of the matrix X, respectively.

[0098] And such as Figure 2 As shown, in this embodiment of the invention, a point-to-point mMIMO-SOFDM system is considered, where the transmitter (Tx) and receiver (Rx) are equipped with I antennas and J antennas, respectively. For the time-domain wireless channel, a general delayed MIMO channel model is adopted. Since the array size of mMIMO is large, the propagation delay of the signal reaching each antenna is different and cannot be ignored. Figure 3 As shown. Therefore, τ l,i,j Defined as the delay between the i-th transmitting antenna and the j-th receiving antenna on the l-th path, its expression is as follows:

[0099]

[0100] Where θ l and φ l τ represents the departure angle (AoD) and arrival angle (AoA) corresponding to path l, respectively. d and c represent the spacing between adjacent antennas and the speed of light, respectively. l Let τ represent the free-space propagation delay of path l. Therefore, the delay τ l,i,j The impulse function is given by δ(τ-τ) l,i,j The channel response matrix between transmitter Tx and receiver Rx is represented by (). Represented as:

[0101]

[0102] in,

[0103]

[0104]

[0105] Let λ be the array steering vector corresponding to path l of transmitter Tx and receiver Rx, respectively, where λ is the carrier wavelength and L represents the number of paths. l It is the gain of path l. Let the delayed pulse matrix be represented by its (i,j)th term as δ(τ-τ l,i,j It can be seen that the mMIMO channel is affected by both spatial and frequency selectivity. Assuming the delay spread of a large-scale MIMO channel is defined as... Greater than small-scale MIMO channel delay spread Therefore, traditional OFDM systems must expend more CP (Conversion Cost) to suppress ISI (Independent Switching). To address this issue, embodiments of the present invention propose an SOFDM modulation method to reduce CP overhead.

[0106] In step one, a point-to-point mMIMO-SOFDM system is constructed using a structured OFDM modulation method;

[0107] In this step, the structured OFDM modulation method refers to:

[0108] All symbols transmitted from the transmitter to the receiver are divided into block structures to obtain multiple subcarriers. Multiple sub-time slots are divided in the wave of any subcarrier. Multiple symbols transmitted on a single subcarrier are inserted into each sub-time slot. A subcarrier frequency domain equalization algorithm is designed at the receiver end to overcome inter-symbol interference within the carrier.

[0109] Accordingly, in the mMIMO-SOFDM system:

[0110] Based on the above configuration, the transmitter Tx and receiver Rx are equipped with I antennas and J antennas respectively; for the time-domain wireless channel, a delayed MIMO channel model is adopted.

[0111] Suppose Tx emits N symbols to Rx, denoted as Based on the structured OFDM modulation method, a pre-blocking process is performed on the baseband unit to obtain multiple subcarriers corresponding to the symbol vector s, and M symbols are allocated in each subcarrier. Then, the transmitted symbol vector s is rewritten in matrix form.

[0112] S = [s0, ..., s k ,…,s K-1 ]

[0113] in, K represents the number of subcarriers, and M represents the length of the modulated symbol in each subcarrier, i.e., N = MK;

[0114] make This represents the transmission precoding vector for the k-th subcarrier. Due to the block structure of the transmitted symbols, all symbols on each subcarrier utilize the same precoding vector w. k , The permutation precoding matrix transmitted at subcarrier k is then defined as:

[0115]

[0116] Represents an identity matrix of dimension M×M;

[0117] Transmitted signal on the k-th subcarrier Represented as:

[0118]

[0119] in, Let Tx represent the pre-equalization matrix for subcarrier k at position Tx;

[0120] By using the inverse discrete Fourier transform (IDFT), the transmitted signal in the time domain... It is given by the following formula:

[0121]

[0122] Based on time-domain channels and block-structured transmission signals Received signal in the time domain Represented as:

[0123]

[0124] in, This represents the noise vector.

[0125] Then, the received signal with block structure at subcarrier k in the frequency domain is given by the following proposition:

[0126] Proposition 1: In a SOFDM-modulated MIMO system, dividing every M time-domain symbols into a group yields a received signal with a block structure at subcarrier k.

[0127]

[0128] in, This represents the received permutation precoding matrix; It is the received precoding vector of subcarrier k; The channel matrix η represents the block structure of subcarrier k. k It is an additive Gaussian noise vector;

[0129] It can be seen that the received signal vector y k , Each entry is a mixture of M symbols. Therefore, frequency equalization is needed to suppress ISI on each subcarrier. For this purpose, Defined as the equalization matrix of subcarrier k at position Rx, the signal received by the equalizer Written as:

[0130]

[0131] Therefore, the spectral efficiency on subcarrier k is given by the following equation:

[0132]

[0133] in, This represents the noise covariance matrix at subcarrier k after receiving precoding and frequency domain equalization.

[0134] In step two, based on the joint spatial precoding and structured frequency domain equalization scheme, the closed-form solutions for each subcarrier frequency domain equalizer, transmit precoding, and receive precoding of the mMIMO-SOFDM system are solved.

[0135] Since the objective of this invention is to maximize overall spectral efficiency by designing transmit / receive precoders and frequency domain equalizers, the following steps are performed before proposing the joint spatial precoding and structured frequency domain equalization scheme:

[0136] By designing transmit / receive precoders and frequency domain equalizers to maximize the overall spectral efficiency of the system, and considering the total power constraint, the optimization problem is formulated as follows:

[0137]

[0138]

[0139] Here, P represents the total transmit power. Since the pre-encoder and equalizer need to be processed in the spatial and frequency domains respectively, the pre-encoder and equalizer matrices must be designed separately. Furthermore, the coupling of optimization variables and the non-convexity of the objective function make the optimization problem difficult to solve directly.

[0140] In summary, the design of encoders and equalizers for mMIMO-SOFDM systems is based on a block-structured channel matrix H. k , By utilizing the characteristics of [the system / mechanism], the equalizer and pre-encoder are decoupled, and the frequency domain equalizer {U} is obtained by solving the problem. t,k U r,k}; According to the frequency domain equalizer {U t,k U r,k}, solve sequentially to obtain the transmit precoding {w k} and receive pre-encoded {v k The closed-form solution of}.

[0141] First, due to the block structure channel matrix H k , It is a factor cyclic matrix.

[0142] To illustrate this, a lemma concerning factorial cyclic matrix factorization is provided here:

[0143] Lemma 1: When H k When it is a factored cyclic matrix, it can be decomposed into a block diagonal form:

[0144]

[0145]

[0146] in, Λ is the DFT matrix; k =diag(1,…,e -j2π(M-1)k / N ) indicates frequency shift The corresponding diagonal matrix; H k This represents the channel of subcarrier k obtained by multiplying the time-domain channel H(τ) by the DFT matrix.

[0147] Due to the block channel matrix H k , Decoupling any two submatrices can be achieved by designing an equilibrium matrix {U}. t,k U r,k To eliminate interference between symbol blocks. Furthermore, the DFT matrix G and the diagonal matrix Λ k It is independent of the channel matrix and precoding vector, and only depends on the symbol length M and the total number of symbols on each subcarrier. Therefore, by applying variables... The change in , the received signal is rewritten as:

[0148]

[0149] Note that Λ k G is a unitary matrix (i.e., the conjugate transpose matrix) because it is the product of the DFT matrix and a diagonal matrix. Therefore, in this embodiment of the invention, the frequency domain equalizer can be designed as follows:

[0150]

[0151] The remaining spectral efficiency of subcarrier k is:

[0152]

[0153] Please note that due to channel H k And the block diagonal structure of the precoding matrix, and It is a diagonal matrix. At this point, the remaining spectral efficiency of each subcarrier further simplifies to:

[0154]

[0155] Therefore, using the equilibrium matrix {U t,k U r,k The transmit and receive precoders are designed to maximize the overall spectral efficiency of the system by addressing the following issues:

[0156]

[0157] Please note that maximizing the overall spectral efficiency requires joint optimization of the transmit and receive precoders. However, joint optimization is difficult due to the coupling between the transmit and receive precoders in the objective function and power constraints.

[0158] To solve for the precoder, we first obtain the upper limit of the spectral efficiency for each subcarrier, which is given by the following equation:

[0159]

[0160] in, Represents set {H k ,…,H k+MK The channel matrix corresponding to the maximum spectral norm in}, where i is the block index corresponding to the maximum spectral norm; (a) indicates the use of Jensen's inequality, and (b) indicates that Tx transmits single-stream data within a symbol period;

[0161] Therefore, the optimization problem is further transformed into maximizing the upper bound of the system's overall spectral efficiency by designing the transmit and receive precoders:

[0162]

[0163]

[0164] Please note that the solution for the optimal receive precoder can be obtained through channel H. k+iK The singular value decomposition (SVD) is given directly because the problem is an unconstrained optimization problem for the receive precoder. However, due to the total power constraint, the solution for the optimal transmit precoder in the optimization problem is not derived by a simple SVD of the channel.

[0165] The optimal precoder for the optimization problem can be obtained under the following propositions:

[0166] Proposition 2: Define the channel SVD decomposition at subcarrier k as... Therefore, the optimal receive and transmit precoders are expressed as follows:

[0167]

[0168] Among them, F k , Σ k , H respectively k+iK The left singular matrix, singular value matrix, and right singular matrix of F; k (1,:) and Q k (1,:) represent matrix F respectively. k and Q k The first column represents the left and right eigenvectors corresponding to the maximum singular value; p k It is the power control factor of subcarrier k using the water-filling power allocation strategy, that is:

[0169]

[0170] And μ satisfies:

[0171]

[0172] Ultimately, by using Proposition 2, the embodiments of the present invention are also able to find the optimal solution for the precoder.

[0173] To better illustrate the advantages of the embodiments of the present invention, the following specific examples are provided:

[0174] Assume the number of transmitted symbols is N = 64, and the symbol sampling period is T. s =0.25ms, therefore the total symbol period is T = NT s =16ms. For an mMIMO channel, assuming the number of taps is L=7, AoA and AoD are in the interval... Furthermore, the symbol length modulated in each subcarrier is set to M=2.

[0175] See Figure 4 This paper describes the relationship between spectral efficiency and SNR under different parameter settings. It can be seen that, based on the proposed SOFDM equalization and precoding strategies, the performance of the proposed SOFDM modulation scheme is superior to that of typical OFDM schemes. Specifically, the proposed scheme achieves intra-block diversity and multiplexing gain by dividing symbols into block structures and using frequency domain equalization. Furthermore, the precoding designed at the transceiver can optimally allocate power in symbols and subcarriers. Moreover, when the length of the CP is not less than the channel length, i.e., N... cp When the length of the CP (Content Processing) is ≥L, the spectral efficiency can increase as the length of the CP decreases. This is because the spectral resources saved by reducing the CP can be used for data transmission, thus improving spectral efficiency.

[0176] See also Figure 5 The figure shows the relationship between the complementary cumulative distribution function (CCDF) and peak-to-average power ratio (PAPR) for different modulation types, with the number of transmit and receive antennas set to 128. As expected, the performance of SOFDM modulation lies between OFDM and single-carrier frequency domain equalization (SC-FDE), because SOFDM systems have fewer subcarriers than OFDM but more than SC-FDE. Furthermore, the PAPR gradually decreases as the symbol length M increases. An intuitive explanation is that the system uses fewer subcarriers to transmit the same number of symbols.

[0177] In summary, compared with existing technologies, it has the following beneficial effects:

[0178] 1. In this embodiment of the invention, considering the more severe inter-symbol interference caused by the dual broadband effect under large-scale MIMO systems, a structured OFDM scheme is proposed. By dividing a subcarrier wave into multiple sub-time slots and transmitting multiple symbols, the total number of transmitted symbols is increased, and the CP overhead is relatively reduced.

[0179] 2. The embodiments of the present invention clearly characterize the transceiver model of a structured OFDM system with dual broadband effect of large-scale MIMO.

[0180] 3. This invention proposes a joint spatial precoding and structured frequency domain equalization scheme for mMIMO-SOFDM systems. Specifically, it maximizes overall spectral efficiency by designing transmit / receive precoders and frequency domain equalizers, while the system is constrained by total power. The challenge lies in the fact that the precoder and equalizer process data in the spatial and frequency domains respectively, and cannot be designed as a whole. Furthermore, the coupling of variables and the non-convexity of the objective function make the problem difficult to solve directly.

[0181] 4. This invention proposes a low-complexity algorithm based on a closed-loop solution for the precoder and equalizer. The algorithm first decouples the precoder and equalizer using the factor cyclic property of the block channel matrix, then designs the equalizer using this property. Next, by transforming the optimization problem into an upper bound problem, the precoder is designed using SVD decomposition and water-filled power allocation.

[0182] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0183] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. 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 of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A joint structured OFDM modulation and precoding design method for a large-scale MIMO system, characterized in that, include: A point-to-point mMIMO-SOFDM system is constructed using a structured OFDM modulation method. Based on the joint spatial precoding and structured frequency domain equalization scheme, the closed-form solutions for each subcarrier frequency domain equalizer, transmit precoding, and receive precoding of the mMIMO-SOFDM system are obtained; In the mMIMO-SOFDM system: The transmitter Tx and receiver Rx are respectively equipped with root antenna and Root antenna; for time-domain wireless channels, a delayed MIMO channel model is adopted; Assume Tx emits to Rx A symbol, represented as ; Based on the structured OFDM modulation method, the symbol vector is obtained. Multiple corresponding subcarriers, and allocation within each subcarrier If there are 1 symbol, then the symbol vector sent is... Rewritten in matrix form : in, , Indicates the number of subcarriers. This represents the length of the modulated symbol in each subcarrier, i.e. ; make Indicates the first The transmission precoding vector of each subcarrier, then the subcarrier The permutation precoding matrix emitted at point is defined as: in, The dimension is The identity matrix; In the Transmitted signals on each subcarrier Represented as: in, Indicates the subcarrier at Tx The pre-equilibrium matrix; By using the inverse discrete Fourier transform (IDFT), the transmitted signal in the time domain... It is given by the following formula: Based on time-domain channels and block-structured transmission signals Received signal in the time domain Represented as: in, Represents a noise vector; Subcarriers in the frequency domain Received signal with block structure : in, This represents the received permutation precoding matrix; It is a subcarrier The received precoding vector; Indicates subcarrier The channel matrix with block structure, It is an additive Gaussian noise vector; Will Defined as a subcarrier at Rx The equalization matrix, then the signal received by the equalizer Written as: subcarrier The spectral efficiency on the spectral surface is given by the following formula: in, Indicates the received precoding and frequency domain equalization of the subcarriers. The noise covariance matrix at that location; Before proposing the joint spatial precoding and subcarrier frequency domain equalization scheme, the following is also performed: By designing transmit / receive precoders and frequency domain equalizers to maximize the overall spectral efficiency of the system, and considering the total power constraint, the optimization problem is formulated as follows: in, That is the total transmission power.

2. The joint structured OFDM modulation and precoding design method as described in claim 1, characterized in that, The structured OFDM modulation method refers to: All symbols transmitted from the transmitter to the receiver are divided into block structures to obtain multiple subcarriers. Multiple sub-time slots are divided in the wave of any subcarrier. Multiple symbols transmitted on a single subcarrier are inserted into each sub-time slot. A subcarrier frequency domain equalization algorithm is designed at the receiver end to overcome inter-symbol interference within the carrier.

3. The joint structured OFDM modulation and precoding design method as described in claim 1, characterized in that, The closed-form solution for each subcarrier frequency domain equalizer, transmit precoder, and receive precoder of the mMIMO-SOFDM system based on the joint spatial precoding and subcarrier frequency domain equalization scheme includes: Based on block structure channel matrix By leveraging the characteristics of [the system / mechanism], the equalizer and pre-encoder are decoupled, and the frequency domain equalizer is obtained through solution. ; According to the frequency domain equalizer The transmit precode is obtained by solving the problem sequentially. and receive precoding The closed-form solution.

4. The joint structured OFDM modulation and precoding design method as described in claim 3, characterized in that, The block-structured channel matrix By leveraging the characteristics of [the system / mechanism], the equalizer and pre-encoder are decoupled, and the frequency domain equalizer is obtained through solution. ,include: block structure channel matrix Decompose into block diagonal form: in, It is a DFT matrix; Indicates frequency shift The corresponding diagonal matrix; Representing the time-domain channel Subcarriers obtained by multiplying by the DFT matrix The channel; By applying variables The change in , the received signal is rewritten as: The frequency domain equalizer is then designed as follows: and subcarriers The remaining spectral efficiency is: And abbreviated as: Using the equilibrium matrix The transmit and receive precoders are designed to maximize the overall spectral efficiency of the system by addressing the following issues: 。 5. The joint structured OFDM modulation and precoding design method as described in claim 4, characterized in that, According to the frequency domain equalizer The transmit precode is obtained by solving the problem sequentially. and receive precoding The closed-form solutions include: The upper limit of the spectral efficiency for each subcarrier is given by the following formula: in, Representative set The channel matrix corresponding to the maximum spectral norm. For the block index corresponding to the maximum spectral norm; (a) indicates the use of Jensen's inequality, and (b) indicates that Tx transmits a single stream of data within a symbol period; The optimization problem is then further transformed into designing the transmit and receive precoders to maximize the upper bound of the system's overall spectral efficiency: Among them, through the channel The singular value decomposition (SVD) is used to obtain the optimal solution for the receiver precoder; subcarrier The channel SVD decomposition at point is defined as The optimal receive and transmit precoders are then expressed as follows: in, They represent The left singular matrix, singular value matrix, and right singular matrix; and Represent matrices respectively and The first column contains the left and right eigenvectors corresponding to the maximum singular value; It is a subcarrier that adopts a water-filling power allocation strategy. The power control factor, namely: and satisfy: in, express The maximum singular value.

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