Beneficial interference precoding solving method and system based on symbol-level extrapolation

Abstract

The invention discloses a beneficial interference precoding solving method and system based on symbol-level extrapolation, and belongs to the technical field of wireless communication, and the solving method comprises the steps: extrapolating a precoding matrix of an mth time slot by using a precoding matrix corresponding to an nth symbol time slot in the same transmission block, obtaining a closed-form solution structure of a beneficial interference precoding matrix of symbol-level extrapolation; based on the closed-form solution structure of the beneficial interference precoding matrix of symbol-level extrapolation, a phase scaling criterion under PSK modulation and a symbol scaling criterion under QAM modulation are combined, and the closed-form solution structure of the precoding matrix under the total transmitting power constraint is obtained; and solving a scaling coefficient corresponding to the symbol time slot, and substituting the scaling coefficient into the closed-form solution structure of the precoding matrix to obtain the precoding matrix. According to the method, the precoding matrixes of different symbol time slots are extrapolated by utilizing the mathematical relationship among different time slot symbols in a transmission block, a large amount of calculation is avoided, PSK modulation and QAM modulation are considered at the same time, and the time complexity is low.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and particularly relates to a method and system for solving beneficial interference precoding based on symbol-level extrapolation. Background Art

[0002] With the continuous evolution of wireless communication technology, traditional spectrum resources are gradually unable to meet the rapidly growing demand for communication rates, which poses a severe challenge to the design of communication systems. Against this background, MIMO (Multiple Input Multiple Output) can more effectively utilize limited spectrum resources. By transmitting data simultaneously on multiple channels, MIMO can support more users within a smaller channel bandwidth, thereby increasing the overall capacity of the system, achieving higher data transmission rates, and further improving spectrum efficiency. However, in a multi-user MIMO system, signals between different users may affect each other, especially in a user-dense environment. Each user receives multiple signals from the transmitting antennas and is also interfered by the signals of other users. In the downlink, considering the complexity of the receiving-end users, MIMO design usually adopts the method of placing interference management at the transmitting end, that is, using precoding technology. Precoding technology performs a linear transformation or processing on the signal before it is transmitted to optimize the transmission mode of the signal on multiple antennas, and maximizes the reliability and rate of data transmission considering channel characteristics and receiving conditions.

[0003] Traditional precoding schemes regard interference in MIMO systems as an adverse factor, and the core of their precoding design is to eliminate interference as much as possible. In recent years, the industry has proposed a symbol-level precoding scheme based on beneficial interference. The core is to divide the interference between users in a communication system into beneficial interference and destructive interference. By retaining beneficial interference and eliminating destructive interference in the precoding design, the bit error rate performance and energy efficiency of the system can be effectively improved. Among them, beneficial interference refers to the interference that can push the constellation points at the receiving end away from the detection threshold, while destructive interference refers to the interference that makes the constellation points at the receiving end approach the detection threshold. In addition, recent studies have also shown that destructive interference can be converted into beneficial interference, and this conversion criterion depends on the modulation method of the transmitted signal, that is, the symbol scaling criterion under phase shift keying (PSK) modulation and the symbol scaling criterion under quadrature amplitude modulation (QAM), which will further improve the performance of the system. However, this beneficial interference precoding scheme is symbol-level, that is, the precoding matrix needs to be updated once in each time slot, which is different from the traditional block-level precoding scheme, so it will bring high complexity. Currently, the prior art has proposed a closed-form solution structure for the symbol scaling criteria of PSK modulation and QAM modulation, which can effectively reduce the complexity of solving the beneficial interference precoding problem.

[0004] However, the solution methods under the above-mentioned PSK modulation and QAM modulation only consider the solution of the precoding matrix in one time slot, while ignoring the mathematical relationship between symbols in different time slots within a transmission block, resulting in a still high complexity of the solution scheme. Summary of the Invention

[0005] The purpose of the present invention is to provide a beneficial interference precoding solution method and system based on symbol-level extrapolation for the problems in the above-mentioned existing technologies. By utilizing the mathematical relationship between symbols in different time slots of a transmission block, a large amount of calculation is avoided, the precoding matrix of different symbol time slots is extrapolated, and both PSK modulation and QAM modulation are considered simultaneously. The iterative algorithm has a fast convergence speed, low time complexity, and improves the efficiency of solving the beneficial interference precoding problem.

[0006] To achieve the above purpose, the present invention has the following technical solutions:

[0007] In the first aspect, a beneficial interference precoding solution method based on symbol-level extrapolation is provided, including:

[0008] Using the precoding matrix corresponding to the nth symbol time slot in the same transmission block to extrapolate the precoding matrix of the mth time slot, and obtaining the closed-form solution structure of the beneficial interference precoding matrix with symbol-level extrapolation;

[0009] Based on the closed-form solution structure of the beneficial interference precoding matrix with symbol-level extrapolation, combining the phase scaling criterion under PSK modulation and the symbol scaling criterion under QAM modulation, obtaining the closed-form solution structure of the precoding matrix under the total transmit power constraint;

[0010] Solving the scaling coefficient corresponding to the symbol time slot and substituting it into the closed-form solution structure of the precoding matrix to obtain the precoding matrix.

[0011] As a preferred solution, under the total transmit power constraint, the optimization problem corresponding to the symbol scaling criterion of beneficial interference precoding in the nth symbol time slot is constructed according to the phase scaling criterion under PSK modulation as:

[0012]

[0013] where is the precoding matrix of the nth symbol time slot, H = [h 1 , h 2 , …, h K T is the channel matrix, is the transmit signal vector of the nth time slot, and the set represents the set of scaling coefficients corresponding to the constellation points using beneficial interference within the nth time slot, ​and respectively represent the vectors obtained by decomposing the constellation points of the k-th user along the detection threshold, and represent the scaling factor of the k-th user; for PSK modulation, within one transmission block, the optimization problem forms corresponding to the symbol scaling criteria for beneficial interference precoding in the m-th symbol time slot are the same.

[0014] As a preferred solution, for the symbol scaling criteria under QAM modulation, under the total transmit power constraint, the optimization problem for symbol-level precoding of beneficial interference is:

[0015]

[0016] wherein, the set contains the real or imaginary parts of the constellation points in the QAM constellation diagram that can be used for interference utilization, and the set contains the real or imaginary parts of the constellation points in the QAM constellation diagram that cannot be used for interference utilization.

[0017] As a preferred solution, in the step of extrapolating the precoding matrix for the m-th time slot from the precoding matrix corresponding to the n-th symbol time slot in the same transmission block, the closed-form solution structure of the beneficial interference precoding matrix under PSK modulation with total power constraint is:

[0018]

[0019] wherein, s (m) = As (n) , Q n = U H (HH H ) - 1 U, represents the mapping function between the matrix V n corresponding to the n-th symbol time slot and the scaling factor corresponding to the m-th symbol time slot;

[0020] The closed-form solution structure of the beneficial interference precoding matrix for symbol-level extrapolation under QAM modulation is:

[0021]

[0022] wherein, represents the mapping function between the matrix V n corresponding to the n-th symbol time slot and the scaling factor corresponding to the m-th symbol time slot.

[0023] As a preferred solution, under PSK modulation, the optimization problem corresponding to the symbol scaling criterion of the beneficial interference precoding in the nth symbol time slot is simplified to:

[0024]

[0025] s.t. Ω (n) V n Ω (n) -p 0 = 0

[0026]

[0027] Under QAM modulation, the optimization problem of symbol-level precoding of beneficial interference is simplified to:

[0028]

[0029] s.t. Ω (n) V n Ω (n) -p 0 = 0

[0030]

[0031] In the formula, Ω (n) represents the scaling coefficient corresponding to the nth symbol time slot.

[0032] As a preferred solution, under PSK modulation, calculate the variable corresponding to the nth symbol time slot according to the following formula:

[0033] Q n = U H (HH H ) -1 U

[0034]

[0035] Deduce the variable corresponding to the mth symbol time slot by using the variable corresponding to the nth symbol time slot:

[0036] s (m) = As (n)

[0037]

[0038] Solve for the scaling coefficient corresponding to the mth time slot through the matrix V m The iterative algorithm updates only one scaling coefficient each time. The update method of the symbol scaling coefficient is to calculate the variable q of the mth symbol time slot (m) , and the calculation formula is as follows:

[0039]

[0040] Select the index of the element with the smallest value less than 0 among the selected variables as the position where the symbol scaling factor will be updated; initialize the scaling factor Ω (m) = 1. When updating the k-th scaling factor, the update expression of the scaling factor is:

[0041]

[0042] After obtaining the symbol scaling factor, perform power normalization according to the following formula:

[0043]

[0044] Substitute the closed-form solution structure of the precoding matrix to obtain the precoding matrix.

[0045] Furthermore, or omit the iterative calculation process of solving the symbol scaling factor, directly solve the symbol scaling factor, and set a threshold to force the solved symbol scaling factor to be greater than or equal to 1. The expression for solving the symbol scaling factor is as follows:

[0046]

[0047] After power normalization, substitute the symbol scaling factor into the closed-form solution structure of the precoding matrix to obtain the precoding matrix. As a preferred solution, under QAM modulation, calculate the variable corresponding to the n-th symbol time slot according to the following formula:

[0048] Q n = U H (HH H ) -1 U

[0049] Calculate the variable V corresponding to the m-th time slot through the variable Q corresponding to the n-th time slot according to the following formula n Extrapolate the variable V corresponding to the m-th time slot m :

[0050]

[0051] Solve the scaling factor corresponding to the m-th time slot through V m The iterative algorithm updates only one scaling factor each time. The update method of the symbol scaling factor is to calculate the variable q of the m-th symbol time slot (m) , and the calculation formula is as follows:

[0052]

[0053] For QAM modulation, according to whether the symbol scaling factor can utilize beneficial interference, the indices of the symbol scaling factor are divided into two sets A set of indices representing scaling factors that cannot utilize beneficial interference, A set of indices representing scaling factors that can utilize beneficial interference;

[0054] Take q according to the following formula (m) Extract the scaling factors that can utilize beneficial interference in it:

[0055]

[0056] For the iterative algorithm, only one scaling factor is updated each time, and the variable The index of the element less than 0 and with the smallest value in is selected as the position to update the symbol scaling factor, and the update expression of the symbol scaling factor for each iteration is:

[0057]

[0058] After obtaining the scaling factor of the symbol, perform power normalization according to the following formula:

[0059]

[0060] Substitute into the closed-form solution structure of the precoding matrix to obtain the precoding matrix.

[0061] Furthermore, either omit the iterative calculation process of solving the symbol scaling factor, directly solve the symbol scaling factor, and set a threshold to force the solved symbol scaling factor to be greater than or equal to 1. The expression for solving the symbol scaling factor is as follows:

[0062]

[0063] After power normalization, substitute the symbol scaling factor into the closed-form solution structure of the precoding matrix to obtain the precoding matrix.

[0064] In a second aspect, a beneficial interference precoding solution system based on symbol-level extrapolation is provided, including:

[0065] A closed-form solution structure acquisition module, configured to extrapolate the precoding matrix of the m-th time slot from the precoding matrix corresponding to the n-th symbol time slot in the same transmission block, and obtain the closed-form solution structure of the beneficial interference precoding matrix of symbol-level extrapolation;

[0066] A closed-form solution structure constraint module, configured to obtain the closed-form solution structure of the precoding matrix under the total transmit power constraint by combining the phase scaling criterion under PSK modulation and the symbol scaling criterion under QAM modulation based on the closed-form solution structure of the beneficial interference precoding matrix of symbol-level extrapolation;

[0067] A precoding matrix solution module, configured to solve the scaling factor corresponding to the symbol time slot and substitute it into the closed-form solution structure of the precoding matrix to obtain the precoding matrix.

[0068] Compared with the prior art, the present invention has at least the following beneficial effects:

[0069] The beneficial interference precoding solution method based on symbol-level extrapolation of the present invention has a lower solution complexity and a faster convergence speed compared with the prior art. The present invention utilizes the mathematical relationship between the transmitted symbols in different symbol time slots, and proposes a closed-form solution structure of the beneficial interference precoding matrix based on symbol-level extrapolation, reducing the complexity of solving the original problem. The present invention uses an iterative algorithm to solve the simplified optimization problem. By reasonably selecting the initial point, this iterative algorithm can converge quickly, reducing the complexity of solving the beneficial interference precoding problem and promoting the application of constructive interference (CI) precoding in practical scenarios. The low-complexity algorithm proposed by the present invention can not only be applied to PSK modulation, but also to QAM modulation. Compared with the algorithms used in the prior art, the present invention utilizes the mathematical relationship between the symbols in different time slots of a transmission block to extrapolate the precoding matrix of different symbol time slots, avoiding a large amount of calculations, and simultaneously considering both PSK modulation and QAM modulation. The iterative algorithm has a fast convergence speed and a low time complexity, improving the efficiency of solving the beneficial interference precoding problem.

[0070] Furthermore, the present invention proposes a closed-form suboptimal algorithm, which omits the iterative calculation process of solving the symbol scaling coefficient, directly solves the symbol scaling coefficient, and sets a threshold to force the solved symbol scaling coefficient to be greater than or equal to 1, further reducing the complexity of solving the beneficial interference precoding problem with a small performance loss. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required in the embodiments. It should be understood that the following drawings only show some embodiments of the present invention, and those of ordinary skill in the art can obtain other relevant drawings without creative efforts based on these drawings.

[0072] Figure 1 Schematic diagram of the symbol scaling criterion principle of beneficial interference precoding under PSK modulation in an embodiment of the present invention;

[0073] Figure 2 Schematic diagram of the symbol scaling criterion principle of beneficial interference precoding under QAM modulation in an embodiment of the present invention;

[0074] Figure 3 Graph of the bit error rate varying with the signal-to-noise ratio of the beneficial interference precoding solution method based on symbol-level extrapolation in an embodiment of the present invention, using QPSK modulation, with M equipped at the transmitter t= 8 antennas, and the number of single-antenna users at the receiving end is K = 8 respectively.

[0075] Figure 4 This is the graph of the bit error rate varying with the signal-to-noise ratio for the beneficial interference precoding solution method based on symbol-level extrapolation in the embodiments of the present invention. 8PSK modulation is adopted, and M t = 12 antennas are equipped at the transmitting end, and the number of single-antenna users at the receiving end is K = 12 respectively.

[0076] Figure 5 This is the graph of the bit error rate of the method of the present invention varying with the average number of iterations under 8PSK modulation.

[0077] Figure 6 This is the graph of the average running time of the method of the present invention varying with the number of users K under 8PSK modulation.

[0078] Figure 7 This is the graph of the bit error rate varying with the signal-to-noise ratio for the beneficial interference precoding solution method based on symbol-level extrapolation in the embodiments of the present invention under 16QAM modulation. M t = 12 antennas are equipped at the transmitting end, and the number of single-antenna users at the receiving end is K = 12 respectively. Specific embodiments

[0079] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, those of ordinary skill in the art can also obtain other embodiments without making creative efforts.

[0080] Embodiment 1

[0081] The embodiments of the present invention propose a beneficial interference precoding solution method based on symbol-level extrapolation, including:

[0082] Using the precoding matrix corresponding to the nth symbol time slot in the same transmission block to extrapolate the precoding matrix of the mth time slot, and obtaining the closed-form solution structure of the beneficial interference precoding matrix of symbol-level extrapolation;

[0083] Based on the closed-form solution structure of the beneficial interference precoding matrix of symbol-level extrapolation, combining the phase scaling criterion under PSK modulation and the symbol scaling criterion under QAM modulation, obtaining the closed-form solution structure of the precoding matrix under the total transmit power constraint;

[0084] Solving the scaling coefficient corresponding to the symbol time slot, and substituting it into the closed-form solution structure of the precoding matrix to obtain the precoding matrix.

[0085] The applicable scenario of the beneficial interference precoding solution method based on symbol-level extrapolation in the embodiments of the present invention is:

[0086] The base station is equipped with M t antennas, the receiving end is K single-antenna users, and the transmitting end utilizes beneficial interference through symbol-level precoding design. The scenario considered is the downlink of multi-user MIMO.

[0087] In a possible implementation, first consider the correspondence between mathematics under different symbol time slots. In a transmission block, S (n) represents the transmitted symbol in the nth symbol time slot, and S (m) represents the transmitted symbol in the mth symbol time slot. The mathematical relationship between the transmitted symbols in two different time slots can be expressed as:

[0088] s (m) = As (n)

[0089] In the formula, represents a diagonal conversion matrix, and β k represent the phase and amplitude differences between symbols.

[0090] Furthermore, the symbol-level extrapolation (SLE) precoding design under PSK modulation. Within a transmission block, the precoding matrix corresponding to the mth symbol time slot is extrapolated through the precoding matrix corresponding to the nth symbol time slot. The original optimization problem corresponding to the nth time slot is:

[0091]

[0092] where is the precoding matrix in the nth symbol time slot, H = [h 1 , h 2 , …, h K T is the channel matrix, is the transmitted signal vector in the nth time slot, the set represents the set of scaling factors corresponding to the constellation points that can utilize beneficial interference within the nth time slot, and respectively represent the vectors obtained by decomposing the constellation points of the kth user along the detection threshold, and represent the scaling factors of the kth user. Please refer to Figure 1 . For PSK modulation, it is considered that all constellation points can utilize beneficial interference. Problem ​The optimization objective is to maximize t, that is, to push the received - end constellation points as far as possible from the detection boundary, which is also the core idea of CI precoding. Within a transmission block, the form of the precoding matrix optimization problem corresponding to the m - th time slot is the same as that of the n - th time slot. For this optimization problem, the prior art gives a closed - form solution structure based on the scaling criterion for symbol - level precoding, and the formula is as follows:

[0093]

[0094] Among them, each variable in the formula can be expressed as:

[0095]

[0096] Further, to obtain the simplified form of the above - mentioned optimization problem, under PSK modulation, for the n - th symbol time slot, the simplified optimization problem is:

[0097]

[0098] s.t.Ω (n) V n Ω (n) -p 0 =0

[0099]

[0100] Among them, Ω (n) represents the scaling coefficient corresponding to the n - th symbol time slot, and the calculation formulas for each variable in the optimization problem are as follows:

[0101] Q n =U H (HH H ) -1 U

[0102]

[0103] The optimization problem corresponding to the m - th symbol time slot has the same simplified form as that of the n - th time slot. In a transmission block, explore the correspondence between the matrix V n of the n - th symbol time slot and the matrix V m of the m - th symbol time slot, and connect the optimization problems and as:

[0104] s (m) =As (n)

[0105]

[0106] Based on the above derivation and the closed - form solution structure of the symbol - level precoding matrix in the prior art, the closed - form solution structure of the precoding matrix for the beneficial interference of symbol - level extrapolation can be obtained, and the expression is as follows:

[0107]

[0108] Wherein, represents the mapping function between the matrix V corresponding to the n - th symbol time slot n and the scaling coefficient corresponding to the m - th symbol time slot.

[0109] When the matrix V n is extrapolated to obtain the matrix V m after that, the scaling coefficient corresponding to the m - th symbol time slot is calculated through the matrix V m . When the optimization problem obtains the optimal solution, the transmitting end must be at the maximum transmitting power, and the formula can be obtained:

[0110] (Ω (m) ) T V m Ω (m) -p 0 =0

[0111] Based on this formula, a power normalization factor can be defined, and the expression is as follows:

[0112]

[0113] When the scaling coefficients of the symbols are calculated using an iterative or sub - optimal algorithm, the power scaling factor can be used to perform power normalization on the scaling coefficients to meet the power constraint conditions, and the expression is as follows:

[0114]

[0115] Wherein, p 0 represents the total power of the transmitting end.

[0116] By calculating the symbol scaling departure coefficients through the matrix V m , the power constraint in the optimization problem can be expanded, and the obtained expression is:

[0117]

[0118] In the formula, represents the i - th scaling coefficient within the m - th symbol time slot. This expansion formula can be simply understood as the accumulation of 2K univariate quadratic equations. Based on this understanding, the embodiments of the present invention respectively propose a low - complexity iterative algorithm and a sub - optimal closed - form solution algorithm for the beneficial interference precoding of symbol - level extrapolation for PSK modulation.

[0119] For the iterative algorithm, initialize the symbol scaling factor to Ω (m) = 1. The iterative algorithm updates only one scaling factor each time. Specifically, first calculate the variable q corresponding to the m-th symbol time slot (m) , and the calculation formula is as follows:

[0120]

[0121] Select the index of the element in the variable that is less than 0 and has the smallest value as the position where the symbol scaling factor will be updated, and initialize the scaling factor Ω (m) = 1. When selecting the k-th scaling factor for update, the update formula for the scaling factor is:

[0122]

[0123] After obtaining the scaling factor of the symbol, in order to meet the power constraint, perform power normalization, and the expression is:

[0124]

[0125] Substitute the closed-form solution of the precoding matrix to obtain the final precoding matrix.

[0126] Furthermore, an embodiment of the present invention proposes a suboptimal closed-form algorithm based on symbol-level extrapolation. Compared with the iterative algorithm based on symbol-level extrapolation proposed in the above embodiment of the present invention, this suboptimal algorithm omits the iterative calculation process of solving the symbol scaling factor, directly solves the scaling factor of the symbol, and sets a threshold to force the solved symbol scaling factor to be greater than or equal to 1, further reducing the complexity. The specific expression formula for the symbol scaling factor is:

[0127]

[0128] Similarly, after power normalization, the scaling factor can be substituted into the closed-form solution of the precoding matrix to obtain the final precoding matrix, completing the solution of the problem.

[0129] Furthermore, next, consider a low-complexity solution scheme for beneficial interference based on symbol extrapolation under QAM modulation. The solution idea is similar to the method under PSK modulation.

[0130] Specifically, first give the symbol-level precoding optimization problem of beneficial interference under QAM modulation as:

[0131]

[0132] Among them, the set The elements in are the real part or the imaginary part of the constellation points in the QAM constellation that can utilize interference, and the set The elements in are the real or imaginary parts of the constellation points in the QAM constellation diagram that cannot be used for interference exploitation (please refer to Figure 2 , where only the real and imaginary parts of point C, the real part of point B, and the imaginary part of point D can be used for interference exploitation, while the real and imaginary parts of point A, the imaginary part of point B, and the real part of point D cannot be used for interference).

[0133] For this optimization problem, a closed-form solution structure based on the scaling criterion is given in the prior art, and the formula is as follows:

[0134]

[0135] Furthermore, to obtain the simplified form of the above optimization problem, under QAM modulation, for the nth symbol time slot, the simplified optimization problem is:

[0136]

[0137] s.t. Ω (n) V n Ω (n) -p 0 = 0

[0138]

[0139]

[0140] In the formula, Ω (n) represents the scaling coefficient corresponding to the nth symbol time slot. The optimization problem corresponding to the mth symbol time slot is the same as the optimization problem of the nth symbol time slot, and an iterative algorithm and a sub-optimal closed-form solution algorithm are used for solving. The calculation formulas of each variable in the optimization problem are as follows:

[0141] Q n = U H (HH H ) -1 U

[0142]

[0143] Furthermore, in a transmission block, explore the correspondence between the matrix V n of the nth symbol time slot and the matrix V m of the mth symbol time slot, and relate the optimization problems and to each other, which is expressed as:

[0144]

[0145] Based on the above derivations and the closed-form solution structure of the symbol-level precoding matrix in the prior art, the closed-form solution structure of the precoding matrix for the beneficial interference of symbol-level extrapolation under QAM modulation can be obtained, and the expression is as follows:

[0146]

[0147] In the formula, represents the mapping function between the matrix Q corresponding to the nth symbol time slot and the scaling factor corresponding to the mth symbol time slot. n

[0148] Next, it is explained that when the matrix V n is extrapolated through the matrix Q m , if the scaling factor corresponding to the mth symbol time slot is calculated through the matrix V m . Each iteration of the iterative algorithm updates only one scaling factor. The update method of the symbol scaling factor is to first calculate the variable q (m) corresponding to the mth symbol time slot, and the calculation formula is as follows:

[0149]

[0150] For QAM modulation, only some scaling factors can utilize the beneficial interference. According to whether the symbol scaling factor can utilize the beneficial interference, the indices of the symbol scaling factors can be divided into two sets. represents the index set of the scaling factors that cannot utilize the beneficial interference. represents the index set of the scaling factors that can utilize the beneficial interference. The scaling factors in q (m) that can utilize the beneficial interference are taken out, and the expression is:

[0151]

[0152] For the iterative algorithm, each iteration updates only one scaling factor. The index of the element that is less than 0 and has the smallest value among the variables is selected as the position where the symbol scaling factor will be updated. The update formula for the symbol scaling factor in each iteration is:

[0153]

[0154] When the scaling factor of the symbol is obtained, power normalization is performed, and the expression is:

[0155]

[0156] Substituting the closed-form solution of the precoding matrix, the final precoding matrix can be obtained.

[0157] ​Furthermore, an embodiment of the present invention proposes a sub-optimal closed-form algorithm based on symbol-level extrapolation. Compared with the iterative algorithm based on symbol-level extrapolation proposed in the above embodiment of the present invention, this sub-optimal algorithm omits the iterative calculation process of solving the symbol scaling coefficient, directly solves the scaling coefficient of the symbol, and sets a threshold to force the solved symbol scaling coefficient to be greater than or equal to 1, further reducing the complexity. The specific expression formula of the symbol scaling coefficient is:

[0158]

[0159] Similarly, after power normalization, the scaling coefficient can be substituted into the closed-form solution of the precoding matrix to obtain the final precoding matrix.

[0160] Embodiment 2

[0161] Taking PSK modulation as an example, the beneficial interference precoding solution method based on symbol-level extrapolation proposed in the embodiment of the present invention includes the following steps:

[0162] S1. The transmitting end obtains the channel state information H and the transmitted symbol s at the nth symbol time slot. Based on the transmitted symbol s at the current time slot and the channel matrix H, the following matrices and vectors are constructed: Q (n) , based on the transmitted symbol s at the current time slot (n) and the channel matrix H, construct the following matrices and vectors: Q n = U H (HH H ) -1 U,

[0163] S2. According to the modulation order M of PSK and the number of single-antenna users K, construct the following matrices and vectors

[0164] S3. Start extrapolating different symbol time slots within a transmission block, and initialize the symbol scaling factor in the ith time slot as Ω (i) = 1.

[0165] S4. Calculate the mathematical relationship s (i) between the symbol s in the ith symbol time slot and the symbol s in the nth symbol time slot (n) as s (i) = As (n) .

[0166] S5. Calculate the matrices and vectors corresponding to the ith symbol time slot Initialize the iteration count = 0.

[0167] S6. Enter the iterative loop, calculate the vector corresponding to the ith symbol time slot and select the vector q(i) The smallest value a in

[0168] S7. If a < 0, update the iteration count count = count + 1, and find the index corresponding to the value a in the vector q (i) in it. Assume the index is index.

[0169] S8. Update according to the index by selecting the scaling factor

[0170] S9. If a > 0, directly jump out of the entire iteration loop.

[0171] S10. When the iteration count is less than the required iteration count, repeat S6, S7, S8, S9.

[0172] S11. Perform power normalization processing

[0173] S12. Substitute into the closed-form solution to solve the precoding matrix:

[0174]

[0175] S13. Calculate the precoding matrix corresponding to the next symbol time slot, and return to S3.

[0176] Embodiment 3

[0177] Taking PSK modulation as an example, the low-complexity closed-form sub-optimal solution scheme proposed in the embodiment of the present invention includes the following steps:

[0178] S1. The transmitter obtains the channel state information H, the transmitted symbol s of the (n) th symbol time slot, and based on the transmitted symbol s of the current time slot (n) and the channel matrix H, construct the following matrices and vectors: Q n = U H (HH H ) -1 U,

[0179] S2. According to the modulation order of PSK and the number of single-antenna users K, construct the following matrices and vectors

[0180] S3. Start extrapolating different symbol time slots within a transmission block, and initialize the symbol scaling factor in the ith time slot to Ω (i) = 1.

[0181] S4. Calculate the symbol s within the ith symbol time slot (i)The mathematical relationship s between the symbol s within the nth symbol time slot (n) is s (i) = As (n) .

[0182] S5. Calculate the matrix and vector corresponding to the ith symbol time slot

[0183] S6. Calculate

[0184] S7. Perform power normalization processing

[0185] S8. Substitute into the closed-form solution to solve for the precoding matrix:

[0186]

[0187] S9. Calculate the precoding matrix corresponding to the next symbol time slot, and return to S3.

[0188] Embodiment 4

[0189] Taking QAM modulation as an example, the beneficial interference precoding solution method based on symbol-level extrapolation proposed in the embodiment of the present invention includes the following steps:

[0190] S1. According to the number of users K, construct the following matrix and vector

[0191] S2. The transmitting end obtains the channel state information H, and the transmitted symbol s of the th symbol time slot (n) , based on the transmitted symbol s of the current time slot (n) and the channel matrix H, construct the following matrix and vector: Q n = U H (HH H ) -1 U, T n =

[0192] S3. Start extrapolating different symbol time slots within a transmission block, initialize the symbol scaling factor within the ith time slot to Ω (i) = 1, and initialize the number of iterations to count = 0.

[0193] S5. Calculate the matrix and vector corresponding to the ith symbol time slot

[0194] S6. Calculate the vector corresponding to the ith symbol time slot

[0195] S7. If the set q (i) is not an empty set, then proceed to the next step.

[0196] S8. The minimum value of the vector is a. If a < 0, update the iteration count count = count + 1, find the index corresponding to the value a in the vector , and assume the index is index.

[0197] S9. Select a scaling factor for update according to the index,

[0198] S10. Update the vector q (i) and

[0199] S11. If a > 0, directly jump out of the entire iteration loop.

[0200] S12. When the iteration count is less than the required iteration count, repeat S8, S9, S10.

[0201] S13. If it is an empty set, then directly start the calculation from S12.

[0202] S14. Perform power normalization processing

[0203] S15. Substitute into the closed - form solution to solve for the precoding matrix:

[0204]

[0205] S16. Calculate the precoding matrix corresponding to the next symbol time slot, and return to S3.

[0206] Example 5

[0207] Taking QAM modulation as an example, the low - complexity closed - form sub - optimal solution scheme proposed in the embodiment of the present invention includes the following steps:

[0208] 1. According to the number of users K, construct the following matrices and vectors

[0209] S2. The transmitting end obtains the channel state information H, the transmitted symbol s (n) of the th symbol time slot, and based on the transmitted symbol s (n) of the current time slot and the channel matrix H, construct the following matrices and vectors: Q n = U H (HH H ) -1 U,

[0210] S3. Start extrapolating different symbol time slots within a transport block, and initialize the symbol scaling factor in the \(i\)-th time slot to \(\Omega\) (i) = 1.

[0211] S5. Calculate the matrix and vector corresponding to the \(i\)-th symbol time slot

[0212] S6. Calculate the symbol scaling coefficient corresponding to the \(i\)-th symbol time slot

[0213] S7. Perform power normalization processing

[0214] S8. Substitute into the closed-form solution to solve for the precoding matrix:

[0215]

[0216] S9. Calculate the precoding matrix corresponding to the next symbol time slot, and go back to S3.

[0217] The implementation effect of the beneficial interference precoding solution method based on symbol-level extrapolation in the embodiments of the present invention is further illustrated by the following simulation experiments.

[0218] The proposed scheme is simulated using the Monte Carlo simulation method.

[0219] The test conditions are as follows:

[0220] In a multi-user MIMO downlink, the transmitter is equipped with \(M\) t transmit antennas, and the receiver is \(K\) single-antenna users. Assuming that the transmitter can obtain perfect channel state information, the received vector \(r\) can be expressed as:

[0221] \(r = H W s + n\)

[0222] where \(s\) is the modulated transmit vector, \(W\) is the precoding matrix, \(H\) is the channel matrix, and \(n\) is the noise vector. Specifically, assuming that the channel is a flat fading Rayleigh channel, each element of \(H\) follows a standard complex Gaussian distribution; the noise is additive white Gaussian noise, and each element of \(n\) follows a Gaussian distribution with a mean of 0 and a variance of \(\sigma\) 2 . Assuming that the transmit power \(p\) per time slot 0 = 1, the transmitter SNR can be expressed as \(\rho = 1 / \sigma\) 2 .

[0223] The simulation results are as Figures 3 to 7As shown in the figure. Among them, zero-forcing precoding, the closed-form iterative method in the existing literature, and the method of directly using the optimization package CVX are added in the simulation. These three methods can be regarded as the baseline schemes of the solution of the present invention.

[0224] Please refer to Figure 3 and Figure 4 . Figure 3 The bit error rate curves of different precoding schemes under QPSK modulation are simulated in it. The number of transmitting antennas M t = K = 8. First of all, the zero-forcing precoding scheme has the worst performance. Compared with the method of solving with the CVX optimization package, there is some performance loss for the low-complexity iterative scheme based on extrapolation proposed by the present invention. The performance of the closed-form suboptimal scheme proposed by the present invention is better than that of the zero-forcing precoding scheme. Although the performance of the closed-form iterative scheme in the reference literature is slightly better than the scheme proposed by the present invention, the complexity is greatly increased. Figure 4 The bit error rate curves of different precoding schemes under 8PSK modulation are simulated. The number of transmitting antennas M t = K = 12. From Figure 4 the results, it can be seen that the low-complexity scheme of the present invention is still available under 8PSK modulation, and the performance difference from the optimal solution is not large.

[0225] Please refer to Figures 5 to 7 . Figure 5 The average number of iterations of the low-complexity scheme proposed by the present invention is simulated. It can be seen that the proposed iterative algorithm only needs five iterations to converge, and the convergence speed is very fast. Figure 6 The average running time of different precoding schemes is simulated. First of all, the closed form of zero-forcing precoding makes its complexity the lowest, but the bit error rate performance is very poor; secondly, the complexity of the low-complexity scheme proposed by the present invention is greatly reduced compared with the two baseline schemes. At the same time, the performance gap between the extrapolation iterative scheme proposed by the present invention and the optimal solution is very small, further verifying the performance advantages and practical availability of the solution of the embodiment of the present invention.

[0226] Another embodiment of the present invention also proposes an electronic device, which is characterized by including:

[0227] A memory that stores at least one instruction; and a processor that executes the instruction stored in the memory to implement the beneficial interference precoding solution method based on symbol-level extrapolation.

[0228] Another embodiment of the present invention also proposes a computer-readable storage medium. At least one instruction is stored in the computer-readable storage medium, and the at least one instruction is executed by a processor in an electronic device to implement the beneficial interference precoding solution method based on symbol-level extrapolation.

[0229] Exemplarily, the instructions stored in the memory can be divided into one or more modules / units. The one or more modules / units are stored in a computer-readable storage medium and executed by the processor to implement the beneficial interference precoding solution method based on symbol-level extrapolation according to the present invention. The one or more modules / units can be a series of computer-readable instruction segments capable of accomplishing specific functions, and these instruction segments are used to describe the execution process of the computer program in the server.

[0230] The electronic device can be a computing device such as a smart phone, a notebook, a palm computer, and a cloud server. The electronic device may include, but is not limited to, a processor and a memory. Those skilled in the art can understand that the electronic device may further include more or fewer components, or combine certain components, or different components. For example, the electronic device may further include input / output devices, network access devices, a bus, etc.

[0231] The processor may be a central processing unit (CPU), or may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0232] The memory may be an internal storage unit of the server, such as the hard disk or memory of the server. The memory may also be an external storage device of the server, such as a plug-in hard disk equipped on the server, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. Further, the memory may also include both the internal storage unit and the external storage device of the server. The memory is used to store the computer-readable instructions and other programs and data required by the server. The memory may also be used to temporarily store data that has been output or is to be output.

[0233] It should be noted that for the information interaction, execution process, etc. between the above-mentioned module units, since they are based on the same concept as the method embodiment, for their specific functions and the technical effects brought, reference may be specifically made to the method embodiment section, and details are not elaborated herein.

[0234] Those skilled in the art can clearly understand that, for the convenience and conciseness of description, only the division of the above-mentioned functional units and modules is used as an example. In actual applications, the above-mentioned functions can be assigned to different functional units and modules according to needs, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. Each functional unit and module in the embodiments can be integrated into a processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of a software functional unit. In addition, the specific names of the functional units and modules are only for the convenience of mutual distinction and do not limit the protection scope of this application. The specific working processes of the units and modules in the above system can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0235] If the above-mentioned integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, to implement all or part of the processes in the above-mentioned method embodiments of this application, a computer program can be used to instruct relevant hardware to complete. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, the steps of the above-mentioned method embodiments can be implemented. Among them, the computer program includes computer program code, and the computer program code can be in the form of source code, object code, executable file or some intermediate form, etc. The computer-readable medium can at least include: any entity or device that can carry the computer program code to the photographing device / terminal device, recording medium, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electrical carrier signal, telecommunication signal, and software distribution medium. For example, a USB flash drive, a mobile hard disk, a magnetic disk, or an optical disc, etc.

[0236] In the above embodiments, the descriptions of the various embodiments have their own emphases. For the parts not detailed or recorded in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0237] The above embodiments are only used to illustrate the technical solutions of this application, rather than to limit it; although this application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included in the protection scope of this application.

Claims

1. A method for solving beneficial interference precoding based on symbol-level extrapolation, characterized in that: include: Using the precoding matrix corresponding to the nth symbol time slot in the same transmission block to extrapolate the precoding matrix of the mth time slot, and obtaining a closed-form solution structure of the symbol-level extrapolated beneficial interference precoding matrix; Based on the closed-form solution structure of the beneficial interference precoding matrix extrapolated at the symbol level, the closed-form solution structure of the precoding matrix under the total transmit power constraint is obtained by combining the phase scaling criterion under PSK modulation and the symbol scaling criterion under QAM modulation. The scaling coefficient corresponding to the symbol time slot is solved and substituted into the closed-form solution structure of the precoding matrix to obtain the precoding matrix.

2. The method for solving beneficial interference precoding based on symbol-level extrapolation according to claim 1, characterized in that: The phase scaling criterion under the PSK modulation, under the total transmit power constraint, the optimization problem corresponding to the symbol scaling criterion of the nth symbol time slot beneficial interference precoding is constructed as follows: In the formula, is the precoding matrix of the nth symbol slot, H = [h1,h2,…,h K ] T is the channel matrix, is the transmitted signal vector of the nth time slot, the set represents the set of scaling factors corresponding to the constellation points utilizing beneficial interference in the nth time slot, and They represent the vectors of the constellation points of the kth user decomposed along the detection threshold, and represents the scaling factor of the kth user; for PSK modulation, within a transmission block, the optimization problem corresponding to the symbol scaling criterion of the beneficial interference precoding of the mth symbol time slot is in the same form.

3. The method for solving beneficial interference precoding based on symbol-level extrapolation according to claim 2, characterized in that: The symbol scaling criterion under the QAM modulation, under the total transmit power constraint, the symbol-level precoding optimization problem of beneficial interference is: In the formula, the set The elements in are the real or imaginary parts of the constellation points in the QAM constellation diagram that can be used for interference. The elements in are the real or imaginary parts of the constellation points in the QAM constellation diagram that cannot be used for interference.

4. The method for solving beneficial interference precoding based on symbol-level extrapolation according to claim 3, characterized in that: In the step of extrapolating the precoding matrix of the mth time slot using the precoding matrix corresponding to the nth symbol time slot in the same transmission block, the extrapolated closed-form solution structure of the beneficial interference precoding matrix with total power constraint under PSK modulation is: In the formula, s (m) =As (n) , Q n =U H (HH H ) -1 U, Represents the matrix V corresponding to the nth symbol slot n A mapping function between the scaling factors corresponding to the mth symbol slot; The closed-form solution structure of the symbol-level extrapolated beneficial interference precoding matrix under QAM modulation is: In the formula, Represents the matrix V corresponding to the nth symbol slot n A mapping function between the scaling factors corresponding to the mth symbol slot.

5. The method for solving beneficial interference precoding based on symbol-level extrapolation according to claim 4 is characterized in that: Under PSK modulation, the optimization problem corresponding to the symbol scaling criterion of the beneficial interference precoding in the nth symbol time slot is simplified to: s.t.Ω (n) V n Ω (n) -p0=0 Under QAM modulation, the symbol-level precoding optimization problem of beneficial interference is simplified to: s.t.Ω (n) V n Ω (n) -p0=0 In the formula, Ω (n) Indicates the scaling factor corresponding to the nth symbol slot.

6. The method for solving beneficial interference precoding based on symbol-level extrapolation according to claim 5, characterized in that: Under PSK modulation, the variable corresponding to the nth symbol time slot is calculated as follows: Q n =U H (HH H ) -1 U The variable corresponding to the nth symbol time slot is used to extrapolate the variable corresponding to the mth symbol time slot: s (m) =As (n) Through the matrix V m Solve the scaling factor corresponding to the mth time slot. The iterative algorithm updates only one scaling factor each time. The symbol scaling factor is updated by calculating the variable q of the mth symbol time slot. (m) , the calculation formula is as follows: Select the index of the element with the smallest value less than 0 in the variable as the position to update the symbolic scaling factor; initialize the scaling factor Ω (m) =1, when the kth scaling factor is selected for update, the updating expression of the scaling factor is: After the symbol scaling factor is obtained, power normalization is performed as follows: Substitute into the closed-form solution structure of the precoding matrix to obtain the precoding matrix.

7. The method for solving beneficial interference precoding based on symbol-level extrapolation according to claim 6, characterized in that: Alternatively, the iterative calculation process of solving the symbol scaling factor can be omitted, and the symbol scaling factor can be solved directly. A threshold can be set to force the solved symbol scaling factor to be greater than or equal to 1. The expression for solving the symbol scaling factor is as follows: After power normalization, the scaling coefficients of the symbols are substituted into the closed-form solution structure of the precoding matrix to obtain the precoding matrix.

8. The method for solving beneficial interference precoding based on symbol-level extrapolation according to claim 5, characterized in that: Under QAM modulation, the variable corresponding to the nth symbol time slot is calculated as follows: Q n =U H (HH H ) -1 U According to the formula, the variable Q corresponding to the nth time slot is n Extrapolate the variable V corresponding to the mth time slot m : By V m Solve the scaling factor corresponding to the mth time slot. The iterative algorithm updates only one scaling factor each time. The symbol scaling factor is updated by calculating the variable q of the mth symbol time slot. (m) , the calculation formula is as follows: For QAM modulation, the index of the symbol scaling factor is divided into two sets according to whether the symbol scaling factor can utilize beneficial interference. represents the set of indices of scaling factors that cannot exploit beneficial interference, A set of indices representing scaling factors capable of exploiting beneficial interference; Press the formula to change q (m) The scaling factor of the beneficial interference can be used to extract: For the iterative algorithm, only one scaling factor is updated each time, and the variable The index of the element with the smallest value less than 0 in is used as the position to update the symbol scaling coefficient. The update expression of the symbol scaling coefficient for each iteration is: After the symbol scaling factor is obtained, power normalization is performed as follows: Substitute into the closed-form solution structure of the precoding matrix to obtain the precoding matrix.

9. The method for solving beneficial interference precoding based on symbol-level extrapolation according to claim 8, characterized in that: Alternatively, the iterative calculation process of solving the symbol scaling factor can be omitted, and the symbol scaling factor can be solved directly. A threshold can be set to force the solved symbol scaling factor to be greater than or equal to 1. The expression for solving the symbol scaling factor is as follows: After power normalization, the scaling coefficients of the symbols are substituted into the closed-form solution structure of the precoding matrix to obtain the precoding matrix.

10. A beneficial interference precoding solution system based on symbol-level extrapolation, characterized in that: include: A closed-form solution structure acquisition module is used to use the precoding matrix corresponding to the n-th symbol time slot in the same transmission block to extrapolate the precoding matrix of the m-th time slot, and obtain the closed-form solution structure of the beneficial interference precoding matrix extrapolated at the symbol level; A closed-form solution structure constraint module is used for obtaining a closed-form solution structure of a beneficial interference precoding matrix based on symbol-level extrapolation, combining a phase scaling criterion under PSK modulation and a symbol scaling criterion under QAM modulation, to obtain a closed-form solution structure of the precoding matrix under total transmit power constraints; The precoding matrix solving module is used to solve the scaling coefficient corresponding to the symbol time slot, and substitute it into the closed solution structure of the precoding matrix to obtain the precoding matrix.

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