CN111404634B - Large-scale MIMO detection method, system and application based on variable step length iteration - Google Patents
Large-scale MIMO detection method, system and application based on variable step length iteration Download PDFInfo
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Abstract
The invention belongs to the field of wireless communication, and discloses a large-scale MIMO detection method, a large-scale MIMO detection system and application based on variable step length iteration. Determining an iteration formula of a variable step size iteration algorithm based on a discrete ZNN model and a Newton iteration formula of matrix inversion, giving an optimal step size updating formula, aiming at a filter matrix of an MMSE detection method, approximating the inversion result of the filter matrix through the variable step size iteration algorithm, substituting the obtained approximation value of the inversion of the filter matrix into the MMSE detection method, calculating a receiving estimation value by using the MMSE detection method formula, and evaluating whether the error rate verification algorithm can accelerate iterative convergence. Compared with an MMSE detection method, the method avoids a direct inversion process of a filter matrix, reduces the operation complexity and accelerates the convergence speed; under the iterative operation of the same order, the error rate obtained by the variable step iteration detection method is obviously lower than the error rate obtained by the conjugate gradient algorithm and the Newton iterative algorithm.
Description
Technical Field
The invention belongs to the field of wireless communication, and particularly relates to a large-scale MIMO detection method and system based on variable step length iteration and application.
Background
Compared with a single-antenna and small-scale MIMO system, the large-scale MIMO system greatly enlarges the scale of the antenna array, the number of the large-scale MIMO system can reach hundreds or more, and larger system capacity and higher spectrum utilization rate can be provided. However, as the number of antennas increases, the massive MIMO system also faces some problems, and it is one of the most important loops to achieve efficient and reliable signal detection at the receiving end.
In the conventional MIMO system signal detection, a nonlinear detection method and a linear detection method are mainly included. The nonlinear detection method comprises a Serial Interference Cancellation (SIC) algorithm, a QR decomposition algorithm, a spherical detection method and the like. Compared with the linear detection method, the nonlinear detection method has better performance, but the calculation complexity is greatly increased along with the increase of the number of transmitting and receiving antennas, the realization is difficult, and the method is not suitable for a large-scale MIMO system. The linear detection method has low complexity and good performance of minimum mean square error detection (MMSE) algorithm, and the calculation complexity is mainly concentrated on a filter matrix A ═ HHH+σ2And I, the inverse operation. Due to the large number of antennas in the large-scale MIMO system, the size of the filter matrix becomes large, and the complexity of directly performing the inversion operation is too high. There are two main research directions to solve this problem, one is to approximate with a polynomial expansion, such as the Neumann series expansion (Neumanneries), and the other is to estimate the inverse of the matrix by an iterative algorithm, such as the Newton iteration method. Under the same system configuration, the Newton iterative method is much faster in convergence speed than the Neumann series expansion method. However, the relatively precise values needed to obtain the inverse of the matrix still require multiple iterations.
In summary, the problems of the prior art are as follows: the traditional large-scale MIMO system signal detection method is low in convergence speed and high in detection system calculation complexity.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a large-scale MIMO detection method with variable step length iteration.
The invention is realized in this way, a large-scale MIMO detection method of variable step length iteration, comprising the following steps:
firstly, aiming at a filter matrix of an MMSE detection method, a variable step size iterative algorithm is adopted to approximate an inversion result;
secondly, replacing the inverse of the filter matrix in the MMSE detection method with the approximate result of the obtained inverse of the filter matrix, and calculating a receiving estimation value through an MMSE detection method formula;
and thirdly, verifying the performance of the MIMO detection method of variable step size iteration by analyzing the error rate.
Further, the first step specifically includes: filter matrix A ═ H for MMSE detection methodHH+σ2I, where σ2Is the noise variance, I is the identity matrix; solving the approximate inverse of the filter matrix A by adopting variable step length iteration, wherein the iteration formula of the variable step length iterative algorithm is Xk+1＝Xk-hkXk(AXk-I), wherein XkIs an approximation of the inverse of the matrix obtained for the kth iteration, hkIs the step size factor.
Further, the second step specifically includes: obtaining an approximate value X of the inverse of the filter matrix after the kth time variable step size iterative operationkThe receiving estimation value of the transmitting signal vector X is obtained by the MMSE detection method
Further, in the iterative formula of the variable step size iterative algorithm, a larger step size is selected during initial iteration, and as the number of iterations increases, the value of the step size gradually decreases and finally approaches to 1. Specifically, the optimal step size update formula is
hk＝1/(1-θ·trace(Ek)/N)
Wherein E iskIs an error matrix, N is the order of the matrix, and θ is an adjustment factor.
Further, the value range of the adjusting factor theta is [0,1], the larger the value of theta is, the larger the value of the step length in the initial iteration is, the worse the stability of the algorithm is, the smaller the value of theta is, the smaller the value of the step length in the initial iteration is, and the better the stability of the algorithm is. In order to meet the compromise between performance and stability, the value of theta can be taken to be about 0.8.
Another objective of the present invention is to provide a step-size-variable iterative massive MIMO detection system for implementing the step-size-variable iterative massive MIMO detection method, wherein the step-size-variable iterative massive MIMO detection system comprises: a transmitter and a receiver.
The transmitter transmits the required transmitted data to the receiver through a large-scale antenna through a wireless channel, and the receiver detects the signals by using a large-scale MIMO detection method based on variable step iteration.
Another object of the present invention is to provide a massive MIMO system applying the massive MIMO detection method based on variable step size iteration.
In summary, the advantages and positive effects of the invention are: the direct inversion operation of the filter matrix in the MMSE detection method is avoided, and on the basis of the Newton iterative algorithm, the step length of each iterative operation is changed, so that the convergence speed of the algorithm is increased, and the calculation complexity of the detection system is reduced.
The invention is mainly used for solving the problem of overhigh complexity of inversion operation of a large-scale matrix in large-scale MIMO linear detection, which is a difficult point in the key technology of 5G or even the next generation communication system. According to the invention, on the basis of a Newton iteration method, the step length of each step in the iteration of the algorithm is adjusted, so that the convergence speed of the algorithm is accelerated, and the BER curve after three iterations is obviously superior to the BER curve obtained by three iterations of the Newton iteration method; on the other hand, the computational complexity is greatly reduced, MMSE (minimum mean square error) needs to directly perform inversion operation on a large-scale matrix, the complexity is very high, and the complexity of a common linear detection method is O (N)t 3) The invention only needs O (N)t 2). The invention can accelerate the convergence speed of the algorithm and reduce the calculation complexity of the detection system.
Drawings
Fig. 1 is a flowchart of a large-scale MIMO detection method based on variable step size iteration according to an embodiment of the present invention.
Fig. 2 is a specific iteration flowchart of a variable step size iteration algorithm for matrix inversion in the large-scale MIMO detection method based on variable step size iteration according to the embodiment of the present invention.
Fig. 3 is a schematic structural diagram of a large-scale MIMO detection system based on variable step size iteration according to an embodiment of the present invention.
FIG. 4 shows a diagram of N provided by an embodiment of the present inventiont＝32，NrUnder the condition of 256, simulation results of the algorithm disclosed by the invention are compared with simulation results of a Newton iteration algorithm, a CG algorithm and an MMSE algorithm.
FIG. 5 shows a diagram of N provided by an embodiment of the present inventiont＝64，NrThe simulation results of the inventive algorithm and the Newton iterative algorithm, the CG algorithm and the MMSE algorithm are shown in a comparison schematic diagram under the condition of 512.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In view of the problems in the prior art, the present invention provides a method and a system for large-scale MIMO detection with variable step size iteration, which are described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the method for detecting a large-scale MIMO with variable step size iteration provided by the embodiment of the present invention includes the following steps:
s101: aiming at a filter matrix of an MMSE detection method, a variable step size iterative algorithm is adopted to approximate an inversion result;
s102: replacing the inverse of the filter matrix in the MMSE detection method with the approximate result of the obtained inverse of the filter matrix, and calculating a receiving estimation value through an MMSE detection method formula;
s103: and verifying the performance of the MIMO detection method of variable step length iteration by analyzing the error rate.
The large-scale MIMO detection method based on variable step iteration provided by the embodiment of the invention comprises the following steps:
first, the filter matrix a ═ H for the MMSE detection methodHH+σ2I, where σ2Is the noise variance, I is the identity matrix; solving the approximate inverse of the filter matrix A by adopting variable step length iteration, wherein the iteration formula of the variable step length iterative algorithm is Xk+1＝Xk-hkXk(AXk-I), wherein XkIs an approximation of the inverse of the matrix obtained for the kth iteration, hkIs the step size factor.
Step two, obtaining an approximate value X of the inverse of the filter matrix after the kth variable step size iterative operationkThe receiving estimation value of the transmitting signal vector X is obtained by the MMSE detection method
And thirdly, verifying the performance of the MIMO detection method of variable step size iteration by analyzing the error rate.
In a preferred embodiment of the invention, the optimal step-size factor in the step-size-variable iterative formula is given by
hk＝1/(1-θ·trace(Ek)/N)
Wherein E iskIs an error matrix, i.e. Ek＝I-XkA. The value range of the regulating factor theta is [0, 1%]In this embodiment, in order to balance the iteration speed and the algorithm stability, the optimal adjustment factor θ is 0.8.
As shown in fig. 3, the step-size-variable iterative massive MIMO detection system provided in the embodiment of the present invention includes: a transmitter and a receiver.
The transmitter transmits the required transmitted data to the receiver through a large-scale antenna through a wireless channel, and the receiver detects the signals by using a large-scale MIMO detection method based on variable step iteration.
The technical solution of the present invention is further described with reference to the following specific examples.
The large-scale MIMO detection method with variable step size iteration provided by the embodiment of the invention comprises the following steps:
(1) determining the initial value of the step size-variable iterative algorithm, wherein in a large-scale MIMO system, the filter matrix A of MMSE detection has a better property along with the transmitting antenna NtAnd a receiving antenna NrIncrease (both increase, ratio tends to be constant), matrix HHThe eigenvalues of H almost tend to determine the distribution, with the ratio of the main diagonal elements to the non-main diagonal elements becoming larger and larger, i.e. the channel hardening phenomenon. As the number of antennas tends to infinity, it can be assumed that the off-diagonal element strength tends to zero, i.e., as N approaches infinityt,Nr→∞，HHH/N→INt. The matrix inversion at this time only needs to take the reciprocal of the diagonal elements respectively. In the Newton iterative method, therefore, the initial value is generally set by taking the reciprocal of the diagonal component of the matrix a
Where D is the diagonal component of a. Initial value setting and Newton iteration of variable step size iterative algorithmThe substitution algorithm initial value setting is the same, taking the reciprocal of the diagonal component of the matrix a.
(2) Determining the size of the step size factor of the iteration, determining the initial value of the variable step size iterative algorithm in the last step, and recording as X0An error matrix of E can be obtained0＝I-X0A, then obtaining the step length h of the iteration according to a step length updating formula0＝1/(1-θ·trace(E0)/N)。
(3) Calculating the next approximate value by the step-length-variable iterative formula, and substituting the value obtained in the previous steps into the step-length-variable iterative formula to obtain X1＝X0-h0X0(AX0-I). Available of X1The initial value in the step (1) is replaced by a new iteration operation to obtain a more accurate approximate value of the inverse of the matrix a, and a specific iteration operation flow is shown in fig. 2.
(4) Detecting the received signal, substituting the approximate value of the inverse of the filter matrix A obtained by the iteration operation of the previous steps into the MMSE detection method formula
To obtain a signal detection value
The technical effects of the present invention will be described in detail with reference to simulations.
1. Simulation system parameter setting
The system adopts a typical modulation mode 64QAM in a 5G communication system for modulation; the channel parameter is a rayleigh fading channel; the noise parameter is complex additive white Gaussian noise vector, the mean value of the elements is zero, and the variance is
2. Emulated content
First simulation, 32 transmitting antennas and 256 receiving antennas are adopted to perform simulation comparison on the bit error rate curves of the variable step size iterative algorithm, the Newton iterative algorithm, the CG algorithm and the MMSE algorithm, and the result is shown in FIG. 4, so that the following conclusion can be obtained:
the performance of the algorithm is obviously superior to that of a CG algorithm with 3 iterations after the algorithm is used for 3 iterations; the error rate curve of the algorithm is superior to that of a Newton iterative algorithm after the signal-to-noise ratio is 16dB, and the requirement of the error rate is 10-5Compared with the Newton iterative algorithm, the performance of the method can be improved by at least 1 dB.
And secondly, increasing the number of antennas on the basis of the first simulation, adopting 64 transmitting antennas and 512 receiving antennas, performing 3 iterations on the algorithm, the Newton iteration algorithm and the CG algorithm, and performing simulation comparison on error rate curves of the two algorithms, wherein the results are shown in FIG. 5, the same results as the second simulation can be obtained, and the advantage that the algorithm can accelerate convergence is further illustrated.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (4)
1. A large-scale MIMO detection method based on variable step length iteration is characterized by comprising the following steps:
firstly, aiming at a filter matrix of an MMSE detection method, a variable step size iterative algorithm is adopted to approximate an inversion result;
substituting the obtained approximate result of the inverse of the filter matrix into an MMSE detection method, and calculating a receiving estimation value through an MMSE detection method formula;
thirdly, verifying the performance of the large-scale MIMO detection method of variable step length iteration by analyzing the error rate;
the first step specifically comprises: filter matrix A ═ H for MMSE detection methodHH+σ2I, where σ2Is the noise variance, I is the identity matrix; solving the approximate inverse of the filter matrix A by adopting variable step length iteration, wherein the iteration formula of the variable step length iterative algorithm is Xk+1＝Xk-hkXk(AXk-I), wherein XkIs an approximation of the inverse of the filter matrix, h, obtained for the kth iterationkIs a step size factor;
in an iteration formula of the variable-step iteration algorithm, a larger step length is selected during initial iteration, and the value of the step length is gradually reduced with the increase of iteration times and finally approaches to 1; specifically, the step updating formula is
hk＝1/(1-θ·trace(Ek)/N)
Wherein E iskIs an error matrix, N is the order of the matrix, and θ is an adjustment factor.
2. The massive MIMO detection method based on variable step size iteration of claim 1, wherein the second step specifically includes: obtaining an approximate value X of the inverse of the filter matrix after the kth time variable step size iterative operationkThe receiving estimation value of the transmitting signal vector X is obtained by the MMSE detection method
3. The large-scale MIMO detection method based on variable step size iteration as claimed in claim 1, wherein the adjustment factor θ has a value range of [0,1], the larger the value of θ, the larger the initial iteration step size, the worse the stability of the algorithm, the smaller the value of θ, the smaller the initial iteration step size, and the better the stability of the algorithm; in order to meet the compromise between performance and stability, the value of theta is taken as 0.8.
4. A massive MIMO iterative detection system for implementing the massive MIMO detection method based on variable step size iteration according to any one of claims 1 to 3, wherein the massive MIMO iterative detection system based on variable step size iteration comprises: a receiver, a transmitter;
the transmitter transmits the required transmitted data to the receiver through a large-scale antenna and a wireless channel, and the receiver detects the signals by using a large-scale MIMO detection method based on variable step iteration.
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