CN107222246B - Efficient large-scale MIMO detection method and system with approximate MMSE performance - Google Patents

Efficient large-scale MIMO detection method and system with approximate MMSE performance Download PDF

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CN107222246B
CN107222246B CN201710392735.7A CN201710392735A CN107222246B CN 107222246 B CN107222246 B CN 107222246B CN 201710392735 A CN201710392735 A CN 201710392735A CN 107222246 B CN107222246 B CN 107222246B
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张川
吴至榛
尤肖虎
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Southeast University
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    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
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Abstract

The invention discloses a high-efficiency large-scale MIMO detection method and a system with similar MMSE performance, and by introducing a precondition technology, the invention can remarkably accelerate the iteration rate of the traditional GS method, so that the large-scale MIMO detection algorithm provided by the invention can still quickly approach the performance of an accurate MMSE detection algorithm in a severe propagation environment (such as a channel with similar transmitting/receiving antenna number or larger spatial correlation). Numerical simulation results show that the error rate performance of the large-scale MIMO detection algorithm provided by the invention in a severe propagation environment is superior to that of the traditional large-scale MIMO detection algorithm based on Neumann series, GS method and CG method. On the other hand, the system provided by the invention innovatively exploits the cyclic shift characteristic of GS iteration in the element updating process, so that the GS iteration operation can be carried out with low hardware consumption and delay.

Description

Efficient large-scale MIMO detection method and system with approximate MMSE performance
Technical Field
The invention belongs to the field of computer communication and digital circuits, and relates to a high-efficiency large-scale MIMO detection method and system with approximate MMSE performance.
Background
Massive Multiple Input Multiple Output (MIMO) is recognized as one of the important technologies for 5 th generation (5G) wireless communication systems. The technique provides higher spectral efficiency, faster peak data rates and better energy efficiency than conventional small-scale MIMO systems by providing a large number of antennas at the base station and the user end. However, with the large increase in the number of antennas, the complexity of the baseband algorithm is also increasing dramatically in massive MIMO systems. Among them, the optimal multi-user detection methods for the uplink, such as Maximum Likelihood (ML) detection and Maximum A Posteriori (MAP) methods, will become overwhelming in terms of computational complexity (due to their exponential complexity). Therefore, a more practical and efficient detector design has attracted a lot of attention. In recent years, researchers have turned their attention to linear detection methods, such as traditional Zero Forcing (ZF) and Minimum Mean Square Error (MMSE), because of their suboptimal detection performance and low complexity characteristics in massive MIMO systems.
Notably for large scale MIMO systemsThe main computational complexity of the MMSE detection method is the inversion of a high-order matrix. Assuming that M is the number of single-antenna users, if an accurate matrix inversion method, such as Cholesky decomposition, is adopted, the computational complexity is O (M)3). This means that if the number of M is very large, accurate MMSE detection will require a huge amount of computation and hardware consumption.
In recent years, researchers at home and abroad successively propose a large-scale MIMO detection method based on Gauss-Seidel (GS) method, Neumann series and Conjugate Gradient (CG), and performance close to MMSE algorithm is obtained. The common point of these methods is that all are traditional iterative numerical computation methods, and although the computation complexity is reduced to some extent, their performance will be degraded or even unable to converge for the severe propagation environment (such as channels with close number of transmit/receive antennas or large spatial correlation).
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects of the prior art, the invention provides a high-efficiency large-scale MIMO detection method and system with similar MMSE performance.
The technical scheme is as follows: a high-efficiency large-scale MIMO detection method with approximate MMSE performance comprises the following steps:
step 1: pre-treating; inputting the channel matrix H and the received signal vector y into a detector to obtain the output y of the matched filterMF＝HHy and the regularized Gram matrix W ═ G + NoIMWherein Gram matrix G ═ HHH，NoAs a variance of the noise, IMIs an M-dimensional unit matrix, ()HIs a conjugate transpose operation;
step 2: calculating a normalized matrix
Figure BDA0001307898040000021
And normalized vector
Figure BDA0001307898040000022
Wherein D is a diagonal element matrix of W such that coefficient matrix diagonal elements are 1;
and step 3: pre-conditioning; constructing a preconditions matrix P ═ S + IMCalculating a coefficient matrix
Figure BDA0001307898040000023
Vector of sum constants
Figure BDA0001307898040000024
Wherein S is a sum
Figure BDA0001307898040000025
The matrix concerned is:
Figure BDA0001307898040000026
and 4, step 4: according to the coefficient matrix output in step 3
Figure BDA0001307898040000027
Vector of sum constants
Figure BDA0001307898040000028
Setting an iterative initial solution to x(0)When the value is equal to 0, starting iterative operation and outputting a detection result; the algorithm pseudo-code is as follows:
Figure BDA0001307898040000029
after K iterations, x(K)I.e. the estimated result of the signal to be detected.
The invention also provides a high-efficiency large-scale MIMO detection system with approximate MMSE performance, which comprises:
a pre-condition module for completing pre-processing, inputting the channel matrix H and the received signal vector y into the detector to obtain the output y of the matched filterMF＝HHy and the regularized Gram matrix W ═ G + NoIMWherein Gram matrix G ═ HHH，NoAs a variance of the noise, IMIs an M-dimensional unit matrix, ()HIs a conjugate transpose operation; then a normalization matrix is calculated
Figure BDA00013078980400000210
And normalized vector
Figure BDA00013078980400000211
Wherein D is a diagonal element matrix of W such that coefficient matrix diagonal elements are 1; finally constructing a precondition matrix P ═ S + IMCalculating a coefficient matrix
Figure BDA00013078980400000212
Vector of sum constants
Figure BDA00013078980400000213
Wherein S is a sum
Figure BDA00013078980400000214
A matrix of interest;
GS iteration module for completing coefficient matrix output according to precondition module
Figure BDA0001307898040000031
Vector of sum constants
Figure BDA0001307898040000032
Setting an iterative initial solution to x(0)And (5) performing iterative operation and outputting a retrieval result, wherein the algorithm pseudo code is as follows:
Figure BDA0001307898040000033
after K iterations, x(K)I.e. the estimated result of the signal to be detected.
Further, the precondition module comprises a matrix multiplier formed by 6 systolic arrays, 2 adder arrays and 1 reciprocal unit; wherein the matched filter output y is calculated using 2 systolic arraysMF＝HHy and the regularized Gram matrix W ═ G + NoIMWherein the processing unit of the systolic array is a basic complex multiply accumulator; computing a normalization matrix with another 2 systolic arrays
Figure BDA0001307898040000034
And normalized vector
Figure BDA0001307898040000035
Wherein D-1The pulse array is obtained by calculation of a reciprocal unit, the reciprocal unit is generated by a lookup table, and a processing unit of the pulse array is still a basic complex multiplication accumulator; computing a coefficient matrix using the remaining 2 systolic arrays
Figure BDA0001307898040000036
Vector of sum constants
Figure BDA0001307898040000037
Wherein the precondition matrix P is S + IM。
Furthermore, the GS iteration module includes M-1 complex multipliers, adders, and registers, which require M clock cycles for each turn of GS iteration, where M is the number of transmit antennas.
The working principle is as follows: considering that a filter matrix W in MMSE detection of an uplink of a large-scale MIMO system is Hermitian positive definite matrix and a main diagonal line is dominant, the GS iteration method adopted by the invention has certain convergence after multiple iterations. In a severe propagation environment (such as a channel with similar transmitting/receiving antenna numbers or larger spatial correlation), the pre-condition method adopted by the invention can reduce the spectrum radius of the iterative matrix to achieve the effect of accelerating convergence.
Has the advantages that: compared with the prior art, the method and the device mainly consider how to achieve the detection effect of the MMSE performance in a severe propagation environment (such as channels with similar transmitting/receiving antenna numbers or larger spatial correlation) with lower computation complexity. By adopting the pre-conditioning GS iteration method, the invention can obtain better error rate performance than the traditional large-scale MIMO detection algorithm based on Neumann series, GS method and CG method under the condition of the same iteration times, especially under the severe propagation environment (such as channels with similar transmitting/receiving antenna number or larger spatial correlation), and obtain the detection effect similar to MMSE performance after less iteration times. On the other hand, the system provided by the invention innovatively exploits the cyclic shift characteristic of GS iteration in the element updating process, so that the GS iteration operation can be carried out with low hardware consumption and delay. Furthermore, this characteristic also makes the design of the corresponding control circuit very easy.
Drawings
Fig. 1 is a bit error rate comparison graph (when the number of transmitting antennas is 32, the number of receiving antennas is 128, and the correlation coefficient is 0) between the signal detection method of the present invention and other conventional detection methods;
FIG. 2 is a comparison graph of the error rates of the signal detection method of the present invention and other conventional detection methods (when the number of transmitting antennas is 32, the number of receiving antennas is 128, and the correlation coefficient is 0.3);
FIG. 3 is a comparison graph of the error rates of the signal detection method of the present invention and other conventional detection methods (when the number of transmitting antennas is 16, the number of receiving antennas is 128, and the correlation coefficient is 0.3);
FIG. 4 is a bit error rate comparison graph (when the number of transmitting antennas is 8, the number of receiving antennas is 128, and the correlation coefficient is 0.3) using the signal detection algorithm of the present invention and other conventional detection algorithms;
FIG. 5 is a schematic view of the system of the present invention;
FIG. 6 is a schematic diagram of the GS iteration module in the system of the present invention;
fig. 7 is a schematic diagram of the timing scheduling of the GS iteration module in the system of the present invention (when the number of transmit antennas in the system is 4).
Detailed Description
The following describes embodiments of the present invention in detail with reference to the accompanying drawings;
in this embodiment, a massive MIMO uplink system is established for analog operation. In massive MIMO uplink, there is typically N > M (the number of base station antennas N is much larger than the number of transmit antennas, i.e., the number of users M). Firstly, parallel transmission bit streams generated by M different users are respectively encoded through channel coding, then mapped to constellation symbols, and subjected to constellation diagram set energy normalization. Let x be [ x ]1，x2，x3，...，xM]TRepresenting a signal vector, x comprising transmission symbols generated from M users respectivelyAnd adopting a 64-QAM mode for mapping. The H-dimension is an NxM channel matrix, so the received signal vector y at the uplink base station end can be expressed as
y＝Hx+n
Wherein y is an additive white noise vector of dimension Nx 1, and N is an additive white noise vector of dimension Nx 1, whose elements obey a zero mean variance of NoA gaussian distribution of (a). The task of uplink multiuser signal detection is to receive a vector y ═ y from the receiver1，y2，y3，...，yN]TThe transmitted signal symbol x is estimated. Assuming H is known, the estimation of the vector of the transmitted signal is expressed as
Figure BDA0001307898040000051
The estimation process is equivalent to solving a linear system of equations
Figure BDA0001307898040000052
Based on the model, the embodiment of the invention discloses a high-efficiency large-scale MIMO detection method with similar MMSE performance, which comprises the following steps:
step 1: preprocessing, inputting the channel matrix H and the received signal vector y into a detector to obtain the output y of a matched filterMF＝HHy and the regularized Gram matrix W ═ G + NoIMWherein Gram matrix G ═ HHH，NoAs a variance of the noise, IMIs an M-dimensional unit matrix, ()HIs a conjugate transpose operation;
step 2: computing
Figure BDA0001307898040000053
And
Figure BDA0001307898040000054
wherein D is a diagonal element matrix of W such that coefficient matrix diagonal elements are 1;
and step 3: pre-conditioning, constructing a pre-condition matrix P ═ S + IMCalculating
Figure BDA0001307898040000055
And
Figure BDA0001307898040000056
wherein S is a sum
Figure BDA0001307898040000057
The matrix concerned is:
Figure BDA0001307898040000058
and 4, step 4: according to the output of step 3
Figure BDA0001307898040000059
And
Figure BDA00013078980400000510
setting an iterative initial solution to x(0)When the value is equal to 0, starting iterative operation and outputting an estimation retrieval result; the algorithm pseudo-code is as follows:
Figure BDA00013078980400000511
after K iterations, x(K)I.e. the estimated result of the signal to be detected.
For a large-scale MIMO system with the antenna configuration (NxM) of 128 x 32 and the channel correlation coefficient of 0 (namely, the H matrix elements are i.i.d. distributed), 64-QAM mapping is adopted, and the numerical simulation result of the high-efficiency large-scale MIMO detection algorithm with the approximate MMSE performance is shown in figure 1; for a massive MIMO system with a channel correlation coefficient of 0.3 and antenna configurations of 128 × 32, 128 × 16, and 128 × 8, respectively, the numerical simulation results of the algorithm are shown in fig. 2, fig. 3, and fig. 4. Wherein, NS represents a detection algorithm based on Neumann series, CG represents a detection algorithm based on conjugate gradient, GS represents a detection algorithm based on traditional GS, PGS represents an efficient large-scale MIMO detection algorithm with approximate MMSE performance, and Cholesky represents an accurate MMSE detection algorithm. As can be seen from the results of fig. 1 and fig. 2, as the spatial correlation increases, the error rate performance of all compared algorithms is lost a lot at the same iteration number, but the advantages of the algorithm of the present invention compared with other algorithms become more obvious. As can be seen from fig. 2, fig. 3, and fig. 4, when the number of receiving antennas is 128, the error rate performance of all the compared algorithms gradually decreases with the increase of the number of transmitting antennas (the number of users), and the required iteration number gradually increases, however, the performance of the algorithm of the present invention is still better than that of other algorithms, and the error rate performance of the accurate MMSE detection algorithm can be approached after fewer iterations.
As shown in fig. 5, in terms of hardware architecture, the efficient massive MIMO detection system with approximate MMSE performance adopted in this embodiment mainly includes a precondition module and a GS iteration module, and a schematic diagram of the precondition module is shown in a dashed line in the figure.
Specifically, in the precondition module, the calculation process is as follows:
1) as shown in fig. 5, 2 systolic arrays (labeled in fig. 5)
Figure BDA0001307898040000068
) Calculating the matched filter output yMF＝HHy and the regularized Gram matrix W ═ G + NoIMWherein the adder array is represented as
Figure BDA0001307898040000066
The Processing Element (PE) of the systolic array is a basic complex Multiply Accumulator (MAC), noting that the systolic array used to compute the matrix-matrix multiplication is represented by M2The pulse array used for calculating matrix-vector multiplication consists of M PEs;
2) with 2 systolic arrays (labelled in figure 5)
Figure BDA0001307898040000067
) Calculating a normalized matrix
Figure BDA0001307898040000061
And normalized vector
Figure BDA0001307898040000062
Wherein D-1The pulse array is calculated by an inverse unit (marked as inv in fig. 5) (the inverse unit is generated by a lookup table, and a pulse array consists of 2M real number multipliers);
3) with 2 systolic arrays (labelled in figure 5)
Figure BDA0001307898040000063
) Calculating a coefficient matrix
Figure BDA0001307898040000064
Vector of sum constants
Figure BDA0001307898040000065
Wherein the precondition matrix P is S + IMThe elements can be taken directly from 2), noting that the systolic array for computing matrix-matrix multiplications is represented by M2The PE array is composed of M PEs, and the systolic array used for calculating matrix-vector multiplication is composed of M PEs.
As shown in fig. 6, in the GS iteration module, the calculation process is as follows:
1) at each clock cycle, the GS iteration module outputs
Figure BDA0001307898040000071
Wherein the complex multiplier and the complex adder are respectively labeled in FIG. 6
Figure BDA0001307898040000072
And
Figure BDA0001307898040000073
the delay cell is labeled D. After M clock cycles, one GS iteration is completed (timing schedule is shown in fig. 7, the solid line block corresponds to D in fig. 6), the calculation results of the first M-1 clock cycles are stored in a register, note that the values of b and a input by each multiplier are also periodically changed along with the clock cycles;
2) after KM clock cycles, the estimation result of the signal to be detected is obtained from the register, where K is the set GS iteration number, as shown in fig. 7, and M is a schematic diagram of element update in a system of 4.
By introducing a precondition (preconditioning) technology, the invention can remarkably accelerate the iteration rate of the traditional GS method, so that the large-scale MIMO detection algorithm provided by the invention can still quickly approach the performance of an accurate MMSE detection algorithm in a severe propagation environment (such as a channel with similar transmitting/receiving antenna numbers or larger spatial correlation). Numerical simulation results show that the error rate performance of the large-scale MIMO detection algorithm provided by the invention in a severe propagation environment is superior to that of the traditional large-scale MIMO detection algorithm based on Neumann series, GS method and CG method. Furthermore, the present invention provides a circuit design with low hardware consumption and low delay.

Claims (4)

1. A high-efficiency large-scale MIMO detection method with approximate MMSE performance is characterized by comprising the following steps:
step 1: pre-treating; inputting the channel matrix H and the received signal vector y into a detector to obtain the output y of the matched filterMF＝HHy and the regularized Gram matrix W ═ G + NoIMWherein Gram matrix G ═ HHH，NoAs a variance of the noise, IMIs an M-dimensional unit matrix, ()HIs a conjugate transpose operation;
step 2: calculating a normalized matrix
Figure FDA0002446005670000011
And normalized vector
Figure FDA0002446005670000012
Wherein D is a diagonal element matrix of W such that coefficient matrix diagonal elements are 1;
and step 3: pre-conditioning; constructing a preconditions matrix P ═ S + IMCalculating a coefficient matrix
Figure FDA0002446005670000013
Vector of sum constants
Figure FDA0002446005670000014
Wherein S is a sum
Figure FDA0002446005670000015
The matrix concerned is:
Figure FDA0002446005670000016
and 4, step 4: according to the coefficient matrix output in step 3
Figure FDA0002446005670000017
Vector of sum constants
Figure FDA0002446005670000018
Setting an iterative initial solution to x(0)When the value is equal to 0, starting iterative operation and outputting a detection result; the algorithm pseudo-code is as follows:
Figure FDA0002446005670000019
after K iterations, x(K)I.e. the estimated result of the signal to be detected.
2. An efficient massive MIMO detection system with approximate MMSE performance, comprising:
a pre-condition module for completing pre-processing, inputting the channel matrix H and the received signal vector y into the detector to obtain the output y of the matched filterMF＝HHy and the regularized Gram matrix W ═ G + NoIMWherein Gram matrix G ═ HHH，NoAs a variance of the noise, IMIs an M-dimensional unit matrix, ()HIs a conjugate transpose operation; then a normalization matrix is calculated
Figure FDA00024460056700000110
And normalized vector
Figure FDA00024460056700000111
Wherein D is a diagonal element matrix of W such that coefficient matrix diagonal elements are 1; finally constructing a precondition matrix P ═ S + IMCalculating a coefficient matrix
Figure FDA0002446005670000021
Vector of sum constants
Figure FDA0002446005670000022
Wherein S is a sum
Figure FDA0002446005670000023
The matrix concerned is:
Figure FDA0002446005670000024
GS iteration module for completing coefficient matrix output according to precondition module
Figure FDA0002446005670000025
Vector of sum constants
Figure FDA0002446005670000026
Setting an iterative initial solution to x(0)And (5) performing iterative operation and outputting a retrieval result, wherein the algorithm pseudo code is as follows:
Figure FDA0002446005670000027
after K iterations, x(K)I.e. the estimated result of the signal to be detected.
3. The system of claim 2, wherein the pre-conditioning module comprises a matrix multiplier comprising 6 systolic arrays, 2 adder arrays, and 1 reciprocal unit; wherein the matched filter output is calculated by using 2 systolic arraysGo out yMF＝HHy and the regularized Gram matrix W ═ G + NoIMWherein the processing unit of the systolic array is a basic complex multiply accumulator; computing a normalization matrix with another 2 systolic arrays
Figure FDA0002446005670000028
And normalized vector
Figure FDA0002446005670000029
Wherein D-1The pulse array is obtained by calculation of a reciprocal unit, the reciprocal unit is generated by a lookup table, and a processing unit of the pulse array is still a basic complex multiplication accumulator; computing a coefficient matrix using the remaining 2 systolic arrays
Figure FDA00024460056700000210
Vector of sum constants
Figure FDA00024460056700000211
Wherein the precondition matrix P is S + IM。
4. The system of claim 2, wherein the GS iteration module comprises M-1 complex multipliers, adders and registers, which require M clock cycles for each GS iteration, where M is the number of transmit antennas.
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