CN111162828B - Low-complexity signal detection method of large-scale MIMO system - Google Patents

Low-complexity signal detection method of large-scale MIMO system Download PDF

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CN111162828B
CN111162828B CN201911276647.6A CN201911276647A CN111162828B CN 111162828 B CN111162828 B CN 111162828B CN 201911276647 A CN201911276647 A CN 201911276647A CN 111162828 B CN111162828 B CN 111162828B
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vector
value
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CN111162828A (en
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邓炳光
李晨
张旭辉
徐方圆
温鹏瑜
沈艳
禹斯译
张治中
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • 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
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/0848—Joint weighting
    • H04B7/0854—Joint weighting using error minimizing algorithms, e.g. minimum mean squared error [MMSE], "cross-correlation" or matrix inversion
    • H—ELECTRICITY
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H04B7/0486—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting taking channel rank into account
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
    • H04L1/0047—Decoding adapted to other signal detection operation
    • H04L1/0048—Decoding adapted to other signal detection operation in conjunction with detection of multiuser or interfering signals, e.g. iteration between CDMA or MIMO detector and FEC decoder

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Abstract

The invention relates to a low-complexity signal detection method of a large-scale MIMO system, which belongs to the technical field of communication test and comprises the following steps: s1: converting channel model of large-scale MIMO system into equivalent substantial model, constructing filter matrix W, and receiving estimation matrix
Figure DDA0002315740880000011
And matched filter output matrix
Figure DDA0002315740880000012
S2: iteratively solving the received signal by adopting a GS algorithm according to the model constructed in the step S1; s3: and optimizing the GS algorithm detection result, performing region blocking on the constellation diagram by using a Fibonacci search algorithm, and selecting a proper iteration initial value to finish signal detection. The invention ensures that the signal detection performance is close to the foundation of the error rate performance of the MMSE algorithm, and simultaneously reduces the algorithm complexity by one order of magnitude.

Description

Low-complexity signal detection method of large-scale MIMO system
Technical Field
The invention belongs to the technical field of communication test, and relates to a low-complexity signal detection method of a large-scale MIMO system.
Background
The core idea of a large-scale Multiple-Input Multiple-Output (MIMO) technology is to equip hundreds of antennas for a Base Station (BS), so as to implement simultaneous data transmission and reception of a large number of antennas and to simultaneously serve a plurality of users in the same frequency band, thereby improving the spectrum efficiency and system capacity of a wireless communication system.
However, the advantages of massive MIMO systems come at the cost of significantly increased signal processing complexity. For signal reception, hundreds of transmit-receive antennas will complicate the signal at the receiving end, which makes signal detection very difficult, so that it is one of the most challenging tasks for large-scale MIMO systems to develop a signal detection technique with reasonable complexity, especially when high-order modulation is adopted. The Maximum Likelihood (ML) algorithm has the best detection performance, but the algorithm complexity increases exponentially with the increase of the number of antennas and the modulation order, and is difficult to apply to a real communication system. In order to obtain near-optimal detection performance with low complexity, some non-linear algorithms, such as active Tabu Search (RTS) algorithm, Likelihood Ascending Search (LAS) algorithm, and Markov Chain Monte Carlo (MCMC) algorithm, are proposed, but the detection performance under high-order modulation is not ideal. As the number of antennas at the receiving end increases, the channels gradually become orthogonal to each other, and a "channel hardening" phenomenon appears, and at this time, some simple linear detection algorithms, such as Zero Forcing (ZF) and Minimum Mean Square Error (MMSE) algorithms, may obtain near-optimal detection performance, but the algorithms involve high-dimensional matrix inversion. In the face of a large-scale MIMO system with hundreds of antennas, it is a current research hotspot to research an algorithm with high detection performance and low complexity.
The existing linear signal detection method generally adopts a Neumann series approximation algorithm, when the iteration number is not more than 3, the calculated amount is obviously reduced, and when the ratio of the receiving and transmitting antennas is close to 1, larger performance loss is brought. Performance degradation is significant as the number of iterations increases. In addition, Richardson (RI), Newton iteration (Newton), Gaussian iteration (Gauss-Seidel, GS) and the like can be used, matrix inversion is avoided by solving the optimal solution of a linear equation, the algorithm has convergence when the weighting matrix has the characteristics of symmetry positive definite or diagonal dominance and the like, and otherwise, the performance loss of the algorithm is large. The RI algorithm has intermediate performance, the Newton algorithm has local convergence, the algorithm complexity is high due to the fact that high iteration times are needed, the GS algorithm can obtain an initial solution vector which is approximate to MMSE, the convergence speed is low, and the complexity is low compared with other solutions.
Disclosure of Invention
In view of the above, the present invention aims to provide a low-complexity signal detection method for a large-scale MIMO system, and firstly, aiming at the problem that linear detection and nonlinear detection algorithms need high-dimensional matrix inversion due to the increase of antenna scale, the present invention applies a GS algorithm to the large-scale MIMO system, and the algorithm avoids the complex high-dimensional matrix inversion by solving a linear equation, so as to obtain accurate MMSE estimation in an iterative manner. Further, in order to accelerate the convergence speed, a GS optimization algorithm based on a regional constellation diagram is provided, the region blocking is carried out on the constellation diagram by utilizing a Fibonacci search algorithm, and an iterative initial solution is optimized, so that the calculated amount is further reduced. The method ensures that the signal detection performance is close to the base of the error rate performance of the MMSE algorithm, and simultaneously reduces the algorithm complexity by one order of magnitude.
In order to achieve the purpose, the invention provides the following technical scheme:
a low-complexity signal detection method of a large-scale MIMO system comprises the following steps:
s1: converting channel model of large-scale MIMO system into equivalent substantial model, constructing filter matrix W, and receiving estimation matrix
Figure BDA0002315740860000024
And matched filter output matrix
Figure BDA0002315740860000025
S2: iteratively solving the received signal by adopting a GS algorithm according to the model constructed in the step S1;
s3: and optimizing the GS algorithm detection result, performing region blocking on the constellation diagram by using a Fibonacci search algorithm, and selecting a proper iteration initial value to finish signal detection.
Further, step S1 specifically includes the following steps:
s11: when NT transmitting antennas and MR receiving antennas are used and the channel is a quasi-static flat fading channel, the channel model of the system is as follows:
yMR×1＝HMR×NTxNT×1+nMR×1
wherein y represents a received signal, H represents a static flat fading channel matrix, the matrix elements satisfy CN (0,1), x sends a signal vector, n receives a complex additive white Gaussian noise vector, and follows independent distribution CN (0, sigma)2)；
S12: converting the model, wherein the real-valued model is as follows:
Figure BDA0002315740860000021
the received signal estimate for the MMSE algorithm is represented as:
Figure BDA0002315740860000022
wherein W is HHH+δ2I2NTRepresents the MMSE filtering matrix and the MMSE filtering matrix,
Figure BDA0002315740860000023
representing the matched filter output matrix.
Further, step S2 specifically includes the following steps:
s21: when MR > NT, the channel matrix H is full rank, then the equation Hp has a unique solution of 0, i.e., p is a K × 1 zero vector, so for any K × 1 non-zero vector x, there is:
Figure BDA0002315740860000031
the above formula shows that the matrix HHH is Hermitian positive, again because of the noise variance δ2The MMSE filter matrix W is Hermitian positive, and the convergence of the GS iterative algorithm is guaranteed by the characteristics;
s22: decomposing the MMSE filter matrix W:
W＝D+L+U
wherein D represents a matrix formed by diagonal elements of the matrix W, L represents a matrix formed by strictly lower triangular elements of the matrix W, and U represents a matrix formed by strictly upper triangular elements of the matrix W;
s23: applying the GS algorithm to solve the M-dimensional linear equation: ax ═ b, where a is the M × MHermitian positive definite matrix representing the filter matrix W, x is the M × 1 solution vector, and b is the M × 1 measurement vector representing the matched filter output matrix
Figure BDA00023157408600000317
Solving the optimal solution of the linear equation by the GS algorithm through an iteration method; according to the GS algorithm formula, the method comprises the following steps:
Figure BDA0002315740860000032
usually the initial solution vector of the GS iterative algorithm is x(0)For a zero vector matrix, estimating a receiving vector value x through the (i +1) th iteration(i+1)。
Further, step S3 specifically includes the following steps:
s31: initializing regional constellation parameters: dividing the constellation diagram into segments based on the modulation order Q of the signal
Figure BDA0002315740860000033
Regions of mutually non-overlapping blocks, each small region having a width of
Figure BDA0002315740860000034
Square of (2);
s32: roughly judging which region of the mapped constellation diagram the initial value belongs to;
the signal estimation value is received by the linear MMSE algorithm in S1:
Figure BDA0002315740860000035
Figure BDA0002315740860000036
indicating that the transmission is to the ith element,
Figure BDA0002315740860000037
representing the i-th element of the received vector, Wi,jI row and j column representing W;
judging that diagonal elements of the filter matrix W are dominant and are positive numbers according to the characteristics of diagonal dominance, positive definite symmetry and the like:
Figure BDA0002315740860000038
according to the received vector
Figure BDA0002315740860000039
Positive and negative judgment receiving vector estimation value of real and imaginary parts
Figure BDA00023157408600000310
Positive and negative of real and imaginary parts to obtain
Figure BDA00023157408600000311
The area where the device is located;
Figure BDA00023157408600000312
when the concentration of the carbon dioxide is more than 0,
Figure BDA00023157408600000313
the region is [2n,2(n +)1)]，
Figure BDA00023157408600000314
The other case is
Figure BDA00023157408600000315
In the region of [ -2(n +1), -2n [ - ]]，
Figure BDA00023157408600000316
S33: constructing a Fibonacci array F (k), the Fibonacci being defined by a recursive method: f (1) ═ 1, F (2) ═ 1, F (k) ═ F (k-1) + F (k-2) (k > ═ 2);
s34: constructing a search array, initializing a region constellation map range as array [0,2,4, …,2n ] or array [0, -2, -4, …, -2n ] according to the judgment result of the step S32, wherein n is the length of the array to be searched;
calculating the position of the array length n in the Fibonacci sequence: n > F (k) -1; solving a minimum k value meeting the condition;
finally, the length n of the array is expanded to F (k), if elements need to be supplemented, the last element is supplemented and repeated until the length F (k) is met;
s35: carrying out Fibonacci division, namely dividing the search array into F (k-1) elements in the first half part and F (k-2) elements in the second half part, and carrying out recursive search until a stop condition is met;
initializing and searching parameters: the array bit sequence low is 0, high is n-1;
receiving a vector
Figure BDA0002315740860000044
And the boundary value m ═ array [ mid]Performing operation, and updating the boundary bit sequence mid to low + F (k-1) -1;
Figure BDA0002315740860000041
find out
Figure BDA0002315740860000042
Judging whether the array bit sequence is updated to be low or high;
Figure BDA0002315740860000043
the left bit sequence update low + mid +1, k-2 indicates that the boundary value to be searched is [ mid +1, high ═ h ═ m-]Within the range;
updating high-1, k-1 of the else right bit sequence, wherein the boundary value to be searched is in the range of [ low, mid-1 ];
finally, when the value array [ high ] -array [ low ] < ═ Z, the iteration ends; determining the bit sequence of the updated initial value;
s36: finding out new iteration initial value
If the bit sequence high obtained in step S35 is greater than n, it indicates that the found value is an extended value, and the initial value should be array [ n-1], otherwise, it indicates that the found position is the position of the initial value, and the initial value is array [ high ].
The invention has the beneficial effects that: the invention applies the GS algorithm to a large-scale MIMO system, and the algorithm avoids complex high-dimensional matrix inversion by solving a linear equation, and obtains accurate MMSE estimation in an iterative mode. Further, in order to accelerate the convergence speed, a GS optimization algorithm based on a regional constellation diagram is provided, the region blocking is carried out on the constellation diagram by utilizing a Fibonacci search algorithm, and an iterative initial solution is optimized, so that the calculated amount is further reduced. The method ensures that the signal detection performance is close to the base of the error rate performance of the MMSE algorithm, and simultaneously reduces the algorithm complexity by one order of magnitude.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a schematic flow chart of a low complexity signal detection method for a massive MIMO system according to the present invention;
FIG. 2 is a schematic diagram of a massive MIMO system model according to the present invention;
FIG. 3 is an initial solution comparison of a conventional algorithm and an optimization algorithm;
FIG. 4 is a flow chart of optimized GS algorithm signal detection;
fig. 5 is a flowchart of the initial value optimization of the fibonacci search algorithm.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Wherein the showings are for the purpose of illustrating the invention only and not for the purpose of limiting the same, and in which there is shown by way of illustration only and not in the drawings in which there is no intention to limit the invention thereto; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "front", "rear", etc., based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not an indication or suggestion that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes, and are not to be construed as limiting the present invention, and the specific meaning of the terms may be understood by those skilled in the art according to specific situations.
The invention provides a low-complexity signal detection method of a large-scale MIMO system, as can be seen from FIG. 3, the distance from the traditional zero vector initial solution to the transmitting vector is obviously greater than the distance from the optimized initial solution to the transmitting vector, which shows that the initial solution based on the regional constellation diagram provided by the invention is closer to the actual transmission symbol, and the GS iterative algorithm can quickly converge to the final estimated value. Therefore, the number of iterations required for the algorithm to reach the corresponding estimated value is reduced, which further reduces the computational complexity of the algorithm.
The invention is described in more detail below, by way of example, with reference to the accompanying drawings, as shown in figures 1 and 2:
s01, for the NT transmitting antennas, the MR receiving antennas, the channel model of the massive MIMO system is:
yMR×1＝HMR×NTxNT×1+nMR×1
wherein y represents a received signal, H represents a static flat fading channel matrix, the matrix elements satisfy CN (0,1), x sends a signal vector, n receives a complex additive white Gaussian noise vector, and follows independent distribution CN (0, sigma)2)。
S02, converting the model, wherein the real-valued model is as follows:
Figure BDA0002315740860000061
then, in a massive MIMO system, the received signal estimation of the MMSE algorithm can be expressed as:
Figure BDA0002315740860000062
wherein W is HHH+δ2I2NTRepresents the MMSE filtering matrix and the MMSE filtering matrix,
Figure BDA0002315740860000063
representing the matched filter output matrix.
As shown in fig. 4, S03 iteratively solves the received signal by using the GS algorithm:
when MR > NT, the channel matrix H is full rank, then the equation Hp has a unique solution of 0, i.e., p is a K × 1 zero vector, so for any K × 1 non-zero vector x, there is:
Figure BDA0002315740860000064
the above formula shows that the matrix HHH is Hermitian positive, again because of the noise variance δ2Is a positive number, so the MMSE filter matrix W is Hermitian positive definite, and the characteristic ensures the convergence of the GS iterative algorithm.
S04, decomposing an MMSE filter matrix W:
W＝D+L+U
where D represents a matrix composed of diagonal elements of the matrix W, L represents a matrix composed of strictly lower triangular elements of the matrix W, and U represents a matrix composed of strictly upper triangular elements of the matrix W.
The S05, GS algorithm may be applied to solve the M-dimensional linear equation: ax ═ b, where a is the M × MHermitian positive definite matrix representing the filter matrix W, x is the M × 1 solution vector, and b is the M × 1 measurement vector representing the matched filter output matrix
Figure BDA0002315740860000067
Namely, the GS algorithm can solve the optimal solution of the linear equation by an iterative method. According to the GS algorithm formula, the following results are obtained:
Figure BDA0002315740860000068
usually the initial solution vector of the GS iterative algorithm is x(0)Is a zero vector matrix. Estimating a receiving vector value x through the i +1 th iteration(i+1)。
As shown in fig. 5, S06 redefines the initial value using the fibonacci search algorithm.
Firstly, initializing regional constellation map parameters: dividing the constellation diagram into segments based on the modulation order Q of the signal
Figure BDA0002315740860000065
Regions of mutually non-overlapping blocks, each small region having a width of
Figure BDA0002315740860000066
Square of (2).
S07, roughly determining which region of the mapped constellation the initial value belongs to.
The signal estimation value received by the linear MMSE algorithm in S02 can be obtained:
Figure BDA0002315740860000071
Figure BDA0002315740860000072
indicating that the transmission is to the ith element,
Figure BDA0002315740860000073
representing the i-th element of the received vector, Wi,jI-th row and j-th column of W.
Then, according to the characteristics of diagonal dominance, positive definite symmetry and the like, the fact that diagonal elements of the filter matrix W are dominance and are all positive numbers can be judged.
Figure BDA0002315740860000074
Finally according to the received vector
Figure BDA0002315740860000075
Positive and negative judgment receiving vector estimation value of real and imaginary parts
Figure BDA0002315740860000076
Positive and negative for real and imaginary parts. Thereby obtaining
Figure BDA0002315740860000077
The area of the site.
Figure BDA0002315740860000078
When the concentration of the carbon dioxide is more than 0,
Figure BDA0002315740860000079
in the region of [2n,2(n +1) ]]，
Figure BDA00023157408600000710
The other case is
Figure BDA00023157408600000711
In the region of [ -2(n +1), -2n [ - ]]，
Figure BDA00023157408600000712
S08, constructing a Fibonacci array F (k), wherein the Fibonacci is defined by a recursive method: f (1) ═ 1, F (2) ═ 1, F (k) ═ F (k-1) + F (k-2) (k > ═ 2).
S09, constructing and searching an array, initializing the area constellation diagram range as array [0,2,4, …,2n ] or array [0, -2, -4, …, -2n ] by the judgment result of S07, wherein n is the length of the array to be searched.
Calculating the position of the array length n in the Fibonacci sequence: n > F (k) -1. The minimum k value satisfying the condition may be obtained.
Finally, the array length n is extended to F (k), and if the element needs to be supplemented, the last element is complementally repeated until the length F (k) is met.
And S10, carrying out Fibonacci division, namely dividing the search array into F (k-1) elements in the first half and F (k-2) elements in the second half, and carrying out recursive search until a stop condition is met.
Initializing and searching parameters: the array bit sequence low is 0 and high is n-1.
Receiving a vector
Figure BDA00023157408600000716
And the boundary value m ═ array [ mid]The operation is performed to update the boundary bit sequence mid to low + F (k-1) -1.
Figure BDA00023157408600000713
Find out
Figure BDA00023157408600000714
The positive or negative property of (2) can be determined whether the array bit sequence is updated to be low or high.
Figure BDA00023157408600000715
The left-order update low + mid +1, k-2 indicates that the boundary value to be searched is [ mid +1, high ═ 2]Within the range.
And (4) updating the else right bit sequence by high-1 and k-1, wherein the boundary value to be searched is in the range of [ low, mid-1 ].
Finally, the iteration ends when the value array [ high ] -array [ low ] < ═ Z. And determining the bit sequence of the updated initial value.
And S11, solving a new iteration initial value.
If the bit sequence high obtained from S10 is greater than n, it indicates that the found is an extended numerical value, and the initial value should be array [ n-1], otherwise, it indicates that the found position is the position where the initial value is located, and the initial value is array [ high ].
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.

Claims (1)

1. A low-complexity signal detection method of a large-scale MIMO system is characterized in that: the method comprises the following steps:
s1: converting the channel model of large-scale MIMO system into equivalent real-valued model, constructing filter matrix W, and receiving estimation matrix
Figure FDA0003515051800000011
And matched filter output matrix
Figure FDA0003515051800000012
Step S1 specifically includes the following steps:
s11: when NT transmitting antennas and MR receiving antennas are used and the channel is a quasi-static flat fading channel, the channel model of the system is as follows:
yMR×1＝HMR×NTxNT×1+nMR×1
wherein y represents a received signal, H represents a static flat fading channel matrix, the matrix elements satisfy CN (0,1), x represents a transmitted signal vector, n represents a receiving end complex Gaussian white noise vector, and the receiving end complex Gaussian white noise vector follows independent distribution CN (0, sigma)2)；
S12: converting the model, wherein the real-valued model is as follows:
Figure FDA0003515051800000013
the received signal estimate for the MMSE algorithm is represented as:
Figure FDA0003515051800000014
wherein W is HHH+δ2I2NTRepresents the MMSE filtering matrix and the MMSE filtering matrix,
Figure FDA0003515051800000015
representing a matched filter output matrix;
s2: iteratively solving the received signal by adopting a GS algorithm according to the model constructed in the step S1; step S2 specifically includes the following steps:
s21: when MR > NT, the channel matrix H is full rank, then the equation Hp has a unique solution of 0, i.e., p is a K × 1 zero vector, so for any K × 1 non-zero vector x, there is:
Figure FDA0003515051800000016
the above formula shows that the matrix HHH is Hermitian positive, again because of the noise variance δ2The MMSE filter matrix W is Hermitian positive definite, so that the convergence of the GS iterative algorithm is ensured;
s22: decomposing the MMSE filter matrix W:
W＝D+L+U
wherein D represents a matrix formed by diagonal elements of the matrix W, L represents a matrix formed by strictly lower triangular elements of the matrix W, and U represents a matrix formed by strictly upper triangular elements of the matrix W;
s23: applying the GS algorithm to solve the M-dimensional linear equation: ax ═ b, where a is the M × M Hermitian positive definite matrix representing the filter matrix W, x is the M × 1 solution vector, and b is the M × 1 measurement vector representing the matched filter output matrix
Figure FDA0003515051800000017
Solving the optimal solution of the linear equation by the GS algorithm through an iteration method; according to the GS algorithm formula, the method comprises the following steps:
Figure FDA0003515051800000018
the initial solution vector of the GS iterative algorithm is x(0)For a zero vector matrix, estimating a receiving vector value x through the (i +1) th iteration(i +1)；
S3: optimizing a GS algorithm detection result, carrying out region blocking on a constellation diagram by utilizing a Fibonacci search algorithm, selecting a proper iteration initial value, and completing signal detection; step S3 specifically includes the following steps:
S31: initializing regional constellation parameters: dividing the constellation diagram into segments based on the modulation order Q of the signal
Figure FDA0003515051800000021
Regions of mutually non-overlapping blocks, each small region having a width of
Figure FDA0003515051800000022
Square of (2);
s32: roughly judging which region of the mapped constellation diagram the initial value belongs to;
the signal estimation value is received by the linear MMSE algorithm in S1:
Figure FDA0003515051800000023
Figure FDA0003515051800000024
indicating that the transmission is to the ith element,
Figure FDA0003515051800000025
representing the i-th element of the received vector, Wi,jI row and j column representing W;
judging that diagonal elements of the filter matrix W are dominant and are positive numbers according to the diagonal dominance and positive definite symmetry characteristics:
Figure FDA0003515051800000026
according to the received vector
Figure FDA0003515051800000027
Positive and negative judgment receiving vector estimation value of real and imaginary parts
Figure FDA0003515051800000028
Positive and negative of real and imaginary parts, therebyTo obtain
Figure FDA0003515051800000029
The area where the device is located;
Figure FDA00035150518000000210
when the concentration of the carbon dioxide is more than 0,
Figure FDA00035150518000000211
in the region of [2n,2(n +1) ]]，n＝0,1,2,…
Figure FDA00035150518000000212
The other case is
Figure FDA00035150518000000213
In the region of [ -2(n +1), -2n [ - ]]，n＝0,1,2,…
Figure FDA00035150518000000214
S33: constructing a Fibonacci array F (k), the Fibonacci being defined by a recursive method: f (1) ═ 1, F (2) ═ 1, F (k) ═ F (k-1) + F (k-2) (k > ═ 2);
s34: constructing a search array, initializing a region constellation map range as array [0,2,4, …,2n ] or array [0, -2, -4, …, -2n ] according to the judgment result of the step S32, wherein n is the length of the array to be searched;
calculating the position of the array length n in the Fibonacci sequence: n > F (k) -1; solving a minimum k value meeting the condition;
finally, the length n of the array is expanded to F (k), if elements need to be supplemented, the last element is supplemented and repeated until the length F (k) is met;
s35: carrying out Fibonacci division, namely dividing the search array into F (k-1) elements in the first half part and F (k-2) elements in the second half part, and carrying out recursive search until a stop condition is met;
initializing and searching parameters: the array bit sequence low is 0, high is n-1;
receiving a vector
Figure FDA00035150518000000216
And the boundary value m ═ array [ mid]Performing operation, and updating the boundary bit sequence mid to low + F (k-1) -1;
Figure FDA00035150518000000215
find out
Figure FDA0003515051800000031
Judging whether the array bit sequence is updated to be low or high;
if
Figure FDA0003515051800000032
the left bit sequence update low + mid +1, k-2 indicates that the boundary value to be searched is [ mid +1, high ═ h ═ m-]Within the range;
updating high-1, k-1 of the else right bit sequence, wherein the boundary value to be searched is in the range of [ low, mid-1 ];
finally, when the value array [ high ] -array [ low ] < ═ Z, the iteration ends; determining the bit sequence of the updated initial value;
s36: finding out new iteration initial value
If the bit sequence high obtained in step S35 is greater than n, it indicates that the found value is an extended value, and the initial value should be array [ n-1], otherwise, it indicates that the found position is the position of the initial value, and the initial value is array [ high ].
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