CN107835068B - Low-complexity orthogonal space modulation spherical decoding detection algorithm with transmit diversity - Google Patents

Low-complexity orthogonal space modulation spherical decoding detection algorithm with transmit diversity Download PDF

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CN107835068B
CN107835068B CN201711063638.XA CN201711063638A CN107835068B CN 107835068 B CN107835068 B CN 107835068B CN 201711063638 A CN201711063638 A CN 201711063638A CN 107835068 B CN107835068 B CN 107835068B
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CN107835068A (en
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金小萍
赵蒙蒙
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Zhejiang Zhiduo Network Technology Co ltd
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China Jiliang University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03178—Arrangements involving sequence estimation techniques
    • H04L25/03203—Trellis search techniques
    • H04L25/03242—Methods involving sphere decoding
    • 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
    • H04L1/0052—Realisations of complexity reduction techniques, e.g. pipelining or use of look-up tables
    • 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
    • H04L1/02—Arrangements for detecting or preventing errors in the information received by diversity reception
    • H04L1/06—Arrangements for detecting or preventing errors in the information received by diversity reception using space diversity
    • H04L1/0618—Space-time coding
    • H04L1/0631—Receiver arrangements
    • 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
    • H04L1/02—Arrangements for detecting or preventing errors in the information received by diversity reception
    • H04L1/06—Arrangements for detecting or preventing errors in the information received by diversity reception using space diversity
    • H04L1/0618—Space-time coding
    • H04L1/0637—Properties of the code

Abstract

The invention discloses a low-complexity orthogonal space modulation spherical decoding detection algorithm (DQSM-SD) with transmit diversity, which is characterized in that on the basis of activating an antenna by the traditional QSM, the method is converted into an activated space-time matrix to realize the transmit diversity, and meanwhile, the search zero is increased to shorten the search process of tree-shaped spherical decoding by combining the activation combination of a space-domain matrix, thereby reducing the detection complexity.

Description

Low-complexity orthogonal space modulation spherical decoding detection algorithm with transmit diversity
Technical Field
The invention belongs to the technical field of communication, relates to a method for constructing a signal at a transmitting end of a wireless communication system and a method for detecting a signal at a receiving end, and particularly relates to a low-complexity quadrature space modulation spherical decoding detection algorithm (DQSM-SD) with transmit diversity.
Background
Orthogonal spatial modulation (Quadrature spatial modulation QSM) not only retains almost all the advantages of SM, but also improves the transmission efficiency m of spatial modulation by adding a spatial dimension, i.e. loading the real part and imaginary part of the modulation symbol on two carriers for separate transmission, i.e. m is log2(Nt 2M). Wherein N istFor transmit antennas, M is the constellation dimension. At high signal-to-noise ratios, QSM performs better than SM. Unlike the General Spatial Modulation (GSM) which generates channel interference (ICI), QSM successfully avoids ICI even though it also uses two transmit antennas. This is because the symbols transmitted on the two antennas have orthogonality, that is, when the modulated carrier is transmitted, a part of the symbols is loaded to the cosine carrier transmission, and a part of the symbols is loaded to the sine carrier transmission. In addition, QSM improves transmission efficiency compared to GSM. QSM is more robust to channel estimation errors than SM. Based on these advantages, QSM has been applied to cognitive communication systems and amplify-and-forward cooperative communication systems at present. And the analysis is carried out under the Nakagami-m fading channel, under various small-scale fading channel environments and in the aspect of interference among channels. Research results show that the QSM system has better performance compared with the SM system and the GSM system. However, QSM systems suffer from two disadvantages: (1) progressive mean error summary from QSMAs can be seen from the expression, the QSM has only receive diversity but no transmit diversity; (2) the current detection method adopts an ML traversal search method, the complexity of the method is high, and 4 variables are detected, namely an antenna index carrying a symbol real part, an antenna index carrying a symbol imaginary part, a symbol real part and a symbol imaginary part. In order to reduce the detection complexity of QSM, a detection algorithm based on compressed sensing is provided, although the complexity is greatly reduced, under the condition of low signal-to-noise ratio, the detection algorithm is still in the same order of magnitude as the ML detection algorithm, and is greatly related to a threshold.
In contrast, the invention improves the QSM system, the algorithm converts the active antenna into the active space-time matrix to realize the transmit diversity, and simultaneously provides a low-complexity spherical decoding detection algorithm aiming at the problem of overlarge ML traversal detection complexity. The method is characterized in that depth-first spherical decoding is carried out, meanwhile, the combination of activated airspace matrixes is judged, the number of search nodes is changed according to the activation characteristics of the airspace matrixes, and the complexity of the algorithm is reduced on the premise of ensuring that the performance is not lost.
Disclosure of Invention
The invention provides a low-complexity orthogonal space modulation spherical decoding detection algorithm (DQSM-SD) with transmit diversity, aiming at the problems that the transmission end of an orthogonal space modulation system has no transmit diversity and ML detection is complicated and overlarge.
The invention relates to a low-complexity orthogonal space modulation spherical decoding detection algorithm with transmit diversity, which comprises the following steps:
1) firstly, setting the number of transmitting antennas of a QSM system as NtThe number of receiving antennas is NrM-QAM modulation is adopted. Activating N at a time according to QSM system characteristicstTwo of which transmit the real and imaginary parts of the modulation symbols. As can be seen from the QSM progressive average error probability expression, the QSM has only receiving diversity and no transmitting diversity. For this purpose, the invention proposes to convert the active transmit antennas into an active space-domain matrix a, a ═ a (a ═ a), in order to increase the transmit diversity1,A2,...,AQ) Is NtAnd the number of the antenna arrays in the rows T and the columns of each row is Q, and each column only has one non-zero element.
2) The information bits B are divided into B1,B2,B3Three parts according to
Figure BDA0001455292560000021
Represents a rounding down operation to obtain B1,B2A value representing the number of bits that activate the spatial matrix. length b3＝log2M, to obtain B3Representing the number of bits mapped to the modulation symbol s. Modulated real information bits
Figure BDA0001455292560000022
And B1Selected spatial matrix A(1)Multiplying to obtain a signal matrix
Figure BDA0001455292560000023
Imaginary information bits
Figure BDA0001455292560000024
And B2Selected spatial matrix A(2)Multiplying to obtain a signal matrix
Figure BDA0001455292560000025
Then, the two signal matrixes are superposed to obtain a transmission signal matrix S(t)。
When A is(1)＝A(2)Time S(t)Each column of (a) is represented as (1),
Figure BDA0001455292560000026
matrix index representing activation:
Figure BDA0001455292560000027
when A is(1)≠A(2)When S is present(t)Each column of (a) is represented as (2):
Figure BDA0001455292560000028
3) under the influence of complex gaussian noise N, the signal received by the receiving antenna is expressed as:
Y＝HS(t)+N (3)
wherein the content of the first and second substances,
Figure BDA0001455292560000029
for the MIMO channel matrix, obeying the complex Gaussian distribution of CN (0,1),
Figure BDA00014552925600000210
obeying CN (0, sigma) as a noise matrix2) Complex gaussian distribution of (a)2Is the variance of the noise.
4) In order to facilitate the detection of signals, the DQSM-SD system represented in the form of matrix is equivalent to a system represented in the form of vector by using a linearized equivalent system model, and then can be represented as
Figure BDA0001455292560000031
Wherein
Figure BDA0001455292560000032
vec (-) represents vectorization of the matrix, where
Figure BDA0001455292560000033
kron (-) denotes performing a kronecker operation on a matrix,
Figure BDA0001455292560000034
and representing the combined matrix after Q spatial matrix columns are vectorized. When A is(1)＝A(2)When K is [0, …, s,0, …,0 ═ K]T∈CQ× 1, when A is(1)≠A(2)When the temperature of the water is higher than the set temperature,
Figure BDA0001455292560000035
wherein the number of non-zero elements is related to a combination of spatial matrices chosen for the real and imaginary parts. The position of the non-zero element corresponds to the activation of the second spatial matrix.
Figure BDA0001455292560000036
5) According to the idea of conventional sphere decoding, the corresponding search process can be equivalent to:
||U(Z-Y′)||≤d2(5)
wherein
Figure BDA0001455292560000037
U∈CQ×QIs a triangular matrix, (.)HRepresenting a conjugate transpose of a given matrix
Figure BDA0001455292560000038
Representing and taking matrix
Figure BDA0001455292560000039
Pseudo-inverse matrix of, Z ═ CQ×1Representing candidate vectors participating in the search, having the same structure as K. d is the search radius of the sphere decoding, and the initial value is equal to the accumulated metric value when the root node is searched for the first time.
6) In the detection process, the node is searched from the fourth layer, and the node with the minimum metric value after the sorting is used as the root node of the third layer search. The addition of zeros during the test represents the inactive state of the matrix. The positions of the nonzero elements correspond to the corresponding spatial domain matrix. In the searching process, when the first detection node is a modulation symbol, the spatial matrix showing the activation of the real part and the imaginary part is the same, namely: a. the(1)＝A(2)That the remaining search nodes will automatically become zero; similarly, if the first detected node is the real part or the imaginary part of the modulation symbol, the nodes at the remaining position must be the corresponding real part or the imaginary part, and the remaining candidate nodes are decreased accordingly.
According to the signal transmission method of the orthogonal frequency division multiplexing index modulation system, the invention has the beneficial effects that:
1) the scheme of the invention converts the QSM activation antenna transmission signal into an activation space domain matrix, thereby increasing the transmission diversity for a QSM system;
2) the sphere decoding detection at the receiving end uses a method of adding zero points to represent the position of an inactivated space domain matrix, and the position of a non-zero element represents that a corresponding space domain matrix is activated. And judging the matrix activation scheme while detecting the modulation symbols.
3) In the process of detecting the searching nodes, the number of the searching nodes is shortened layer by layer according to the characteristic that if the nodes are modulation symbols, the real part and the imaginary part are activated to be the same, if the nodes are the real part or the imaginary part, one node is left to be the imaginary part or the real part, and the detection complexity of a receiving end is further reduced.
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Fig. 1 is a schematic diagram of an embodiment of a transmitter signal transmission with a transmit diversity orthogonal spatial modulation system according to the present invention.
Fig. 2 is a schematic diagram of an embodiment of a detection node search of the low-complexity orthogonal spatial modulation sphere decoding detection algorithm with transmit diversity according to the present invention.
Fig. 3 is a graph comparing the performance of maximum likelihood detection and sphere decoding with and without transmit diversity applied in QSM systems.
Fig. 4 is a complexity contrast diagram of three detection algorithms when the number of transmitting antennas is unchanged and the modulation order is changed.
Fig. 5 is a complexity contrast diagram of three detection algorithms when the modulation order is unchanged and the number of transmitting antennas is changed.
Detailed Description
Specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
The idea of the low-complexity orthogonal space modulation spherical decoding detection algorithm with transmit diversity provided by the invention is shown in fig. 1 and is carried out according to the following steps:
1) firstly, setting the number of transmitting antennas of a QSM system as NtThe number of receiving antennas is NrM-QAM modulation is adopted. Activating N at a time according to QSM system characteristicstTwo of which transmit the real and imaginary parts of the modulation symbols. As can be seen from the QSM progressive average error probability expression, the QSM has only receiving diversity and no transmitting diversity. For the scheme of the invention, the active transmission antennas are converted into an active space domain matrix A to increase the transmission diversity，A＝(A1,A2,...,AQ) Is NtThe array antenna comprises rows T and columns, wherein each row and column only has one non-zero element, and the number of the array antennas is Q;
2) the information bits B are divided into B1,B2,B3Three parts according to
Figure BDA0001455292560000041
Represents a rounding down operation to obtain B1,B2A value representing the number of bits that activate the spatial matrix. length b3＝log2M, to obtain B3Representing the number of bits mapped to the modulation symbol s. Modulated real information bits
Figure BDA0001455292560000042
And B1Selected spatial matrix A(1)Multiplying to obtain a signal matrix
Figure BDA0001455292560000043
Imaginary information bits
Figure BDA0001455292560000044
And B2Selected spatial matrix A(2)Multiplying to obtain a signal matrix
Figure BDA0001455292560000045
Then, the two signal matrixes are superposed to obtain a transmission signal matrix S(t). When A is(1)＝A(2)Time S(t)Each column of (a) is represented as (1),
Figure BDA0001455292560000051
matrix index representing activation:
Figure BDA0001455292560000052
when A is(1)≠A(2)When S is present(t)Each column of (a) is represented as (2):
Figure BDA0001455292560000053
3) under the influence of complex gaussian noise N, the signal received by the receiving antenna is expressed as:
Y＝HS(t)+N (3)
wherein the content of the first and second substances,
Figure BDA0001455292560000054
for the MIMO channel matrix, obeying the complex Gaussian distribution of CN (0,1),
Figure BDA0001455292560000055
obeying CN (0, sigma) as a noise matrix2) Complex gaussian distribution of (a)2Is the noise variance.
4) In order to facilitate the detection of signals, the DQSM-SD system represented in the form of matrix is equivalent to a system represented in the form of vector by using a linearized equivalent system model, and then can be represented as
Figure BDA0001455292560000056
Wherein
Figure BDA0001455292560000057
vec (-) represents vectorization of the matrix, where
Figure BDA0001455292560000058
kron (-) denotes performing a kronecker operation on a matrix,
Figure BDA0001455292560000059
and representing the combined matrix after Q spatial matrix columns are vectorized. When A is(1)＝A(2)When K is [0, …, s,0, …,0 ═ K]T∈CQ×1(ii) a When A is(1)≠A(2)When the temperature of the water is higher than the set temperature,
Figure BDA00014552925600000510
wherein the number of non-zero elements is related to a combination of spatial matrices chosen for the real and imaginary parts. Position of non-zero elementCorresponding to the activation of the second spatial matrix.
Figure BDA00014552925600000511
5) According to the idea of conventional sphere decoding, the corresponding search process can be equivalent to:
||U(Z-Y′)||≤d2(5)
wherein
Figure BDA00014552925600000512
U∈CQ×QIs a triangular matrix, (.)HRepresenting taking the conjugate transpose of a certain matrix,
Figure BDA00014552925600000513
representing and taking matrix
Figure BDA00014552925600000514
Pseudo-inverse matrix of, Z ═ CQ×1Representing candidate vectors participating in the search, having the same structure as K. d is the search radius of the sphere decoding, and the initial value is equal to the accumulated metric value when the root node is searched for the first time.
The embodiment of searching for a detection node according to the method for detecting a low-complexity orthogonal space modulation sphere decoding algorithm with transmit diversity proposed by the present invention is illustrated in fig. 2 by the following embodiments:
example 1
By the number of transmitting antennas NtThe system with 4QAM modulation scheme is exemplified, where the spatial matrix dimension T is 4, the total number Q of spatial matrices is 4. According to the system model, the number of the selected space domain matrix is 2, and the number of the selected schemes of the space domain matrix is 4. Defining the selection scheme as a matrix F ═ F1,F2,F3,F4]In which F isq(q ═ 1,2,3,4) is a spatial matrix activation scheme. Suppose that
Figure BDA0001455292560000061
Wherein, 1 indicates that the spatial matrix corresponding to the position is activated and carries constellation modulation symbols, and 0 indicates that the spatial matrix corresponding to the position is not activatedIs activated.
1) The invention firstly starts to search from a root node shown in a spherical decoding tree-shaped search composition chart 2, and candidate symbols participating in the search are four constellation symbols, real parts and imaginary parts of the four constellation symbols and a zero point. The black points in the tree structure diagram represent modulation symbols, the gray points represent real parts or imaginary parts of the modulation symbols, and the hollow points represent zero points. The value beside each node represents the accumulated sum of the metric values searched for the node.
1) Firstly, the metric values are sorted in the fourth layer, the node with the minimum metric value after sorting is used as a root node of the third layer search, when the third layer search is carried out, the search is continued on the basis of the symbol corresponding to one gray point (0.15 at the moment) of the minimum metric value in the fourth layer, and before the third layer search is carried out, the node corresponding to the minimum metric value in the fourth layer is judged according to a space domain matrix selection scheme in a matrix F. Since the fourth layer is a gray dot, another transmission symbol should also be a gray dot and not repeated according to the inventive characteristics, the candidate symbols are reduced to 4 calculated distances and sorted at the time of the third layer search; when the third layer is searched, the point corresponding to the minimum metric value is a gray point, that is, the spatial matrix corresponding to the positions of the two points is activated. Through comparison with various schemes in the F matrix, only F2The scheme is matched with the fourth and the third space domain matrixes to be activated, so that the method is based on F2The scheme may set the second, first spatial domain matrix to an inactive state, i.e. [ 1100 ]]TCorresponding to the path having an accumulated metric of 1.9.
2) After the invention finishes the search of a complete path, the value of the search radius d is set to 1.9, the nodes of the previous layer are returned to continue the search, the accumulated metric value of each layer is recorded, the radius d is searched for comparison, and if the accumulated metric value is smaller than d, the value of d is updated. As shown in fig. 2, when the path with the accumulated metric value of 1.7 is searched, the updated d is 1.7 and the searching for other nodes is continued, and since the accumulated metric value of the searching for other nodes under the first node of the fourth layer is already greater than 1.7, the searching for the next node is not required to be continued. 3) When the invention is applied to the fourth layer, the second smallest value is 0.5 smaller than d, and a black dot represents a modulation symbol. Namely A(1)＝A(2)The real and imaginary activated spatial matrices are the same. Through comparison with various schemes in the F matrix, only F1The scheme conforms that the fourth spatial matrix is activated simultaneously, so according to F1The scheme may set the remaining three spatial matrices to an inactive state, i.e., [ 1000 ]]TAnd comparing the accumulated metric value with d by searching layer by layer to obtain a path with the accumulated metric value of 2.1. Finally, it can be seen that 2.1 is less than 1.7. Therefore, the point where the path passes is obtained as the result of (0.15,0.8,1.1,1.7), and finally the space domain matrix activation position is separated from the bits carried by the constellation symbols to be subjected to inverse mapping to obtain the transmitting signal.
The embodiment of the scheme of the invention is verified and explained by the error rate. Fig. 3 is a graph comparing the performance of maximum likelihood detection and low complexity sphere decoding applied to the DQSM system. The four algorithms are respectively maximum likelihood detection with transmit diversity, maximum likelihood detection without transmit diversity, traditional sphere decoding and low-complexity sphere decoding with transmit diversity. Simulation in Nt＝4,NrThe method is carried out under a system with 4, 4 and 4, adopts 4QAM modulation, and simultaneously assumes that a channel is a quasi-static flat Rayleigh fading channel. It can be seen that under the condition of the same modulation order, the DQSM-ML algorithm with the transmission diversity has the best performance, and the error rate is 10 compared with the QSM-ML algorithm-4The method has the advantage of nearly 1 dB. And the performance of the DQSM-SD algorithm is very close to that of the QSM-ML algorithm. Meanwhile, the four algorithms have basically the same performance at low signal-to-noise ratio, and the time difference is larger than 6 dB. The transmission diversity improves the reliability of transmission, so the method is more suitable for a frequency selective transmission model with severe fading.
In addition, fig. 4 and 5 are schematic diagrams illustrating the calculation complexity comparison of the three algorithms of maximum likelihood detection under different conditions, maximum likelihood detection without transmit diversity, and low-complexity sphere decoding with transmit diversity. The invention adopts real number multiplication times to measure when analyzing complexity. For example:
Figure BDA0001455292560000071
for the case of a × B,
Figure BDA0001455292560000072
requiring 4mnp and 2n operations, respectively. Therefore, the complexity of the maximum likelihood detection algorithm under the QSM system is as follows:
CDQSM-ML＝8Nr×Nt 2×M (1)
compared with QSM-ML, the DQSM-ML algorithm has one more space domain dimension T, and the DQSM-ML complexity formula is as follows:
CDQSM-ML＝8Nr×Nt 2×T×M (2)
the complexity formula under the DQSM-SD system is as follows:
CDQSM-SD＝20/3×Q3+22×Q3+4Nt×Nr×Q×T (3)
fig. 4 compares the complexity of the three algorithms under the condition that the number of transmitting antennas is fixed and the modulation order is changed. The DQSM-SD algorithm detects debugging symbols by introducing zero points and judges the spatial domain matrix activation combination at the same time, thereby greatly reducing the detection complexity. Fig. 5 compares the three algorithms when the number of transmit antennas varies when M is 8. The detection complexity of the three antennas is increased along with the increase of the number of the transmitting antennas, and the advantage of the DQSM-SD is more obvious when the number of the transmitting antennas is larger.
The detailed description of the embodiments of the present invention is provided above with reference to the accompanying drawings. The invention is not limited to the embodiments described above. Various modifications or alterations may be made by those skilled in the art without departing from the spirit and scope of the claims of this application.

Claims (1)

1. A low-complexity orthogonal space modulation spherical decoding detection algorithm DQSM-SD with transmit diversity, which is characterized by comprising the following steps:
1) firstly, setting the number of transmitting antennas of a QSM system as NtThe number of receiving antennas is NrM-QAM modulation is adopted; according to QSM system characteristicsActivating NtTwo of them transmit the real and imaginary parts of the modulation symbols, and the active transmit antennas are converted into an active space domain matrix a to increase the transmit diversity, where a ═ is1,A2,...,AQ) Is NtThe array antenna comprises rows T and columns, wherein each row and column only has one non-zero element, and the number of the array antennas is Q;
2) dividing information bits B into B1,B2,B3Three parts according to
Figure FDA0002623815360000011
Figure FDA0002623815360000012
Represents a rounding down operation to obtain B1,B2A value representing the number of bits activating the spatial matrix, length B3＝log2M, to obtain B3A value representing the number of bits mapped to a modulation symbol s; modulated real information bits
Figure FDA0002623815360000013
And B1Spatial matrix A selected from A(1)Multiplying to obtain a signal matrix
Figure FDA0002623815360000014
Imaginary information bits
Figure FDA0002623815360000015
And B2Spatial matrix A selected from A(2)Multiplying to obtain a signal matrix
Figure FDA0002623815360000016
Superposing the two signal matrixes to obtain a transmission signal matrix S(t)I.e. by
Figure FDA0002623815360000017
When A is(1)＝A(2)Time S(t)Each column S of(t) columnExpressed as the formula (1),
Figure FDA0002623815360000018
matrix index representing activation:
Figure FDA0002623815360000019
when selecting matrix A(1)≠A(2)When S is present(t)Is expressed as formula (2):
Figure FDA00026238153600000110
3) under the influence of complex gaussian noise N, the signal received by the receiving antenna is expressed as:
Y＝HS(t)+N (3)
wherein the content of the first and second substances,
Figure FDA00026238153600000111
for the MIMO channel matrix, obeying the complex Gaussian distribution of CN (0,1),
Figure FDA00026238153600000112
obeying CN (0, sigma) as a noise matrix2) Complex gaussian distribution of (a)2Is the variance of the noise;
4) in order to facilitate the detection of signals, the DQSM-SD system represented in a matrix form is equivalent to a system represented in a vector form by using a linear equivalent system model, and the system is represented as
Figure FDA0002623815360000021
Wherein
Figure FDA0002623815360000022
vec (-) represents vectorization of the matrix, where
Figure FDA0002623815360000023
kron (·) denotes performing kronecker operation on a matrix, ζ ═ vec (a)1)…vec(AQ)]∈CNtT×QRepresenting a combined matrix after vectorization of Q airspace matrix arrays; when A is(1)＝A(2)When K is [0, …, s,0, …,0 ═ K]T∈CQ×1(ii) a When A is(1)≠A(2)When the temperature of the water is higher than the set temperature,
Figure FDA0002623815360000024
wherein the number of the non-zero elements is related to the spatial matrix combination selected from the real part and the imaginary part, the position of the non-zero elements corresponds to the activated spatial matrix,
Figure FDA0002623815360000025
5) according to sphere decoding, equation (4) is equivalent to:
||U(Z-Y′)||≤d2(5)
wherein
Figure FDA0002623815360000026
U∈CQ×QIs a triangular matrix, (.)HRepresenting taking the conjugate transpose of a certain matrix,
Figure FDA0002623815360000027
Figure FDA0002623815360000028
representing and taking matrix
Figure FDA0002623815360000029
Pseudo-inverse matrix of, Z ═ CQ×1Representing candidate vectors participating in the search, wherein the structure of the candidate vectors is the same as K, d is the search radius of the spherical decoding, and the initial value of the search radius is equal to the accumulated metric value when the root node is searched for the first time;
6) the detection process is started from the searching node of the fourth layer, and the node with the minimum metric value is used as the searching node of the third layer after being sorted according to the metric valueThe root node of (2) adds a zero point to represent the non-activated state of the matrix in the detection process, the position of the non-zero element corresponds to a corresponding spatial matrix, and in the search process, when the first detection node is a modulation symbol, the spatial matrix with activated real part and imaginary part is the same, namely: a. the(1)＝A(2)That the remaining search nodes will automatically become zero; similarly, if the first detected node is the real part or the imaginary part of the modulation symbol, the nodes at the remaining position must be the corresponding real part or the imaginary part, and the remaining candidate nodes are decreased accordingly.
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