CN109547074B - Lattice reduction assisted ML-SIC signal detection method based on ZF criterion - Google Patents

Lattice reduction assisted ML-SIC signal detection method based on ZF criterion Download PDF

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CN109547074B
CN109547074B CN201811476016.4A CN201811476016A CN109547074B CN 109547074 B CN109547074 B CN 109547074B CN 201811476016 A CN201811476016 A CN 201811476016A CN 109547074 B CN109547074 B CN 109547074B
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李兵兵
杜佳伟
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Xidian University
Xian Cetc Xidian University Radar Technology Collaborative Innovation Research Institute Co Ltd
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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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Abstract

The invention belongs to the technical field of MIMO system signal detection, and discloses a lattice reduction-assisted ML-SIC signal detection method based on a ZF criterion. Firstly, sequencing column vectors of a channel matrix; then, generating candidate signals in the FE stage, and eliminating the signals in the FE stage in the original domain before converting to the reduction domain; then, signal processing is carried out in an SE stage, and LR-ZF-SIC is used in a system model after the signal processing in an FE stage; then, the subsequent processing, which acts on the SE-phase candidate signals: converting the candidate signal from the reduction domain to the original domain, slicing; the candidate signals in the SE stage and the candidate signals in the FE stage form a candidate signal list, and the symbol vector with the minimum Euclidean distance is determined through ML measurement; and finally, reordering the detection vectors, and reordering the detection vectors according to the sequence opposite to the original channel matrix sequence. When MQAM modulation is adopted, the invention can achieve near-optimal detection performance with lower calculation complexity.

Description

Lattice reduction assisted ML-SIC signal detection method based on ZF criterion
Technical Field
The invention belongs to the technical field of MIMO system signal detection, and particularly relates to a Lattice Reduction (LR) assisted ML-SIC signal detection method based on a ZF criterion. The invention can be widely applied to receivers of the MIMO wireless communication system.
Background
Currently, the current state of the art commonly used in the industry is such that:
in recent years, the demand of users for data transmission rate and system capacity is increasing, and new challenges are brought to wireless communication systems. MIMO technology can realize multiple increases in system capacity and spectrum utilization without increasing transmission power and bandwidth, and is becoming one of the most promising communication technologies. In a wireless MIMO communication system, the problem of signal detection at the receiving end is a very critical factor in determining whether it can be applied to an actual system. Therefore, how to realize signal detection with higher detection performance and lower complexity becomes an important issue for the development of MIMO technology. The Maximum Likelihood (ML) detection algorithm is the detection algorithm with the best performance, but the computation complexity of the detection algorithm increases exponentially with the increase of the number of antennas, and the detection algorithm cannot be practically applied, and is often used as a standard for measuring other algorithms. The current research on the MIMO system signal detection method mainly focuses on finding a signal detection method with near ML detection performance and lower complexity. Agrell et al propose a Sphere Decoding (SD) algorithm whose basic idea is to search for lattice points within a hypersphere with the received vector as the center of the sphere, the closest lattice point to the center of the sphere being the final solution. The SD algorithm can obtain lower complexity because only the lattice points in the hyper-sphere are searched, and the ML algorithm searches the whole lattice point set. However, the main disadvantage of the SD algorithm is that its complexity depends on the signal-to-noise ratio SNR, which, although the average complexity can be significantly reduced, is still the same as ML detection in the worst case. The K-best signal detection method is a tree search algorithm with a width priority, and expands currently reserved branches during traversal of tree search, but only reserves K optimal branches in the expanded branches. The computational complexity is fixed. When the K value is larger, the K-best algorithm can reach the ML performance, and when the K value is smaller, the performance of the K-best algorithm is reduced, so that the method has the advantage of reducing the complexity. The K-best algorithm, although having a fixed computational complexity, has some drawbacks: in the case of high snr, few branches need to be processed, but K-best still has K paths per layer and is ordered, so the complexity is correspondingly high. Barbero et al propose a fixed complexity sphere decoding (FSD) detection algorithm, which is also a tree search algorithm, that first sequences the channel matrix, performs full expansion on the previous P layer, and performs single expansion on the remaining other layers, enabling optimal detection performance with fixed complexity. However, when higher order modulation is used or the number of transmit antennas is large, the complexity of the FSD algorithm is still high. Dirk mubben et al propose a linear detector using Lattice Reduction (LR) technique, which processes a channel matrix using LR technique to obtain a channel matrix with better channel conditions before using Zero Forcing (ZF) detection algorithm or Minimum Mean Square Error (MMSE) algorithm for detection. The linear detector can obtain the same diversity degree as the ML detection algorithm with lower complexity, but the detection performance of the linear detector is still far from the optimal detector.
In summary, the problems of the prior art are as follows:
the existing signal detection method can obtain better detection performance but higher computation complexity, or has low computation complexity but poorer detection performance, namely, a good compromise cannot be obtained between the detection performance and the computation complexity.
The difficulty in solving the technical problems is as follows: how to design the algorithm achieves near-optimal signal detection performance through low computational complexity.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a Lattice Reduction (LR) assisted ML-SIC signal detection method based on a ZF criterion.
The invention is realized in this way, a Lattice Reduction (LR) assisted ML-SIC signal detection method based on ZF criterion is characterized in that the Lattice Reduction (LR) assisted ML-SIC signal detection method based on ZF criterion comprises:
step one, sequencing column vectors of a channel matrix;
step two, eliminating signals in an FE stage, generating candidate signals in the FE stage, and eliminating the signals in the FE stage in an original domain before converting into a reduction domain;
thirdly, processing signals in an SE stage, wherein LR-ZF-SIC is used in a system model processed in an FE stage;
step four: post-processing and ML metric, the post-processing acting on the SE phase candidate signals: converting the candidate signal from the reduction domain to the original domain, slicing; the candidate signals in the SE stage and the candidate signals in the FE stage form a candidate signal list, and a symbol vector with the minimum Euclidean distance is determined through ML measurement;
step five: and reordering the detection vectors, and reordering the detection vectors according to the reverse order of the first step.
Further, the step orders the column vectors of the channel matrix according to the magnitude of the norm value, and places the signal with low reliability in the FE stage for processing, and places the signal with high reliability in the SE stage for processing.
Further, the second step generates candidate signals in the FE stage, and assuming that the FE stage includes p-layer signals, the signals in the FE stage are eliminated as follows:
Figure BDA0001892207280000031
wherein N isTIs the number of transmitting antennas, NRIs the number of the receiving antennas and,
Figure BDA0001892207280000032
is the reception of a signal or signals,
Figure BDA0001892207280000033
is the received signal in the modified system and,
Figure BDA0001892207280000034
is a channel matrix
Figure BDA0001892207280000035
The first column of (a) is,
Figure BDA0001892207280000036
(Ω is the real constellation) is the kth candidate signal from the lth transmit antenna; finally, the system model after eliminating the candidate signal in the FE stage is
y′(k)＝H′s′(k)+n
Wherein the content of the first and second substances,
Figure BDA0001892207280000037
is an additive white gaussian noise vector.
Further, the third LR-ZF-SIC step is used in the system model processed by the FE stage, and the LR algorithm is firstly applied to H' to be preprocessed to obtain a base matrix of the reduction domain
Figure BDA0001892207280000039
And the transformation matrix T' is then paired
Figure BDA0001892207280000038
Carrying out QR decomposition and SIC operation:
to y'(k)Transforming and preprocessing H' by applying LR algorithm
Figure BDA0001892207280000041
And T':
Figure BDA0001892207280000042
Figure BDA0001892207280000043
wherein the content of the first and second substances,
Figure BDA0001892207280000044
to pair
Figure BDA00018922072800000416
QR decomposition is carried out to obtain
Figure BDA0001892207280000045
Equation of
Figure BDA0001892207280000046
Two sides respectively take the left
Figure BDA0001892207280000047
Obtaining:
Figure BDA0001892207280000048
the list of candidate signals for the SE stage generated in the SIC mode is represented as follows:
Figure BDA0001892207280000049
wherein the content of the first and second substances,
Figure BDA00018922072800000410
and is
Figure BDA00018922072800000411
Wherein, q'(k),iIs q'(k)The (i) th element of (a),
Figure BDA00018922072800000412
is that
Figure BDA00018922072800000413
The (i, j) th element of (a).
Further, the step four of subsequent processing of the candidate signal acting on the SE stage mainly includes the following two steps: (1) converting the candidate signal from the reduced domain to the original domain, (2) slicing; firstly, converting the candidate signals in the SE stage into the original domain, then slicing the estimation vector converted into the original domain according to the constellation points in the original domain, wherein the candidate signals in the SE stage and the candidate signals in the FE stage form a candidate signal list together:
Figure BDA00018922072800000414
finally, the symbol vector with the minimum euclidean distance is determined by the ML metric:
Figure BDA00018922072800000415
further, the fifth step reorders the detection vectors in the reverse order of the first step.
In summary, the advantages and positive effects of the invention are: for a 4 × 4MIMO system, when MQAM modulation is adopted, compared with a conventional ML-SIC algorithm, the proposed algorithm can achieve near-optimal detection performance with fewer layers in the FE stage, and the fewer layers in the FE stage means lower computation complexity, that is, the proposed algorithm can achieve a good compromise between computation complexity and detection performance. Therefore, the invention has better comprehensive performance.
Drawings
Fig. 1 is a flowchart of a Lattice Reduction (LR) assisted ML-SIC signal detection method based on ZF criterion according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of BER performance of 16QAM signals in a 4 × 4MIMO system according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of BER performance of 64QAM signals in a 4 × 4MIMO system according to an embodiment of the present invention.
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.
The following detailed description of the principles of the invention is provided in connection with the accompanying drawings.
As shown in fig. 1, a Lattice Reduction (LR) assisted ML-SIC signal detection method based on ZF criterion provided by an embodiment of the present invention includes the following steps:
sequencing column vectors of a channel matrix, placing signals with low reliability in an FE stage for processing, and placing signals with high reliability in an SE stage for processing;
step two, FE stage signal elimination, the main obstacle of applying LR algorithm to ML-SIC algorithm is lack of determined candidate signal in reduction domain, the proposed solution is to generate candidate signal in FE stage, and eliminate FE stage signal in original domain before converting to reduction domain;
step three, signal processing is carried out in an SE stage, and in the step, LR-ZF-SIC is used in a system model processed in an FE stage;
step four: the subsequent processing and ML measurement, the subsequent processing acts on the candidate signal in SE stage, mainly include the following two steps: (1) converting the candidate signal from the reduced domain to the original domain, and (2) slicing. The candidate signals in the SE stage and the candidate signals in the FE stage form a candidate signal list, and a symbol vector with the minimum Euclidean distance is determined through ML measurement;
step five: and reordering the detection vectors, and reordering the detection vectors according to the reverse order of the first step.
The application of the principles of the present invention will now be described in further detail with reference to the accompanying drawings.
The ML-SIC signal detection method assisted by Lattice Reduction (LR) based on ZF criterion provided by the embodiment of the invention comprises the following steps:
s1, sorting the column vectors of the channel matrix according to the magnitude of the norm values, putting the signals with low reliability in the FE stage for processing, and putting the signals with high reliability in the SE stage for processing.
S2 performs FE stage signal processing, and the main obstacle in applying LR algorithm to ML-SIC algorithm is the lack of defined candidate signals in the reduced domain after transformation from the original domain to the reduced domain. Assuming that the FE stage contains p-layer signals, the FE stage signals are eliminated as follows:
Figure BDA0001892207280000061
wherein N isTIs the number of transmitting antennas, NRIs the number of the receiving antennas and,
Figure BDA0001892207280000062
is the reception of a signal or signals,
Figure BDA0001892207280000063
is the received signal in the modified system and,
Figure BDA0001892207280000064
is a channel matrix
Figure BDA0001892207280000065
The first column of (a) is,
Figure BDA0001892207280000066
(omega is the real constellation) is the kth candidate signal from the lth transmit antenna. Finally, the system model after eliminating the candidate signal in the FE stage is
y′(k)＝H′s′(k)+n
Wherein the content of the first and second substances,
Figure BDA0001892207280000067
is an additive white gaussian noise vector.
S3 in the step of signal processing in SE stage, LR-ZF-SIC is used in the system model processed in FE stage, and LR algorithm is applied to H' to pre-process to obtain base matrix of reduction domain
Figure BDA0001892207280000068
And the transformation matrix T' is then paired
Figure BDA0001892207280000069
Carrying out QR decomposition and SIC operation:
to y'(k)Transforming and preprocessing H' by applying LR algorithm
Figure BDA00018922072800000715
And T':
Figure BDA0001892207280000071
Figure BDA0001892207280000072
wherein the content of the first and second substances,
Figure BDA0001892207280000073
z(k)＝T′-1x(k)。
to pair
Figure BDA0001892207280000074
QR decomposition is carried out to obtain
Figure BDA0001892207280000075
Equation of
Figure BDA0001892207280000076
Two sides respectively take the left
Figure BDA00018922072800000716
Obtaining:
Figure BDA0001892207280000077
the list of candidate signals for the SE stage generated in the SIC mode is represented as follows:
Figure BDA0001892207280000078
wherein the content of the first and second substances,
Figure BDA0001892207280000079
and is
Figure BDA00018922072800000710
Wherein, q'(k),iIs q'(k)The (i) th element of (a),
Figure BDA00018922072800000711
is that
Figure BDA00018922072800000712
The (i, j) th element of (a).
S4, performing a subsequent process, where the subsequent process acts on the candidate signal in the SE stage, and the subsequent process mainly includes the following two steps: (1) converting the candidate signal from the reduced domain to the original domain, and (2) slicing. First, the candidate signal in SE phase is converted from the reduced domain to the original domain, and then the estimated vector converted to the original domain is sliced according to the constellation points in the original domain.
S5, performing ML measurement, and forming a candidate signal list by the candidate signals in the SE stage and the candidate signals in the FE stage:
Figure BDA00018922072800000713
the symbol vector with the minimum euclidean distance is determined by the ML metric:
Figure BDA00018922072800000714
s6 reorders the test vectors and reorders the test vectors in reverse order of step one.
The application effect of the present invention will be described in detail with reference to the simulation.
To evaluate the performance of the present invention, the following simulation experiments performed simulation verification of the performance of the proposed algorithm. The system employed is configured to: 4 x 4MIMO uncoded system, channel condition is uncorrelated flat fading channel, modulation mode adopts 16QAM and 64 QAM. The simulation results are shown in fig. 2 and 3, and it can be seen from the simulation diagrams that: no matter 16QAM or 64QAM is adopted, the proposed algorithm can achieve near-optimal performance when the number of layers p in the FE stage is 2, while the conventional ML-SIC algorithm can achieve near-optimal performance when the number of layers p in the FE stage is 4, and a smaller number of layers in the FE stage means a lower computational complexity.
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 (1)

1. A lattice reduction aided ML-SIC signal detection method based on ZF criterion is characterized in that the lattice reduction aided ML-SIC signal detection method based on ZF criterion comprises the following steps:
step one, sequencing column vectors of a channel matrix;
step two, eliminating signals in an FE stage, generating candidate signals in the FE stage, and eliminating the signals in the FE stage in an original domain before converting into a reduction domain;
thirdly, processing signals in an SE stage, wherein LR-ZF-SIC is used in a system model processed in an FE stage;
step four: post-processing and ML metric, the post-processing acting on the SE phase candidate signals: converting the candidate signal from the reduction domain to the original domain, slicing; the candidate signals in the SE stage and the candidate signals in the FE stage form a candidate signal list, and a symbol vector with the minimum Euclidean distance is determined through ML measurement;
step five: reordering the detection vectors, and reordering the detection vectors according to the sequence opposite to the first step;
the column vectors of the channel matrix are sorted according to the magnitude of the norm value, the signals with low reliability are processed in an FE stage, and the signals with high reliability are processed in an SE stage;
the second step generates candidate signals in the FE stage, and assuming that the FE stage includes p-layer signals, the signals in the FE stage are eliminated as follows:
Figure FDA0003036870430000011
wherein N isTIs the number of transmitting antennas, NRIs the number of the receiving antennas and,
Figure FDA0003036870430000012
is the reception of a signal or signals,
Figure FDA0003036870430000013
is the received signal in the modified system and,
Figure FDA0003036870430000014
is a channel matrix
Figure FDA0003036870430000015
The first column of (a) is,
Figure FDA0003036870430000016
(Ω is the real constellation) is the kth candidate signal from the lth transmit antenna; finally, the system model after eliminating the candidate signal in the FE stage is:
y″(k)＝H′s′(k)+n；
wherein the content of the first and second substances,
Figure FDA0003036870430000021
is the channel matrix in the modified system,
Figure FDA0003036870430000022
is the transmitted signal vector in the modified system,
Figure FDA0003036870430000023
is an additive white gaussian noise vector;
the third LR-ZF-SIC is used in a system model processed by an FE stage, and the LR algorithm is firstly applied to H' to carry out pretreatment to obtain a base matrix of a reduction domain
Figure FDA0003036870430000024
And the transformation matrix T' is then paired
Figure FDA0003036870430000025
Carrying out QR decomposition and SIC operation:
to y'(k)Transform and apply LR algorithm to HIs pretreated to obtain
Figure FDA0003036870430000026
And T':
Figure FDA0003036870430000027
Figure FDA0003036870430000028
wherein the content of the first and second substances,
Figure FDA0003036870430000029
z(k)＝T′-1x(k)；
to pair
Figure FDA00030368704300000210
QR decomposition is carried out to obtain
Figure FDA00030368704300000211
Equation of
Figure FDA00030368704300000212
Two sides respectively take the left
Figure FDA00030368704300000213
Obtaining:
Figure FDA00030368704300000214
the list of candidate signals for the SE stage generated in the SIC mode is represented as follows:
Figure FDA00030368704300000215
wherein the content of the first and second substances,
Figure FDA00030368704300000216
and:
Figure FDA00030368704300000217
wherein, q'(k),iIs q'(k)The (i) th element of (a),
Figure FDA00030368704300000218
is that
Figure FDA00030368704300000219
The (i, j) th element of (a);
the step four of subsequent processing of the candidate signals for the SE phase includes the following two steps: (1) converting the candidate signal from the reduced domain to the original domain, (2) slicing; converting the candidate signals in the SE stage into an original domain, slicing the estimation vector converted into the original domain according to the constellation points in the original domain, and forming a candidate signal list by the candidate signals in the SE stage and the candidate signals in the FE stage together:
Figure FDA00030368704300000220
finally, the symbol vector with the minimum euclidean distance is determined by the ML metric:
Figure FDA0003036870430000031
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