CN113098603A - Imaging light MIMO pre-coding and decoding method based on lattice reduction - Google Patents
Imaging light MIMO pre-coding and decoding method based on lattice reduction Download PDFInfo
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Abstract
The invention discloses an imaging light MIMO pre-coding and decoding method based on lattice reduction, and relates to the technical field of underwater optical communication. By utilizing the characteristics of the lattice reduction algorithm and combining the traditional minimum mean square error precoding algorithm to solve the precoding matrix to improve the error rate performance, the lattice reduction operation is firstly carried out on the channel matrix at the sending end, MMSE precoding is carried out according to the reduced channel matrix, and the complexity of the receiving end signal detection algorithm is further reduced. Compared with the prior art, the invention has the beneficial effects that: the iterative reduction operation enables the channel to have better orthogonality, the precoding matrix is solved based on the reduced ideal channel, and the linear precoding algorithm is combined, so that the defect that the linear detection is adopted at the receiving end to amplify the noise can be overcome. The method has the advantages that the influence of channel interference is compensated by adopting the lattice reduction precoding operation to carry out signal preprocessing at the transmitting end, the system performance is optimized, and meanwhile, the complexity of the receiving end can be reduced.
Description
Technical Field
The invention relates to the technical field of underwater optical communication, in particular to an imaging optical MIMO pre-coding and decoding method based on lattice reduction.
Background
In recent years, underwater visible light communication (UWOC) has become an underwater wireless communication scheme with great application prospects in the advantages of high rate, low time delay, low cost and the like. UWOC uses blue-green Light Emitting Diodes (LEDs) as light sources, but because LEDs have limited modulation bandwidth and complex underwater environment, Multiple Input Multiple Output (MIMO) technology is used to increase system capacity and achieve high-speed data transmission. Because the underwater visible light MIMO technology adopts a modulation and demodulation mode of intensity modulation/direct detection (IM/DD), and with the gradual increase of the number of LEDs, a VLC system has strong channel correlation, so that the interference between signals is caused, and the system is difficult to obtain higher multiplexing gain.
There are many studies for reducing spatial correlation of MIMO channels, which are mainly classified into optical means and electrical means. An imaging lens is placed in front of the detector to separate the signals from the different LEDs. At the receiving end, however, when the images are overlapped, interference still exists between the signals. There are also some studies that employ means based on angle diversity, optimizing transceiver normal vector tilt angle, and setting link blocking, etc., to reduce channel correlation by changing the physical structure of the transceiver array, which has limitations in terms of device size and universality. In the electrical means, the space modulation technology reduces the intersymbol interference by only adopting partial LEDs to transmit information at each time, so that the realization is simpler, but the improvement of the system capacity is greatly limited. The lattice reduction algorithm (LR) was proposed in 2002 as a signal processing means for effectively reducing channel correlation in polynomial time and applied to signal detection in MIMO systems. And then, a plurality of researches on a signal detection method based on lattice reduction are carried out, and the researches are combined with a receiving end suboptimal linear detection algorithm, so that the algorithm complexity is low, and the better signal detection performance can be achieved. However, the multi-user MIMO receiving end is difficult to cooperate with each other, the difficulty of joint detection is high, and linear signal detection at the receiving end has the disadvantage of amplified noise.
Therefore, the invention can adopt the lattice reduction precoding operation to carry out signal preprocessing at the sending end to compensate the influence of channel interference based on the condition that the sending end can obtain the channel state information, optimize the system performance and simultaneously reduce the complexity of the receiving end.
Disclosure of Invention
The technical problems to be solved by the invention are that the interference between signals is caused by large channel correlation in the prior art, and the noise is amplified by adopting linear detection at a receiving end. The imaging light MIMO pre-coding and decoding method based on the lattice reduction has the characteristics of weak interference and low noise.
In order to solve the technical problems, the technical scheme is as follows:
an imaging optical MIMO pre-coding and decoding method based on lattice reduction, the imaging optical MIMO pre-coding and decoding method based on lattice reduction comprises the following steps:
step one, a sending end adopts a lattice reduction algorithm to reduce the lattice of a channel matrix, and LR-MMSE precoding is carried out on the reduced channel matrix to obtain a precoding matrix
And step two, carrying out clipping processing on the data of the LR-MMSE after the minimum mean square error precoding through lattice reduction to obtain a signal to be sent.
In the foregoing scheme, for optimization, further, the first step further includes preprocessing, where the preprocessing includes:
step 1, inputting a binary random information sequence, carrying out QAM mapping on the binary random information sequence, and carrying out serial-parallel conversion;
step 2, carrying out hermitian symmetry on the data subjected to the serial-parallel conversion;
and 3, performing fast Fourier inverse transformation on the data subjected to hermitian symmetry to obtain the OFDM signal.
wherein σ2Is the variance of white gaussian noise, I is a 2 x 2 identity matrix,in order to update the channel matrix,HHfor the transpose operation, T is the reduction matrix.
Further, the definition may be accomplished by:
step A, selecting an LLL lattice reduction algorithm, wherein the LLL lattice reduction algorithm has the following conditions:
wherein, | mui,j| is μijThe length or the modulus value of (a),for i, j two columns of Schmidt orthogonalization coefficients,is a base vector bjCorresponding Schmidt orthogonalized basis vectors, bjIs the jth column of the channel matrix B, i.e. the jth basis vector,for i, j two columns of Schmidt orthogonalization coefficients,is a base vector biThe corresponding schmitt orthogonalized basis vectors. Delta is an approximate reduction coefficient and satisfies that delta is more than 0.25 and less than or equal to 1;
step B, combining the lattice reduction with the MMSE precoding algorithm at the transmitting end, and transposing H of the channel matrix HHPerforming a lattice reduction to obtain an updated channel matrixWherein, the reduction matrix T is an unimodular matrix, and the determinant value is +/-1;
step C, calculating the precoding matrix of LR-MMSE asWherein σ2I is an identity matrix of 2 × 2, which is the variance of gaussian white noise.
Further, the reduction coefficient δ is 0.75.
Further, the lattice reduction-based imaging optical MIMO pre-coding and decoding method further includes:
the receiving end receives the optical signal through the imaging lens, converts the optical signal into an electric signal, and the electric signal is subjected to fast Fourier transform and extracts a data subcarrier; sub-carriers for signal detection and decoding to recover transmitted signals
Wherein the content of the first and second substances,n is white gaussian noise, which is a signal received by a receiving end,for precoding matrix, betaLR-MMSEIs a constraint factor, G, for making the energy of the transmitted signals before and after precoding identicalLR-MMSEIs a decoding matrix;
GLR-MMSE=TH/βLR-MMSE;
where E is the energy of the transmitted signal and x is the initial transmitted signal.
The invention has the beneficial effects that: the invention enables the channel to have better orthogonality through iteration reduction operation, and can make up the defect of amplifying noise by adopting linear detection at a receiving end by combining with a linear precoding algorithm. The method has the advantages that the influence of channel interference is compensated by adopting the lattice reduction precoding operation to carry out signal preprocessing at the transmitting end, the system performance is optimized, and meanwhile, the complexity of the receiving end can be reduced.
Drawings
The invention is further illustrated with reference to the following figures and examples.
Fig. 1 is a simulation diagram of the error rate performance of a system incorporating the lattice reduction algorithm.
Fig. 2 is a simulation diagram of the systematic error performance of the LR-MMSE precoding algorithm and the MMSE precoding algorithm.
Fig. 3 is a simulation diagram comparing the performance of different precoding algorithms.
Fig. 4 is a simulation diagram comparing error rate performance of a lattice reduction algorithm system under different correlation channels.
Fig. 5 is a schematic diagram of an imaging optical MIMO precoding and decoding method based on lattice reduction in embodiment 1.
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.
Example 1
The present embodiment provides an imaging optical MIMO pre-coding and decoding method based on lattice reduction, as shown in fig. 5, the imaging optical MIMO pre-coding and decoding method based on lattice reduction includes:
step one, a sending end adopts a lattice reduction algorithm to reduce the lattice of a channel matrix, and LR-MMSE precoding is carried out on the reduced channel matrix to obtain a precoding matrix
And step two, carrying out clipping processing on the data of the LR-MMSE after the minimum mean square error precoding through lattice reduction to obtain a signal to be sent.
Preferably, as shown in fig. 5, the first step further comprises a pretreatment, and the pretreatment comprises:
step 1, inputting a binary random information sequence, carrying out QAM mapping on the binary random information sequence, and carrying out serial-parallel conversion;
step 2, carrying out hermitian symmetry on the data subjected to the serial-parallel conversion;
and 3, performing fast Fourier inverse transformation on the data subjected to hermitian symmetry to obtain the OFDM signal.
Precoding matrix in the present embodimentCan be defined as required. Here, the precoding matrixCan be defined as:
wherein σ2Is the variance of white gaussian noise, I is a 2 x 2 identity matrix,in order to update the channel matrix,HH is the transpose operation, and T is the reduction matrix.
Furthermore, if not in a directly defined manner. The definition in this embodiment can also be calculated by the following steps:
step A, selecting an LLL lattice reduction algorithm, wherein the LLL lattice reduction algorithm has the following conditions:
wherein, | mui,j| is μijThe length or the modulus value of (a),for i, j two columns of Schmidt orthogonalization coefficients,is a base vector bjCorresponding Schmidt orthogonalized basis vectors, bjIs the jth column of the channel matrix B, i.e. the jth basis vector,for i, j two columns of Schmidt orthogonalization coefficients,is a base vector biThe corresponding schmitt orthogonalized basis vectors. Delta is an approximate reduction coefficient and satisfies that delta is more than 0.25 and less than or equal to 1;
step B, combining the lattice reduction and MMSE precoding algorithm at the transmitting end, and carrying out the channel matrix HTranspose HHPerforming a lattice reduction to obtain an updated channel matrixWherein, the reduction matrix T is an unimodular matrix, and the determinant value is +/-1;
step C, calculating the precoding matrix of LR-MMSE asWherein σ2I is an identity matrix of 2 × 2, which is the variance of gaussian white noise.
Preferably, the reduction factor δ is 0.75.
In this embodiment, the decoding method and the encoding method in the encoding and decoding method have the opposite path. For example, the decoding is that a receiving end receives an optical signal through an imaging lens, the optical signal is converted into an electric signal, and the electric signal is subjected to fast Fourier transform and data subcarriers are extracted; sub-carriers for signal detection and decoding to recover transmitted signals
Wherein the content of the first and second substances,n is white gaussian noise, which is a signal received by a receiving end,for precoding matrix, betaLR-MMSEIs a constraint factor, G, for making the energy of the transmitted signals before and after precoding identicalLR-MMSEIs a decoding matrix;
GLR-MMSE=TH/βLR-MMSE;
where E is the energy of the transmitted signal and x is the initial transmitted signal.
In fig. 1, after the lattice reduction algorithm is added at the receiving end, the error code performance of the system is obviously improved after 12dB SNR. Further applying the lattice reduction algorithm to the transmitting end, under the condition of low signal to noise ratio, the error code performance of the LR-MMSE detection algorithm at the receiving end is improved by adopting the lattice reduction precoding algorithm, and the error code performance is 10 DEG-4At BER, the system has an SNR gain of about 5dB after the lattice reduction algorithm is added.
In fig. 2, the system error performance of the MMSE precoding algorithm is compared with that of the lattice reduction based precoding algorithm, and it can be seen from the figure that the interference of the received signal is reduced by reducing the channel correlation based on the lattice reduction algorithm, and the system error rate is lower than that of the system only adopting MMSE precoding. In fig. 3, the comparison of the system error rate performances of different precoding algorithms is shown, and it can be seen that, under a low signal-to-noise ratio, the performance of the precoding algorithm with only lattice reduction is superior to that of the joint MMSE precoding algorithm due to the fact that the noise component is large and the noise amplification effect of the power normalization factor of MMSE precoding is significant, while under a high signal-to-noise ratio condition, the LR-MMSE precoding algorithm is 10-4The BER has about a 2dB signal-to-noise gain compared to the LR precoding algorithm.
In fig. 4, BER of the underwater imaging optical MIMO system with the lattice reduction precoding and detection algorithm varies with SNR under different correlation channels, and it can be seen from the figure that the lattice reduction precoding algorithm improves the improvement degree of the system error code performance under the channel condition with larger correlation, and when the channel matrix condition number is 1, because the channel correlation is minimum at this time, the lattice reduction algorithm cannot further improve the channel correlation, and at this time, the lattice reduction algorithm cannot optimize the system error code rate performance. Therefore, when the channel has certain correlation, the lattice reduction precoding algorithm can effectively reduce the channel correlation and improve the error code performance of the system.
Although the illustrative embodiments of the present invention have been described above to enable those skilled in the art to understand the present invention, the present invention is not limited to the scope of the embodiments, and it is apparent to those skilled in the art that all the inventive concepts using the present invention are protected as long as they can be changed within the spirit and scope of the present invention as defined and defined by the appended claims.
Claims (6)
1. An imaging optical MIMO pre-coding and decoding method based on lattice reduction is characterized in that: the imaging optical MIMO pre-coding and decoding method based on the lattice reduction comprises the following steps:
step one, a sending end adopts a lattice reduction algorithm to reduce the lattice of a channel matrix, and LR-MMSE precoding is carried out on the reduced channel matrix to obtain a precoding matrix
And step two, carrying out clipping processing on the data of the LR-MMSE after the minimum mean square error precoding through lattice reduction to obtain a signal to be sent.
2. The lattice reduction-based imaging optical MIMO pre-coding and decoding method according to claim 1, wherein: the pretreatment is also included before the step one, and the pretreatment comprises the following steps:
step 1, inputting a binary random information sequence, carrying out QAM mapping on the binary random information sequence, and carrying out serial-parallel conversion;
step 2, carrying out hermitian symmetry on the data subjected to the serial-parallel conversion;
and 3, performing fast Fourier inverse transformation on the data subjected to hermitian symmetry to obtain the OFDM signal.
3. The lattice reduction-based imaging optical MIMO pre-coding and decoding method according to claim 2, wherein: precoding matrixCan be defined as:
4. The lattice reduction-based imaging optical MIMO pre-coding and decoding method according to claim 3, wherein: the definition can be accomplished by:
step A, selecting an LLL lattice reduction algorithm, wherein the LLL lattice reduction algorithm has the following conditions:
wherein, | mui,j| is μijThe length or the modulus value of (a),for i, j two columns of Schmidt orthogonalization coefficients,is a base vector bjCorresponding Schmidt orthogonalized basis vectors, bjIs the jth column of the channel matrix B, i.e. the jth basis vector,is iJ two columns of Schmidt orthogonalization coefficients, bi *Is a base vector biCorresponding Schmidt orthogonalized basis vectors; delta is an approximate reduction coefficient and satisfies that delta is more than 0.25 and less than or equal to 1;
step B, combining the lattice reduction with the MMSE precoding algorithm at the transmitting end, and transposing H of the channel matrix HHPerforming a lattice reduction to obtain an updated channel matrixWherein, the reduction matrix T is an unimodular matrix, and the determinant value is +/-1;
5. The lattice reduction-based imaging optical MIMO pre-coding and decoding method according to claim 4, wherein: the reduction factor δ is 0.75.
6. The lattice reduction-based imaging optical MIMO pre-coding and decoding method according to claim 4, wherein: the imaging optical MIMO pre-coding and decoding method based on the lattice reduction further comprises the following steps:
the receiving end receives the optical signal through the imaging lens, converts the optical signal into an electric signal, and the electric signal is subjected to fast Fourier transform and extracts a data subcarrier; sub-carriers for signal detection and decoding to recover transmitted signals
Wherein the content of the first and second substances,n is white gaussian noise, which is a signal received by a receiving end,for precoding matrix, betaLR-MMSEIs a constraint factor, G, for making the energy of the transmitted signals before and after precoding identicalLR-MMSEIs a decoding matrix;
GLR-MMSE=TH/βLR-MMSE;
where E is the energy of the transmitted signal and x is the initial transmitted signal.
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