CN113315553A

CN113315553A - Simple and convenient dirty paper coding method capable of approaching information theory limit

Info

Publication number: CN113315553A
Application number: CN202110582091.4A
Authority: CN
Inventors: 杨涛; 刘荣科
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2021-05-27
Filing date: 2021-05-27
Publication date: 2021-08-27
Anticipated expiration: 2041-05-27
Also published as: CN113315553B

Abstract

The invention provides a simple and convenient dirty paper coding method which can approach the limit of information theory. Based on the structural characteristics of the q-system linear modulation code, namely, a plurality of code words fall into an extended codebook of the codebook after being overlapped in an integer field, the dirty paper coding of an n-dimensional space is simplified into the operation of finite field subtraction symbol by symbol, and the optimal performance of the dirty paper coding is kept. The coding complexity of the method is basically consistent with that of a single-user interference-free system, and dirty paper coding is realized with extremely low additional cost. The decoding of the method only needs one symbol-by-symbol soft value output detector and one single-user confidence propagation decoding, and the complexity of the method is basically consistent with the encoding complexity of a single-user interference-free system. Through simulation verification, the method can approach the information theory limit (the difference is about 1 dB) of the downlink multi-user channel, and the throughput and the spectral energy efficiency of the system are remarkably improved at low cost.

Description

Simple and convenient dirty paper coding method capable of approaching information theory limit

[ technical field ] A method for producing a semiconductor device

Aiming at the problems of interference among users, spectrum efficiency and energy efficiency of multi-user downlink channel transmission in wireless communication, the invention provides a novel simple and efficient dirty paper coding method which can approach the information theory limit of a downlink multi-user channel at low cost and substantially improve the throughput and spectrum energy efficiency of a system. The invention belongs to the field of communication and signal processing.

[ background of the invention ]

Present-day and future wireless communications are based on multiple-access (MA) and multiple-input multiple-output (MIMO) systems. For the uplink, i.e. multiple ues transmitting information to a base station equipped with multiple antenna arrays, the Serial Interference Cancellation (SIC) based scheme can reach the uplink multiple subscriber information capacity limit. For a downlink, namely, a base station transmits information to a plurality of user equipments, interference between users needs to be precompensated at the base station end through Dirty Paper Coding (DPC), so that the downlink multi-user information theory capacity limit can be reached, and the maximum information throughput and spectrum energy efficiency are realized. The downlink dirty paper coding and the uplink SIC are dual problems.

However, prior to the present invention, the progress of dirty paper coding was relatively slow and very limited. Most of the work in the existing literature stays in the theoretical analysis stage, and although the dirty paper coding is proved to achieve the same transmission rate as that of a non-interference channel, the feasible method for the dirty paper coding is very rare. The teachings of z.xiong in the united states and s.ten Brink in germany have published a series of works on actual dirty-paper coding, however, their methods are very complex, involve multidimensional quantization, source coding, shaping (mapping), and so on, and the gain of real dirty-paper coding combined with channel coding is unclear, making it difficult to implement in an actual wireless communication system. At present, the theoretical performance of dirty paper coding is largely used to depict the upper limit of the downlink spectral energy efficiency, but the mining degree of the huge performance improvement potential in the practical application is very limited.

[ summary of the invention ]

Objects of the invention

The invention can provide a simple, clear, easy-to-use and high-performance novel dirty paper coding method, approaches the information theory limit of a downlink multi-user channel with low complexity, and obviously improves the throughput rate and the spectral energy efficiency of a system with low cost.

The basic problem and mathematical model of dirty paper coding is described as follows: consider a base station that is to communicate an information sequence w of length k to a user equipment. x represents a coded and modulated (baseband) symbol sequence of length n, sent by the base station. The baseband signal received by the user equipment is:

where x is normalized to the average energy of the interference term s, P_xAnd P_sRespectively representing their energies, z represents mean 0 and variance σ²White additive gaussian noise.

In the dirty paper coding problem model, the interference term s is known at the base station and unknown at the user end. In practical applications, the interference term may be a signal from another user, so that it is known at the transmitting end of the base station and compensates for the interference caused by the other user through precoding.

The problems considered by the invention are: how to design dirty paper coding encoder

Satisfy the power constraint E (x)^Tx) is less than or equal to n, and dirty paper code-decoder

Make the error code error probability

The performance approaches the capacity limit of the clear channel (e.g., the gap is around or within 1 dB).

(II) technical scheme

Early preparation

Multi-system irregular repeat accumulation modulation code

In the present invention, the q-ary linear modulation code is a base stone, and therefore, it is first briefly explained.

A real-valued baseband signal model is considered. For a conventional non-interference additive white noise channel (and s is 0), q-ary linear code coding and modulation are respectively

And

here, the

Representing a modulo q multiplication, G is an (n, k) -dimensional code generator matrix with each element belonging to {0, …, q-1}, and γ is the energy used to normalize x. Here, (4) (5) the message sequence is mapped to a q-PAM symbol sequence of n length with an information rate of

Bit/symbol.

This coding technique is called ring codes (ring codes), and is different from the conventional code modulation method. Conventional coded modulation uses binary coding and then logs₂q bits to one q-PAM symbol. The ring code adopted by the invention is a q-ary coded sequence directly changed from a q-ary message sequence and then mapped to a q-PAM symbol in a one-to-one way. For a complex-valued baseband signal model, two independent paths of codes and IQ modulation are respectively adopted for a real part and an imaginary part of the complex-valued baseband signal model: for the real part, encoding and mapping one path of message sequence to q-PAM; for the imaginary part, another message sequence is encoded and mapped to q-PAM. This forms q²-QAM modulation.

The dirty paper coding method of the present invention builds on the characteristics of this q-ary linear modulation code algebraic structure, which will be explained in detail later in the implementation steps.

In a specific implementation, G employs an Irregular Repeat Accumulate (IRA) algorithm, see fig. 1. The q-system IRA modulation code can realize low-complexity coding, iterative decoding, code optimization of density evolution and the like, and approaches to the limit of channel capacity.

Step oneProposed dirty paper coding encoder (see figure 2)

Wherein

Here Q_ZQuantizing an interference sequence s symbol by symbol to a nearest integer value s_Q，

Representing modulo q subtraction, gamma is used to energy normalize the symbol sequence x.

In particular when interfering with

When the sequence is an integer sequence, the proposed dirty paper coding encoder is simplified into

That is, the dirty paper coding of the present invention can be realized only by performing symbol-by-symbol subtraction on a finite field, and the concept and implementation thereof are very simple. If the interference sequence is not an integer, only one difference term quantized with the interference integer needs to be compensated additionally

Is also simple to implement. In addition, when the modulation order q is large, interference to any non-integer interference sequence is avoided

Is a very small value, and therefore equation (3) can be approximately replaced by equation (5).

Step twoWireless channel transmission: the received baseband signal is shown in equation (1).

Step threeProposed DPC decoder (see FIG. 3)

In addition

Representing the signal plus interference term. By using the dirty paper coding we newly propose in equation (6), the term is

When the receiver receives y ═ r + z, the decoder takes two steps:

the first step is as follows:

let c [ t ], y [ t ] and r [ t ] denote the t-th symbol of the codeword sequence c, the received sequence y and the signal plus interference term r, respectively, t being 1, …, n. The a posteriori probability for the t-th symbol with codeword value c [ t ] ═ i, i ═ 0, q-1 is calculated as follows:

where β is a probability normalization coefficient. The prior probability p (r [ t ] in the above equation]) And expanded constellations

Details will be given later in the detailed description section.

The second step is that:

the symbol-by-symbol posterior probability of the codeword sequence c is sent to an iterative confidence coefficient retransmission decoder of a standard q-system IRA modulation code, and the hard decision of the message sequence is output. The Tanner graph of the iterative decoder is shown in figure 4.

It is emphasized here that this decoding algorithm requires a multilevel linear modulation code, such as the q-ary IRA modulation code mentioned earlier.

Step fourOptimized design

Based on the concept of an external information transfer (EXIT) diagram, the optimal degree distribution of q-system IRA modulation code information nodes and check nodes is obtained by linear programming, and the difference between the performance of dirty paper coding and the channel capacity limit is minimized.

Step fiveSimulation verification

The simulation of the system Bit Error Rate (BER) to the signal-to-noise ratio (SNR) is carried out under a channel model of the dirty paper coding problem. Consider the interference signal as a discrete integer value and the interference signal as a continuous gaussian distributed random variable, respectively.

Step sixPerformance evaluation

The performance at different information rates, different interference energies, and the gap to the information capacity limit are evaluated and compared to the performance of non-dirty paper coding systems and existing dirty paper coding systems.

Step sevenApplication and implementation in downlink multi-user MIMO.

Considering the number of base station antennas as 4,8,16,32, 64, the total number of users is equal to the number of base station antennas. The base station performs RQ decomposition on the MIMO channel to triangulate the MIMO channel, and then performs layer-by-layer dirty paper coding precoding by applying the algorithm in the invention (see the implementation step on page 11 for details). In the middle to high signal-to-noise ratio interval (e.g. 10-25dB), the performance improvement and the difference from the information theory capacity limit are evaluated by comparing with the linear precoding schemes such as zero-forcing (ZF), Regular Channel Inversion (RCI) and the like widely used in the industry.

(III) advantages and effects

Based on the structural characteristics of the q-system linear modulation code, and the fact that a plurality of code words fall into an expansion codebook of the codebook after being overlapped in an integer field, the dirty paper coding of an n-dimensional space is simplified into the operation of symbol-by-symbol finite field subtraction, and the optimal performance of the dirty paper coding is kept. The coding complexity of the scheme is basically consistent with that of a single-user interference-free system, and dirty paper coding is realized with extremely low additional cost. The decoding of the scheme only needs one symbol-by-symbol soft value output detector and one single-user confidence propagation decoding, and the complexity of the decoding is basically consistent with the encoding complexity of a single-user interference-free system. Through simulation verification, the method can approach the information theory limit (the difference is about 1 dB) of the downlink multi-user channel, and the throughput and the spectral energy efficiency of the system are remarkably improved at low cost. The method has strong universality, can be suitable for general multi-user MIMO downlink, and can be expanded to multi-cell multi-base station and even the problem of data hiding. The method can be used for improving the service quality of 5G eMBB scenes or services, and helping to realize the full coverage of a 6G heaven-earth integrated network and the like.

[ description of the drawings ]

Fig. 1 is a block diagram of an embodiment according to the present invention.

FIG. 2 is a block diagram 1 of a dirty paper encoder according to an embodiment of the present invention.

FIG. 3 is a block diagram 2 of a dirty paper encoder according to an embodiment of the present invention.

Fig. 4 is a schematic diagram of an IRA modulation code decoder Tanner.

FIG. 5 is a performance description and evaluation of the present invention.

Fig. 6 is a description of the extended constellation required by the present invention.

Fig. 7 is a schematic diagram of the principle of the dirty paper coding of the present invention under the condition of no channel coding.

[ detailed description ] embodiments

The principles, methods, features and performance advantages of the present invention will now be described in detail for a better understanding and appreciation of the invention.

1. Original constellation and expanded constellation

One q-PAM original constellation (constellation point set) is represented as follows

Repeating the q constellation points in an integer domain to obtain a constellation point

The Expanded Constellation (Expanded Constellation) is expressed as follows:

the expanded constellations are grouped according to their corresponding message values as follows (see fig. 6):

here, the first and second liquid crystal display panels are,

is a set of original constellations,

in order to expand the constellation set, the constellation set is expanded,

to expand the subset of the constellation set corresponding to the message value c,

a set of integers is represented that is,

is a finite set of integers of q elements. Example (c): considering q 5, the original constellation is

For a certain message value such as c-3 as an example,

the subset element is represented in figure 6 by the "□" shape.

2. Dirty paper coding (non-channel coding)

For ease of understanding, interference is first considered

For any integer, the dirty paper coding encoder generation provided by the invention

It is clear that,

belongs to the original constellation and automatically satisfies the power constraint. At the user receiver, the signal plus interference cancellation noise term is

Which falls on the extended constellation.

And the receiver finds the value of c with the maximum posterior probability value on all the expanded constellation points as the decision output. It is clear that the minimum distance after dirty paper coding is equal to that in a non-interfering AWGN channel, indicating that the same performance can be achieved at high signal-to-noise ratios as without interference.

Next, consider any s and P_s. By way of example, consider that

(see FIG. 7.) the dirty paper encoder of this invention generates a signal x of

At the user receiver, the signal plus interference cancellation noise term is

Obviously, this term still falls on the expanded constellation by the dirty-paper coding algorithm of the present invention. The decoding method is the same as the above integer value interference example. Here, the transmission signal x contains an extra interference minus its integer quantized difference, resulting in extra energy consumption. It can be shown that the partial energy consumption decreases rapidly with increasing q-value and can be neglected at medium to large q-values.

3. Dirty paper coding (with channel coding)

The dirty paper code containing the channel code can be regarded as the expansion of the single-dimensional dirty paper code in the n-dimensional code word space. The above-described spreading constellation needs to be generalized to a spreading codebook.

In addition

To be driven from

All the resulting sets of codewords are called codebooks. The code book contains

A code word. Its extended codebook is

Wherein

Note that any of these

The elements in (b) are modulo q to obtain the same codeword c.

The dirty paper coding and coding method of the invention is characterized in that the signal plus the interference term is

Obviously, it belongs to a codeword of the extended codebook. This important property allows us to: 1) the method ensures that the dirty paper coding of the symbol by symbol is equivalent to the dirty paper coding of the n-dimensional vector space, so that the method can approach the performance of the capacity limit of the information theory; 2) it is efficiently decoded with q-ary linear modulation coding. We emphasize that in the binary coding combined with many-to-one modulation schemes, which is commonly used in the literature and industry, the above properties are not applicable, and thus the simple dirty paper coding technique of this invention cannot be derived.

Here we describe the effective range of the extended constellation and the prior probability for r, which will be used in the dirty paper codec in the previous technical description. Consider the interference term s as non-infinite. Another s_maxRepresenting the element of s with the largest magnitude. The effective boundary of the extended constellation (constellation points for which the prior probability is not zero) is

Thus, the prior probability of r is

Can be conveniently obtained.

The foregoing illustrates the basic principles of the dirty paper encoding operation of the present invention, and the implementation steps thereof will be described in detail below.

Coding of first-step dirty paper coding

The encoding flow chart of dirty paper encoding is shown in fig. 2. The message sequence passes through a q-ary IRA encoder to generate a codeword sequence. Code word sequence and interference sequence after integer quantization

And performing modulo q subtraction in a finite cyclic domain. And adding a quantization error term to the generated sequence, and finally obtaining a transmitted symbol sequence through an energy return stroke and an energy amplifier.

And a second step of wireless channel transmission: the received baseband signal is shown in equation (1).

Third step decoding of dirty paper code

The decoding flow chart is shown in fig. 3. The symbol-by-symbol posterior probability of codeword sequence c is first computed, yielding q soft messages for each symbol (the values of the late-delay probability of symbol equal to 0, …, q-1, respectively). Then, the soft information is delivered to a q-system IRA modulation code decoder, decoding is carried out by using an iterative belief propagation algorithm, and finally, hard decision of a message sequence is output.

Fourth step of coding degree distribution optimization

The outer code is a check node and accumulator that connects the dirty paper code symbol-by-symbol APP generator. The inner code (inner code) is a repetition node. The inner code and the outer code are connected by an interleaver.

A target code rate is given. Firstly, a certain external code initial degree distribution is selected, and the optimal internal code degree distribution is found by applying linear programming based on curve fitting of an EXIT graph. The inner codedegree distribution is then locked and the rightmost outer codedegree distribution is obtained using a curve-fitted linear program. And iterating until convergence, and recording the generated code word degree distribution.

Fifth step simulation verification

Firstly, a single-user AWGN channel dirty paper coding model is considered, and Monte-Carlo simulation is carried out on the signal-to-noise ratio (BER overturs SNR) of the system error rate. And (4) stopping simulation after 300 frame errors are collected at each SNR point, and recording the result BER and FER results. Firstly, considering the interference signal as a discrete integer value, and then considering the interference signal as a continuous Gaussian distributed random variable.

Sixth Performance evaluation

As shown in fig. 5, the differences between the simulation performance of the dirty paper coding of the present invention and the capacity of the interference-free AWGN channel are about 1.42, 1.15, and 0.91dB at the spectral utilization rates of 1.5, 2.0, and 2.5 bits/symbol, respectively. It is worth mentioning that the gap to the channel capacity can be further narrowed by the minimum mean square error processing at low code rates, which is beyond the scope of this specification.

The seventh step specifically illustrates the application of multi-user MIMO downlink channel precoding in a 5G cellular network and a new generation WiFI system.

The invention solves the problem of energy spectrum efficiency of multi-user MIMO downlink channel precoding. In this example, K is 16 users, and the number of base station antennas N is 16. The channel parameters are rayleigh distributions without spatial and temporal correlation. Firstly, the MIMO channel matrix is decomposed into RQ

H＝RQ

Where R is the lower triangular matrix and Q is the orthogonal matrix, can be compensated by precoding by multiplying by its transpose, so that the equivalent channel matrix is the lower triangular matrix R.

The first row of R is the channel of user 1, and because of the lower triangular matrix characteristic, no interference is caused by other users, and no paper pollution coding is needed. The second row of R is the user 2 channel, which is the superposition of user 1 and user 2 signals. At a sending end of a base station, a user 1 signal is regarded as interference, and the method is used for carrying out dirty paper coding on a message of a user 2; at the receiving end of the user 2, the information of the user 2 is solved by using the dirty paper codec. The third row of R is user 1-3 signal superposition. The base station sending end regards the superposed signals of the

users

1 and 2 as interference and applies the invention to do dirty paper coding on the information of the user 3; at the receiving end of the user 3, the dirty paper codec of the invention is used for solving the information of the user 3. The operation is carried out until the dirty paper coding and decoding operation of the last user is completed. This operation is called serial dirty paper coding.

The simulation of the invention uses Matlab scientific calculation, and calls C language-based programs of an encoder, a decoder and an optimizer of a q-system IRA modulation code through a mex function. And applying the simulation verification method of the single-user AWGN dirty paper code to the multi-user MIMO serial dirty paper code to obtain a numerical simulation result. The result shows that compared with the traditional linear precoding (such as a zero forcing algorithm, a regular channel inversion method and the like), the method can improve the energy spectrum efficiency by about 83% (the signal-to-noise ratio is 20-25 dB) under 16 users.

Although the present invention has been described with reference to the above embodiments, the embodiments are merely exemplary, and not restrictive, and it should be understood that various changes and substitutions may be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims

1. A simple dirty paper coding method which can approach the limit of information theory,

the preparation work is required as follows:

for the traditional non-interference additive white noise channel, the adopted q-system linear code coding and modulation are respectively

And

here, the

Representing modulo q multiplication, G is an (n, k) -dimensional code generator matrix with each element belonging to {0, …, q-1}, and γ is the energy used to normalize x; here, a message sequence is mapped to a q-PAM symbol sequence of n length with an information rate of

Bit/symbol;

this coding technique is called ring codes (ring codes), and is different from the conventional code modulation method; conventional coded modulation uses binary coding and then logs₂q bits to one q-PAM symbol; the ring code adopted by the dirty paper coding method is a coding sequence which directly changes a q-system message sequence into a q-system, and then one-to-one mapping is carried out on a q-PAM symbol; for a complex baseband signal model, a real part and an imaginary part respectively adopt two paths of independent codes and IQ modulation: for the real part, encoding and mapping one path of message sequence to q-PAM; for the imaginary part, encoding and mapping the other path of message sequence to q-PAM; this forms q²-QAM modulation;

the dirty paper encoding method is now described; the method is characterized by comprising the following steps:

the method comprises the following steps: proposed dirty paper coding encoder

Wherein

Representing modulo q subtraction, γ being used to energy normalize the symbol sequence x;

when interference occurs

That is, dirty paper encoding can be realized only by symbol-by-symbol subtraction in a finite field; if the interference sequence is not an integer, only one difference term quantized with the interference integer needs to be compensated additionally

The implementation is also simple; in addition, when the modulation order q is large, interference to any non-integer interference sequence is avoided

Is a very small value, and therefore equation (3) can be approximately replaced by equation (5);

step two: wireless channel transmission:

considering that a base station needs to transmit an information sequence w with the length k to a user equipment; x represents a coded and modulated symbol sequence sent by the base station, and the length is n; the baseband signal received by the user equipment is:

where x is normalized to the average energy of the interference term s, P_xAnd P_sRespectively representing their energies, z represents mean 0 and variance σ²Additive white gaussian noise of (1);

step three: proposed DPC decoder

Order to

Representing the signal plus an interference term; the dirty paper code applied in equation (3) is

Which is a codeword in the extended codebook;

step four: optimized design

Based on the idea of an external information transfer diagram, the optimal degree distribution of q-system IRA modulation code information nodes and check nodes is obtained by linear programming, and the difference between the performance of dirty paper coding and the channel capacity limit is minimized;

step five: simulation verification

Carrying out simulation of a system bit error rate BER to a signal-to-noise ratio SNR under a channel model of dirty paper coding; respectively considering that the interference signals are discrete integer values and the interference signals are continuous Gaussian distributed random variables;

step six: performance evaluation

Evaluating the performances of different information rates and different interference energies and the difference between the performances and the information capacity limit, and comparing the performances with the performances of a non-dirty paper coding system and the performances of the existing dirty paper coding system;

step seven: application and implementation of downlink multi-user MIMO;

considering the number of base station antennas to be 4,8,16,32 and 64, the total number of users is equal to the number of base station antennas; the base station performs RQ decomposition on the MIMO channel to triangulate the MIMO channel, and then performs layer-by-layer dirty paper coding precoding; and comparing the intermediate-to-high signal-to-noise ratio interval with a zero-forcing and regular-stroke channel inversion linear precoding scheme widely applied in the industry, and evaluating the performance improvement and the difference with the capacity limit of an information theory.

2. The method of claim 1, wherein the method comprises: in the first step, the message sequence passes through a q-system IRA encoder to generate a code word sequence; code word sequence and interference sequence after integer quantization

Performing modulo q subtraction in a finite cyclic domain; and adding a quantization error term to the generated sequence, and finally obtaining a transmitted symbol sequence through an energy return stroke and an energy amplifier.

3. The method of claim 1, wherein the method comprises: in the second step, the interference item s is known at the base station and unknown at the user terminal; in practical applications, the interference term may be a signal from another user, and therefore, the interference caused by the other user is known at the transmitting end of the base station and compensated by precoding.

4. The method of claim 1, wherein the method comprises: in step three, when the receiver receives y ═ r + z, the decoder takes two steps:

the first step is as follows:

let c [ t ], y [ t ] and r [ t ] denote the codeword sequence c, the received sequence y and the tth symbol of the signal plus interference term r, respectively, t is 1, …, n; the a posteriori probability for the t-th symbol with codeword value c [ t ] ═ i, i ═ 0, …, q-1, is calculated as follows:

wherein β is a probability normalization coefficient; the prior probability p (r [ t ]) in the above equation (8)]) And expanded constellations

Details will be given later in the detailed description section;

the second step is that:

the symbol-by-symbol posterior probability of the codeword sequence c is sent to an iterative confidence coefficient retransmission decoder of a standard q-system IRA modulation code, and the hard decision of the message sequence is output.

5. The method of claim 1, wherein the method comprises: in the fourth step, the concrete steps are as follows: the external code is a check node and an accumulator which are connected with a dirty paper coding symbol-by-symbol APP generator; the inner code is a repetition node; the inner code and the outer code are connected through an interleaver;

giving a target code rate; firstly, selecting a certain external code initial degree distribution, and finding out the optimal internal code degree distribution by using a linear programming based on EXIT graph curve fitting; then, locking the inner code degree distribution, and obtaining the rightmost outer code degree distribution by using linear programming of curve fitting; and iterating until convergence, and recording the generated code word degree distribution.

6. The method of claim 1, wherein the method comprises: in the fifth step, the method specifically comprises the following steps: firstly, considering a dirty paper coding model of a single-user AWGN channel, and carrying out Monte-Carlo simulation on the signal-to-noise ratio of the system bit error rate; stopping simulation after 300 frame errors are collected by each SNR point, and recording the result BER and FER results; firstly, considering the interference signal as a discrete integer value, and then considering the interference signal as a continuous Gaussian distributed random variable.

7. The method of claim 1, wherein the method comprises: in the sixth step, specifically: under the spectrum utilization rates of 1.5, 2.0 and 2.5 bits/symbol, the differences between the dirty paper coding simulation performance and the interference-free AWGN channel capacity are respectively about 1.42 dB, 1.15 dB and 0.91 dB; the gap to channel capacity is further narrowed by minimum mean square error processing at low code rates.

8. The method of claim 1, wherein the method comprises: in the seventh step, specifically: the application of the multi-user MIMO downlink channel precoding in a 5G cellular network and a new generation WiFI system;

adopting 16 users, and the number of base station antennas N is 16; the channel parameters are Rayleigh distribution without space-time correlation; firstly, the MIMO channel matrix is decomposed into RQ

H＝RQ

Wherein R is a lower triangular matrix, Q is an orthogonal matrix which can be pre-coded and compensated by multiplying the transpose of the orthogonal matrix, so that the equivalent channel matrix is the lower triangular matrix R;

the first row of R is the channel of user 1, and because the lower triangular matrix characteristic of the channel has no interference of other users, the channel does not need to be subjected to dirty paper coding; the second behavior of R is the channel of user 2, and the signals of user 1 and user 2 are superposed; at a sending end of a base station, regarding a user 1 signal as interference, and performing dirty paper coding on a message of a user 2; at a receiving end of the user 2, the information of the user 2 is solved by using a dirty paper codec; the third row of R is user 1-3 signal superposition; a base station sending end regards the superposed signals of the users 1 and 2 as interference and carries out dirty paper coding on the information of the user 3; at a receiving end of a user 3, a dirty paper codec is utilized to solve the message of the user 3; the operation is carried out until the dirty paper coding and decoding operation of the last user is completed.