CN108900448B - Low-complexity packet decoding method based on MIMO system - Google Patents

Abstract

The present invention claims to protect a low-complexity packet decoding method based on a MIMO system, a packet-forcing decoding method, which belongs to the technical field of communications and is used for reducing the complexity of the MIMO system decoding. The proposed algorithm is based on the forced integer decoding algorithm. The received signals are grouped, each group is independently decoded using the forced integer algorithm, and then the transmitted codewords decoded by each group are aggregated to obtain the most primitive before grouping. transmit information. The packet forcing algorithm reduces the complexity of decoding by grouping the received symbols. Therefore, compared with the forcing detection algorithm, the grouping forcing has an advantage in the decoding complexity. At the same time, it can be seen from the simulation results that the grouping is Compared with the forced adjustment algorithm, the system performance has an advantage, and the gap of system performance becomes larger and larger with the increase of the number of antennas.

Description

A low-complexity block decoding method based on MIMO system

technical field

The invention belongs to the field of communication technologies, and relates to the design of a decoding algorithm at a receiving end in a multiple-input multiple-output (Multiple-Input Multiple-Output, MIMO for short) system, in particular to a packet-forcing decoding algorithm based on a forced-integration decoding algorithm structure design.

Background technique

Multiple-input multiple-output technology can double the channel capacity of the system without increasing additional system bandwidth and antenna transmit power, so MIMO technology has been widely used in the field of wireless mobile communications [1]. The quality of the decoding algorithm at the receiving end determines the performance of the MIMO system, so it is particularly important to seek a low-complexity and high-performance algorithm [2]. The decoding algorithms at the receiving end can be divided into two categories. One is the Maximum Likelihood (ML) decoding algorithm. The ML decoding algorithm is the optimal decoding algorithm, but its decoding complexity will vary with the transmission. The antenna and modulation constellations increase exponentially [2], [3]. The other type is the traditional linear decoding algorithm, including Zero-Forcing (ZF) decoding algorithm and Minimum Mean Square Error (MMSE) decoding algorithm. The complexity of the linear decoding algorithm is Much lower than ML algorithms, but its performance is poor compared to ML [2], [4]. Recently, a new linear decoding algorithm based on MIMO system called Integer-Forcing Linear Receivers (IF) decoding algorithm has been widely studied [2], [5]. The IF decoding algorithm has more advantages than the ML algorithm. Lower complexity, but its performance is close to the ML decoding algorithm.

The most prominent feature of the IF detection algorithm is that unlike the traditional linear detection algorithm, it directly recovers the transmission codeword. It uses the receiving antenna to generate an effective integer channel matrix, and recovers the integer combination of the transmitted codeword through the effective channel matrix. [2]. The effective integer channel matrix must be invertible and non-singular. There are various algorithms that can be used to find this effective integer channel matrix, such as HKZ, Minkowski, LLL, and CLLL algorithm[6]–[8]. Although the forcing decoding algorithm has lower decoding complexity, it is still necessary to find a decoding algorithm to further reduce the complexity and make it better for applications with a large number of antennas or requiring lower complexity and general system performance Therefore, in-depth analysis and research are carried out based on the forced integer decoding algorithm.

[1] G.J.Foschini and M.J.Gans, "On limits of wireless communications in a fading environment when using multiple antennas," Wireless Personal Communications, vol.6, no.3, pp.311–335, 1998.

[2] J. Zhan, B. Nazer, U. Erez, and M. Gastpar, “Integer-forcing linearreceivers,” IEEE Transactions on Information Theory, vol.60, no.12, pp.7661–7685, Dec 2014.

[3] M.O.Damen, H.E.Gamal, and G.Caire, “On maximum-likelihood detection and the search for the closest lattice point,” IEEE Transactions on Information Theory, vol.49, no.10, pp.2389–2402, Oct 2003 .

[4] K.R.Kumar, G.Caire, and A.L. Moustakas, “Asymptotic performance of linear receivers in mimo fading channels,” IEEE Transactions on InformationTheory, vol.55, no.10, pp.4398–4418, Oct 2009.

[5] J.Zhan, B.Nazer, U.Erez, and M.Gastpar, "Integer-forcing linearreceivers: A new low-complexity mimo architecture," in 2010IEEE 72nd VehicularTechnology Conference-Fall, Sept 2010, pp.1– 5.

[6] W. Zhang, S. Qiao, and Y. Wei, “Hkz and minkowski reduction algorithms for lattice-reduction-aided mimo detection,” IEEE Transactions on SignalProcessing, vol.60, no.11, pp.5963–5976, Nov 2012.

[7] A. Sakzad, J. Harshan, and E. Viterbo, “On complex lll algorithm forinteger forcing linear receivers,” in 2013 Australian Communications TheoryWorkshop (AusCTW), Jan 2013, pp.13–17.

[8]——, "Integer-forcing mimo linear receivers based on latticereduction," IEEE Transactions on Wireless Communications, vol.12, no.10, pp.4905–4915, October 2013.

SUMMARY OF THE INVENTION

The present invention aims to solve the above problems of the prior art. Based on the forced integer decoding algorithm, a packet forced integer decoding algorithm is proposed. Since the decoding complexity of the forced integer decoding algorithm mainly comes from using the lattice reduction algorithm to make the channel matrix into an effective integer channel matrix, the packet forced integer algorithm passes The received symbols are grouped to reduce the dimension of the channel matrix and thus reduce the complexity of decoding. The technical scheme of the present invention is as follows:

A low-complexity packet decoding algorithm based on a MIMO system, comprising the following steps:

First, the received symbols are grouped, and each group of received signals is decoded independently using the forcing algorithm to obtain the transmitted codeword. The idea of the forcing algorithm is to find an effective integer matrix A and an equalization matrix B, and each group is decoded to obtain their group. The transmitted codewords decoded independently by each group are the total transmitted symbols before grouping, so as to obtain the most original transmitted information before grouping.

Further, the grouping of the received signals specifically includes: first, the two columns of the channel matrix H are used as a group, and the received symbols are divided into L groups, where L=N/2, and N is the number of receiving and transmitting antennas, then the MIMO system The equation is

SNR表示每根接收天线处的平均信噪比，X_q表示第q组的发送符号，q表示第q个组，在不失一般性的情况下，只对第一分组进行研究，找到有效整数矩阵A和均衡矩阵B,在研究一个分组时，把其他分组当成噪声，第一组的信号模型为in

SNR represents the average signal-to-noise ratio at each receiving antenna, X _q represents the transmitted symbols of the qth group, and q represents the qth group. Without loss of generality, only the first group is studied to find a valid integer Matrix A and equalization matrix B. When studying one group, other groups are regarded as noise. The signal model of the first group is

被当作有效信号成分，其中

表示一个N×2 复数矩阵，而

都被当作有效噪声成分。Although the signal model of Equation (2) is the same as the system equation of Equation (1), in Equation (2), only

is regarded as a valid signal component, where

represents an N×2 complex matrix, and

are regarded as effective noise components.

后得到Further, the equalization matrix is used for the first grouped signal

get after

是第一分组的有效整数信道矩阵；in

is the effective integer channel matrix of the first grouping;

分别表示

B₁,A₁的第m行use

Respectively

B ₁ , the mth row of A ₁

公式(4)变成Let

Equation (4) becomes

Further, the use of the improved forcing algorithm for decoding specifically includes:

上有限格译码：将

中每个元素译码到整数域

中得到离其最近的点，即

其中

表示取整操作；step one

Upper bounded decoding: the

decodes each element into the integer domain

to get the closest point to it, that is,

in

Indicates the rounding operation;

对

进行取模操作得到

J表示星座阶数；Step 2: Grid word projection:

right

Take the modulo operation to get

J represents the constellation order;

获得译码向量

Step 3: Lattice Codeword Decoupling: Based on Linear Equations

get decoded vector

After the above steps, the decoded symbols of the first group are obtained, and then the same steps as the first group are used in the remaining groups to obtain the decoded symbols of other groups, and the decoded symbols of all the groups are collected to get The original sent message before being grouped.

Further, the expression of the optimal effective integer channel matrix A ₁

The expression of the optimal equilibrium matrix B ₁

The advantages and beneficial effects of the present invention are as follows:

The invention reduces the dimension of the channel matrix by grouping the received signals, further reduces the complexity of using the lattice reduction algorithm to reduce the channel matrix to an effective integer channel matrix, thereby reducing the overall complexity of the forced integer decoding algorithm. Compared with the forcing decoding algorithm, the packet forcing decoding algorithm has lower decoding complexity and better decoding performance than the forcing decoding algorithm, and with the increase of the number of antennas, the performance gap increases. getting bigger. Based on these characteristics of the grouping algorithm, it can be applied to the case where the decoding complexity is low and the decoding performance is general or the number of antennas is large.

Description of drawings

1 is a block diagram of a forcing system in a preferred embodiment provided by the present invention;

Fig. 2 is the bit error rate performance comparison schematic diagram of the packet-forcing decoding algorithm of the present invention and the forcing decoding algorithm using the 4-QAM constellation in 4 × 4 channels;

3 is a schematic diagram showing the comparison of the bit error rate performance of the packet-forcing decoding algorithm of the present invention and the forcing-forcing decoding algorithm using a 4-QAM constellation in an 8×8 channel;

FIG. 4 is a schematic diagram showing the comparison of the bit error rate performance of the packet-forcing decoding algorithm of the present invention and the forcing decoding algorithm using the 4-QAM constellation in a 12×12 channel.

Detailed ways

The technical solutions in the embodiments of the present invention will be described clearly and in detail below with reference to the accompanying drawings in the embodiments of the present invention. The described embodiments are only some of the embodiments of the invention.

The technical scheme that the present invention solves the above-mentioned technical problems is:

A low-complexity packet decoding algorithm based on a MIMO system, which includes the following steps at the receiving end: first, the received symbols are divided into L groups with two columns of a channel matrix H as a group, L=N/2, and N is The number of receive and transmit antennas, then the MIMO system equation is

SNR表示每根接收天线处的平均信噪比，q表示第q个组。在不失一般性的情况下，只对第一分组进行研究，第一组的信号模型为in

SNR denotes the average signal-to-noise ratio at each receive antenna, and q denotes the qth group. Without loss of generality, only the first group is studied, and the signal model of the first group is

被当作有效信号成分，其中

而

都被当作有效噪声成分。Although the signal model of Equation (2) is the same as the system equation of Equation (1), in Equation (2), only

is regarded as a valid signal component, where

and

are regarded as effective noise components.

后得到Further, using an equalization matrix for the first grouped signal

get after

是第一分组的有效整数信道矩阵。in

is the effective integer channel matrix of the first packet.

分别表示

B₁，A₁的第m行Further, with

Respectively

B ₁ , the mth row of A ₁

公式(4)变成Let

Equation (4) becomes

Further, the effective noise variance can be obtained as

Further, take the reciprocal of b _1m

Equation (7) equals zero to get

_An expression for the optimal equalization matrix B1 is then obtained, and the resulting equalization matrix _B1 can minimize the effective noise.

a_1m＝a₁，公式(8)变为further, make

a _1m =a ₁ , formula (8) becomes

便可得到最优有效整数信道矩阵A₁的表达式Substituting b _opt,1m of formula (9) into formula (6), we get

Then the expression of the optimal effective integer channel matrix A ₁ can be obtained

Further, after replacing H ₁ in formula (10) with the singular value decomposition (SVD) of H ₁ , we get

的特征向量所构成的矩阵，D₁是对角矩阵，它的第m的项表示为

p_m是H₁矩阵的第m个奇异值。where _V1 is determined by

The matrix formed by the eigenvectors of , D ₁ is a diagonal matrix, and its mth item is expressed as

p _m is the mth singular value _of the H1 matrix.

Through the above steps, two important matrices are obtained when the received symbols are grouped and then used for integer detection, the equalization matrix B ₁ and the effective integer channel matrix A ₁ .

中产生N个相互独立的、均匀的、长度为k的信息序列w₁,…,w_N。信道矩阵用

表示，Η的元素都服从独立同分布

且设定Η在M时隙中保持不变并独立于下一个时隙。此系统模型使用N层的水平编码方案，即使用不同的天线独立的发送信息，第r (1≤r≤N)层的发送信息被馈送到格编码器ε中：

即将消息

映射成格码字

其中格Λ是

的一个离散加性子群，并且加性运算和反射运算在格中被封闭。格码书的码字是格的元素，且格码的任意线性组合本身就是格码。使用

表示发送码字矩阵，则接收矩阵

可表示为A block diagram of a MIMO system based on the idea of a forced integer decoding algorithm is shown in FIG. 1 . The number of transmit antennas in the system is N, the number of receive antennas is N, and N is an even number. Suppose from

Generate N mutually independent and uniform information sequences w ₁ ,...,w _N of length k. For channel matrix

It means that the elements of H are all independent and identically distributed

And setting H remains unchanged in M slots and independent of the next slot. This system model uses a horizontal coding scheme of N layers, i.e., the information is transmitted independently using different antennas, and the transmitted information of the r (1≤r≤N)th layer is fed into the trellis encoder ε:

upcoming news

Mapping to Trellis Codewords

where lattice Λ is

is a discrete additive subgroup of , and the additive and reflex operations are closed in the lattice. The code words of the trellis code book are the elements of the trellis, and any linear combination of the trellis codes is itself a trellis code. use

represents the transmit codeword matrix, then the receive matrix

can be expressed as

表示噪声矩阵，其元素为独立同分布的高斯随机变量。信道信息只能被接收机知道。在迫整系统模型中，将公式(12)左乘一个均衡矩阵B得到有效整数信道矩阵A，有效整数信道矩阵必须是可逆的，可得

represents a noise matrix whose elements are independent and identically distributed Gaussian random variables. Channel information can only be known by the receiver. In the forcing system model, multiply the equation (12) to the left by an equalization matrix B to obtain an effective integer channel matrix A, which must be invertible, and can be obtained

为信号成分，

为有效噪声。in

is the signal component,

is the effective noise.

中的极小问题是具有Gram矩阵G₁＝V₁D₁V₁ ^H的格的最短向量问题，又因为G₁是对称正定矩阵，则可以将G₁写成G₁＝L₁L₁ ^H，

而又L₁＝V₁D₁ ^1/2的行可以生成格Λ。用LLL算法使L₁变成一个格生成矩阵L'₁，L₁和L'₁生成相同的格Λ，然后通过

的行向量便可得到有效整数信道矩阵A₁，这个步骤的伪代码如下所示：The optimal integer channel matrix A ₁ obtained by grouping forcing, namely formula (11)

The minimal problem in is the shortest vector problem of the lattice with Gram matrix G ₁ =V ₁ D ₁ V ₁ ^H , and because G ₁ is a symmetric positive definite matrix, G ₁ can be written as G ₁ =L ₁ L ₁ ^H ,

And the row where L ₁ =V ₁ D ₁ ^1/2 can generate lattice Λ. Use the LLL algorithm to make L ₁ into a lattice generator matrix L' ₁ , L ₁ and L' ₁ generate the same lattice Λ, and then pass

The effective integer channel matrix A ₁ can be obtained by the row vector of , and the pseudocode of this step is as follows:

Input: H,H ₁

Output: A ₁ ,B ₁

1:S←ρ ^-1 I+HH ^H

2: (U ₁ ,Σ,V ₁ )←SVD(H ₁ ), where Σ=diag(p ₁ ,p ₂ )

3:

4:L ₁ ←V ₁ D ₁ ^1/2

5:L ₁ '←LLL(L ₁ )

6: get A ₁ =L ₁ 'L ₁ ^-1 and

It is obvious from the above that in the grouping forcing algorithm, only the LLL algorithm is used to find a 2×2 integer matrix, instead of finding an N×N integer matrix like the forcing algorithm, so the grouping forcing has lower decoding complexity.

Set M=1, and linearly vectorize the received matrix Y ₁ to get

分别表示第一分组中的接收和发送符号向量，而y₁,w₁分别表示第一个接收和发送符号，注意

和y₁,w₁表示含义之间的差别。之后利用

与

之间标准的一对一映射关系，将第一组的接收复数向量变成实数向量，则公式(14)变为It should be noted that,

represent the received and transmitted symbol vectors in the first packet, respectively, and y ₁ , w ₁ represent the first received and transmitted symbols, respectively, note that

and y ₁ , w ₁ represent the difference between meanings. use later

and

The standard one-to-one mapping relationship between , and the received complex vector of the first group becomes a real vector, then formula (14) becomes

有限环

J是2的幂次方。在这些设定下，使用分组迫整算法译码的过程如下：in

finite ring

J is a power of 2. Under these settings, the decoding process using the packet forcing algorithm is as follows:

上有限格译码：将

中每个元素译码到整数域

中得到离其最近的点，即

其中

表示取整操作。step one

Upper bounded decoding: the

decodes each element into the integer domain

to get the closest point to it, that is,

in

Indicates a rounding operation.

对

进行取模操作得到

Step 2: Grid word projection:

right

Take the modulo operation to get

获得译码向量

Step 3: Lattice Codeword Decoupling: Based on Linear Equations

get decoded vector

After the above steps, the decoded symbols of the first group can be obtained, and then the same steps as the first group are used in the remaining groups to obtain the decoded symbols of other groups, and the decoded symbols of all the groups are collected to obtain The original sent information before it was grouped.

The simulation platform of this embodiment is a flat Rayleigh fading channel, using 4-QAM modulation, the code word is generated from a two-dimensional integer lattice code, and the number of antennas is 4 to 4 to receive, 8 to 8 to receive, and 12 to 12 to receive. This implementation is listed under the above simulation platform, simulates the packet-forcing decoding algorithm and the zero-forcing decoding algorithm, and compares and analyzes the bit error rate (Bit ErrorRate, BER for short) performance obtained. Figure 2 shows the BER performance of the packet-forcing decoding algorithm and the zero-forcing decoding algorithm in the 4×4 channel, and Figure 3 shows the packet-forcing decoding algorithm and the zero-forcing decoding algorithm in the 8×8 channel, respectively. The BER performance of the coding algorithm, Figure 4 shows the BER performance of the packet-forcing decoding algorithm and the zero-forcing decoding algorithm in a 12×12 channel. From the figures of these embodiments, it can be known that the packet forcing decoding algorithm has better BER performance than the forcing detection, and as the number of antennas increases, the performance advantage of grouping forcing becomes more and more obvious.

The above embodiments should be understood as only for illustrating the present invention and not for limiting the protection scope of the present invention. After reading the contents of the description of the present invention, the skilled person can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims (1)

1. A low complexity packet decoding method based on MIMO system is characterized in that the method comprises the following steps:

firstly, grouping received symbols, wherein each group of received signals are independently decoded by using a forced integer algorithm to obtain a transmitted code word, the concept of the forced integer algorithm is to find an effective integer matrix A and an equilibrium matrix B, each group decodes the symbols of the groups respectively, and the transmitted code words which are independently decoded by each group are aggregated and are the total transmitted symbols before no grouping, so that the most original transmitted information before no grouping is obtained;

the decoding by using the improved rounding algorithm specifically comprises:

step one is

Upper lattice decoding: will be provided with

In which each element is decoded into an integer field

To obtain the point closest thereto, i.e.

Wherein

Representing a rounding operation;

in order to equalize the matrix, the matrix is,

a vector of received symbols for a first packet;

receiving a signal matrix Y for a first packet ₁ Is represented by a vectorization of (a),

to represent

Vector after getting whole according to element;

step two, code word projection:

to pair

Performing a mold-taking operation to obtain

J represents the constellation order;

step three-lattice code word decoupling: based on linear equations

Obtaining a decoded vector

Obtaining the decoding symbols of the first grouping through the steps, then obtaining the decoding symbols of other groups in the rest grouping by using the same steps as the first grouping, and collecting the decoding symbols of all the groupings to obtain the original sending information before the grouping;

optimal effective integer matrix A ₁ Expression (2)

Optimal equalization matrix B ₁ Expression (2)

For the optimal equalization matrix B ₁ Row m;

the grouping of the received signals specifically includes: firstly, two columns of a channel matrix H are taken as a group, received symbols are divided into L groups, L is N/2, N is the number of receiving and transmitting antennas, and then the MIMO system equation is

Is a receiving matrix; h _q Represents the q-th group after the channel matrix H grouping, wherein

SNR represents the average signal-to-noise ratio, X, at each receive antenna _q Representing the transmitted symbols of the q-th group, q representing the q-th group, and under the condition of no loss of generality, only the first group is studied to find the effective integer matrix A and the equalization matrix B, and when one group is studied, other groups are used as noise, and the signal model of the first group is

H ₁ 、X ₁ Representing the first grouping of the channel matrix H and the transmit codeword matrix X, respectively, although the signal model of equation (2) is the same as the system equation of equation (1), in equation (2), only

Is taken as an effective signal component, wherein

Represents an N x 2 complex matrix, and

are all considered as effective noise components;

the use of an equalization matrix for the first packet signal

Then obtain

Wherein

Is the effective integer channel matrix of the first packet;

by using

Respectively represent

B ₁ ,A ₁ Line m of

Let

Equation (4) becomes

Using a horizontal coding scheme of N layers, i.e., using different antenna-independent transmission information, the transmission information of the r (1 ≦ r ≦ N) th layer is fed into the trellis encoder ε:

i.e. a message

Mapping to trellis code words

Wherein Λ is

And the additive operation and the reflection operation are enclosed in the cell; the code words of the trellis code book are elements of the trellis, and any linear combination of the trellis codes is the trellis code; use of

Indicating the matrix of the transmitted code word, then the received matrix

Can be expressed as

Representing a noise matrix, wherein elements of the noise matrix are independent and identically distributed Gaussian random variables; channel information can only beIs known by the receiver; in the forced integer system model, the equation (12) is multiplied by an equalization matrix B to obtain an effective integer channel matrix A, which must be reversible to obtain

Wherein

As a component of the signal, the signal component,

is effective noise;

optimal integer channel matrix A obtained in group forced integer ₁ Namely formula (11)

Has a Gram matrix G ₁ ＝V ₁ D ₁ V ₁ ^H The shortest vector problem of the lattice of (2), and because of G ₁ Is a symmetric positive definite matrix, G can be set ₁ Write to G ₁ ＝L ₁ L ₁ ^H ，

L ₁ Represents an intermediate variable, which is L ₁ ＝V ₁ D ₁ ^1/2 May generate a lattice Λ; using LLL algorithm to make L ₁ Becomes a lattice generating matrix L' ₁ ，L ₁ And L' ₁ Generate the same lattice Λ and then pass

The row vector of the channel matrix A is obtained ₁ 。

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