CN105790820A

CN105790820A - MIMO-FBMC based maximum likelihood detecting algorithm

Info

Publication number: CN105790820A
Application number: CN201610105585.2A
Authority: CN
Inventors: 刘文旭; 夏鹏敏; 万晨
Original assignee: Huazhong University of Science and Technology
Current assignee: Huazhong University of Science and Technology
Priority date: 2016-02-25
Filing date: 2016-02-25
Publication date: 2016-07-20

Abstract

The present invention relates to a maximum likelihood detection algorithm based on MIMO-FBMC. The steps of the scheme are briefly described as follows: 1. Construct a channel model; 2. Use the MMSE algorithm to estimate interference; due to the existence of intersymbol interference ( This is also the main reason why there is no better channel equalization algorithm in MIMO-FBMC), that is, S is a random value and cannot be traversed directly, so this scheme uses MMSE to make a preliminary estimate of the interference and narrow its scope; 3. Use The ML algorithm estimates the effective signal, and after obtaining the estimate of the interference, estimates the effective signal, so as to achieve the purpose of the present invention.

Description

A Maximum Likelihood Detection Algorithm Based on MIMO-FBMC

技术领域technical field

本发明属于通信技术领域，更具体地，涉及MIMO‐FBMC(Multiple‐InputMultiple‐Output‐FilterbankMulticarrier，多输入多输出滤波器多载波)的检测算法。The invention belongs to the technical field of communication, and more specifically relates to a detection algorithm of MIMO-FBMC (Multiple-Input Multiple-Output-Filterbank Multicarrier, multiple-input multiple-output filter multicarrier).

背景技术Background technique

通过研究我们可以得知，FBMC的一个关键特性是其可能传输独立的无重叠覆盖的子载波，也有可能传输有重叠覆盖的子载波，因此，在基于FBMC的传输系统中存在子载波不重叠和子载波重叠这两种情况。在子载波不重叠的情况下的MIMO技术与OFDM(OrthogonalFrequencyDivisionMultiplexing，正交频分复用)下的技术并无不同，前人与业界都进行了大量的研究，有了很多成熟的算法。而对于后者，算法并不成熟，如迫零检测、最小均方误差检测算法及最大似然检测算法，都有一定的缺陷。Through research, we can know that a key feature of FBMC is that it may transmit independent non-overlapping subcarriers, and may also transmit subcarriers with overlapping coverage. Therefore, there are non-overlapping subcarriers and subcarriers in FBMC-based transmission systems Carriers overlap in both cases. The MIMO technology in the case of non-overlapping subcarriers is no different from the technology under OFDM (Orthogonal Frequency Division Multiplexing, Orthogonal Frequency Division Multiplexing). The predecessors and the industry have conducted a lot of research, and there are many mature algorithms. For the latter, the algorithm is not mature, such as zero-forcing detection, minimum mean square error detection algorithm and maximum likelihood detection algorithm, all have certain defects.

下面介绍上文所提三种算法:The three algorithms mentioned above are introduced below:

1.迫零检测算法(ZF,Zeroforcing检测算法)1. Zero-forcing detection algorithm (ZF, Zeroforcing detection algorithm)

迫零检测算法是最简单的MIMO检测算法，其目的是消除其他天线的干扰，将接受信号映射到其他天线的正交子空间，强制干扰为0。ZF算法依据的是最小二乘估计准则，找到一个估计值，通过信道矩阵后与信号的误差平方和最小。但接收机噪声通过迫零检测之后被放大。从这一点上来说，迫零算法抑制了发送天线间的干扰，却同时放大了噪声。The zero-forcing detection algorithm is the simplest MIMO detection algorithm. Its purpose is to eliminate the interference of other antennas, map the received signal to the orthogonal subspace of other antennas, and force the interference to be 0. The ZF algorithm is based on the least squares estimation criterion, finds an estimated value, and the sum of squares of the error with the signal is the smallest after passing through the channel matrix. But receiver noise is amplified after zero-forcing detection. From this point of view, the zero-forcing algorithm suppresses the interference between transmitting antennas, but at the same time amplifies the noise.

2.最小均方差误差检测算法(MMSE,MinimumMeanSquareError检测算法)2. Minimum mean square error detection algorithm (MMSE, MinimumMeanSquareError detection algorithm)

MMSE算法同为线性检测算法，却能兼顾抑制天线间间干扰和降低噪声，从而提升系统性能。其原理是找到一个发射信号的估计值，使估计值与真实值的平方误差值最小。MMSE检测算法是线性的。复杂度较低。并且，同时抑制了天线干扰和噪声。在性能上，MMSE要优于ZF，适用于更广泛的信噪比。从而得到更广泛应用。The MMSE algorithm is also a linear detection algorithm, but it can suppress interference between antennas and reduce noise, thereby improving system performance. Its principle is to find an estimated value of the transmitted signal, so that the square error value between the estimated value and the true value is the smallest. The MMSE detection algorithm is linear. Less complex. Also, antenna interference and noise are suppressed at the same time. In terms of performance, MMSE is better than ZF and is suitable for a wider range of signal-to-noise ratios. resulting in wider application.

3.最大似然检测算法(ML，Maximumlikelihood检测算法)3. Maximum likelihood detection algorithm (ML, Maximumlikelihood detection algorithm)

ML算法与前文所提两种算法，其为非线性算法，基本思想为历所有可能的发送信号，求该信号经过给定信道后与接收信号的欧几里德距离。使其最小的一个信号即为检测信号，相对于MMSE算法而言，其有精度更高。The ML algorithm and the two algorithms mentioned above are nonlinear algorithms. The basic idea is to go through all possible sending signals and find the Euclidean distance between the signal and the receiving signal after passing through a given channel. The signal that makes it the smallest is the detection signal, which has higher precision than the MMSE algorithm.

但由于在FBMC系统当中，干扰值随机而非固定的集合，不可能遍历，因此并不可试用与存在子载波重叠的FBMC系统当中。However, in the FBMC system, the interference value is random rather than a fixed set, and it is impossible to traverse, so it cannot be tried in the FBMC system with overlapping subcarriers.

从上文可以看出，ML算法相对于令两种算法精度更高，但由于FBMC系统存在符号间干扰，因此不可行。It can be seen from the above that the ML algorithm is more accurate than the two algorithms, but it is not feasible due to the intersymbol interference in the FBMC system.

发明内容Contents of the invention

本发明的目的就是为了克服上述现有MIMO‐FBMC信道均衡并没有精度较高的信道均衡算法的问题，提供一种基于MIMO-FBMC的最大似然检测算法，本发明通过对干扰做估计，运用这个干扰值进一步进行ML检测。干扰估计用MMSE实现。The purpose of the present invention is to overcome the problem that the above-mentioned existing MIMO-FBMC channel equalization does not have a channel equalization algorithm with higher precision, and to provide a maximum likelihood detection algorithm based on MIMO-FBMC. The present invention estimates the interference and uses This noise value is further subjected to ML detection. Interference estimation is realized with MMSE.

本发明的技术方案为：Technical scheme of the present invention is:

一种基于MIMO-FBMC的最大似然检测算法，其特征在于按以下步骤进行：A maximum likelihood detection algorithm based on MIMO-FBMC is characterized in that it proceeds in the following steps:

步骤一构建信道模型：发射天线和接收天线的数目都为n，n为大于1的偶数，假设n根发射天线分别发送数据d₁,d₂,…,d_n，而此时的有效信道矩阵H为：Step 1: Construct a channel model: the number of transmitting antennas and receiving antennas is n, and n is an even number greater than 1. Assume that n transmitting antennas respectively transmit data d ₁ , d ₂ ,...,d _n , and the effective channel matrix at this time H is:

理想状况下，接收机收到的有效信号s为，Ideally, the effective signal s received by the receiver is,

s₁＝d₁+ju₁ s ₁ =d ₁ +ju ₁

s₂＝d₂+ju₂ s ₂ =d ₂ +ju ₂

……

s_n＝d_n+ju_n s _n = d _n + ju _n

其中u为干扰值，j为虚数符号，加上噪声b和信道h，接收信号x为：Where u is the interference value, j is the imaginary symbol, plus noise b and channel h, the received signal x is:

${x x}_{11} = = {Σ Σ}_{i i = = 11}^{n no} {h h}_{11 i i} (({d d}_{i i} + + {ju ju}_{i i})) + + {b b}_{11}$

${x x}_{22} = = {Σ Σ}_{i i = = 11}^{n no} {h h}_{22 i i} (({d d}_{i i} + + {ju ju}_{i i})) + + {b b}_{22}$

……

${x x}_{n no} = = {Σ Σ}_{i i = = 11}^{n no} {h h}_{n no i i} + + (({b b}_{i i} + + {ju ju}_{i i})) + + {b b}_{n no}$

写成接收信号矩阵形式：Written in the form of the received signal matrix:

X＝HS+BX=HS+B

其中H为有效信道矩阵，S为信号矩阵，B为噪声矩阵；Where H is the effective channel matrix, S is the signal matrix, and B is the noise matrix;

步骤二使用MMSE算法对干扰进行估计：由于干扰值u的值是由周围符号决定的，故有效信号s的值是随机的，因此无法遍历，对此使用MMSE算法对有效信号s进行检测，即找出矩阵系数G，使得下面的开销函数值最小：Step 2 uses the MMSE algorithm to estimate the interference: Since the value of the interference value u is determined by the surrounding symbols, the value of the effective signal s is random, so it cannot be traversed, and the MMSE algorithm is used to detect the effective signal s, namely Find the matrix coefficients G such that the following cost function is minimized:

${J J}_{M m M m S S E E.} = = E E. [[{Σ Σ}_{i i = = 11}^{n no} | | {s the s}_{i i} - - {Σ Σ}_{j j = = 11}^{n no} {g g}_{i i j j} {x x}_{i i} {| |}^{22}]]$

在MMSE算法中得到，其中δ_n为噪声，N_r为接收天线数目：It is obtained in the MMSE algorithm, where δ _n is the noise, and N _r is the number of receiving antennas:

$G G = = {(({H h}^{H h} H h + + {δ δ}_{n no}^{22} {I I}_{{N N}_{r r}}))}^{- - 11} {H h}^{H h}$

则信号矩阵S的估值由下式决定：Then the evaluation of the signal matrix S is determined by the following formula:

$\overset{~ ~}{S S} = = G G X x = = G G H h S S + + G G B B;;$

步骤三使用ML算法对有效信号进行估计，得到干扰的估值后，对信号进行估值：得到的估值之后，通过下式得到干扰的估值，Step 3 Use the ML algorithm to estimate the effective signal, and after obtaining the estimate of the interference, estimate the signal: get After the valuation of , the interference is obtained by the following formula valuation,

${\overset{~ ~}{s the s}}_{11} = = {\overset{~ ~}{d d}}_{11} + + j j {\overset{~ ~}{u u}}_{11}$

${\overset{~ ~}{s the s}}_{22} = = {\overset{~ ~}{d d}}_{22} + + j j {\overset{~ ~}{u u}}_{22}$

……

${\overset{~ ~}{s the s}}_{n no} = = {\overset{~ ~}{d d}}_{n no} + + j j {\overset{~ ~}{u u}}_{n no}$

根据ML准则，在所有可能的信号矩阵S中遍历，以寻求有效信号的估值；ML准则中的判决函数J_ML，定义如下According to the ML criterion, traverse through all possible signal matrices S to find an estimate of the effective signal; the decision function J _ML in the ML criterion is defined as follows

${J J}_{M m L L} = = {Σ Σ}_{i i = = 11}^{n no} | | {x x}_{i i} - - {Σ Σ}_{j j = = 11}^{n no} {h h}_{i i j j} {\overset{~ ~}{s the s}}_{i i} {| |}^{22} . .$

本发明利用MMSE估计干扰，然后再利用ML算法进行检测。性能较其他算法更高。The present invention uses MMSE to estimate interference, and then uses ML algorithm to detect. The performance is higher than other algorithms.

附图说明Description of drawings

图1为本发明的接收机MMSE‐ML检测方案示意图。Fig. 1 is a schematic diagram of the receiver MMSE-ML detection scheme of the present invention.

图2为本发明的4*4MIMO‐FBMCMMSE‐ML仿真结果示意图。Fig. 2 is a schematic diagram of 4*4MIMO-FBMCMMSE-ML simulation results of the present invention.

具体实施方式detailed description

使用MMSE‐ML算法的接收机结构如图1所示：The receiver structure using the MMSE-ML algorithm is shown in Figure 1:

为了研究简洁明了，假定发射和接收天线的数目都为2，也就是n＝2，这通常是MIMO复用研究的最简单常用的情况。假设两根发射天线分别发送数据d₁和d₂，而此时的有效信道矩阵H为：For the sake of simplicity and clarity of research, it is assumed that the number of transmitting and receiving antennas is 2, that is, n=2, which is usually the simplest and commonly used case of MIMO multiplexing research. Assume that two transmit antennas transmit data d ₁ and d ₂ respectively, and the effective channel matrix H at this time is:

$H h = = [\begin{matrix} {h h}_{1111} & {h h}_{1212} \\ {h h}_{21 twenty one} & {h h}_{22 twenty two} \end{matrix}]$

理想状况下，接收机收到的信号S，Ideally, the signal S received by the receiver,

s₁＝d₁+ju₁ s ₁ =d ₁ +ju ₁

s₂＝d₂+ju₂ s ₂ =d ₂ +ju ₂

x₁＝h₁₁(d₁+ju₁)+h₁₂(d₂+ju₂)+b₁ x ₁ ＝h ₁₁ (d ₁ +ju ₁ )+h ₁₂ (d ₂ +ju ₂ )+b ₁

x₂＝h₂₁(d₁+ju₁)+h₂₂(d₂+ju₂)+b₂ x ₂ ＝h ₂₁ (d ₁ +ju ₁ )+h ₂₂ (d ₂ +ju ₂ )+b ₂

X＝HS+BX=HS+B

其中H为有效信道矩阵，S为有效信号矩阵，B为噪声矩阵；Where H is the effective channel matrix, S is the effective signal matrix, and B is the noise matrix;

由于干扰值u的值是由周围符号决定的，故有效信号s的值是随机的，因此无法遍历，对此使用MMSE算法对有效信号s进行检测，即找出矩阵系数G，使得下面的开销函数值最小：Since the value of the interference value u is determined by the surrounding symbols, the value of the effective signal s is random, so it cannot be traversed. For this, the MMSE algorithm is used to detect the effective signal s, that is, to find the matrix coefficient G, so that the following overhead The minimum value of the function:

在MMSE算法中，我们可以得到，其中δ_n为噪声，N_r为接收天线数目：In the MMSE algorithm, we can get, where δ _n is the noise, and N _r is the number of receiving antennas:

接下来，信号矩阵S的估值由下式决定：Next, the estimation of the signal matrix S It is determined by the following formula:

$\overset{~ ~}{S S} = = G G X x = = G G H h S S + + G G B B;;$

得到的估值之后我们可以得到干扰的估值，如下式get After the valuation of , we can get the disturbance valuation, as follows

$\overset{~ ~}{s the s} = = {\overset{~ ~}{d d}}_{11} + + j j {\overset{~ ~}{u u}}_{11}$

根据ML准则，在所有可能的信号矩阵S中遍历，以寻求信号s的估值；ML准则中的判决函数J_ML定义如下According to the ML criterion, traverse all possible signal matrices S to seek the evaluation of the signal s; the decision function J _ML in the ML criterion is defined as follows

${J J}_{M m L L} = = {Σ Σ}_{i i = = 11}^{n no} | | {x x}_{i i} - - {Σ Σ}_{j j = = 11}^{n no} {h h}_{i i j j} {\overset{~ ~}{s the s}}_{i i} {| |}^{22}$

本发明利用MMSE估计干扰，然后再利用ML算法进行检测。性能较其他算法更高。下面对FBMC‐MMSE‐ML算法进行仿真，并与FBMC‐MMSE算法进行了对比，仿真参数如下：The present invention uses MMSE to estimate interference, and then uses ML algorithm to detect. The performance is higher than other algorithms. The FBMC-MMSE-ML algorithm is simulated below and compared with the FBMC-MMSE algorithm. The simulation parameters are as follows:

表1空间复用MMSE‐ML算法仿真参数Table 1 Simulation parameters of spatial multiplexing MMSE‐ML algorithm

系统带宽system bandwidth 2MHz2MHz 载波频率carrier frequency 2.4GHz2.4GHz 子载波数目number of subcarriers 256256 子载波间隔/子信道带宽Subcarrier spacing/subchannel bandwidth 7.8125KHz7.8125KHz 信道channel 平坦瑞利信道flat Rayleigh channel 帧包含数据符号数Frame contains number of data symbols 1414 帧持续时间frame duration 4.352ms4.352ms 调制方式Modulation 16QAM16QAM 发射天线transmitting antenna 44 接收天线Receive antenna 44 MIMO方案MIMO scheme 4×4空间复用4×4 spatial multiplexing

仿真结果如图2所示:The simulation results are shown in Figure 2:

从图2中可以看到，相比于MMSE检测算法，提出的MMSE‐ML算法性能增益。From Fig. 2, we can see the performance gain of the proposed MMSE‐ML algorithm compared to the MMSE detection algorithm.

本方案提出了一种创新的MMSE‐ML算法，首先利用MMSE估计干扰，然后再利用ML算法进行检测。性能较其他算法更高。This scheme proposes an innovative MMSE-ML algorithm, which first uses MMSE to estimate interference, and then uses ML algorithm for detection. The performance is higher than other algorithms.

Claims

1. A maximum likelihood detection algorithm based on MIMO-FBMC, characterized in that it is carried out in the following steps:

Step 1: Construct a channel model: the number of transmitting antennas and receiving antennas is n, and n is an even number greater than 1. Assume that n transmitting antennas respectively transmit data d ₁ , d ₂ ,...,d _n , and the effective channel matrix at this time H is:

Ideally, the effective signal s received by the receiver is,

s ₁ =d ₁ +ju ₁

s ₂ =d ₂ +ju ₂

…

s _n = d _n + ju _n

Where u is the interference value, j is the imaginary symbol, plus noise b and channel h, the received signal x is:

{x x}_{11} = = {Σ Σ}_{i i = = 11}^{n no} {h h}_{11 i i} (({d d}_{i i} + + {ju ju}_{i i})) + + {b b}_{11}

{x x}_{22} = = {Σ Σ}_{i i = = 11}^{n no} {h h}_{22 i i} (({d d}_{i i} + + {ju ju}_{i i})) + + {b b}_{22}

…

{x x}_{n no} = = {Σ Σ}_{i i = = 11}^{n no} {h h}_{n no i i} (({d d}_{i i} + + {ju ju}_{i i})) + + {b b}_{n no}

Written in the form of the received signal matrix:

X=HS+B

Where H is the effective channel matrix, S is the effective signal matrix, and B is the noise matrix;

Step 2 Use the MMSE algorithm to estimate the interference: Since the value of the interference value u is determined by the surrounding symbols, the value of the signal s is random, so it cannot be traversed, and the MMSE algorithm is used to detect the signal s, that is, find out The matrix coefficient G minimizes the value of the following cost function:

{J J}_{MMSE MMSE} = = E E. [[{Σ Σ}_{i i = = 11}^{n no} {| | {s the s}_{i i} - - {Σ Σ}_{j j = = 11}^{n no} {g g}_{ij ij} {x x}_{i i} | |}^{22}]]

It is obtained in the MMSE algorithm, where δ _n is the noise, and N _r is the number of receiving antennas:

G G = = {(({H h}^{H h} H h + + {δ δ}_{n no}^{22} {I I}_{{N N}_{r r}}))}^{- - 11} {H h}^{H h}

Then the evaluation of the signal matrix S is determined by the following formula:

\overset{~ ~}{S S} = = G G X x = = G G H h S S + + G G B B;;

Step 3 Use the ML algorithm to estimate the effective signal, and after obtaining the estimate of the interference, estimate s: get After the valuation of , the interference is obtained by the following formula valuation,

{\overset{~ ~}{s the s}}_{11} = = {\overset{~ ~}{d d}}_{11} + + j j {\overset{~ ~}{u u}}_{11}

{\overset{~ ~}{s the s}}_{22} = = {\overset{~ ~}{d d}}_{22} + + j j {\overset{~ ~}{u u}}_{22}

…

{\overset{~ ~}{s the s}}_{n no} = = {\overset{~ ~}{d d}}_{n no} + + j j {\overset{~ ~}{u u}}_{n no}

According to the ML criterion, traverse through all possible signal matrices S to find an estimate of the effective signal; the decision function J _ML in the ML criterion is defined as follows

{J J}_{M m L L} = = {Σ Σ}_{i i = = 11}^{n no} {| | {x x}_{i i} - - {Σ Σ}_{j j = = 11}^{n no} {h h}_{i i j j} {\overset{~ ~}{s the s}}_{i i} | |}^{22} . .