CN1188975C

CN1188975C - Space-time iterative multiuser detecting algorithm based on soft sensitive bit and space grouping

Info

Publication number: CN1188975C
Application number: CNB031208207A
Authority: CN
Inventors: 李俊强; 曹志刚; K·B·李德富
Original assignee: Tsinghua University
Current assignee: Tsinghua University
Priority date: 2003-03-21
Filing date: 2003-03-21
Publication date: 2005-02-09
Anticipated expiration: 2023-03-21
Also published as: CN1437345A

Abstract

The space-time iterative multi-user detection method based on soft-sensitive bits and space grouping is applied to the field of multi-user access technology in wireless communication. The outer group, and then use the simplified MA∏ iterative multiuser detection algorithm based on soft sensitive bits for the sub-multiusers in each group, that is, first distinguish the sensitive bits to obtain prior information, and then Perform MA∏ detection in the small subset, and then use the external information output by the iteratively processed channel MA∏ decoding of users in each group to realize soft interference cancellation outside the group. It can be used in the coded multi-user access system in broadband wireless communication, and can approach the single-user multi-antenna coded system with a small number of iterations when accessing 20 users at the same time in the AΩΓN channel and the frequency selective fading channel performance.

Description

Spatiotemporal Iterative Multiuser Detection Method Based on Soft Sensitive Bits and Spatial Grouping

技术领域technical field

无线通信中编码的多用户接入系统：编码的直接序列码分多址接入(Direct Sequence-CodeDivision Multiple Access，DS-CDMA)，编码的多载波MC-CDMA(Multicarrier-CDMA)和编码的空分多址接入(Space Division Multiple Access，SDMA)系统。Coded multi-user access system in wireless communication: coded Direct Sequence Code Division Multiple Access (DS-CDMA), coded multi-carrier MC-CDMA (Multicarrier-CDMA) and coded space Space Division Multiple Access (SDMA) system.

背景技术Background technique

在宽带无线通信系统中，多址接入干扰(Multiple Access Interference，MAI)和符号间干扰(Inter-Symbol Interference，ISI)构成了影响系统稳定通信的主要障碍。为了更好地解决符号间干扰和多址干扰MAI问题，提高系统容量，我们发明了联合采用了智能天线和简化迭代MAP多用户检测(Turbo Multiuser Detection，Turbo MUD)技术的算法，及基于软敏感比特和空间分组的时空迭代多用户检测方法，应用于编码的多用户接入系统中。In broadband wireless communication systems, Multiple Access Interference (MAI) and Inter-Symbol Interference (ISI) constitute the main obstacles affecting the stable communication of the system. In order to better solve the problems of inter-symbol interference and multiple access interference (MAI) and improve system capacity, we invented an algorithm that jointly adopts smart antennas and simplified iterative MAP multi-user detection (Turbo Multiuser Detection, Turbo MUD) technology, and based on soft sensitive A spatio-temporal iterative multi-user detection method based on bit and space grouping, applied to coded multi-user access systems.

智能天线技术在移动通信中的应用是通信领域的研究热点。该技术能在不增加频谱资源的情况下大大地增加系统的容量，提高功率和频谱的效率。这是因为空间滤波能有效地抑制不同于目标用户入射方向的多址接入干扰，同时由于天线阵上目标信号的分集合并能增强目标信号。近年来，随着强纠错能力的Turbo Code的发明，迭代(Turbo)处理技术在无线通信系统中越来越受到重视。Turbo code技术能获得稳定通信且性能接近香依理论值。基于MAP的迭代(Turbo)多用户检测技术应用与编码的CDMA系统时，此算法性能即使在稍低的SNR范围也能逼近单用户编码CDMA系统的性能。因此，结合Turbo多用户检测技术和智能天线技术将进一步提高系统的性能。近来，已有不同的结合天线阵的Turbo多用户检测技术提出用于增强系统的性能[1，2]。在[1]和[2]中，将结合基于干扰消除方法的天线阵Turbo多用户检测技术用于衰落信道下的DS-CDMA和MC-CDMA系统。该多用户检测算法类似于串行干扰消除方法(Successive Interference Cancellation，SIC)。类似的Turbo多用户检测技术也在[3，4]中被提出，只是其在干扰消除后用了最小均方误差(Minimum Mean Square Error，MMSE)滤波来提高性能。虽然这些基于干扰消除的方法的复杂度跟用户数呈线性关系，但为了逼近最优MAP迭代多用户检测算法需要更多的迭代次数。在[5]中，提出结合智能天线的MAP迭代多用户检测算法，用于多波束(Multibeam)系统，但此算法的复杂度跟用户数呈指数关系，在实际中不可实现。The application of smart antenna technology in mobile communication is a research hotspot in the field of communication. This technology can greatly increase system capacity and improve power and spectrum efficiency without increasing spectrum resources. This is because the spatial filtering can effectively suppress the multiple access interference from the incident direction of the target user, and at the same time, the diversity combination of the target signal on the antenna array can enhance the target signal. In recent years, with the invention of Turbo Code with strong error correction capability, iterative (Turbo) processing technology has received more and more attention in wireless communication systems. Turbo code technology can obtain stable communication and its performance is close to the theoretical value of Shannon. When the iterative (Turbo) multi-user detection technology based on MAP is applied to a coded CDMA system, the performance of this algorithm can approach the performance of a single-user coded CDMA system even in a slightly lower SNR range. Therefore, combining Turbo multi-user detection technology and smart antenna technology will further improve the performance of the system. Recently, different Turbo multiuser detection techniques combined with antenna arrays have been proposed to enhance the performance of the system [1, 2]. In [1] and [2], the antenna array Turbo multi-user detection technology based on the interference elimination method will be used for DS-CDMA and MC-CDMA systems under fading channels. The multi-user detection algorithm is similar to the serial interference cancellation method (Successive Interference Cancellation, SIC). A similar Turbo multi-user detection technology was also proposed in [3, 4], but it uses the minimum mean square error (Minimum Mean Square Error, MMSE) filter to improve performance after interference elimination. Although the complexity of these interference cancellation-based methods is linear with the number of users, more iterations are required to approach the optimal MAP iterative multi-user detection algorithm. In [5], a MAP iterative multi-user detection algorithm combined with smart antennas is proposed for use in multi-beam (Multibeam) systems, but the complexity of this algorithm is exponentially related to the number of users, which cannot be realized in practice.

为了使MAP迭代多用户检测技术应用在实际系统中(在扇区内同时有几十甚至上百个用户接入)成为可能，我们发明了结合智能天线和迭代多用户检测技术的时空迭代(Turbo)多用户检测算法用于编码的多用户接入系统。In order to make it possible for MAP iterative multi-user detection technology to be applied in practical systems (with dozens or even hundreds of users accessing in a sector at the same time), we invented the space-time iterative (Turbo ) multi-user detection algorithm for coded multi-user access systems.

[1]M.C.Reed and P.D.A.exander，“Iterative multiuser detection using antenna arrays and FEC on multipathchannels，”IEEE JSAC，Vol.17，No.12，pp.2082-89，Dec 1999.[1]M.C.Reed and P.D.A.exander, "Iterative multiuser detection using antenna arrays and FEC on multipathchannels," IEEE JSAC, Vol.17, No.12, pp.2082-89, Dec 1999.

[2]M.S.Akhter and J.Asenstorfer，“Iterative detection for MC-CDMA system with Base station antenna array forfading chanels，”IEEE GLOBECOM’98.Sydney，NSW，Australia，1998.[2] M.S.Akhter and J.Asenstorfer, "Iterative detection for MC-CDMA system with Base station antenna array forfading channels," IEEE GLOBECOM'98.Sydney, NSW, Australia, 1998.

[3]X.D.Wang and H.V.Poor，“Iterative(Turbo)soft interference cancellation and decodig for coded CDMA，”IEEE Trans.Commun.，Vol.47，No.7，pp.1046-1061，July 1999.[3] X.D.Wang and H.V.Poor, "Iterative (Turbo) soft interference cancellation and decoding for coded CDMA," IEEE Trans.Commun., Vol.47, No.7, pp.1046-1061, July 1999.

[4]H.E.Gamal，and E.Geraniotis，“Iterative multiuser detection for coded CDMA signals in AWGN and Fadingchannels，”IEEE JSAC，Vol.18，No.1，pp.30-41，January 2000.[4] H.E.Gamal, and E.Geraniotis, "Iterative multiuser detection for coded CDMA signals in AWGN and Fading channels," IEEE JSAC, Vol.18, No.1, pp.30-41, January 2000.

[5]Michael L.Moher，“Multiuser decoding for multibeam systems，”IEEE Trans.Vehicular Technology，Vol.49，No.4，pp.1226-34，July 2000[5] Michael L. Moher, "Multiuser decoding for multibeam systems," IEEE Trans. Vehicular Technology, Vol.49, No.4, pp.1226-34, July 2000

发明内容Contents of the invention

结合智能天线和简化MAP迭代多用户检测技术的基于软敏感比特和空间分组时空迭代(Turbo)多用户检测算法可应用于宽带无线通信中编码的多用户接入系统。举例如附图1、2、3中，我们将时空迭代多用户检测算法应用于多载波CDMA系统以显著地提高系统的容量和性能。时空迭代多用户检测算法描述如下：时空迭代多用户接收机将所有用户根据空间相关性归类分成若干组和相应的“外组”，所有用户被归类到不同的组。分组后，基于MAP迭代的多用户检测算法应用于各减少有效用户数的组内。虽然各组内的有效用户数相对于扇区内所有的用户数是大大地减少了，但当组内用户数接近或超过10时，传统的MAP迭代多用户检测算法是不可行的。为了减少组内MAP多用户检测算法的复杂度，我们提出了基于软敏感比特的简化的迭代MAP多用户检测算法作为各组内的子多用户检测算法。基于敏感比特的MAP迭代多用户检测算法的基本思想是首先我们分辨出敏感比特，这样做可获得“粗”的先验信息，它给出了各编码比特是可能估计对还是错的信息。有了这些先验信息，我们可在对应分辨出的敏感比特的小子集中进行MAP检测。另外，因为空间滤波方法抑制组间用户干扰是有限的，在各组内进行MAP迭代多用户检测前，先消除“外组”干扰用户的多址接入干扰即MAI，算法中我们采用软的干扰消除方法。由于组内的Turbo(迭代)处理，各组内用户的信道MAP译码输出的外信息可用于实现组外的软干扰消除以提高算法性能。因为若用硬干扰消除方法，当硬判决估计错误时会导致硬干扰消除时出错。通过这样处理，基于软敏感比特和空间分组的时空迭代多用户检测算法可明显地减少算法的复杂度，并且可获得比传统结合天线阵的软干扰消除的多用户检测更好的性能。在编码的MC-CDMA系统中，时空迭代多用户检测算法能在同时接入二十个用户时在AWGN信道和频选衰落信道下都能在很少的迭代次数下逼近单用户多天线编码系统的性能。我们发明的时空迭代多用户检测算法的算法复杂度跟用户数呈线性关系，本算法的提出为MAP多用户检测算法在实际的应用中成为可能。The time-space iterative (Turbo) multi-user detection algorithm based on soft-sensitive bits and space grouping combined with smart antenna and simplified MAP iterative multi-user detection technology can be applied to coded multi-user access systems in broadband wireless communications. For example, in accompanying drawings 1, 2, and 3, we apply the space-time iterative multi-user detection algorithm to a multi-carrier CDMA system to significantly improve system capacity and performance. The space-time iterative multi-user detection algorithm is described as follows: the space-time iterative multi-user receiver classifies all users into several groups and corresponding "outer groups" according to the spatial correlation, and all users are classified into different groups. After grouping, the multi-user detection algorithm based on MAP iteration is applied to each group that reduces the effective number of users. Although the number of effective users in each group is greatly reduced relative to the number of all users in the sector, when the number of users in a group is close to or exceeds 10, the traditional MAP iterative multi-user detection algorithm is not feasible. In order to reduce the complexity of intra-group MAP multi-user detection algorithm, we propose a simplified iterative MAP multi-user detection algorithm based on soft sensitive bits as sub multi-user detection algorithm within each group. The basic idea of the MAP iterative multiuser detection algorithm based on sensitive bits is that we first distinguish the sensitive bits, and by doing so, we can obtain "coarse" prior information, which gives information about whether each coded bit may be estimated to be right or wrong. With this prior information, we can perform MAP detection on a small subset of sensitive bits that correspond to the resolution. In addition, because the spatial filtering method is limited to suppress inter-group user interference, before performing MAP iterative multi-user detection in each group, the multiple access interference (MAI) of the "outside group" interfering users is eliminated first. In the algorithm, we use soft Interference Cancellation Method. Due to the Turbo (iterative) processing in the group, the external information output by the channel MAP decoding of the users in each group can be used to realize the soft interference cancellation outside the group to improve the performance of the algorithm. Because if the hard interference cancellation method is used, errors in the hard interference cancellation will result when the hard decision estimates are wrong. By doing this, the space-time iterative multiuser detection algorithm based on soft sensitive bits and space grouping can significantly reduce the complexity of the algorithm, and can obtain better performance than traditional multiuser detection combined with soft interference cancellation of antenna array. In the coded MC-CDMA system, the space-time iterative multi-user detection algorithm can approach the single-user multi-antenna coding system with a small number of iterations when accessing 20 users simultaneously. performance. The algorithm complexity of the spatio-temporal iterative multi-user detection algorithm we invented has a linear relationship with the number of users. This algorithm is proposed to make the MAP multi-user detection algorithm possible in practical applications.

因此，本发明的目的在于提出一种基于软敏感比特和空间分组的时空迭代多用户检测法。Therefore, the object of the present invention is to propose a space-time iterative multi-user detection method based on soft sensitive bits and space grouping.

本发明的特征在于：它把所有用户根据空间相关性归类到若干组和相应各组以外的组即“外组”，再对各组内的子多用户使用基于软敏感比特的简化的MAP迭代多用户检测算法，即首先分辨出敏感比特以获得先验信息，再在对应分辨出的敏感比特的小子集中进行MAP检测，然后再用经迭代处理的各组内用户的信道MAP译码输出的外信息实现组外的软干扰消除；它依次含有以下步骤：The present invention is characterized in that: it classifies all users according to the spatial correlation into several groups and groups outside the corresponding groups, i.e. "outer group", and then uses the simplified MAP based on soft sensitive bits for the sub-multi-users in each group Iterative multi-user detection algorithm, that is, first distinguish the sensitive bits to obtain prior information, then perform MAP detection in the small subset of the corresponding distinguished sensitive bits, and then use the iteratively processed channel MAP decoding output of the users in each group The outer information of the group realizes the soft interference cancellation outside the group; it contains the following steps in turn:

1)用多天线矩阵接收多用户，设M个用户接入信号，根据用户信号入射方向做空间滤波和频域匹配滤波；根据用户间空间滤波权重系数的相关性，把所有M个用户归类并分到G个组和相应的“外组”；1) Use a multi-antenna matrix to receive multiple users, set M users to access signals, perform spatial filtering and frequency domain matching filtering according to the incident direction of user signals; classify all M users according to the correlation of spatial filtering weight coefficients between users And divided into G groups and corresponding "outer groups";

即：根据下式获得各用户的空间滤波权重矢量再由分组准则把所有M个用户归类分成G个组和相应的“外组”：That is, according to the following formula, the spatial filtering weight vector of each user is obtained Then all M users are classified into G groups and corresponding "outer groups" according to the grouping criteria:

${\overset{&RightArrow;}{W}}_{m} = \frac{{\overset{&RightArrow;}{a}}_{m}}{| | {\overset{&RightArrow;}{a}}_{m} | |} = k \cdot {\overset{&RightArrow;}{a}}_{m},$ 1≤m≤M $k = \frac{1}{\sqrt{Q}}$ ${\overset{&Right Arrow;}{W}}_{m} = \frac{{\overset{&Right Arrow;}{a}}_{m}}{| | {\overset{&Right Arrow;}{a}}_{m} | |} = k &Center Dot; {\overset{&Right Arrow;}{a}}_{m},$ 1≤m≤M $k = \frac{1}{\sqrt{Q}}$

其中：Q为天线元素数；Where: Q is the number of antenna elements;

${\overset{&RightArrow;}{a}}_{m} = {[1, e^{- jπ \sin Q_{m}}, . . . . . . ., e^{- j (Q - 1) π \sin θ_{m}}]}^{T}$ 为第m个用户在入射角为Q_m下的天线阵列响应； ${\overset{&Right Arrow;}{a}}_{m} = {[1, e^{- jπ \sin Q_{m}}, . . . . . . ., e^{- j (Q - 1) π \sin θ_{m}}]}^{T}$ is the antenna array response of the mth user at an incident angle of Q _m ;

所述的分组准则为：The grouping criteria described are:

1.1)当β_μ，ν≥β₁且β_v，μ≥β₂时，分配μ，ν，v用户为同组Ω_g，即{μ，ν，v}∈Ω_g；1.1) When β _{μ, ν} ≥ β ₁ and β _{v, μ} ≥ β ₂ , assign μ, ν, v users to be in the same group Ω _g , that is, {μ, ν, v}∈Ω _g ;

其中，μ＝1，...，M，ν＝1，...μ，v＝2，....，ν-1，Among them, μ=1, ..., M, ν = 1, ... μ, v = 2, ..., ν-1,

β₁，β₂为设定的门限，且β₁＞β₂，β ₁ and β ₂ are the set thresholds, and β ₁ > β ₂ ,

β_μ，v为用户μ，v间的空间滤波矢量W_μ，的相关系数，如：β _{μ, v} is the spatial filter vector W _μ between users μ and v, The correlation coefficient, such as:

${β β}_{μ μ,, v v} = = \frac{| | | | {\overset{&RightArrow; &Right Arrow;}{W W}}_{μ μ}^{H h} \cdot &Center Dot; {\overset{&RightArrow; &Right Arrow;}{W W}}_{v v} | | | |}{| | | | {W W}_{μ μ} | | | | | | | | {W W}_{v v} | | | |}$

上标(·)^H为共轭转置，“·”表示向量点积；The superscript (·) ^H is the conjugate transpose, and "·" represents the vector dot product;

1.2)当β_μ，v≥β₁且β_ν，v≤β₂下，分配用户μ，ν为同组Ω_g中的成员，即{μ，ν}∈Ω_g且 ${v} &NotElement; Ω_{g},$ 1.2) When β _{μ, v} ≥ β ₁ and β _{ν, v} ≤ β ₂ , assign users μ, ν to be members of the same group Ω _g , that is, {μ, ν} ∈ Ω _g and ${v} &NotElement; Ω_{g},$

于是，所有分配到G个组中的用户总数满足 $Σ_{g = 0}^{G = 1} k_{g} = M,$ 其中k_g为第g个组的用户总数，“外组”即为第g个组Ω_g以外的用户，用Ω_g ^I表示，其用户数满足 $k_{g}^{I} = M - k_{g}, k_{g}^{I},$ 表示Ω_g ^I的用户总数；Therefore, the total number of users assigned to G groups satisfies $Σ_{g = 0}^{G = 1} k_{g} = m,$ Among them, k _g is the total number of users in the gth group, and the "outer group" is the users outside the gth group Ω _g , represented by Ω _g ^I , whose number of users satisfies $k_{g}^{I} = m - k_{g}, k_{g}^{I},$ Indicates the total number of users of Ω _g ^I ;

2)计算所有M个用户的编码比特的初始硬估计和软估计，并把真值分配到G个组和相应的“外组”；2) Compute the initial hard and soft estimates of the coded bits for all M users, and assign the true values to the G groups and the corresponding "outer groups";

在接收端经过波束形成和传统的匹配滤波后，得到所有M个用户的编码比特初始硬估计和软估计，它们依次分别为：After beamforming and traditional matched filtering at the receiving end, the initial hard and soft estimates of coded bits of all M users are obtained, which are respectively:

${\overset{^^}{g g}}_{\overset{&OverBar; &OverBar;}{g g},, t t}^{((R R))} = = sign sign ((real real (({y the y}_{m m ((k k,, \overset{&OverBar; &OverBar;}{g g}))})))),,$

${\overset{~ ~}{d d}}_{\overset{&OverBar; &OverBar;}{g g},, t t}^{((k k))} = = real real (({y the y}_{m m ((k k,, \overset{&OverBar; &OverBar;}{g g}))}));;$

是第m个用户被归类为第g个“外组”中的第k个用户的接收信号匹配滤波(MF)输出； is the received signal matched filter (MF) output of the mth user classified as the kth user in the gth "outer group";

3)定义各组最大的敏感比特数目和最大迭代次数；3) Define the maximum number of sensitive bits and the maximum number of iterations in each group;

3.1)根据下述不等式来分辨估计的多用户编码比特矢量

的似然度量和传统的单用户匹配滤波(MF)估计的初始各用户的编码比特的似然度量差值的上限，

的值越大则对应调整的比特越可能估计错误，即敏感比特；3.1) According to the following inequality to resolve the estimated multi-user coded bit vector

The likelihood metric of and the traditional single-user matched filter (MF) estimate the initial coding bits of each user The upper bound on the likelihood measure difference of ,

The larger the value of , the more likely the corresponding adjusted bit is to be incorrectly estimated, that is, the sensitive bit;

3.2)再在k_g个中搜索f(f＜k_g)个最大的度量值，f为第g个组内的敏感比特数；3.2) Then in k _g Search for f(f<k _g ) maximum metric values, f is the number of sensitive bits in the gth group;

4)在第g个组内执行基于软敏感比特的简化的迭代MAP多用户检测算法，它依次有以下步骤：4) Execute the simplified iterative MAP multi-user detection algorithm based on soft sensitive bits in the g group, it has the following steps successively:

4.1)根据“外组”软估计实现软干扰消除；4.1) Realize soft interference cancellation according to the "outer group" soft estimation;

根据“外组”Ω_g ^I内用户传输的编码比特

的软估计来实现软干扰消除：According to the coded bits transmitted by users in the "outer group" Ω _g ^I

Soft estimation of to achieve soft interference cancellation:

上述软估计above soft estimate

${\overset{~ ~}{d d}}_{\overset{&OverBar; &OverBar;}{g g},, k k}^{((k k))} = = real real (({y the y}_{m m ((k k,, \overset{&OverBar; &OverBar;}{g g}))}));;$

则干扰消除后，有 ${\overset{&RightArrow;}{X}}_{g}^{n} = H_{g} G_{g, t} {\overset{&RightArrow;}{d}}_{g, t} + {\overset{&RightArrow;}{Z}}_{g,}$ 而的自相关矩阵R_g，

为After the interference is eliminated, there is

{\overset{&Right Arrow;}{x}}_{g}^{no} = h_{g} G_{g, t} {\overset{&Right Arrow;}{d}}_{g, t} + {\overset{&Right Arrow;}{Z}}_{g,}

and The autocorrelation matrix R _g ,

for

$E E. [[{\overset{&RightArrow; &Right Arrow;}{Z Z}}_{g g} {\overset{&RightArrow; &Right Arrow;}{Z Z}}_{g g}^{H h}]] = = {H h}_{\overset{&OverBar; &OverBar;}{g g}} \cdot &Center Dot; E E. [[Δ Δ {\overset{&RightArrow; &Right Arrow;}{d d}}_{\overset{&OverBar; &OverBar;}{g g}} \cdot &Center Dot; Δ Δ {\overset{&RightArrow; &Right Arrow;}{d d}}_{\overset{&OverBar; &OverBar;}{g g}}^{H h}]] \cdot \cdot {H h}_{\overset{&OverBar; &OverBar;}{g g}}^{H h} + + \frac{11}{\sqrt{Q Q}} {H h}_{g g} {σ σ}_{n no}^{22};;$

其中，H_g是第g组Ω_g内用户和相关矩阵，是组Ω_g内用户和相应“外组”Ω_g ^I内用户间的相关矩阵，G_g，t为组内Ω_g用户的平均功率，

为组Ω_g中用户传输的编码比特矢量，是外组Ω_g ^I内用户传输的编码比特的软估计，是“外组”Ω_g ^I中用户的MAP信道译码输出的估计误差，σ_n ²是加性高斯白噪声即AWGN的方差；Among them, H _g is the user and correlation matrix in the gth group Ω _g , is the correlation matrix between the users in the group Ω _g and the users in the corresponding "outer group" Ω _g ^I , G _{g, t} is the average power of the users in the group Ω _g ,

is the coded bit vector transmitted by users in group Ω _g , are the coded bits transmitted by users in the outer group Ω _g ^I The soft estimate of is the estimated error of the user's MAP channel decoding output in the "outer group" Ω _g ^I , and σ _n ² is the variance of additive white Gaussian noise, namely AWGN;

4.2)用敏感比特算法找出f个敏感比特，根据这些敏感比特用简化的MAP多用户检测算法计算输出的第g组内各用户的外信息；4.2) Find out f sensitive bits with sensitive bit algorithm, calculate the extrinsic information of each user in the g group output with simplified MAP multi-user detection algorithm according to these sensitive bits;

当我们要第一次迭代时设敏感比特的先验概率为等概率分布且非敏感比特的先验概率为1时，则MAP多用户检测算法可仅考虑对应f个敏感比特的2^f个编码比特矢量

When we want to set the prior probability of sensitive bits to equal probability distribution and the prior probability of non-sensitive bits to 1 in the first iteration, then the MAP multi-user detection algorithm can only consider 2 ^f codes corresponding to f sensitive bits bit vector

4.2.1)计算第g组内第k个用户的外信息λ_1e ^k；4.2.1) Calculate the extrinsic information λ _1e ^k of the kth user in the gth group;

4.2.2)用MAP算法算出第k个用户的后验LOG似然率即LLR，用Λ₂表示，则用户译码输出的外信息为 $λ_{2 e}^{k} = Λ_{2} - λ_{1 e}^{k};$ 4.2.2) Use the MAP algorithm to calculate the a posteriori LOG likelihood rate of the kth user, which is LLR, expressed by _Λ2 , then the external information of the user's decoding output is $λ_{2 e}^{k} = Λ_{2} - λ_{1 e}^{k};$

4.2.3)把λ_2e ^k反馈到MAP多用户检测模块，在迭代结束时，计算信息比特的后验LOG似然率，由此来作接收比特译码；4.2.3) Feedback λ _2e ^k to the MAP multi-user detection module, and calculate the posterior LOG likelihood rate of the information bits at the end of the iteration, so as to decode the received bits;

4.2.4)根据各用户信道译码反馈的外信息得到改进的编码比特先验信息即： $λ_{1 σ}^{k} = λ_{2 e}^{k},$ 从而得到更准确的用户编码比特的硬估计和软估计；4.2.4) According to the external information fed back by each user channel decoding, the improved coded bit prior information is: $λ_{1 σ}^{k} = λ_{2 e}^{k},$ So as to obtain more accurate hard and soft estimates of user coded bits;

4.3)判断迭代是否结束：4.3) Determine whether the iteration is over:

若未结束，则各用户MAP信道译码器计算编码比特的外信息并返回步骤(2)；If not finished, then each user MAP channel decoder calculates the external information of coded bits and returns to step (2);

若已结束，即计算完G个组，则各用户MAP信道译码器计算出信息比特的外信息作为多用户检测信号输出；If it is over, that is, the calculation of G groups is completed, then the external information of the information bits is calculated by each user MAP channel decoder as a multi-user detection signal output;

3)获得所有M个用户的改进的硬估计和软估计，返回步骤(3)。3) Obtain the improved hard and soft estimates of all M users, and return to step (3).

使用证明本发明使MAP迭代多用户检测技术在实际系统中的应用成为可能。The application proves that the invention makes it possible to apply the MAP iterative multi-user detection technology in the actual system.

附图说明Description of drawings

图1：Turbo时空多用户检测的多载波CDMA系统模型。Figure 1: Multi-carrier CDMA system model for Turbo spatio-temporal multi-user detection.

图2：Turbo时空多用户接收机。Figure 2: Turbo space-time multi-user receiver.

图3：第g组内基于软敏感比特算法的Turbo多用户检测算法框图。Figure 3: Block diagram of Turbo multi-user detection algorithm based on soft sensitive bit algorithm in group g.

图4：AWGN信道单天线接收的简化Turbo多用户检测算法性能(M＝10，L＝15)。Figure 4: Simplified Turbo multi-user detection algorithm performance (M=10, L=15) for AWGN channel single-antenna reception.

图5：AWGN信道下Turbo时空多用户检测算法性能(M＝20，L＝7)，4组，组间隔15°。Figure 5: Performance of Turbo spatio-temporal multi-user detection algorithm in AWGN channel (M=20, L=7), 4 groups, group interval 15°.

图6：AWGN信道下Turbo时空多用户检测算法性能(M＝20)， $ρ_{{m, m}^{'}}^{s} = 0.4 .$ Figure 6: Turbo space-time multi-user detection algorithm performance under AWGN channel (M=20), $ρ_{{m, m}^{'}}^{the s} = 0.4 .$

图7：频选衰落信道下Turbo时空多用户检测算法性能(M＝20，L＝7)。Figure 7: Performance of Turbo space-time multi-user detection algorithm in frequency-selective fading channel (M=20, L=7).

图8：本方法的程序流程扼图。Figure 8: Schematic diagram of the program flow of the method.

具体的实施方式specific implementation

具体地，在应用于编码的多载波CDMA系统时，算法的实现如下。Specifically, when applied to a coded multi-carrier CDMA system, the implementation of the algorithm is as follows.

为方便理解公式，首先我们定义公式中符号的意义：上面箭头的变量表向量；大写黑体变量表矩阵；下横线变量表时间序列。公式中的小点表乘积；符号定义为Kronecker乘积。上标(·)^T定义转置；上标(·)^H定义共厄转置。For the convenience of understanding the formula, first we define the meaning of the symbols in the formula: the variable table vector of the arrow above; the matrix of the uppercase bold variable table; the time series of the variable table under the horizontal line. The dots in the formula represent products; the symbol  is defined as the Kronecker product. A superscript (·) ^T defines a transpose; a superscript (·) ^H defines a co-Er transpose.

如图1示有M个用户的编码的MC-CDMA系统。用户在120°的扇区内随机分布。由于实际系统中移动终端不易使用天线阵，只有基站装置了Q个元素的天线阵。系统中，第m个用户的信息比特序列b(m)通过卷积编码(或Turbo编码)器后经交织得到编码比特序列d_t ^(m)，以避免深衰落导致的突发误码。第m个用户、第t时间的编码比特序列d_t ^(m)用伪随机(PN)序列扩频后，用MC-CDMA技术传输，其中子载波数N等于PN序列长L。这里，我们假设各子信道是平坦衰落的，且各子信道间的信道响应是独立的，这可以通过频域交织来实现。第m用户的第l子信道的频域信道响应为 $H_{t, l}^{m} = ρ_{m . l} \exp (θ_{m, l}),$ 其中ρ_m，l和θ_m，l分别为幅度和相位。在接收端，系统实现了完全的帧同步，这可以用已有的各种时间同步技术来实现。另外，我们还假设各用户的天线阵列响应 a_m(0≤m≤M-1)已被准确地估计。在波束形成后，每个用户的信号在频域解扩并作最大比率合并。定义 r_t为第r时间间隔的天线阵接收信号Figure 1 shows a coded MC-CDMA system with M users. Users are randomly distributed within a 120° sector. Since it is difficult for the mobile terminal to use the antenna array in the actual system, only the base station is equipped with an antenna array with Q elements. In the system, the information bit sequence b(m) of the mth user passes through a convolutional coder (or Turbo coder) and is interleaved to obtain a coded bit sequence d _t ^(m) to avoid burst errors caused by deep fading. The coded bit sequence d _t ^(m) of the mth user and the tth time is spread with a pseudo-random (PN) sequence, and then transmitted using MC-CDMA technology, where the number of subcarriers N is equal to the length L of the PN sequence. Here, we assume that each sub-channel is flat fading, and the channel responses between each sub-channel are independent, which can be realized through frequency domain interleaving. The frequency domain channel response of the lth subchannel of the mth user is $h_{t, l}^{m} = ρ_{m . l} \exp (θ_{m, l}),$ Where ρ _{m, l} and θ _{m, l} are amplitude and phase, respectively. At the receiving end, the system achieves complete frame synchronization, which can be achieved with various existing time synchronization techniques. In addition, we also assume that the antenna array response a _m (0≤m≤M-1) of each user has been accurately estimated. After beamforming, each user's signal is despread in the frequency domain and combined for maximum ratio. Define r _t as the antenna array receiving signal at the rth time interval

${\overset{&OverBar; &OverBar;}{r r}}_{t t} = = {Σ Σ}_{m m = = 11}^{M m} {d d}_{t t}^{((m m))} \cdot &Center Dot; {\overset{&OverBar; &OverBar;}{a a}}_{m m} \cdot &Center Dot; {Σ Σ}_{l l = = 00}^{N N - - 11} {ρ ρ}_{m m,, l l} \cdot &Center Dot; {c c}_{m m} [[l l]] \cdot &Center Dot; exp exp {{{ω ω}_{l l} t t + + {θ θ}_{m m,, l l}}} + + {\overset{&RightArrow; &Right Arrow;}{n no}}_{t t} - - - - - - ((11))$

其中，

是Q×1维的块矢量in,

is a Q×1-dimensional block vector

${\overset{&RightArrow;}{a}}_{m} = {[1, e^{- jπ \sin θ_{m}}, \cdot \cdot \cdot, e^{- j (Q - 1) π \sin θ_{m}}]}^{T}$ 定义为第m用户在入射角为θ_m时的天线阵列响应。 n_t是天线阵上的加性高斯白噪声(AWGN)矢量，并认为天线阵各元素上的噪声是独立的。c_m[l]是随机序列 c ^m＝{c_m[l]}_{l＝1，…，L}的第l个码片。由于信号带宽远小于射频的频率，因而可近似认为各用户所有子载波上的天线阵列响应

是相同的。考虑第t时间间隔、第q个天线上的接收信号，信号的矩阵形式表示

{\overset{&Right Arrow;}{a}}_{m} = {[1, e^{- jπ \sin θ_{m}}, &Center Dot; &Center Dot; &Center Dot;, e^{- j (Q - 1) π \sin θ_{m}}]}^{T}

Defined as the antenna array response of the mth user when the incident angle is θ _m . n _t is the additive white Gaussian noise (AWGN) vector on the antenna array, and the noise on each element of the antenna array is considered to be independent. c _m [l] is the lth chip of the random sequence c ^m ={c _m [l]} _l=1,...,L . Since the signal bandwidth is much smaller than the frequency of the radio frequency, the antenna array response on all subcarriers of each user can be approximately considered as

Are the same. Considering the received signal on the tth time interval and the qth antenna, the matrix representation of the signal

${\overset{&RightArrow; &Right Arrow;}{r r}}_{t t}^{q q} = = IFFT IFFT {{{A A}_{t t}^{q q} {G G}_{t t} {\overset{&OverBar; &OverBar;}{d d}}_{t t}}} + + {\overset{&RightArrow; &Right Arrow;}{n no}}_{t t} - - - - - - ((22))$

其中，A_t ^q是L×M维矩阵，A_t ^q的第m列矢量包含了第m个用户所有子载波上的信道响应和PN序列的信息。

是M个用户传输的编码比特矢量。而G_t定义为所有用户平均功率矩阵。Among them, A _t ^q is an L×M dimensional matrix, and the m-th column vector of A _t ^q contains the channel response and PN sequence information on all subcarriers of the m-th user.

is the coded bit vector transmitted by M users. And G _t is defined as the average power matrix of all users.

具体地specifically

$A_{t}^{q} = [α_{1, t}^{q} {\overset{&RightArrow;}{s}}_{t}^{1}, α_{2, t}^{q} {\overset{&RightArrow;}{s}}_{t}^{2}, \cdot \cdot \cdot, α_{M, t}^{q} {\overset{&RightArrow;}{s}}_{t}^{M}],$ g＝1，…，Q $A_{t}^{q} = [α_{1, t}^{q} {\overset{&Right Arrow;}{the s}}_{t}^{1}, α_{2, t}^{q} {\overset{&Right Arrow;}{the s}}_{t}^{2}, \cdot \cdot \cdot, α_{m, t}^{q} {\overset{&Right Arrow;}{the s}}_{t}^{m}],$ g=1,...,Q

其中，in,

${\overset{&RightArrow;}{s}}_{t}^{m} = {{[s}_{t, 1}^{m}, s_{t, 2}^{m}, \cdot \cdot \cdot, s_{t, L}^{m}]}^{T},$ m＝1，…，M， ${\overset{&Right Arrow;}{the s}}_{t}^{m} = {{[the s}_{t, 1}^{m}, {the s}_{t, 2}^{m}, &Center Dot; \cdot &Center Dot;, {the s}_{t, L}^{m}]}^{T},$ m=1,...,M,

$s_{t, l}^{m} = H_{t, l}^{m} \cdot c_{m} [l],$ i＝1，…L， ${the s}_{t, l}^{m} = h_{t, l}^{m} \cdot c_{m} [l],$ i=1,...L,

${α α}_{m m}^{q q} = = exp exp {{jπ jπ ((q q - - 11)) sin sin (({θ θ}_{m m}))}}$

和and

${G G}_{t t} = = Diag Diag {{\sqrt{{p p}_{}^{t t}},, \sqrt{{p p}_{}^{t t}},, \cdot &Center Dot; \cdot \cdot \cdot &Center Dot;,, \sqrt{{p p}_{t t}^{M m}}}},,$ ${\overset{&RightArrow; &Right Arrow;}{d d}}_{t t} = = {[[{d d}_{t t}^{((11))},, {d d}_{t t}^{((22))},, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; {,, d d}_{t t}^{((M m))}]]}^{T T}$

其中，H_t，i ^m是第t时刻、第m用户、第i子载波上的频域信道响应，p_t ^m是第t时刻、第m用户的接收功率。因此，第q个天线元素上的频域接收信号可表示为Among them, H _t,i ^m is the channel response in the frequency domain of the mth user and the i-th subcarrier at the tth moment, and p _t ^m is the received power of the mth user at the tth moment. Therefore, the frequency-domain received signal on the qth antenna element can be expressed as

${\overset{&RightArrow; &Right Arrow;}{R R}}_{t t}^{q q} = = FFT FFT \cdot &Center Dot; IFFT IFFT {{{A A}_{t t}^{q q} \cdot &Center Dot; {G G}_{t t} \cdot &Center Dot; {\overset{&RightArrow; &Right Arrow;}{d d}}_{t t}}} + + FFT FFT {{{\overset{&RightArrow; &Right Arrow;}{n no}}_{t t}^{q q}}} . . - - - - - - ((33))$

我们定义

为第m用户的空间滤波矢量，它可根据第m用户的天线阵列响应

用维纳(Winener)算法给出为we define

is the spatial filter vector of the mth user, which can respond according to the antenna array of the mth user

Using the Winner algorithm is given as

${\overset{&RightArrow; &Right Arrow;}{W W}}_{m m} = = \frac{{R R}_{uu u u}^{- - 11} {\overset{&RightArrow; &Right Arrow;}{a a}}_{m m}}{{\overset{&RightArrow; &Right Arrow;}{a a}}_{m m}^{H h} {R R}_{uu u u}^{- - 11} {\overset{&RightArrow; &Right Arrow;}{a a}}_{m m}} = = κ κ \cdot &Center Dot; {\overset{&RightArrow; &Right Arrow;}{a a}}_{m m} ((κ κ : : cons cons tan the tan t t)) - - - - - - ((44))$

其中，R_uu是第m用户的干扰和噪声的协方差矩阵。则第m用户的波束形成和频域匹配滤波输出为where R _uu is the covariance matrix of the interference and noise of the mth user. Then the beamforming and frequency-domain matched filtering output of the mth user is

${y the y}_{m m} = = {\overset{&RightArrow; &Right Arrow;}{s the s}}_{t t}^{{m m}^{T T}} \cdot \cdot {{{\overset{&RightArrow; &Right Arrow;}{W W}}_{m m} \cdot &Center Dot; {[[{\overset{&RightArrow; &Right Arrow;}{R R}}_{t t}^{11},, \cdot \cdot \cdot &Center Dot; \cdot &Center Dot;,, {\overset{&RightArrow; &Right Arrow;}{R R}}_{t t}^{q q},, \cdot &Center Dot; \cdot \cdot \cdot &Center Dot;,, {\overset{&RightArrow; &Right Arrow;}{R R}}_{t t}^{Q Q}]]}^{T T}}}$

$= = {\overset{&RightArrow; &Right Arrow;}{s the s}}_{t t}^{{m m}^{T T}} \cdot \cdot {{{\overset{&RightArrow; &Right Arrow;}{W W}}_{m m} \cdot \cdot (([\begin{matrix} {A A}_{t t}^{11} \\ . . \\ . . \\ . . \\ {A A}_{t t}^{Q Q} \end{matrix}] &CircleTimes; &CircleTimes; {G G}_{t t} \cdot \cdot {\overset{&RightArrow; &Right Arrow;}{d d}}_{t t} + + [\begin{matrix} {\overset{&RightArrow; &Right Arrow;}{η η}}_{t t}^{11} \\ . . \\ . . \\ . . \\ {\overset{&RightArrow; &Right Arrow;}{η η}}_{t t}^{Q Q} \end{matrix}]))}}$

其中，空间和随机序列相关性系数分别为where the spatial and random sequence correlation coefficients are

$ρ_{m, m^{'}}^{a} = {\overset{&RightArrow;}{W}}_{m} \cdot {\overset{&RightArrow;}{a}}_{m^{'}},$ $ρ_{m, m^{'}}^{s} = {\overset{&RightArrow;}{s}}_{t}^{m^{T}} \cdot {\overset{&RightArrow;}{s}}_{t}^{m^{'}}$ (1≤m≤M：1≤m′≤M) $ρ_{m, m^{'}}^{a} = {\overset{&Right Arrow;}{W}}_{m} \cdot {\overset{&Right Arrow;}{a}}_{m^{'}},$ $ρ_{m, m^{'}}^{the s} = {\overset{&Right Arrow;}{the s}}_{t}^{m^{T}} \cdot {\overset{&Right Arrow;}{the s}}_{t}^{m^{'}}$ (1≤m≤M: 1≤m′≤M)

${\overset{&RightArrow;}{η}}_{t}^{q} = FFT {{\overset{&RightArrow;}{n}}_{t}^{q}}$ 是另一复高斯白噪声随机过程，且其方差满足 $σ_{η}^{2} = σ_{n}^{2} .$ σ_n ²是高斯噪声n_t ^q(q＝1，…，Q)的方差。因此，我们可给出整个系统的信号模型为 ${\overset{&Right Arrow;}{η}}_{t}^{q} = FFT {{\overset{&Right Arrow;}{no}}_{t}^{q}}$ is another complex Gaussian white noise stochastic process, and its variance satisfies $σ_{η}^{2} = σ_{no}^{2} .$ σ _n ² is the variance of Gaussian noise n _t ^q (q=1, . . . , Q). Therefore, we can give the signal model of the whole system as

或记作or written as

$\overset{&RightArrow; &Right Arrow;}{y the y} = = H h {G G}_{t t} {\overset{&RightArrow; &Right Arrow;}{d d}}_{t t} + + \overset{&RightArrow; &Right Arrow;}{N N} - - - - - - ((66))$

其中，H是所有用户间的相关矩阵。是有色复高斯噪声，其均值为零，方差为Among them, H is the correlation matrix among all users. is colored complex Gaussian noise with zero mean and variance

$E E. ((\overset{&RightArrow; &Right Arrow;}{N N} \cdot \cdot {\overset{&RightArrow; &Right Arrow;}{N N}}^{H h})) = = \frac{11}{\sqrt{Q Q}} H h {σ σ}_{n no}^{22} . .$

从公式(6)可知，当扇区内有几十甚至上百个用户接入时，在基站用最优MAP的迭代多用户检测算法是不可行的。It can be seen from formula (6) that when there are tens or even hundreds of users accessing the sector, it is not feasible to use the optimal MAP iterative multi-user detection algorithm at the base station.

如图2所示，我们给出了结合智能天线和MAP迭代多用户检测的Turbo时空多用户检测算法结构框图。Turbo时空多用户接收机将所有用户根据空间相关性归类分成若干组和相应的“外组”，在各组内进行MAP迭代多用户检测前，先消除“外组”干扰用户的MAI。本算法中我们采用软的干扰消除方法。由于组内的Turbo(迭代)处理，各组内用户的信道MAP译码输出的外信息可用于实现组外的软干扰消除以提高算法性能。因为若用硬干扰消除方法，当硬判决估计错误时会导致硬干扰消除时出错。另外，为了减少组内MAP多用户检测算法的复杂度，我们应用基于软敏感比特的简化MAP多用户检测算法作为组内的子多用户检测算法。具体地，Turbo时空多用户检测算法描述如下：As shown in Figure 2, we give a structural block diagram of the Turbo spatio-temporal multi-user detection algorithm combined with smart antennas and MAP iterative multi-user detection. The Turbo spatio-temporal multi-user receiver classifies all users into several groups and corresponding "outer groups" according to the spatial correlation. Before performing MAP iterative multi-user detection in each group, the MAI of the "outer group" interfering users is eliminated first. In this algorithm, we adopt the soft interference elimination method. Due to the Turbo (iterative) processing in the group, the external information output by the channel MAP decoding of the users in each group can be used to realize the soft interference cancellation outside the group to improve the performance of the algorithm. Because if the hard interference cancellation method is used, errors in the hard interference cancellation will be caused when the hard decision estimation is wrong. In addition, in order to reduce the complexity of the MAP multiuser detection algorithm within the group, we apply the simplified MAP multiuser detection algorithm based on soft sensitive bits as the sub-multiuser detection algorithm within the group. Specifically, the Turbo space-time multi-user detection algorithm is described as follows:

假设基站可正确地估计各用户的天线阵列响应。为简化算法我们取空间滤波权重矢量为It is assumed that the base station can correctly estimate the antenna array response of each user. To simplify the algorithm, we take the spatial filtering weight vector as

${\overset{&RightArrow; &Right Arrow;}{W W}}_{m m} = = \frac{{\overset{&RightArrow; &Right Arrow;}{a a}}_{m m}}{| | | | {\overset{&RightArrow; &Right Arrow;}{a a}}_{m m} | | | |} = = κ κ \cdot &Center Dot; {\overset{&RightArrow; &Right Arrow;}{a a}}_{m m},, 11 \leq \leq m m \leq \leq M m - - - - - - ((77))$

其中“‖·‖”定义为向量的模， $κ = 1 / \sqrt{Q} .$ 根据用户间空间滤波权重系数的相关性，将所有M个用户归类分到G个组中。我们定义用户间空间滤波矢量

的相关系数为Where "‖·‖" is defined as the modulus of the vector,

κ = 1 / \sqrt{Q} .

According to the correlation of spatial filtering weight coefficients among users, all M users are classified into G groups. We define the inter-user spatial filter vector

The correlation coefficient is

${β β}_{μ μ,, v v} = = \frac{| | | | {\overset{&RightArrow; &Right Arrow;}{W W}}_{u u}^{H h} \cdot &Center Dot; {\overset{&RightArrow; &Right Arrow;}{W W}}_{v v} | | | |}{| | | | {\overset{&RightArrow; &Right Arrow;}{W W}}_{u u} | | | | | | | | {\overset{&RightArrow; &Right Arrow;}{W W}}_{v v} | | | |} u u = = 11,, \cdot \cdot \cdot \cdot \cdot \cdot,, M m,, v v = = 11,, \cdot \cdot \cdot &Center Dot; \cdot \cdot,, u u - - 11 . . - - - - - - ((88))$

其中“·”定义为两向量的点积．定义β₁和β₂为门限且有β₁＞β₂。根据相关系数，我们用下述归类准则来分组：Where "·" is defined as the dot product of two vectors. Define β ₁ and β ₂ as thresholds and have β ₁ > β ₂ . According to the correlation coefficient, we use the following classification criteria to group:

1.当β_μ，ν≥β₁和β_ν，υ≥β₂时，我们分配用户u、用户v、用户υ为同组Ω_g，及满足{u，ν，υ}∈Ω_g 1. When β _{μ, ν} ≥ β ₁ and β _{ν, υ} ≥ β ₂ , we assign user u, user v, and user υ to the same group Ω _g , and satisfy {u, ν, υ} ∈ _{Ω g}

2.当β_μ，ν≥β₁和β_ν，υ≤β₂时，我们分配用户u和用户v为组Ω_g中成员。则有{u，ν，υ}∈Ω_g，and ${ν} &NotElement; Ω_{g}$ 其中，u＝1…，M，ν＝1，…u，υ＝2，…，ν-1，定义K_g为第g组的用户数。则所有分配到G个组中的用户总数满足2. When β _{μ, ν} ≥ β ₁ and β _{ν, υ} ≤ β ₂ , we assign user u and user v as members of group Ω _g . Then we have {u, ν, υ}∈Ω _g , and ${ν} &NotElement; Ω_{g}$ Among them, u=1..., M, ν=1,...u, ν=2,...,ν-1, and K _g is defined as the number of users in the gth group. Then the total number of users assigned to G groups satisfies

${Σ Σ}_{g g = = 00}^{G G - - 11} {K K}_{g g} = = M m . . - - - - - - ((99))$

因为空间滤波干扰抑制的有限性，组外用户仍能对组内用户产生严重的干扰。因此，我们把第g组Ω_g外的用户归类为相应的“外组”Ω_g ^I，其用户数K_g ^I满足Because of the limitation of interference suppression by spatial filtering, users outside the group can still cause serious interference to users in the group. Therefore, we classify the users outside the gth group Ω _g as the corresponding "outer group" Ω _g ^I , and the number of users K _g ^I satisfies

${K K}_{g g}^{I I} = = M m - - {K K}_{g g} . . - - - - - - ((1010))$

根据上述准则，根据用户的入射角(DOA)，扇区内所有用户被分配到若干个组和相应的“外组”。According to the above criteria, all users within a sector are assigned to several groups and corresponding "outer groups" according to their angle of incidence (DOA).

为了减少组间多址干扰MAI的影响，组间干扰消除方法采用软干扰消除方法。如果把一个组看成一个用户，则该方法可以看成是软的并行干扰消除(PIC)方法。不失一般性，如图3示，我们考虑有K_g个有效用户的第g组Ω_g和相应有K_g ^I个干扰用户的“外组”Ω_g ^I。根据公式(6)，第g组的K_g个匹配滤波(MF)输出为In order to reduce the impact of multiple access interference (MAI) between groups, the inter-group interference elimination method adopts a soft interference elimination method. If a group is regarded as a user, the method can be regarded as a soft parallel interference cancellation (PIC) method. Without loss of generality, as shown in Figure 3, we consider the gth group Ω _g with K _g effective users and the "outer group" Ω _g ^I with K _g ^I interference users. According to formula (6), the output of _K matched filter (MF) of group g is

${\overset{&RightArrow; &Right Arrow;}{y the y}}_{g g} = = {H h}_{g g} {G G}_{g g,, t t} {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t} + + {H h}_{\overset{&OverBar; &OverBar;}{g g}} {G G}_{\overset{&OverBar; &OverBar;}{g g},, t t} {\overset{&RightArrow; &Right Arrow;}{d d}}_{\overset{&OverBar; &OverBar;}{g g},, t t} + + {\overset{&RightArrow; &Right Arrow;}{N N}}_{g g} - - - - - - ((1111))$

其中，H_g第g组Ω_g内用户的相关矩阵，而

是组Ω_g内用户和相应“外组”Ω_g ^I内用户间的相关矩阵。

和

分别定义为组Ω_g和外组Ω_g ^I中用户传输的编码比特矢量。另外，G_g，t和分别定义为Ω_g和Ω_g ^I中用户的平均功率。具体地，我们定义Among them, H _g is the correlation matrix of users in the gth group Ω _g , and

is ^the correlation matrix between users in group _Ωg and users in the corresponding "outer group" _ΩgI .

and

Defined as the encoded bit vectors transmitted by users in the group Ω _g and the outer group Ω _g ^I , respectively. In addition, G _{g, t} and Defined as the average power of the user in Ω _g and Ω _g ^I , respectively. Specifically, we define

而噪声矢量为And the noise vector is

它是零均值有色复高斯噪声，且方差为It is zero-mean colored complex Gaussian noise with variance

$E E. (({\overset{&RightArrow; &Right Arrow;}{N N}}_{g g} \cdot &Center Dot; {\overset{&RightArrow; &Right Arrow;}{N N}}_{g g}^{H h})) = = \frac{11}{\sqrt{Q Q}} {H h}_{g g} {σ σ}_{n no}^{22} . . - - - - - - ((1515))$

在公式(11)中的第一项为Ω_g中用户的目标信号，而第二项为来至Ω_g ^I的干扰MAI。因此，干扰消除操作是根据“外组”Ω_g ^I内用户传输的编码比特的估计来实现干扰消除，则消除干扰后有The first term in formula (11) is the user's target signal in _Ωg , and the second term is ^the interference MAI from _ΩgI . Therefore, the interference cancellation operation is based on the coded bits transmitted by users within the "outer group" Ω _g ^I is estimated to achieve interference elimination, then after interference elimination, there is

${\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} = = {H h}_{g g} {G G}_{g g,, t t} {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t} + + {H h}_{\overset{&OverBar; &OverBar;}{g g}} {G G}_{\overset{&OverBar; &OverBar;}{g g},, t t} (({\overset{&RightArrow; &Right Arrow;}{d d}}_{\overset{&OverBar; &OverBar;}{g g},, t t} - - {\overset{\overset{~ ~}{&OverBar; &OverBar;}}{d d}}_{\overset{&OverBar; &OverBar;}{g g},, t t}^{n no})) + + {\overset{&RightArrow; &Right Arrow;}{N N}}_{g g}$

$= = {H h}_{g g} {G G}_{g g,, t t} {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t} + + {H h}_{\overset{&OverBar; &OverBar;}{g g}} {G G}_{\overset{&OverBar; &OverBar;}{g g},, t t} Δ Δ {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t} + + {\overset{&RightArrow; &Right Arrow;}{N N}}_{g g}$

$= = {H h}_{g g} {G G}_{g g,, t t} {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t} + + {\overset{&OverBar; &OverBar;}{Z Z}}_{g g} - - - - - - ((1616))$

其中，是

的软估计，它由第n次迭代的各用户MAP信道译码给出的反馈软信息来获得。是“外组”Ω_g ^I中用户的MAP信道译码输出的估计误差。假设各用户MAP信道译码输出的估计误差是高斯白噪声，则估计误差矢量的协相关矩阵为in, yes

The soft estimate of is obtained from the feedback soft information given by each user's MAP channel decoding in the nth iteration. is the estimated error of the MAP channel decoding output of users in the "outer group" Ω _g ^I. Assuming that the estimated error of each user's MAP channel decoding output is Gaussian white noise, the co-correlation matrix of the estimated error vector is

$E E. [[Δ Δ {\overset{&RightArrow; &Right Arrow;}{d d}}_{\overset{&OverBar; &OverBar;}{g g}} \cdot &Center Dot; Δ Δ {\overset{&RightArrow; &Right Arrow;}{d d}}_{\overset{&OverBar; &OverBar;}{g g}}^{H h}]] = = diag diag (([[{σ σ}_{e e,, 11,, \overset{&OverBar; &OverBar;}{g g}}^{22},, {σ σ}_{e e,, 22,, \overset{&OverBar; &OverBar;}{g g}}^{22},, \cdot \cdot \cdot \cdot \cdot &Center Dot;,, {σ σ}_{e e,, {K K}_{g g}^{l l},, \overset{&OverBar; &OverBar;}{g g}}^{22}]])) . . - - - - - - ((1717))$

因此，式(16)中的总噪声矢量也是高斯的，且有协方差矩阵Therefore, the total noise vector in equation (16) is also Gaussian and has a covariance matrix

$E E. [[{\overset{&RightArrow; &Right Arrow;}{Z Z}}_{g g} {\overset{&RightArrow; &Right Arrow;}{Z Z}}_{g g}^{H h}]] = = {H h}_{\overset{&OverBar; &OverBar;}{g g}} \cdot \cdot E E. [[Δ Δ {\overset{&RightArrow; &Right Arrow;}{d d}}_{\overset{&OverBar; &OverBar;}{g g}} \cdot \cdot Δ Δ {\overset{&RightArrow; &Right Arrow;}{d d}}_{\overset{&OverBar; &OverBar;}{g g}}^{H h}]] \cdot &Center Dot; {H h}_{\overset{&OverBar; &OverBar;}{g g}}^{H h} + + \frac{11}{\sqrt{Q Q}} {H h}_{g g} {σ σ}_{n no}^{22} = = {R R}_{g g,, \overset{&RightArrow; &Right Arrow;}{Z Z} \overset{&RightArrow; &Right Arrow;}{Z Z}} - - - - - - ((1818))$

其中，总噪声协方差矩阵包括剩余干扰和噪声两部分。可以看出，如果我们能计算每次迭代Ω_g ^I内的第k个用户的信道译码的误差方差

和AWGN噪声的方差σ_n ²，则传统的最优的MAP迭代多用户检测算法就可作为各组内的子多用户检测算法。我们定义信道译码输出的误差方差为Among them, the total noise covariance matrix includes two parts: residual interference and noise. It can be seen that if we can calculate the channel decoding error variance of the kth user within Ω _g ^I in each iteration

and the variance σ _n ² of the AWGN noise, the traditional optimal MAP iterative multi-user detection algorithm can be used as the sub-multi-user detection algorithm in each group. We define the error variance of the channel decoding output as

${σ σ}_{e e,, k k,, \overset{&OverBar; &OverBar;}{g g}}^{22} = = E E. [[{(({d d}_{\overset{&OverBar; &OverBar;}{g g},, t t}^{((k k))} - - {\overset{~ ~}{d d}}_{\overset{&OverBar; &OverBar;}{g g},, t t}^{((k k))}))}^{22}]] - - - - - - ((1919))$

其中，是Ω_g ^I中第k个用户实际传输的编码比特，而是该编码比特的软估计。在实际的接收机中，是不可能知道的。因此，我们给出了近似的误差方差估计in, is the coded bits actually transmitted by the kth user in Ω _g ^I , and is a soft estimate of the coded bits. In a real receiver, It is impossible to know. Therefore, we give an approximate error variance estimate

其中，

是编码比特的硬判决估计。而是该编码比特的软估计。根据各用户MAP信道译码反馈的外信息可获得编码比特的先验概率

p (d_{\overset{&OverBar;}{g}, t}^{(k)} = &PlusMinus; 1) .

则，

为的期望值in,

are coded bits Hard-judgment estimates for . and is a soft estimate of the coded bits. According to the external information fed back by each user's MAP channel decoding, the prior probability of the coded bits can be obtained

p (d_{\overset{&OverBar;}{g}, t}^{(k)} = &PlusMinus; 1) .

but,

for expectations

应该注意的是在第一次迭代中编码比特是没有先验概率信息的，因此，我们让It should be noted that there is no prior probability information about the encoded bits in the first iteration, so we let

${\tilde{d}}_{\overset{&OverBar;}{g}, t}^{(k)} = real (y_{m (k, \overset{&OverBar;}{g})})$ 和 ${\tilde{d}}_{\overset{&OverBar;}{g}, t}^{(k)} = real ({the y}_{m (k, \overset{&OverBar;}{g})})$ and

其中，y_m(k，g)是式(6)中的接收信号匹配滤波(MF)输出，而m(k， g)表示第m个用户被归类为第g个“外组”中的第k个用户。where y _{m(k, g)} is the output of the received signal matched filter (MF) in Equation (6), and m(k, g) indicates that the mth user is classified into the gth "outer group" the kth user.

虽然可应用最优的MAP迭代多用户检测算法作为在各组内子多用户检测算法，但其算法的复杂度是跟组内的用户数呈指数关系的。因此，当组内用户数多时，比如大于10个用户时，最优的MAP迭代多用户检测算法是不可行的。以下，我们将应用基于软敏感比特的简化MAP多用户检测算法作为各组的子多用户检测算法。Although the optimal MAP iterative multi-user detection algorithm can be used as a sub-multi-user detection algorithm in each group, the complexity of the algorithm is exponentially related to the number of users in the group. Therefore, when the number of users in the group is large, such as more than 10 users, the optimal MAP iterative multi-user detection algorithm is not feasible. In the following, we will apply the simplified MAP multiuser detection algorithm based on soft sensitive bits as the sub-multiuser detection algorithm for each group.

各组内的MAP迭代多用户检测算法如图3示。不失一般性，我们考虑第t时刻、第g组内的MAP迭代多用户检测。其输出的第k个用户的编码比特d_g，t ^(k)的后验LOG似然率为The MAP iterative multi-user detection algorithm in each group is shown in Figure 3. Without loss of generality, we consider MAP iterative multi-user detection in group g at time t. The a posteriori LOG likelihood of the coded bits d _g,t ^(k) of the kth user outputted by it is

${Λ Λ}_{11} (({d d}_{g g,, t t}^{((k k))})) \overset{Δ Δ}{= =} log log \frac{P P (({d d}_{g g,, l l}^{((k k))} = = + + 11 | | {\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no}))}{P P (({d d}_{g g,, t t}^{((k k))} = = - - 11 | | {\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no}))} = = log log \frac{p p (({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} | | {d d}_{g g,, t t}^{((k k))} = = + + 11))}{p p (({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} | | {d d}_{g g,, t t}^{((k k))} = = - - 11))} + + log log \frac{p p (({d d}_{g g,, t t}^{((k k))} = = + + 11))}{p p (({d d}_{g g,, t t}^{((k k))} = = - - 11))},,$

k＝1，…，K_g (23)k=1,..., K _g (23)

其中，等式(23)中的第一项作为MAP多用户检测给出的外信息(extrinsic information)，定义为λ_1e ^k。第二项为先验信息，用λ_1o ^k来表示。它们通过上次迭代的第k个用户的信道译码来得到。根据等式(15)，的条件概率分布可用K_g维多元高斯概率密度函数来表示，Wherein, the first item in equation (23) is defined as λ _1e ^k as extrinsic information given by MAP multi-user detection. The second item is the prior information, represented by λ _1o ^k . They are obtained by channel decoding of the kth user in the last iteration. According to equation (15), The conditional probability distribution of can be expressed by the K _g- dimensional multivariate Gaussian probability density function,

$p p (({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} | | {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t})) = = \frac{11}{\sqrt{{((22 π π))}^{{K K}_{g g}} det det (({R R}_{g g,, \overset{&OverBar; &OverBar;}{Z Z} \overset{&OverBar; &OverBar;}{Z Z}}))}} exp exp [[- - \frac{11}{22} {(({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} - - {H h}_{g g} {G G}_{g g,, t t} {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t}))}^{H h} {R R}_{g g,, \overset{&OverBar; &OverBar;}{Z Z} \overset{&OverBar; &OverBar;}{Z Z}}^{- - 11} (({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} - - {H h}_{g g} {G G}_{g g,, t t} {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t}))]] - - - - - - ((24 twenty four))$

为了计算λ_1e ^k需要 x_g ⁿ关于第k个用户的编码比特d_g，t ^k的联合概率分布To compute λ _1e ^k requires the joint probability distribution of x _g ⁿ with respect to the coded bits d _g,t ^k of the kth user

$p p (({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no},, {d d}_{g g,, t t}^{((k k))} = = d d)) = = \underset{{\overset{&OverBar; &OverBar;}{d d}}_{g g,, t t};; {d d}_{g g,, t t}^{((k k))} = = d d}{Σ Σ} Pr PR {{{\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} | | {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t}}} \cdot \cdot Pr PR {{{\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t}}} - - - - - - ((2525))$

因为不同用户的编码比特是相互独立的，所以式(25)的条件概率分布可写为Because the coded bits of different users are independent of each other, the conditional probability distribution of Equation (25) can be written as

$p p (({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} | | {d d}_{g g,, t t}^{((k k))} = = d d)) = = \frac{p p (({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no},, {d d}_{g g,, t t}^{((k k))} = = d d))}{p p (({d d}_{t t}^{k k} = = d d))} = = \underset{{\overset{&RightArrow; &Right Arrow;}{d d}}_{t t};; {d d}_{t t}^{k k} = = d d}{Σ Σ} Pr PR {{{\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} | | {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t}}} \cdot &Center Dot; {Π Π}_{\underset{i i &NotEqual; &NotEqual; k k}{i i = = 11}}^{{K K}_{g g}} Pr PR {{{d d}_{g g,, t t}^{((i i))}}} . . - - - - - - ((2626))$

为了简化最优MAP算法的复杂度，我们提出了基于敏感比特的简化MAP多用户检测算法。基于敏感比特的MAP迭代多用户检测算法的基本思想是首先我们分辨出敏感比特，这样做可获得“粗”的先验信息。它给出了各编码比特是可能估计对还是错的信息。有了这些先验信息，我们可在对应分辨出的敏感比特的小子集中进行MAP检测。定义似然度量为In order to simplify the complexity of the optimal MAP algorithm, we propose a simplified MAP multi-user detection algorithm based on sensitive bits. The basic idea of the MAP iterative multi-user detection algorithm based on sensitive bits is that we distinguish the sensitive bits first, so as to obtain "coarse" prior information. It gives information on whether each encoded bit is likely to be estimated right or wrong. With this prior information, we can perform MAP detection on a small subset of sensitive bits that correspond to the resolution. Define the likelihood measure as

$Ψ Ψ (({\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t})) = = {(({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} - - {H h}_{g g} {G G}_{g g,, t t} {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t}))}^{H h} {R R}_{g g,, \overset{&OverBar; &OverBar;}{Z Z} \overset{&OverBar; &OverBar;}{Z Z}}^{- - 11} (({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} - - {H h}_{g g} {G G}_{g g,, t t} {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t})) - - - - - - ((2727))$

并让and let

其中，

是估计的多用户编码比特矢量。另外，让定义为一新的比特矢量，它对应于反转

中的一个且仅一个比特的极性(及-1→1或1→-1)。我们已经证明了当估计比特矢量中有一个或多个比特错误时，且我们反转中的错误的比特的极性得到

则有in,

is the estimated multiuser encoding bit vector. Additionally, let is defined as a new bit vector corresponding to the inverted

The polarity of one and only one bit in (and -1→1 or 1→-1). We have shown that when estimating the bit vector When one or more bits are wrong in , and we invert The polarity of the wrong bit in the

then there is

换一种说法，当

的值越大则对应调整的比特越可能估计错误，即敏感比特。一般的，估计的编码比特矢量中错误的比特数是很少的。比如，若编码比特的的误比特率是10^-2，这意味着平均来说每一百个比特中有一个比特出错，因此，一般敏感比特的数目不会很大。我们通过如下处理来分辨敏感比特：首先我们用传统的单用户匹配滤波(MF)来估计初始各用户的编码比特。然后根据不等式(29)来分辨出敏感比特。我们定义第g组内的敏感比特数目为f，在所有K_g个新调整比特矢量的度量

中搜索f(f＜K_g)个最大的度量值。定义敏感比特为对应于此f个编码比特矢量中调整的比特。为了实现迭代的MAP多用户检测算法，在第一次迭代，我们假设敏感比特的先验概率

为等概分布。而非敏感比特的先验概率为1，因为这些比特假设是正确估计的。则MAP多用户检测算法可以仅考虑对应f敏感比特的2^f所有可能的编码比特矢量 (其中，这些向量中菲敏感比特保持初始估计不变)。则不同于传统最优的MAP准则，式(26)的条件概率的计算可以简化为In other words, when

The larger the value of , the more likely the corresponding adjusted bit will be incorrectly estimated, that is, the sensitive bit. In general, the number of erroneous bits in the estimated coded bit vector is very small. For example, if the bit error rate of coded bits is 10 ^-2 , it means that on average, one bit is wrong in every one hundred bits, and therefore, the number of sensitive bits is generally not very large. We identify sensitive bits by the following process: First, we use traditional single-user matched filtering (MF) to estimate the initial coded bits for each user. Sensitive bits are then identified according to inequality (29). We define the number of sensitive bits in the g-th group as f, the metric of all K _g newly adjusted bit vectors

Search f(f<K _g ) largest metric values in . Sensitive bits are defined as bits corresponding to adjustments in this vector of f coded bits. In order to implement the iterative MAP multiuser detection algorithm, in the first iteration, we assume the prior probability of sensitive bits

is an equiprobable distribution. The prior probability of insensitive bits is 1 because these bits are assumed to be correctly estimated. Then the MAP multi-user detection algorithm can only consider all possible coded bit vectors of 2 ^f corresponding to f sensitive bits (Wherein, the Fei-sensitive bits in these vectors remain unchanged from the initial estimation). Then, unlike the traditional optimal MAP criterion, the calculation of the conditional probability in formula (26) can be simplified as

$p p (({\overset{&RightArrow; &Right Arrow;}{y the y}}_{t t} | | {d d}_{t t}^{((k k))} = = d d)) \approx \approx \underset{{\overset{~ ~}{d d}}_{t t} &Element; &Element; {{{\overset{&RightArrow; &Right Arrow;}{d d}}_{t t}^{s the s}}}_{s the s = = 1, 1, \cdot \cdot \cdot \cdot \cdot &Center Dot;,, 22} f f;; {d d}_{t t}^{((k k))} = = d d}{Σ Σ} Pr PR {{{\overset{&RightArrow; &Right Arrow;}{y the y}}_{t t} | | {\overset{&RightArrow; &Right Arrow;}{d d}}_{t t}}} \cdot &Center Dot; {Π Π}_{\underset{i i &NotEqual; &NotEqual; k k}{i i = = 11}}^{K K} Pr PR {{{d d}_{t t}^{((i i))}}},, k k = = 11,, \cdot \cdot \cdot &Center Dot; \cdot &Center Dot; K K - - - - - - ((3030))$

其中，只考虑2^f(当第k个编码比特为敏感比特时为2^f-1)个重要编码比特矢量，而其它2^kg-f-1个矢量作为不重要的编码比特矢量，在计算式(30)时可以忽略它们因为等式主要取决于2^f重要矢量。Among them, only 2 ^f (2 ^f-1 when the k-th coded bit is a sensitive bit) important coded bit vectors are considered, and the other 2 ^kg-f-1 vectors are regarded as unimportant coded bit vectors, in the calculation formula They can be ignored in (30) because the equation mainly depends on the 2 ^f importance vectors.

根据上述分析，我们初始化第一次迭代时MAP多用户检测的编码比特先验概率为According to the above analysis, when we initialize the first iteration, the coding bit prior probability of MAP multi-user detection is

在下一次迭代，根据各用户MAP信道译码反馈的外信息λ_2e ^k，MAP多用户检测模块可得到更准确的先验概率和传输编码比特的硬判决In the next iteration, according to the external information λ _2ek fed back by the MAP channel decoding ^of each user, the MAP multi-user detection module can obtain more accurate prior probability and hard decision of transmission coding bits

其中，

λ_{10}^{k} = λ_{2 e}^{k} - - - (32)

in,

λ_{10}^{k} = λ_{2 e}^{k} - - - (32)

随着传输编码比特的硬判决

的改善，敏感比特也将重新调整。注意的是，不同于第一次迭代，此时用于MAP多用户检测的编码比特先验概率Pr{d_g，t ^(k)}为With the hard decision of the transmitted coding bits

, the sensitive bits will also be rescaled. Note that, different from the first iteration, the prior probability Pr{d _{g, t} ^(k) } of coded bits used for MAP multi-user detection at this time is

$Pr PR {{{d d}_{g g,, t t}^{((k k))} = = d d}} = = \frac{exp exp ((d d \cdot &Center Dot; {λ λ}_{11 o o}^{k k}))}{11 + + exp exp ((d d \cdot &Center Dot; {λ λ}_{11 o o}^{k k}))} . . - - - - - - ((3333))$

因此，第t时刻、第g组内第k个用户的软编码比估计

可由式(21)和式(33)得到。Therefore, at the tth moment, the soft coding ratio estimation of the kth user in the gth group

It can be obtained by formula (21) and formula (33).

在第g组内，在MAP多用户检测模块后是K_g个用户的信道译码，应用MAP算法给出编码比特的后验概率和在最后迭代给出信息比特的后验概率。假设我们用码率为R＝1/n的卷积码，每n个编码比特d_g，t ^(k)对应一个编码前信息比特b_g，j ^(k)。此n个信道比特定义为 $(d_{g, t}^{(k)}, \cdot \cdot \cdot, d_{g, t + n - 1}^{(k)}) = {\underset{&OverBar;}{d}}_{g, j}^{(k)} .$ 因此，我们有In group g, after the MAP multi-user detection module is channel decoding of K _g users, the MAP algorithm is used to give the posterior probability of coded bits and the posterior probability of information bits in the last iteration. Assuming that we use a convolutional code with code rate R=1/n, every n encoded bits d _g,t ^(k) corresponds to one pre-encoded information bit b _g,j ^(k) . The n channel bits are defined as $(d_{g, t}^{(k)}, &Center Dot; &Center Dot; &Center Dot;, d_{g, t + no - 1}^{(k)}) = {\underset{&OverBar;}{d}}_{g, j}^{(k)} .$ Therefore, we have

$Pr PR {{{d d}_{g g,, {t t}^{' '}}^{((k k))} = = d d | | {\underset{&OverBar; &OverBar;}{x x}}_{g g}^{((K K))}}} = = \underset{{m m}^{' '}}{Σ Σ} \underset{{\underset{&OverBar; &OverBar;}{d d}}_{g g,, j j}^{k k};; {d d}_{g g,, {t t}^{' '}}^{k k} = = d d}{Σ Σ} Pr PR {{- - {S S}_{j j - - 11} = = - - {m m}^{' '};; - - {\underset{&OverBar; &OverBar;}{d d}}_{g g,, j j}^{((k k))} | | {\underset{&OverBar; &OverBar;}{x x}}_{g g}^{((k k))}}} - - - - - - ((3434))$

其中，x_g ^(k)是第g组内第k个用户的接收信号序列。S_j是在j时刻的状态和m’覆盖所有可能的状态。该指出的是等式(34)可以用已有的MAP信道译码算法或简化的log-MAP信道译码算法来实现。有了前端MAP多用户检测输出的外信息，信道译码MAP网格译码状态间的分支度量为Wherein, x _g ^(k) is the received signal sequence of the kth user in the gth group. S _j is the state at time j and m' covers all possible states. It should be noted that equation (34) can be implemented with the existing MAP channel decoding algorithm or the simplified log-MAP channel decoding algorithm. With the extrinsic information output by the front-end MAP multi-user detection, the branch metric between the channel decoding MAP trellis decoding states is

${γ γ}_{j j} (({m m}^{' '},, m m)) = = Pr PR {{{S S}_{j j} = = m m | | {S S}_{j j - - 11} = = {m m}^{' '}}} {Π Π}_{{t t}^{' '} = = t t}^{t t + + n no - - 11} Pr PR {{{\overset{&RightArrow; &Right Arrow;}{x x}}_{g g,, {t t}^{' '}} | | {d d}_{g g,, {t t}^{' '}}^{((k k))}}} - - - - - - ((3535))$

因此，第k个用户的后验LOG似然率(LLR)为Therefore, the posterior LOG likelihood ratio (LLR) of the kth user is

${Λ Λ}_{22} \overset{Δ Δ}{= =} log log \frac{Pr PR {{{d d}_{g g,, {t t}^{' '}}^{((k k))} = = 11 | | {\underset{&OverBar; &OverBar;}{x x}}_{g g}^{((k k))}}}}{Pr PR {{{d d}_{g g,, {t t}^{' '}}^{((k k))} = = - - 11 | | {\underset{&OverBar; &OverBar;}{x x}}_{g g}^{((k k))}}}} \approx \approx {λ λ}_{22 e e}^{k k} + + {λ λ}_{11 e e}^{k k} - - - - - - ((3636))$

其中，用户译码输出外信息为 $λ_{2 e}^{k} = Λ_{2} - λ_{1 e}^{k} .$ 这些信息又反馈给MAP多用户检测模块，且通过式(33)可获得改进的MAP多用户检测的先验信息。Among them, the user decodes and outputs the external information as $λ_{2 e}^{k} = Λ_{2} - λ_{1 e}^{k} .$ These information are fed back to the MAP multi-user detection module, and the prior information of the improved MAP multi-user detection can be obtained through formula (33).

以下简要地总结Turbo时空多用户检测算法。让f_max定义为各组最大的敏感比特数目和I定义为最大迭代次数。则基于软敏感比特算法的Turbo时空多用户检测算法可描述为：初始化：根据式(7)获得各用户的空间滤波权重矢量然后，由分组准则将所有M个用户归类分成G个组和相应的“外组”。在接收端，经过波束形成和传统的匹配滤波后，可得所有M用户的编码比特的初始硬估计和软估计分别为The following briefly summarizes the Turbo spatio-temporal multi-user detection algorithm. Let f _max be defined as the maximum number of sensitive bits for each group and I be defined as the maximum number of iterations. Then the Turbo spatio-temporal multi-user detection algorithm based on the soft-sensitive bit algorithm can be described as: Initialization: According to formula (7), the spatial filtering weight vector of each user is obtained Then, all M users are classified into G groups and corresponding "outer groups" by grouping criteria. At the receiving end, after beamforming and traditional matched filtering, the initial hard and soft estimates of coded bits of all M users are obtained as

和 ${\tilde{d}}_{\overset{&OverBar;}{g}, t}^{(k)} = real (y_{m (k, \overset{&OverBar;}{g})})$ and ${\tilde{d}}_{\overset{&OverBar;}{g}, t}^{(k)} = real ({the y}_{m (k, \overset{&OverBar;}{g})})$

并将其分配到G组和相应的“外组”迭化处理：For n＝1 to IAnd assign it to G group and corresponding "outer group" iterative processing: For n=1 to I

第—步：(软干扰消除)获得第g个“外组”Ω_g ^I的编码比特的软估计

通过消除来至Ω_g ^I的MAI，软干扰消除表示为Step 1: (Soft Interference Cancellation) Obtain a soft estimate of the coded bits of the gth "outer group" Ω _g ^I

By canceling the MAI from Ω _g ^I , the soft interference cancellation is expressed as

${\overset{&OverBar; &OverBar;}{x x}}_{g g}^{n no} = = {H h}_{g g} {G G}_{g g,, t t} {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t} + + {H h}_{\overset{&OverBar; &OverBar;}{g g}} {G G}_{\overset{&OverBar; &OverBar;}{g g},, t t} (({\overset{&RightArrow; &Right Arrow;}{d d}}_{\overset{&OverBar; &OverBar;}{g g},, t t} - - {\overset{&RightArrow; &Right Arrow;}{d d}}_{\overset{&OverBar; &OverBar;}{g g},, t t}^{n no})) + + {\overset{&RightArrow; &Right Arrow;}{N N}}_{g g}$

$= = {H h}_{g g} {G G}_{g g,, t t} {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t} + + {\overset{&RightArrow; &Right Arrow;}{Z Z}}_{g g}$

其中的协相关矩阵

为in The co-correlation matrix of

for

$E E. [[{\overset{&RightArrow; &Right Arrow;}{Z Z}}_{g g} {\overset{&RightArrow; &Right Arrow;}{Z Z}}_{g g}^{H h}]] = = {H h}_{\overset{&OverBar; &OverBar;}{g g}} \cdot \cdot E E. [[Δ Δ {\overset{&RightArrow; &Right Arrow;}{d d}}_{\overset{&OverBar; &OverBar;}{g g}} \cdot \cdot Δ Δ {\overset{&RightArrow; &Right Arrow;}{d d}}_{\overset{&OverBar; &OverBar;}{g g}}^{H h}]] \cdot &Center Dot; {H h}_{\overset{&OverBar; &OverBar;}{g g}}^{H h} + + \frac{11}{\sqrt{Q Q}} {H h}_{g g} {σ σ}_{n no}^{22}$

第二步：(简化的MAP迭代多用户检测)i)根据敏感比特算法，找出f个敏感比特。根据这些敏感比特，由简化的MAP多用户检测算法输出的第g组内第k个用户的外信息为The second step: (simplified MAP iterative multi-user detection) i) Find out f sensitive bits according to the sensitive bit algorithm. According to these sensitive bits, the extrinsic information of the kth user in the gth group output by the simplified MAP multiuser detection algorithm is

${λ λ}_{11 e e}^{k k} = = log log \frac{p p (({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} | | {d d}_{g g,, t t}^{((k k))} = = + + 11))}{p p (({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} | | {d d}_{g g,, t t}^{((k k))} = = - - 11))}$

其中，in,

$p p (({\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} | | {d d}_{g g,, t t}^{((k k))} = = d d)) \approx \approx \underset{{\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t} &Element; &Element; {{{\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t}^{s the s}}}_{s the s = = 11,, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, 22} f f;; {d d}_{g g,, t t}^{((k k))} = = d d}{Σ Σ} Pr PR {{{\overset{&RightArrow; &Right Arrow;}{x x}}_{g g}^{n no} | | {\overset{&RightArrow; &Right Arrow;}{d d}}_{g g,, t t}}} \cdot &Center Dot; {Π Π}_{\underset{i i &NotEqual; &NotEqual; k k}{i i = = 11}}^{{K K}_{g g}} Pr PR {{{d d}_{g g,, t t}^{((i i))}}} . .$

注意，在第一次迭代，编码比特的先验概率Pr{d_g，t ^(k)}由式(31)求的。而在下一次迭代，先验概率Pr{d_g，t ^(k)}由式(33)给出。ii)获得MAP多用户检测输出的外信息λ_1e ^k后，根据公式(36)可的第k个用户的信道译码的外信息λ_2e ^k。然后，将外信息λ_2e ^k反馈到MAP多用户检测模块。当i＝I时，计算信息比特的后验LOG似然率，由此来作接收比特译码。结束本算法。Note that in the first iteration, the prior probability Pr{d _g,t ^(k) } of the coded bits is obtained by Equation (31). And in the next iteration, the prior probability Pr {d _{g, t} ^(k) } is given by equation (33). ii) After obtaining the extrinsic information λ _1e ^k output by the MAP multi-user detection, the extrinsic information λ _2e ^k of channel decoding of the k-th user can be obtained according to formula (36). Then, ^the external information λ _2ek is fed back to the MAP multi-user detection module. When i=I, the posterior LOG likelihood rate of the information bits is calculated, so as to decode the received bits. end this algorithm.

iii)根据各用户信道译码反馈的外信息可获得改进的编码比特先验信息(及 $λ_{1 o}^{k} = λ_{2 e}^{k}$ )，由此可获得更准确的用户编码比特的硬估计和软估计。iii) According to the external information fed back by channel decoding of each user, the improved coded bit prior information (and $λ_{1 o}^{k} = λ_{2 e}^{k}$ ), so that more accurate hard and soft estimates of the user coded bits can be obtained.

和and

第三步：.获得所有M用户改进的硬估计和软估计，返回到第一步。Step 3:. Obtain improved hard and soft estimates for all M users, return to Step 1.

本节给出了在AWGN信道和频率选择性衰落信道下我们建议的分组多用户检测算法的仿真结果和性能比较。仿真实验中，所有用户采用相同的码率为1/2的卷积码。我们采用了两种卷积码：约束长度为5，八进制生成因子为(23，35)和约束长度为3，八进制生成因子为(5，7)的卷积码。每块信息比特的长为128，且采用随机交织方法。所有用户等传输功率(及G＝I)。并设置分组准则的门限β₁和β₂分别为0.9和0.95。假设接收端知道噪声方差σ_n ²和各用户的扩频序列。最后，定义信噪比为信息比特功率和噪声功率的比，仿真图中，(AqBmIn)定义为q个接收天线，m敏感比特和n次迭代。应该注意地是n＝1表示没有反馈信息用于提高系统性能。This section presents the simulation results and performance comparison of our proposed packet multiuser detection algorithm under AWGN channel and frequency selective fading channel. In the simulation experiment, all users adopt the same code rate of 1/2 convolutional code. We adopted two kinds of convolutional codes: a convolutional code with a constraint length of 5 and an octal generation factor of (23, 35) and a constraint length of 3 with an octal generation factor of (5, 7). The length of each piece of information bits is 128, and a random interleaving method is adopted. Equal transmission power (and G=I) for all users. And set the thresholds β ₁ and β ₂ of the grouping criterion as 0.9 and 0.95 respectively. Assume that the receiving end knows the noise variance σ _n ² and the spreading sequence of each user. Finally, the signal-to-noise ratio is defined as the ratio of information bit power to noise power. In the simulation diagram, (AqBmIn) is defined as q receiving antennas, m sensitive bits and n iterations. It should be noted that n=1 means that no feedback information is used to improve system performance.

图4给出了基于敏感比特算法的Turbo多用户检测算法在单天线的编码多载波CDMA系统中的仿真性能，系统中用户数M＝10，PN序列长L＝15。我们采用生成因子为(23，35)的卷积码。从图可以看出即使敏感比特数目远小于用户总数，简化的MAP迭代多用户检测算法能有效工作，并且在敏感比特数f＝3和迭代次数n＝3时，它和单用户编码系统的性能在BER＝10^-4处仅差0.15dB。另外，简化MAP多用户检测算法的复杂度由最优算法的0(K₁2^K1)降到0((K₁-f/2)2^f)，其中K₁＝M，且只有一组。具体地，当K₁＝10和f＝3.时算法复杂度由0(10240)降到0(78)。由此，我们可知简化的MAP迭代多用户检测算法可作为Turbo时空多用户检测中各组内的子多用户检测算法。Figure 4 shows the simulation performance of the Turbo multi-user detection algorithm based on the sensitive bit algorithm in a single-antenna coded multi-carrier CDMA system. The number of users in the system is M=10, and the PN sequence length L=15. We use a convolutional code with a generation factor of (23, 35). It can be seen from the figure that even if the number of sensitive bits is much smaller than the total number of users, the simplified MAP iterative multi-user detection algorithm can work effectively, and when the number of sensitive bits f=3 and the number of iterations n=3, it has the same performance as the single-user coding system The difference is only 0.15dB at BER= ^10-4 . In addition, the complexity of the simplified MAP multi-user detection algorithm is reduced from 0(K ₁ 2 ^K1 ) of the optimal algorithm to 0((K ₁ -f/2)2 ^f ), where K ₁ =M, and there is only one group. Specifically, when K ₁ =10 and f=3, the algorithm complexity is reduced from 0 (10240) to 0 (78). From this, we know that the simplified MAP iterative multi-user detection algorithm can be used as a sub-multi-user detection algorithm in each group in Turbo spatio-temporal multi-user detection.

在下面的仿真中，我们给出了Turbo时空MUD算法在编码多载波CDMA系统中的仿真性能，系统有用户数M＝20，有Q＝3个接收天线。另外，为了减少仿真时间我们采用低状态数的(5，7)卷积码。扇区的大小为2π/3，各用户的DOA入射方向在(π/6)＜θ＜(5π/6)内随机分布，且假设基站可理想地估计出用户的DOA。最后，我们设置各组内简化Turbo多用户检测算法的最大敏感比特数f_max＝3。In the following simulation, we give the simulation performance of the Turbo space-time MUD algorithm in the coded multi-carrier CDMA system. The system has the number of users M=20 and Q=3 receiving antennas. In addition, in order to reduce the simulation time, we adopt (5, 7) convolutional codes with low state numbers. The size of the sector is 2π/3, and the DOA incident direction of each user is randomly distributed within (π/6)<θ<(5π/6), and it is assumed that the base station can ideally estimate the user's DOA. Finally, we set the maximum number of sensitive bits f _max =3 of the simplified Turbo multi-user detection algorithm in each group.

在图5中给出了在AWGN信道下等分组的情况下的Turbo时空多用户检测算法性能。所有用户均匀地分成4组，并有K_g＝5且g＝1，…，4。并且考虑约束，让不同组间的用户DOA最小夹角为15°。这一点可以通过基站的管理软件来保证，及把不在组内的干扰用户切换到其它时间槽或频域信道。这样的空间约束确保各组间用户在空间上的部分分割。因此，在不同的组可以重复地用相同的PN序列，PN序列长为L＝7(L＞K_g)。为了便于比较，我们还给出了单用户编码MC-CDMA系统在使用单天线和多天线阵时的性能。从图中可以看出，在单用户情况，使用天线阵波束形成技术可获得5dB的性能增益。同时，可见Turbo时空多用户算法在很少的迭代次数(n＝3)下就能逼近多天线单用户时的性能。In Fig. 5, the Turbo space-time multi-user detection algorithm performance under the condition of equal grouping under the AWGN channel is given. All users are evenly divided into 4 groups with K _g =5 and g=1, . . . ,4. And considering the constraints, let the minimum angle of user DOA between different groups be 15°. This point can be guaranteed by the management software of the base station, and the interfering users who are not in the group are switched to other time slots or frequency domain channels. Such spatial constraints ensure a partial spatial segmentation of users between groups. Therefore, the same PN sequence can be used repeatedly in different groups, and the length of the PN sequence is L=7 (L>K _g ). For the convenience of comparison, we also provide the performance of the single-user coded MC-CDMA system when using single-antenna and multi-antenna arrays. It can be seen from the figure that in the case of a single user, the performance gain of 5dB can be obtained by using the antenna array beamforming technology. At the same time, it can be seen that the Turbo space-time multi-user algorithm can approach the performance of multi-antenna single-user with a small number of iterations (n=3).

在图6中，我们考虑各用户间等交叉相关性的情况，并设置在式(5)中定义的交叉相关系数 $ρ_{m, m^{'}}^{s} = 0.4,$ 且1≤m，m′≤20。此时没有组间用户的空间约束，所有用户随机分布在扇区内。仿真结果表明我们建议的Turbo时空多用户检测算法在SNR大于-1dB时可获得几乎和单用户多天线编码的多载波CDMA系统的性能。In Figure 6, we consider the case of equal cross-correlation among users, and set the cross-correlation coefficient defined in Equation (5) $ρ_{m, m^{'}}^{the s} = 0.4,$ And 1≤m, m'≤20. At this time, there is no space constraint for users between groups, and all users are randomly distributed in sectors. Simulation results show that our proposed Turbo space-time multi-user detection algorithm can achieve almost the same performance as single-user multi-antenna coding multi-carrier CDMA system when the SNR is greater than -1dB.

Turbo时空多用户检测算法在频域选择性衰落信道下的性能在图7中给出。可以看出，在衰落信道下，本算法可以在比在AWGN信道下更少的迭代次数就能达到理想的结果。例如，在m＝3和n＝2(仅一次迭代)时，我们建议的算法就可逼近单用户在衰落信道下的性能。The performance of Turbo spatio-temporal multi-user detection algorithm in frequency-domain selective fading channel is given in Fig.7. It can be seen that under the fading channel, this algorithm can achieve the ideal result with fewer iterations than under the AWGN channel. For example, when m=3 and n=2 (only one iteration), our proposed algorithm can approximate the performance of a single user in a fading channel.

可见在实际系统中，即使在120°的扇区内有大量用户(几十甚至上百用户)同时接入基站时，我们建议的算法仍能实现。此时，我们算法有和用户数呈线性关系的算法复杂度It can be seen that in the actual system, even if there are a large number of users (dozens or even hundreds of users) accessing the base station at the same time in the sector of 120°, the algorithm we propose can still be implemented. At this point, our algorithm has an algorithmic complexity that is linearly related to the number of users

$O (Σ_{g = 1}^{G} (K_{g} - f / 2) \cdot 2^{f}),$ f≤f_max $o (Σ_{g = 1}^{G} (K_{g} - f / 2) &Center Dot; 2^{f}),$ _f≤fmax

基于软敏感比特和空间分组时空迭代(Turbo)多用户检测算法可应用于宽带无线通信中编码的多用户接入系统。时空迭代多用户检测算法能在同时接入二十个用户时在AWGN信道和频选衰落信道下都能在很少的迭代次数下逼近单用户多天线编码系统的性能。我们发明的时空迭代多用户检测算法的算法复杂度跟用户数呈线性关系，它的提出为MAP多用户检测算法在实际的应用中成为可能。可应用于编码的CDMA、SDM(Space Division Multiplexing)SDMA系统中。The time-space iterative (Turbo) multi-user detection algorithm based on soft-sensitive bits and space grouping can be applied to coded multi-user access systems in broadband wireless communications. The space-time iterative multi-user detection algorithm can approach the performance of the single-user multi-antenna coding system with a small number of iterations when accessing 20 users at the same time in the AWGN channel and the frequency-selective fading channel. The computational complexity of the space-time iterative multi-user detection algorithm we invented has a linear relationship with the number of users. It is proposed that the MAP multi-user detection algorithm becomes possible in practical applications. It can be applied to coded CDMA and SDM (Space Division Multiplexing) SDMA systems.

Claims

1. A space-time iterative multi-user detection method based on soft sensitive bits and space grouping comprises a maximum posterior probability (MAP iterative multi-user detection algorithm) combined with an intelligent antenna, and is characterized in that: classifying all users into a plurality of groups and corresponding groups except the groups, namely 'outer groups', according to spatial correlation, and then using a simplified MAP iterative multi-user detection algorithm based on soft sensitive bits for sub-multi-users in each group, namely firstly distinguishing the sensitive bits to obtain prior information, then carrying out MAP detection in a small subset corresponding to the distinguished sensitive bits, and then using outer information output by channel MAP decoding of users in each group after iterative processing to realize soft interference elimination outside the groups; it comprises the following steps in sequence:

1) receiving multiple users by using a multi-antenna matrix, setting M user access signals, and performing spatial filtering and frequency domain matching filtering according to the incident direction of user signals; according to the correlation of spatial filtering weight coefficients among users, all M users are classified and divided into G groups and corresponding 'outer groups'; namely: obtaining a spatial filtering weight vector of each user according to the following formula

All M users are classified into G groups and corresponding 'outer groups' by grouping criteria:

{\overset{&RightArrow;}{W}}_{m} = \frac{{\overset{&RightArrow;}{a}}_{m}}{| | {\overset{&RightArrow;}{a}}_{m} | |} = k \cdot {\overset{&RightArrow;}{a}}_{m},

1≤m≤M

k = \frac{1}{\sqrt{Q}}

wherein: q is the number of antenna elements;

{\overset{&RightArrow;}{a}}_{m} = {[1, e^{- jπ \sin Q_{m}}, . . . . . . ., e^{- j (Q - 1) π \sin θ_{m}}]}^{T}

for the mth user at an incident angle of Q_mA lower antenna array response; the grouping criterion is as follows:

1.1) when beta_μ，ν≥β₁And beta is_ν，μ≥β₂When the users are distributed to the same group omega_gI.e. { μ, ν, ν }. epsilon. OMEGA_g(ii) a Wherein, mu is 1, 1.. mu, v is 1, 2.. mu, v-1, beta₁，β₂Is a set threshold, and₁＞β₂，β_μ，νfor spatial filtering vectors W between users mu, v_μ， Such as:

β_{μ, ν} = \frac{| | {\overset{&RightArrow;}{W}}_{μ}^{H} \cdot {\overset{&RightArrow;}{W}}_{ν} | |}{| | W_{μ} | | | | W_{ν} | |}

superscript (·)^HFor conjugate transpose, "·" denotes vector dot product;

1.2) when beta_μ，ν≥β₁And beta is_ν，ν≤β₂And then distributing the users mu and v to be the same group omega_gIs { mu, v }. epsilon.omega_gAnd is

{ν} &NotElement; Ω_{g},

Thus, the total number of all users assigned to the G groups satisfies

Σ_{g = 0}^{G = 1} k_{g} = M,

Wherein k is_gThe total number of users in the g-th group, and the 'outer group' is the g-th group omega_gFor other users, using Ω_g ^IIndicates the number of users

k_{g}^{I} = M - k_{g}, k_{g}^{I},

Represents omega_g ^IThe total number of users;

2) calculating initial hard and soft estimates of the coded bits for all M users and assigning truth values to G groups and corresponding "outer groups";

after the receiving end is processed by beam forming and traditional matched filtering, the initial hard estimation and soft estimation of the coded bits of all M users are obtained, and the initial hard estimation and the soft estimation sequentially and respectively comprise:

{\hat{d}}_{\overset{&OverBar;}{g}, t}^{(R)} = sign (real (y_{m (k, \overset{&OverBar;}{g})})),

{\tilde{d}}_{\overset{&OverBar;}{g}, t}^{(k)} = real (y_{m (k, \overset{&OverBar;}{g})});

y_{m(k， g)}is the received signal Matched Filtered (MF) output of the kth user classified as the g "outer group" by the mth user;

3) defining the maximum sensitive bit number and the maximum iteration number of each group;

3.1) according to the following inequality

To resolve estimated multi-user coded bit vectors

Likelihood metric of (d) and the original individual user code bits of a conventional single-user Matched Filter (MF) estimate

The upper limit of the likelihood metric difference value of (c),

the larger the value of (d), the more likely the corresponding adjusted bit is to estimate an error, i.e., a sensitive bit;

3.2) then k_gAn

Middle search f (f < k)_g) F is the number of sensitive bits in the g group;

4) a simplified iterative MAP multi-user detection algorithm based on soft-sensitive bits is performed in the g-th group, which in turn has the following steps:

4.1) realizing soft interference elimination according to the 'outer group' soft estimation;

according to "Outer group omega_g ^ICoded bits for inter-user transmission

To achieve soft interference cancellation: the above soft estimation

{\tilde{d}}_{\overset{&OverBar;}{g}, k}^{(k)} = real (y_{m (k, \overset{&OverBar;}{g})});

After the interference is eliminated, there is

{\overset{&RightArrow;}{X}}_{g}^{n} = H_{g} G_{g, t} {\overset{&RightArrow;}{d}}_{g, t} + {\overset{&RightArrow;}{Z}}_{g},

While

Is self-correlation matrix ofIs composed of

E [{\overset{&RightArrow;}{Z}}_{g} {\overset{&RightArrow;}{Z}}_{g}^{H}] = H_{\overset{&OverBar;}{g}} \cdot E [Δ {\overset{&RightArrow;}{d}}_{\overset{&OverBar;}{g}} \cdot Δ {\overset{&RightArrow;}{d}}_{\overset{&OverBar;}{g}}^{H}] \cdot {H_{\overset{&OverBar;}{g}}}^{H} + \frac{1}{\sqrt{Q}} H_{g} {σ_{n}}^{2};

Wherein H_gIs the g-th group omega_gInner users and correlation matrix, H_gIs group omega_gInner users and corresponding "outer groups" omega_g ^ICorrelation matrix between inner users, G_g，tIs an internal omega of the group_gThe average power of the users is then calculated,is a group omega_gThe vector of coded bits transmitted by the users,

is an outer group omega_g ^ICoded bits for inter-user transmission

The soft-state estimation of (a) is performed,

is an "outer group" omega_g ^IEstimation error, σ, of MAP channel decoded output of a user_n ²Is the variance of additive white gaussian noise, AWGN;

4.2) finding out f sensitive bits by using a sensitive bit algorithm, and calculating the output extrinsic information of each user in the g group by using a simplified MAP multi-user detection algorithm according to the sensitive bits;

when we want to beWhen the prior probability of the sensitive bits is equal probability distribution and the prior probability of the non-sensitive bits is 1 in one iteration, the MAP multi-user detection algorithm can only consider 2 corresponding to f sensitive bits^fA vector of coded bits

4.2.1) computing extrinsic information λ of the kth user in the g-th group_1e ^k；

4.2.2) calculating the posterior LOG Likelihood Ratio (LLR) of the kth user by using MAP algorithm and using Lambda₂Indicating that the user decodes the output extrinsic information into

λ_{2 e}^{k} = Λ_{2} - λ_{1 e}^{k};

4.2.3) treatment of Lambda_2e ^kFeeding back to MAP multi-user detection module, calculating posterior LOG likelihood of information bit when iteration is finished, so as to decode received bit;

4.2.4) obtaining improved prior information of the coding bits according to the external information fed back by each user channel decoding, namely:

λ_{1 σ}^{k} = λ_{2 e}^{k},

thereby obtaining more accurate hard and soft estimates of the user coded bits;

4.3) judging whether the iteration is finished:

if not, each user MAP channel decoder calculates the extrinsic information of the coded bit and returns to the step (2);

if the calculation is finished, namely G groups are calculated, the MAP channel decoder of each user calculates the extrinsic information of the information bit to be output as a multi-user detection signal;

5) and (4) obtaining improved hard estimation and soft estimation of all M users, and returning to the step (3).