CN103078710A - Method for resisting interference in multiple-group multiple-user two-way relay network - Google Patents

Abstract

A method of anti-interference in multi-group multi-user two-way relay network, the implementation of this method requires two stages: (1) multiple access stage, all users send messages to the relay node at the same time; (2) broadcast stage, the relay node The signals received in the multiple access stage are processed and broadcast to all users, and the users complete two-way information exchange through decoding. The processing operation of the relay node on the naturally superimposed signal received in the multiple access stage is the core of the present invention, and the operation steps are as follows: (a) the relay decodes the received signal to recover the user information; The information of the same group of users performs the physical layer network coding operation; (c) performs superposition coding on the network coding symbols obtained in step (b) and broadcasts to all users by way of space-time code. The present invention can resist system performance deterioration caused by intergroup interference and intragroup interference by adopting physical layer network coding and superposition coding. Specifically, physical layer network coding can eliminate intra-group interference, and superposition coding can counteract inter-group interference. Theoretical analysis and simulation experiments prove that the present invention can obtain good system performance.

Description

A method of anti-jamming in multi-group multi-user two-way relay network

technical field

The invention relates to a method for combining physical layer network coding and superposition coding against two types of interference in a multi-group multi-user bidirectional relay network - intra-group interference and inter-group interference, belonging to the technical field of wireless communication.

Background technique

Bidirectional relay networks have attracted the attention of both academia and industry due to their potential advantages in extending network coverage and improving system spectral efficiency. The concept of relay technology first originated in the Ad hoc network. Since the power of radio waves attenuates with the increase of the transmission distance, when the attenuation reaches a certain level, the receiving end cannot detect the expected information from the weak received signal. That is to say, if the distance between two nodes exceeds the effective coverage range of the antenna, then the two nodes cannot complete the communication. At this time, if the communication is still to be continued, other nodes other than these two nodes need to be used for cooperative transmission, that is, the communication process is completed through the relay. Relay technology first appeared in the concept of one-way relay, that is, it is applied in one-way communication system. Two-way relay network, that is, the two parties in the communication need to exchange information with each other, which is a very practical communication scenario. In a typical three-node wireless two-way relay network, two end nodes conduct two-way information exchange through the relay node, that is, the data flow is bidirectional. The communication process needs to be completed in two stages: a multiple-access (MA) stage and a broadcast (BC) stage. In the MA phase, two end nodes send messages to the relay node at the same time; in the BC phase, the relay node processes the received signal and broadcasts it to the two end nodes. A typical three-node bidirectional relay network can be regarded as a single group situation, that is, two end nodes belong to the same group, and two users in the group communicate bidirectionally through the relay node.

Physical-layer network coding (PNC) is an advanced communication technology that utilizes the broadcast characteristics of wireless transmission media and the natural superposition characteristics of signals. A two-way relay network is a very suitable scenario for physical layer network coding. Only two time slots are needed to complete the two-way information exchange between two end nodes by adopting the physical layer network coding technology. According to whether the relay decodes the received mixed signal, the physical layer network coding can be divided into two categories: decoding and forwarding (Decode-and-Forward, DF) based physical layer network coding and amplification and forwarding (Amplify-and-Forward, AF) physical layer network coding (also known as analog network coding, Analog Network Coding, ANC). In DF-based PNC, the relay decodes the received naturally superimposed signal and maps it to a network coded symbol and broadcasts it to the end node; in AF-based ANC, the relay simply performs a simple After amplification, it is directly forwarded to the end node.

Superposition coding has gained extensive research and attention due to its advantages in enhancing the capacity performance of communication systems, and its essence is a layered coding modulation technique. In downlinks with additive white Gaussian noise where all nodes are configured with a single antenna, superposition coding has been proven to be an optimal technique to obtain channel capacity. For a non-fading uplink (multiple transmitters and a receiver), the optimal multiple access strategy is that all users spread their signals to the entire bandwidth, occupying all degrees of freedom, and CDMA systems very similar. However, instead of decoding each user with interference from other users treated as noise, serial interference cancellation receivers are required to achieve capacity. Specifically, after decoding a user, its estimated signal should be subtracted from the total received signal before decoding the next user. A similar transmission strategy is also optimal for the downlink (one transmitter and multiple receivers). The signals of users are mixed and superimposed on each other, and the serial interference cancellation is performed separately: each user firstly compares the signals sent to other signals. Weak user information is decoded, and then the decoded information of other users is eliminated before decoding its own information. It has been proved that when the channel conditions from the user to the base station are completely different, the combination of serial interference cancellation and code division multiple access can make the system obtain greater performance improvement than traditional multiple access technology.

The traditional three-node bidirectional relay network can be regarded as a single-group situation, that is, two end nodes belong to the same group. As a natural extension of the single-group scenario, a multi-group multi-user bidirectional relay network is a more practical communication scenario. Consider the case where each user communicates only with partners belonging to one group and not with users of other groups. However, compared with the single-group situation, the multi-group multi-user scenario can increase the number of users served by the system and improve frequency utilization; however, there are two types of interference that may seriously deteriorate the system performance in this scenario, namely intra-group interference and inter-group interference. interference. For the processing of intra-group interference, a processing scheme similar to that of a single group can be adopted, that is, the physical layer network coding is used to eliminate intra-group interference; and the processing of inter-group interference is a very challenging problem. The specific processing method is related to the system Antenna configuration has a lot to do with it. For multi-group multi-user two-way relay networks with different antenna configurations, the ideas for dealing with the two types of interference are different. According to the configuration of the number of relay antennas and the number of user antennas, the multi-group multi-user two-way relay network is divided into the following three categories: (I) the relay and the user are only equipped with a single antenna; (II) the relay is equipped with multiple antennas The user is equipped with a single antenna; (III) both the relay and the user are equipped with multiple antennas. For Type I two-way relay network, physical layer network coding can be used to deal with intra-group interference, and code division multiple access can be used to combat inter-group interference. For Class II and III two-way relay networks, beamforming is an effective method to combat interference, but the beamforming method has very strict requirements on the antenna configuration of the system: the number of relay antennas must be greater than or at least equal to that of all users The sum of the number of antennas, otherwise the relay will not have enough degrees of freedom to resist interference. When the antenna configuration of the system does not meet the requirements of beamforming, how to counteract the deterioration of system performance caused by the two types of interference is a very challenging problem.

Contents of the invention

The purpose of the present invention is to explore a method that can reduce the degradation of system performance caused by two types of interference in a multi-group multi-user two-way relay network when the system antenna configuration does not meet the application requirements of beamforming. The invention proposes a method for combining physical layer network coding and superposition coding to combat two types of interference. Specifically, physical layer network coding can be used to eliminate intra-group interference, and superposition coding can be used to combat inter-group interference.

表示用户U_ki到中继节点的信道矩阵，其每个元素都是独立同分布的，即每个元素服从

分布；假设上行链路信道和下行链路信道具有互易性，那么中继节点到用户的信道为

其中上标(·)^H代表向量或矩阵的共轭转置操作。其特征在于，所述方法包括两个阶段：Consider a two-way relay network consisting of 2K single-antenna users and a relay node equipped with two antennas, each user communicates only with partners belonging to the same group. U _ki represents the i-th user of the k-th group, where k=1, 2, . . . , K, i=1, 2.

Represents the channel matrix from the user U _ki to the relay node, each element of which is independent and identically distributed, that is, each element obeys

distribution; assuming that the uplink channel and downlink channel have reciprocity, then the channel from the relay node to the user is

where the superscript (·) ^H represents the conjugate transpose operation of a vector or matrix. It is characterized in that the method comprises two stages:

(1) Multiple access stage: all users send information to the relay node at the same time;

(2) Broadcast stage: the relay node performs certain processing operations on the signal received in the multiple access stage and broadcasts it to all users, and each user recovers the desired purpose information through decoding to complete the two-way information exchange. This stage includes the following steps: (a) the relay decodes the received signal to recover the user information; (b) performs the physical layer network coding operation on the information belonging to the same group of users; (c) performs step (b) ) is superimposed on the network coding symbols obtained and broadcast to all users through space-time codes.

The present invention proposes a method for countering intra-group interference and inter-group interference when the multi-group multi-user two-way relay network does not meet the application conditions of beamforming. Corresponding serial interference cancellation at the user end can counteract inter-group interference, thereby alleviating the deterioration of system performance caused by the two types of interference, and effectively improving system performance. In addition, the present invention also provides the expressions of sum rate and outage probability of the system.

Description of drawings

In order to more intuitively and clearly illustrate the technical solutions in the embodiments of the present invention, the drawings that need to be used in the implementation process will be briefly introduced below.

FIG. 1 is a communication scenario where the present invention is applied: a schematic diagram of a multi-group multi-user two-way relay network.

Fig. 2 is a flow chart of joint physical layer network coding and superposition coding proposed by the present invention to combat intra-group interference and inter-group interference in multi-group multi-user two-way relay network.

Fig. 3 is a schematic diagram showing the comparison between the average sum rate of the system and the performance of existing solutions in the embodiment of the present invention.

Fig. 4 is a schematic diagram of comparison between the system outage probability and the performance of existing solutions in the embodiment of the present invention.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

分布。根据通信过程中的具体条件，本发明做出如下三项合理假设：Referring to FIG. 1 , FIG. 1 is an application scenario of an example of the present invention. As shown in Fig. 1, the considered multi-group multi-user two-way relay network consists of 2K single-antenna users and a relay node equipped with two antennas, and each user only communicates with partners belonging to the same group. U _ki represents the i-th user of the k-th group, where k=1, 2, . . . , K, i=1, 2. Represents the channel matrix from the user U _ki to the relay node, each element of which is independent and identically distributed, and obeys

distributed. According to the specific conditions in the communication process, the present invention makes the following three reasonable assumptions:

1. All nodes work in half-duplex mode, and the channel has reciprocity. like Represents the channel matrix from the user U _ki to the relay node. According to the channel reciprocity, the channel from the relay node to the user is Wherein the superscript (·) ^H represents the conjugate transpose operation of the vector or matrix, k=1, 2, . . . , K, i=1, 2. And it is assumed that the channel is quasi-static, that is, the channel does not change during the transmission time interval of several consecutive data packets.

2. Since the channel estimation technology in the current two-way relay network is relatively mature, it is assumed that the relay node can obtain global channel information through channel estimation, and each user can obtain local channel information, that is, the channel information from the user to the relay node.

3. Assume that all users are perfectly synchronized with the relay node, that is, the signals of all users in the multiple access phase arrive at the relay node at the same time.

With reference to Fig. 2, introduce two operation steps that the present invention implements:

Step (1), multiple access stage: all users send information to the relay node at the same time.

Step (2), broadcasting stage: the relay node performs certain processing operations on the signal received in the multiple access stage and broadcasts it to all users, and each user recovers the desired purpose information through decoding to complete the two-way information exchange.

Step (2) further includes the following operations:

其中Ω＝{-1，1}，

代表中继节点解码出的用户U_ki的信息，k＝1，2，…，K，i＝1，2，||·||²表示其元素的Frobenius范数。(21) The baseband signals sent by all users in the multiple access stage received by the relay node are denoted by y, then The relay node uses the global channel information it has mastered to perform maximum likelihood decoding on y, and this operation process is expressed by the following formula:

where Ω={-1, 1},

represents the information of the user U _ki decoded by the relay node, k=1, 2, ..., K, i=1, 2, and ||·|| ² represents the Frobenius norm of its elements.

式中k＝1，2，…，K。(22) Apply bit-based XOR-based physical layer network coding to the decoded information of each group of users at the relay node, which can be expressed as follows:

In the formula, k=1, 2, ..., K.

(23) Perform superposition coding operation on the symbols of the physical layer network codes of each group of users obtained after the execution of (22), and the obtained signal is: In the formula, P _k represents the power allocated to symbol _sk , and the total relay power is the sum of all users. In addition, it is necessary to make P _m ≠ P _n to m ≠ n, so as to ensure that the mapping from (s ₁ , s ₂ , . . . , s _K ) to S _sc is a one-to-one mapping.

(24) In order to make full use of the two antennas of the relay node, Alamouti coding is adopted to obtain space diversity gain. Let S _sc1 and S _sc2 represent two consecutive superimposed coded symbols, and the relay node broadcasts to all users according to the following formula: $S=\left[\begin{array}{cc}{S}_{\mathrm{sc}1}& -{\mathrm{<figure-callout\; id="2"\; label="S\; sc"\; filenames="HSA00000835735200031.png"\; state="\{\{state\}\}">S</figure-callout>}}_{\mathrm{sc}}^2\\ S_{\mathrm{sc}2}& S_{\mathrm{sc}1}^{*}\end{array}\right],$ In the formula (·)* represents the conjugation operation.

(25) At the user end, after receiving the signal broadcast by the relay, each group of users performs serial interference cancellation to recover their desired information, and then detects the desired physical layer network coding symbols using the maximum likelihood criterion.

Operation (25) further includes the following:

(25A) User U ₁₁ first performs serial interference cancellation operations to eliminate interference caused to it by other groups of users.

和

(25B) Next, the user U ₁₁ recovers the expected physical layer network coding symbols through the maximum likelihood criterion, and the physical layer network coding symbols of two consecutive time slots are expressed as

and

与

异或操作，可以得到期望的信息

类似地与

进行异或操作可得到

相关操作可表示如下：

(25C) User U ₁₁ passes self-information

and

XOR operation, you can get the desired information

Similarly and

Exclusive OR operation can be obtained

The related operations can be expressed as follows:

$\stackrel{<span\; class="notranslate">\; ^</span>}{{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="12"\; label="s"\; filenames="HSA00000835735200021.png"\; state="\{\{state\}\}">s</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CirclePlus;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; sc</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Other users perform similar operations to user U ₁₁ , thus completing two-way information exchange among multiple groups of users.

In order to demonstrate the practical performance of the method of the present invention, the applicant has carried out several simulation implementation tests. The test system is a multi-group multi-user two-way relay network shown in Figure 1, including 2K single-antenna users and a relay node equipped with two antennas. Each node adopts binary phase shift keying (Binary Phase Shift Keying, BPSK) modulation mode, and all channels between users and relay nodes are quasi-static Rayleigh fading channels. The power of the relay node is the sum of the power of all user nodes. A physical layer network coding (Time-Division PNC, TD-PNC) method based on decoding and forwarding time division is selected as a comparison scheme. The simulation results about the sum rate are shown in Figure 3. It can be seen from Fig. 3 that the present invention observes that the present invention can obtain a higher sum rate than the TD-PNC method. Fig. 4 plots the curves of the system outage probability changing with the signal-to-noise ratio in the case of different numbers of user groups, and the value of the target rate is set as R ^t =0.2b/s/Hz. It can be seen from Fig. 4 that both the present invention and TD-PNC can obtain a diversity order of 2, but the interruption performance obtained by the present invention is better than that of the TD-PNC method, and the performance gain increases with the number of users.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention should be included in the protection of the present invention. within range.

Claims (3)

1. organize in multi-user's bilateral relay network a kind of to anti-disturbance method more, the scene that is suitable for is: the bilateral relay network that is equipped with the via node (RelayNode, RN) of two antennas to form by K group (every group comprises two users) single antenna user and.Two users that belong to same group carry out bi-directional exchanges of information under the help of RN.U _KiI the user who represents k group, k=1 wherein, 2 ..., K, i=1,2.s _KiExpression user U _KiThe information that sends; Expression user U _KiTo the channel matrix of via node, its each element is independent identically distributed, and obeys Distribute; P _KiExpression user U _KiTransmitting power; N represents 2 * 1 multiple gaussian additive noise vectors of via node.Suppose that uplink channel and downlink channel have reciprocity, via node to user's channel is so

Subscript () wherein ^HThe conjugate transpose operation of representation vector or matrix.It is characterized in that: institute's extracting method comprises following two operating procedures:

(1) the multiple access stage: all users send information to via node simultaneously;

(2) the broadcasting stage: the signal that via node received the multiple access stage carries out being broadcast to all users after certain processing operation, thereby each user finishes bi-directional exchanges of information by the purpose information that decoding recovers expectation.

2. method according to claim 1, it is characterized in that: institute's extracting method is in application process, and communication system also must meet the following conditions: all nodes all are operated in semiduplex mode, and namely the sending and receiving of each node can not carry out simultaneously; Channel between all users and via node is the independent same distribution quasistatic Rayleigh fading channel, and namely channel is invariable within the delivery time of continuous several packets; Via node is grasped global channel information and is used for the mixed signal that the multiple access stage receives is carried out maximum likelihood decoding.

3. method according to claim 2, it is characterized in that: the operation in the step (2) comprises following content:

(21) baseband signal that sends of all users of via node multiple access stage of receiving represents with y, then

Via node utilizes the global channel information of its grasp that y is carried out maximum likelihood decoding, and this operating process represents with following formula:

Wherein Ω=1,1},

Represent the user U that via node decodes _KiInformation, k=1,2 ..., K, i=1,2, || || ²The Frobenius norm that represents its element.

(22) at the via node place every group of user's decoding information is used physical-layer network coding based on the bit XOR, can be expressed as follows:

K=1 in the formula, 2 ..., K.

The symbol of the every group of user's who (23) obtains after (22) are executed physical-layer network coding carries out the supercomposed coding operation, and the gained signal is:

P in the formula _kSymbol s is distributed in representative _kPower, the relaying gross power is all user's sums.Need so that P in addition _m≠ P _nTo m ≠ n, to guarantee (s ₁, s ₂..., s _K) to S _ScMapping be to shine upon one by one.

(24) in order to take full advantage of two antennas of via node, adopt Alamouti to encode to obtain space diversity gain.Make S _Sc1And S _Sc2Represent two symbols behind the continuous process supercomposed coding, via node is broadcast to all users according to following formula: $S=\left[\begin{array}{cc}{S}_{\mathrm{sc}1}& -S_{\mathrm{sc}2}^{*}\\ S_{\mathrm{sc}2}& S_{\mathrm{sc}1}^{*}\end{array}\right],$ () * represents conjugate operation in the formula.

(25) at user side, receive the signal of repeat broadcast after, every group of user carries out serial interference elimination to recover the information of its expectation, then utilizes maximum-likelihood criterion to detect the physical-layer network coding symbol of expectation.For the consideration of symmetry and simplicity, this sentences user U ₁₁Be operating as example explanation: user U ₁₁At first carry out serial interference elimination and operate to eliminate other group user to its interference that causes.User U ₁₁Next recover the physical-layer network coding symbol of expectation by maximum-likelihood criterion, the physical-layer network coding symbolic representation of continuous two time slots is

With

Distribute to the power of the physical-layer network coding symbol of each user's group herein when impliedly requiring each user to know supercomposed coding, can utilize maximum-likelihood criterion to decode the physical-layer network coding symbol of expectation.User U ₁₁Pass through self information

With

Xor operation, the information that can obtain expecting

Similarly

With

Carrying out xor operation can obtain

Associative operation can be expressed as follows:

Other user carries out and user U ₁₁The two-way communication between many groups user has so just been finished in similar operation.

(26) the obtainable average and speed of taking into account system.Consider the situation of certain given channel under realizing, in the multiple access stage, each user's transmission rate and total should satisfy following constraint with speed: $R_{\mathrm{ki}}^{\mathrm{MA}}\&le;{\log }_2(1+\frac{P{\left|\right|h_{\mathrm{ki}}\left|\right|}^2}{{\mathrm{\&sigma;}}^2}),$ $\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{2}{\mathrm{\&Sigma;}}}{R}_{\mathrm{ki}}^{\mathrm{MA}}\&le;R^{\mathrm{MA}}={\log }_2\det (I_2+\frac{P}{{\mathrm{\&sigma;}}^2}\mathrm{HH}*),$ P represents the transmitting power of each symbol, I in the formula ₂Expression 2 * 2 unit matrixs,

K=1,2 ..., K, i=1,2.Can not surpassing with speed that second formula shows all users of multiple access stage regarded the communication scenes of considering as by 2K cooperate the at all capacity of the multiaerial system that transmitting antenna and 2 reception antennas form.

In the broadcasting stage, each user's transmission rate can be represented by the formula:

Constant 2 in the formula right-hand member logarithmic function on second denominator is because repeat broadcast is the power loss that adopts the Alamouti coding to cause.Owing to organize the identical symbol sebolic addressing of emission at broadcasting stage via node to the user, therefore less speed is determining the information rate that finally can reliably transmit, then user U among every group of user _KiSpeed be:

In the formula || g _k|| ²=min (|| h _K1|| ², || h _K2|| ²), k=1,2 ..., K, i=1,2.

Consider that supercomposed coding is on the impact of speed.Discuss for convenient, suppose || g ₁|| ²≤ || g ₂|| ²≤ ... ≤ || g _K|| ², the user who belongs to same group is regarded as an integral body, from top hypothesis as can be known, when m＞n, the user organizes m and organizes n than the user and have better channel quality.This sentences two groups of users and is the signal processing operations of example explanation user side.Because the user organizes 2 and organizes 1 than the user and have better channel quality, so the user organizes 2 data that any user's group can decode of can decoding.The user organizes 1 decoding and the user is organized 2 signal during its purpose information and be treated to noise.The user organizes 2 signals of decode users group 1 at first, then deducts the information of its expectation of decoding at last from receive signal.K group user's achievable rate can be represented by the formula: $R_k=\min (R_{\mathrm{ki}}^{\mathrm{MA}},R_{\mathrm{ki}}^{\mathrm{BC}},R_k^{\mathrm{SC}})={\log }_2(1+\frac{\frac{P_k}{2}{\left|\right|g_k\left|\right|}^2}{{\mathrm{\&sigma;}}^2+\left(\underset{m=k+1}{\overset{K}{\mathrm{\&Sigma;}}}\frac{P_m}{2}\right){\left|\right|g_k\left|\right|}^2}),$ Wherein

K group user's speed behind the expression employing supercomposed coding.

By asking expectation just can obtain average and speed to mutual information at all possible channel status, can be expressed as: $R_{\mathrm{sum}}=\frac{1}{2}E\left[\min (\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}2R_k,R^{\mathrm{MA}})\right]=E\left[\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{R}_k\right],$ Invariant in the formula Because need 2 time slots to finish bi-directional exchanges of information.

(27) interruption performance of taking into account system.When the instantaneous transmission speed of user in the system is lower than targeted rate, be referred to as to have occured interrupt event one time.As long as there is one group of user that interruption has occured, interruption has occured in system with regard to title.The outage probability of system can be expressed as so: p _Out(R ^t)=Pr{min (R ₁..., R _k)＜R ^tR in the formula ^tBe targeted rate.Still suppose || g ₁|| ²≤ || g ₂|| ²≤ ... ≤ || g _K|| ², consider the speed that every group of user finally can realize, outage probability can be written as again: p _Out(R ^t)=Pr{R ₁＜R ^t, R in the formula ₁Be the user organize two users in 1 traffic rate and: $R_1={\log }_2(1+\frac{P{\left|\right|g_1\left|\right|}^2}{{\mathrm{\&sigma;}}^2+(K-1)P{\left|\right|g_1\left|\right|}^2})={\log }_2(1+\frac{\mathrm{\&rho;}{\left|\right|g_1\left|\right|}^2}{1+(K-1)\mathrm{\&rho;}{\left|\right|g_1\left|\right|}^2}),$ In the formula

When || h _Ki|| ²Value hour its probability density function can be approximated to be: f (x) ≈ x, x 〉=0.Notice || g ₁|| ²=min (|| g ₁|| ², || g ₂|| ²..., || g _K|| ²), || g ₁|| ²Cumulative distribution function can obtain by calculating: $\mathrm{Pr}({\left|\right|g_1\left|\right|}^2<z)=1-{(1-{\&Integral;}_0^{z}f\left(x\right)\mathrm{dx})}^{2K}\&ap;{\mathrm{Kz}}^2,z\&GreaterEqual;0.$ In the high s/n ratio zone, the outage probability of system can further be derived as: $p_{\mathrm{out}}\left(R^t\right)=\mathrm{Pr}({\left|\right|g_1\left|\right|}^2<\frac{2R^t-1}{\mathrm{\&rho;}(K+2R^t-K2R^t)})\&ap;\frac{K{(2R^t-1)}^2}{{\mathrm{\&rho;}}^2{(K+{2R}^t-K2R^t)}^2}.$ The diversity order that obtains of the user of the poorest user of channel quality group is 2 as can be seen from the above equation.Yet the diversity order that other user with better channel quality user group obtains is greater than 2, because they benefit from the serial interference elimination operation.In a word, the diversity order that system obtains is 2, can the poorest user determine because the final performance of system is do as one likes.

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