CN103684523B - Method for transmitting and receiving signal of complementary stirring code division multiple access system on basis of multi-path attenuation channels - Google Patents

Abstract

The invention discloses a method for transmitting and receiving signals of a complementary stirring code division multiple access system on the basis of multi-path attenuation channels, and relates to the field of communication. The method aims to solve problems of high bandwidth requirements and bit error rate and low transmission rate of the traditional direct-sequence spread-spectrum multiple-input-multiple-output complementary code division multiple access system. The method has the advantages that the method is combined with an MIMO (multiple-input-multiple-output) technology, a plurality of transmitting antennas and a plurality of receiving antennas are arranged at a transmitting end and a receiving end, accordingly, a bit error rate can be reduced and is comparably reduced by 15%, and a transmission rate can be increased and is comparably increased by 17%; bandwidth resources required by the complementary stirring code division multiple access system can be reduced and are comparably reduced by 20%; a stirring technology is combined with the traditional orthogonal complementary codes; a wireless channel transmission system is established among multiple users via multiple access; the method is applicable to the field of communication.

Description

The signal transmitting and receiving method of code division multiple access system is stirred in complementation based on multipath fading channels

Technical field

The present invention relates to the communications field.

Background technology

Tradition straight sequence exhibition frequently complementary code division multiple access (the Direct-sequence Multiple Access) system of multiple-input and multiple-output uses code to distinguish antenna, transmission data due to different antennae can use coding to be separated so can realize multicast or space diversity, but the demand too increased bandwidth, does not meet the main concept of multiple-input and multiple-output simultaneously.

The straight sequence exhibition of tradition frequently multiple-input and multiple-output mutual-complementing code division multiple access system uses the spreading codes of straight sequence to eliminate interference, and straight sequence exhibition frequently technology can consume a large amount of bandwidth especially transmit data grows fast time.Due to the data separating that traditional multiple antennas mutual-complementing code technology uses code different antennae to be transmitted, so traditional multiple antennas mutual-complementing code technology is not really wanted to use multiaerial system, and multiple antennas is used whether to meet benefit or a problem to realize traditional multiple antennas mutual-complementing code technology.

Summary of the invention

The present invention is that the demand of multiple-input and multiple-output mutual-complementing code division multiple access system to bandwidth is high frequently in order to solve the exhibition of tradition straight sequence, the error rate is high, the problem that transmission rate is low, and then the signal transmitting and receiving method providing the complementation stirring code division multiple access system based on multipath fading channels.

The signal transmitting method of code division multiple access system is stirred in complementation based on multipath fading channels, and described launching technique is:

Step one, by signal B to be sent ^(k)data Replica becomes N _tindividual, N _tfor being greater than the positive integer of zero, k=1,2 ... K;

Step 2, by each signal B ^(k)data are copied into M signal again, M be greater than zero positive integer;

By n-th _tm signal in M the signal that individual signal is corresponding and coding carry out stirring operation, obtain signal n _t=1,2 ... N _t, m is the positive integer being greater than zero and being less than M;

Step 3, to be outputed signal in step 2 with carry out product, after product, obtain signal by n-th _tby the end n-th after M the modulation signal that individual signal is corresponding superposes _tindividual transmission antennas transmit.

The signal acceptance method of code division multiple access system is stirred in complementation based on multipath fading channels, and the signal acceptance method of user k is:

The N of step 4, receiving terminal _rindividual reception antenna receives the signal that transmitting terminal is launched, N _rfor being greater than the positive integer of zero, and N _tbe less than or equal to N _r, n-th _rindividual reception antenna receives n-th _tsignal after the superposition of individual transmission antennas transmit, and by N _r× 1 dimensional signal merges formation vector Y _t, n _r=1,2 ... N _r, vector Y _tsignal U is obtained after superposing with N _t, N is coding degree;

Step 5, the signal U that will obtain _tdata Replica becomes N _rindividual;

Step 6, by each signal U _tat f _mcarrier frequency carries out demodulation operation, and the signal after demodulation operation by obtaining two signal datas after low pass filter filtering is respectively and P _m,t;

Signal signal is obtained by channel estimator by described signal carry out pseudo-inverse operation, obtain signal signal P _m,tsample in time t, obtain signal R _m,t; By signal with signal R _m,tcarry out product, after product, obtain signal

Step 7, the signal that will obtain with carry out solution and stir operation, obtain solution stir after signal by N _rindividual solution stir after signal data superpose after obtain signal then carry out adjudicating rear output final signal B ^(k).

In the present invention, adopt multiple transmitting antenna and multiple reception antenna in conjunction with MIMO (Multiple-Input-Multiple-Output) technology at transmitting terminal and receiving terminal, reduce the error rate, reduce 15% on year-on-year basis, improve transmission rate, improve 17% on year-on-year basis; The complementary code division multiple access system that stirs can reduce the demand of system to bandwidth resources, decreases 20% on year-on-year basis; Stirring technique is combined with conventional orthogonal mutual-complementing code; The wireless channel transmission system set up between multi-user is accessed by multiple access.

Channel is multipath frequency decay channel, and time delay expansion L must meet L≤N _t≤ N _r.Use table 1 represents ITU-R M.1225 channel model, is wherein indoor test environment tapped delay line parameter, as follows:

Use table 2 represents the probability that the inverse matrix element number range of channel matrix is greater than 1, as follows:

The Performance Evaluation of channel A under indoor environment:

In Performance Evaluation, suppose that indoor test environment adopts channel A as shown in table 1, we are 100ns the conventional letter duration, so we have selected time constant [0 110 170 290] ns as delay path, corresponding average power is [0-10-18-26] dB.

As shown in Figure 8, the complementary code division multiple access system that stirs uses transmitting antenna N _t=4, reception antenna N _r=[4 56 7].Delay path L is limited to the sum of transmitting antenna, thus extend path L=4, so we need more than 4 accept antenna to overcome multi-path jamming.Because symbol duration is chosen to be 100ns so the message transmission rate of each user is 10Mbps.Because system user sum K=2 is so the overall transmission rate of system is 2 × 10Mbps.Because each carrier wave occupies the bandwidth of 10MHz and the total carrier wave M=2 of system, so the total bandwidth that system occupies is 2 × 10MHz.

The performance of the increase system that we can find along with reception antenna quantity is become better and better, and when the quantity of transmitting antenna is equal with the quantity accepting antenna, systematic function is the poorest.This phenomenon produces, because when complementary stirring code division multiple access system performs pseudo-inverse operation to first channel matrix, so the number range of the element of the pseudo-inverse matrix of non-side's channel matrix will suppose that the inverse matrix of channel matrix is much little due to squeeze theorem.Stir in code division multiple access system in complementation, the element on first path of the inverse matrix of the channel matrix of side is the chief component of system MAI and MI, and when we use the transmitting antenna of varying number and accept antenna, the performance of system increases significantly.Systematic function is very responsive to the element in the inverse matrix of channel matrix, and when coefficient is less than 1, when the number range of element becomes large, interference and noise are also exaggerated.If channel matrix is square matrix, the value of the determinant of channel matrix directly affects the number range of the inverse matrix element of channel matrix, when channel matrix determinant value close to zero time, the number range of the inverse matrix of channel matrix will become very large result and produce worse performance, when coefficient is greater than 1, when the value of channel matrix determinant becomes very large, the number range of the inverse matrix of channel matrix will become very little result and produce good performance.

When code division multiple access execution pseudo inverse matrix operation is stirred in complementation, along with the increase of reception antenna quantity, channel matrix the number range of element of inverse matrix diminish.Table 2 represents the absolute value probability that is greater than 1, when absolute value when being greater than 1 will become very poor of the performance of system because bit error rate function into:

Along with reception antenna, to compare transmitting antenna increasing, absolute value be greater than that the probability of 1 will become more and more less, the performance of system will be become better and better.When transmitting antenna is equal with reception antenna quantity time, absolute value be greater than the probability of 1 close to 0.534, so the performance of system becomes very poor.

As shown in Figure 9, the complementary code division multiple access system that stirs uses transmitting antenna N _t=4, reception antenna N _r=6.Delay path L is limited to the sum of transmitting antenna, thus extend path L=4, in order to complete pseudoinverse inverse matrix we need more than 4 accept antenna to overcome multi-path jamming.According to formula (4-45), if K=M formula can abbreviation be:

According to formula, we can analyze: as K=M the error rate only and the signal to noise ratio of signal have relation and carrier number and number of users irrelevant.And as K<M, can analyze from formula (4-45), along with the increase of number of carriers, the error rate is more and more less, and then the performance of system improves.

As shown in Figure 10, the complementary code division multiple access system that stirs uses transmitting antenna N _t=4, reception antenna N _r=6.Delay path L is limited to the sum of transmitting antenna, thus extend path L=4, in order to complete pseudoinverse inverse matrix we need more than 4 accept antenna to overcome multi-path jamming.According to formula, we can analyze: as K=M the error rate only and the signal to noise ratio of signal have relation and carrier number and number of users irrelevant.And as K<M, can analyze from formula (4-45), along with the minimizing of number of users, the error rate is more and more less, and then the performance of system improves.

The Performance Evaluation of channel B under indoor environment:

In Performance Evaluation, suppose that indoor test environment adopts channel B as shown in table 1, we are 100ns the conventional letter duration, so we have selected time constant [0 100 200 300] ns as delay path, corresponding average power is [0-3.6-7.2-10.8] dB.

As shown in figure 11, the complementary code division multiple access system that stirs uses transmitting antenna N _t=5, reception antenna N _r=[5 67 8].Delay path L is limited to the sum of transmitting antenna, thus extend path L=5, so we need more than 5 accept antenna to overcome multi-path jamming.Because symbol duration is chosen to be 100ns so the message transmission rate of each user is 10Mbps.Because system user sum K=2 is so the overall transmission rate of system is 2 × 10Mbps.Because each carrier wave occupies the bandwidth of 10MHz and the total carrier wave M=2 of system, so the total bandwidth that system occupies is 2 × 10MHz.

The performance of the increase system that we can find along with reception antenna quantity is become better and better, and when the quantity of transmitting antenna is equal with the quantity accepting antenna, systematic function is the poorest.This phenomenon produces, because when complementary stirring code division multiple access system performs pseudo-inverse operation to first channel matrix, so the number range of the element of the pseudo-inverse matrix of non-side's channel matrix will suppose that the inverse matrix of channel matrix is much little due to squeeze theorem.Stir in code division multiple access system in complementation, the element on first path of the inverse matrix of the channel matrix of side is the chief component of system MAI and MI, and when we use the transmitting antenna of varying number and accept antenna, the performance of system increases significantly.Systematic function is very responsive to the element in the inverse matrix of channel matrix, and when coefficient is less than 1, when the number range of element becomes large, interference and noise are also exaggerated.If channel matrix is square matrix, the value of the determinant of channel matrix directly affects the number range of the inverse matrix element of channel matrix, when channel matrix determinant value close to zero time, the number range of the inverse matrix of channel matrix will become very large result and produce worse performance, when coefficient is greater than 1, when the value of channel matrix determinant becomes very large, the number range of the inverse matrix of channel matrix will become very little result and produce good performance.

When code division multiple access execution pseudo inverse matrix operation is stirred in complementation, along with the increase of reception antenna quantity, channel matrix the number range of element of inverse matrix diminish.Table 2 represents the absolute value probability that is greater than 1, when absolute value when being greater than 1 will become very poor of the performance of system because bit error rate function into:

Along with reception antenna, to compare transmitting antenna increasing, absolute value be greater than that the probability of 1 will become more and more less, the performance of system will be become better and better.When transmitting antenna is equal with reception antenna quantity time, absolute value be greater than the probability of 1 close to 0.534, so the performance of system becomes very poor.

As shown in figure 12, the complementary code division multiple access system that stirs uses transmitting antenna N _t=5, reception antenna N _r=7.Delay path L is limited to the sum of transmitting antenna, so latency path L=5, in order to complete pseudo inverse matrix we need more than 5 accept antenna to overcome multi-path jamming.According to formula (4-45), if K=M formula can abbreviation be:

According to formula, we can analyze: as K=M the error rate only and the signal to noise ratio of signal have relation and carrier number and number of users irrelevant.And as K<M, can analyze from formula (4-45), along with the increase of number of carriers, the error rate is more and more less, and then the performance of system improves.

As shown in figure 13, the complementary code division multiple access system that stirs uses transmitting antenna N _t=5, reception antenna N _r=7.Delay path L is limited to the sum of transmitting antenna, thus extend path L=5, in order to complete pseudoinverse inverse matrix we need more than 5 accept antenna to overcome multi-path jamming.According to formula, we can analyze: as K=M the error rate only and the signal to noise ratio of signal have relation and carrier number and number of users irrelevant.And as K<M, can analyze from formula (4-45), along with the minimizing of number of users, the error rate is more and more less, and then the performance of system improves.

Accompanying drawing explanation

Fig. 1 is that the present invention stirs mutual-complementing code emission system;

Fig. 2 is the flow chart of stirring operation in step 2;

Fig. 3 is that coding receiving system is stirred in the present invention's complementation;

Fig. 4 is step 6 baseband equivalence channel impulse response model flow figure;

Fig. 5 is step 6 baseband equivalence channel model flow chart;

Fig. 6 is the lag characteristic distribution map of baseband channel equivalent model;

Fig. 7 is the flow chart separating stirring operation in step 7;

Fig. 8 is the error rate of multi-user K=M=2, and system uses transmitting antenna N _t=4, reception antenna N _r=[4 56 7];

Fig. 9 is the error rate of multi-user K=2, M=[2 46 8], and system uses transmitting antenna N _t=4, reception antenna N _r=6;

Figure 10 is the error rate of multi-user M=8, K=[2 46 8], and system uses transmitting antenna N _t=4, reception antenna N _r=6;

Figure 11 is the error rate of multi-user K=M=2, and system uses transmitting antenna N _t=5, reception antenna N _r=[5 67 8];

Figure 12 is the error rate of multi-user K=2, M=[2 46 8], and system uses transmitting antenna N _t=5, reception antenna N _r=7;

Figure 13 is multi-user K=[2 46 8], the error rate of M=8, and system uses transmitting antenna N _t=5, reception antenna N _r=7.

Embodiment

Embodiment one: present embodiment is described below in conjunction with Fig. 1 and Fig. 2, stir the signal transmitting method of code division multiple access system described in present embodiment based on the complementation of multipath fading channels, described launching technique is:

Step one, by signal B to be sent ^(k)data Replica becomes N _tindividual, N _tfor being greater than the positive integer of zero, k=1,2 ... K;

Step 2, by each signal B ^(k)data are copied into M signal again, M be greater than zero positive integer;

By n-th _tm signal in M the signal that individual signal is corresponding and coding carry out stirring operation, obtain signal n _t=1,2 ... N _t, m is the positive integer being greater than zero and being less than M;

Step 3, to be outputed signal in step 2 with carry out product, after product, obtain signal by n-th _tby the end n-th after M the modulation signal that individual signal is corresponding superposes _tindividual transmission antennas transmit.

Embodiment two: present embodiment is further qualified the signal transmitting method that code division multiple access system is stirred in the complementation based on multipath fading channels described in embodiment one, in present embodiment, the method for stirring operation in step 2:

Initial transmit for $B^{\left(k\right)}=[b_1^{\left(k\right)},b_2^{\left(k\right)},...,b_N^{\left(k\right)}],---(2-1)$

$b_t^{\left(t\right)}=b^{\left(k\right)}{p}_t,---(2-2)$

Signal $B^{\left(k\right)}={[b_1^{\left(k\right)},b_2^{\left(k\right)},...,b_N^{\left(k\right)}]}_{1\&times;N}$ With coding $C_{n_t,m}^{\left(k\right)}={[c_{n_t,m,1}^{\left(k\right)},c_{n_t,m,2}^{\left(k\right)},...,c_{n_t,m,N}^{\left(k\right)}]}_{1\&times;N}$ In corresponding element stir formed output signal $T_{n_t,m}^{\left(k\right)}={[b_1^{\left(k\right)}{c}_{n_t,m,1}^{\left(k\right)},b_2^{\left(k\right)}{c}_{n_t,m,2}^{\left(k\right)},...,b_N^{\left(k\right)}{c}_{n_t,m,N}^{\left(k\right)}]}_{1\&times;N}.$

Described in above-mentioned execution mode, the complementary code that stirs is obtained by following steps:

Steps A: set up orthogonal matrix A and D

Then step B is performed;

Step B: utilize orthogonal matrix A to be multiplied by orthogonal matrix D, obtains complementary stirring code division multiple access encoder matrix C ^(k)

$C^{\left(k\right)}=\left[\begin{array}{c}{C}_{n_t,1,t}^{\left(k\right)}\\ C_{n_t,2,t}^{\left(k\right)}\\ .\\ .\\ .\\ C_{n_t,M,t}^{\left(k\right)}\end{array}\right]=a_{t,n_t}\left[\begin{array}{c}{d}_{1,k}\\ d_{2,k}\\ .\\ .\\ .\\ d_{M,k}\end{array}\right]$

Wherein, n is positive integer and n≤N.

Embodiment three: present embodiment is described below in conjunction with Fig. 3 to Fig. 7, stir the signal acceptance method of code division multiple access system described in present embodiment based on the complementation of multipath fading channels, the signal acceptance method of user k is:

The N of step 4, receiving terminal _rindividual reception antenna receives the signal that transmitting terminal is launched, N _rfor being greater than the positive integer of zero, and N _tbe less than or equal to N _r, n-th _rindividual reception antenna receives n-th _tsignal after the superposition of individual transmission antennas transmit, and by N _r× 1 dimensional signal merges formation vector Y _t, n _r=1,2 ... N _r, vector Y _tsignal U is obtained after superposing with N _t, N is coding degree;

Step 5, the signal U that will obtain _tdata Replica becomes N _rindividual;

Step 6, by each signal U _tat f _mcarrier frequency carries out demodulation operation, and the signal after demodulation operation by obtaining two signal datas after low pass filter filtering is respectively and P _m,t;

Signal signal is obtained by channel estimator by described signal carry out pseudo-inverse operation, obtain signal signal P _m,tsample in time t, obtain signal R _m,t; By signal with signal R _m,tcarry out product, after product, obtain signal

Step 7, the signal that will obtain with carry out solution and stir operation, obtain solution stir after signal by N _rindividual solution stir after signal data superpose after obtain signal then carry out adjudicating rear output final signal B ^(k).

Embodiment four: present embodiment is further qualified the signal transmitting and receiving method that code division multiple access system is stirred in the complementation based on multipath fading channels described in embodiment three, in present embodiment, the detailed process of step 6 and step 7 is:

The detailed process of corresponding step 6 is: signal U _tat carrier wave f _mbe in time t from transmitting antenna n _tto reception antenna n _rchannel gain be

${\tilde{H}}_{n_t,n_r,m,t}^{\left(k\right)}=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\tilde{h}}_{n_t,n_r,m,t-l}^{\left(k\right)}=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{n_t,n_r,m,t}^{\left(k\right)}{e}^{i{\mathrm{\&theta;}}_{n_t,n_r,m,t}^{\left(k\right)}}{\mathrm{\&delta;}}_{t-l},---(4-1)$

Channel postpones distribution by L and forms, and time of delay, t+1 to t+L was formed continuously, parameter represent l path, l=0,1,2 ..., L-1, obtains:

${\tilde{h}}_{n_t,n_r,m,t-l}^{\left(k\right)}={\mathrm{\&beta;}}_{n_t,n_r,m,t}^{\left(k\right)}{e}^{i{\mathrm{\&theta;}}_{n_t,n_{r}m,t}^{\left(k\right)}}---(4-2)$

The overall attenuation factor depends on the complex Gaussian random variables of attenuation channel:

${\mathrm{\&beta;}}_{n_t,n_r,m,t}^{\left(k\right)}{e}^{i{\mathrm{\&theta;}}_{n_t,n_{r}m,t}^{\left(k\right)}}---(4-3)$

The phase place of signal is: ${\mathrm{\&theta;}}_{n_t,n_r,m,t}^{\left(k\right)}={\mathrm{\&zeta;}}_{n_t,n_r,m,t}^{\left(k\right)}-2\mathrm{\&pi;}{f}_{c}t$ And rayleigh distributed;

Multipath time of delay of time in units of a symbol of what l represented is time t; L represents the channel quantity of multipath fading, N _t=L≤N _r;

L is in units of the delay of a symbol time and a total L path, postpones expansion L and is less than N;

real part be then:

$H_{n_t,n_r,m,t}^{\left(k\right)}=\mathrm{Re}\left[{\tilde{H}}_{n_t,n_r,m,t}^{\left(k\right)}\right]=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{n_t,n_r,m,t}^{\left(k\right)}\cos \left({\mathrm{\&theta;}}_{n_t,n_r,m,t}^{\left(k\right)}\right){\mathrm{\&delta;}}_{n_t,n_r,m,t-l}$

Or $h_{n_t,n_r,m,t}^{\left(k\right)}=\mathrm{Re}\left[{\tilde{h}}_{n_t,n_r,m,t-l}^{\left(k\right)}\right]={\mathrm{\&beta;}}_{n_t,n_r,m,t}^{\left(k\right)}\cos \left({\mathrm{\&theta;}}_{n_t,n_r,m,t}^{\left(k\right)}\right){\mathrm{\&delta;}}_{t-l};---(4-4)$

The signal of user k is by transmitting antenna n _tlaunch, reception antenna n _rreceive, signal U _tby carrier wave f _mbe expressed as after demodulation after low pass filter be:

$p_{n_t,n_r,m,t}^{\left(k\right)}=H_{n_t,n_r,m,t}^{\left(k\right)}*t_{n_t,m,t}^{\left(k\right)}+n_{n_{r}m,t}^{\left(k\right)},$

The signal that user k' receives comprises the signal that all users launch:

$p_{n_t,n_r,m,t}=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}(H_{n_t,n_r,m,t}^{\left(k\right)}*t_{n_t,m,t}^{\left(k\right)}+n_{n_r,m,t}^{\left(k\right)}),---(4-6)$

Multiple transmit antennas model, reception antenna n _rwhat receive is the signal launched of each transmitting antenna and is:

$p_{n_r,m,t}=\underset{n_t=1}{\overset{N_t}{\mathrm{\&Sigma;}}}{p}_{n_t,n_r,m,t}=\underset{n_t=1}{\overset{N_t}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}(H_{n_t,n_r,m,t}^{\left(k\right)}*t_{n_t,m,t}^{\left(k\right)}+n_{n_r,m,t}^{\left(k\right)}),---(4-7)$

What perform is demodulation operation, obtains:

By

P _m,t=[p _1,m,tp _2,m,t ... p _Nr,m,t] ^T， (4-9)

Obtain signal phasor P _m,t:

obey independent Gaussian distribution and itself and also Gaussian distributed:

$\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{n}_{n_r,m,t}^{\left(k\right)}=n_{n_r},---(4-11)$

Channel matrix be divided into different path:

Above-mentionedly to obtain:

represent at carrier wave f _mthe impulse response square of the baseband equivalence channel on l path, signal phasor P _m,tbecome:

$\begin{array}{c}{P}_{m,t}=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\{H_{m,t}^{\left(k\right)}*\left[\begin{array}{c}{b}_t^{\left(k\right)}{c}_{1,m,t}^{\left(k\right)}\\ b_t^{\left(k\right)}{c}_{2,m,t}^{\left(k\right)}\\ .\\ .\\ .\\ b_t^{\left(k\right)}{c}_{N_t,m,t}^{\left(k\right)}\end{array}\right]\}+\left[\begin{array}{c}{n}_1\\ n_2\\ .\\ .\\ .\\ n_{N_r}\end{array}\right]\\ =\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\{H_{m,t}^{(k,0)}*\left[\begin{array}{c}{b}_t^{\left(k\right)}{c}_{1,m,t}^{\left(k\right)}\\ b_t^{\left(k\right)}{c}_{2,m,t}^{\left(k\right)}\\ .\\ .\\ .\\ b_t^{\left(k\right)}{c}_{N_t,m,t}^{\left(k\right)}\end{array}\right]+\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_{m,t}^{(k,l)}*\left[\begin{array}{c}{b}_t^{\left(k\right)}{c}_{1,m,t}^{\left(k\right)}\\ b_t^{\left(k\right)}{c}_{2,m,t}^{\left(k\right)}\\ .\\ .\\ .\\ b_t^{\left(k\right)}{c}_{N_t,m,t}^{\left(k\right)}\end{array}\right]\end{array},---(4-14)$

To P _m,tsample at time t':

$\begin{array}{c}{R}_{{m,t}^{\&prime;}}=\underset{t=-\&infin;}{\overset{\&infin;}{\&Integral;}}{P}_{m,t}{\mathrm{\&delta;}}_{t-t^{\&prime;}}\mathrm{dt}\\ =\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\{H_{m,t^{\&prime;}}^{(k,0)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_{m,t^{\&prime;}}^{(k,l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_{t.},m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]\}+\left[\begin{array}{c}{n}_1\\ n_2\\ .\\ .\\ .\\ n_{N_r}\end{array}\right]\end{array},---(4-15)$

Channel receiver is estimated at carrier wave f by the control signal receiving receiver known _mfor the impulse response matrix of the baseband equivalence channel of desired signal (l=0) on first path, matrix is:

Here l=0 represents first path of acknowledge(ment) signal:

$h_{n_t,n_r,m,t^{\&prime;}-l}^{\left(k\right)}={\mathrm{\&beta;}}_{n_t,n_r,m,t^{\&prime;}}^{\left(k\right)}{\mathrm{\&delta;}}_{n_t,n_r,m,t^{\&prime;}-l}^{\left(k\right)}\cos {\mathrm{\&theta;}}_{n_t,n_r,m,t^{\&prime;}}^{\left(k\right)},---(4-17)$

Channel estimator obtains gain and the phase data in Article 1 path, that is:

Launch data receive by user k', signal is broken down into:

$\begin{array}{c}{R}_{m,t^{\&prime;}}=H_{m,t^{\&prime;}}^{(k^{\&prime;},0)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]+\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]\\ +\underset{k\&NotEqual;k^{\&prime;}}{\overset{K}{\underset{k=1}{\mathrm{\&Sigma;}}}}\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_{m,t^{\&prime;}}^{(k,l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+\left[\begin{array}{c}{n}_1\\ n_2\\ .\\ .\\ .\\ n_{N_r}\end{array}\right]\end{array},---(4-19)$

The signal of different user will face identical channel, that is:

$H_{m,t^{\&prime;}}^{\left(\mathrm{1,0}\right)}=H_{m,t^{\&prime;}}^{\left(\mathrm{2,0}\right)}=...=H_{m,t^{\&prime;}}^{(K,0)}=H_{m,t^{\&prime;}}^{(k^{\&prime;},0)},---(4-20)$

Substituting into formula (4-19) abbreviation is:

$\begin{array}{c}{R}_{m,t^{\&prime;}}=H_{m,t^{\&prime;}}^{(k^{\&prime;},0)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]+\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]\\ +\underset{k\&NotEqual;k^{\&prime;}}{\overset{K}{\underset{k=1}{\mathrm{\&Sigma;}}}}\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_{m,t^{\&prime;}}^{(k,l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+\left[\begin{array}{c}{n}_1\\ n_2\\ .\\ .\\ .\\ n_{N_r}\end{array}\right]\end{array},---(4-21)$

Signal phasor R _m,t' and the N of user k' _t× N _rdimension pseudo inverse matrix is multiplied the signal being separated different antennae transmitting, N _t× N _rtie up pseudo-inverse channel-matrix for:

${\left({\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right)}^{+}={\left[{\left({\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{\left(k^{\&prime;,}0\right)}\right)}^H{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{-1}{\left({\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right)}^H,---(4-22)$

with signal R _m,tobtain after product:

$\begin{array}{c}{\tilde{R}}_{m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}={\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{R}_{m,t^{\&prime;}}\\ ={\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]+\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]\\ +\underset{k\&NotEqual;k^{\&prime;}}{\overset{K}{\underset{k=1}{\mathrm{\&Sigma;}}}}{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+\underset{k\&NotEqual;k^{\&prime;}}{\overset{K}{\underset{k=1}{\mathrm{\&Sigma;}}}}\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{\left(k^{\&prime;,}l\right)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}\left[\begin{array}{c}{n}_1\\ n_2\\ .\\ .\\ .\\ n_{N_r}\end{array}\right]\end{array},---(4-23)$

Above formula is reduced to:

$\begin{array}{c}{\tilde{R}}_{m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}=\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]+\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]\\ +\underset{k\&NotEqual;k^{\&prime;}}{\overset{K}{\underset{k=1}{\mathrm{\&Sigma;}}}}\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+\underset{k\&NotEqual;k^{\&prime;}}{\overset{K}{\underset{k=1}{\mathrm{\&Sigma;}}}}\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}\left[\begin{array}{c}{n}_1\\ n_2\\ .\\ .\\ .\\ n_{N_r}\end{array}\right]\end{array},---(4-24)$

Embodiment five: present embodiment stirs the signal acceptance method of code division multiple access system to the complementation based on multipath fading channels described in embodiment three, and in present embodiment, the detailed process of corresponding step 7 is:

The solution process of stirring is:

Signal the input signal separating stirring operation, and signal will by relevant coding separate and stir, for:

$C_{m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}=[c_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)},c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)},...,c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}],---(4-25)$

with coding $C_{m,t}^{\left(k^{\&prime;}\right)}={[c_{1,m,t}^{\left(k^{\&prime;}\right)},c_{2,m,t}^{\left(k^{\&prime;}\right)},...,c_{N_t,m,t}^{\left(k^{\&prime;}\right)}]}_{1\&times;N_t}$ In corresponding element solution stir formed output signal $s_{m,t}^{\left(k^{\&prime;}\right)}=C_{m,t}^{\left(k^{\&prime;}\right)}\&times;{\tilde{R}}_{m,t}^{\left(k^{\&prime;}\right)},$

$\begin{array}{c}\underset{k\&NotEqual;k^{\&prime;}}{\overset{K}{\underset{k=1}{\mathrm{\&Sigma;}}}}{\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]}^T\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]=\underset{k\&NotEqual;k^{\&prime;}}{\overset{K}{\underset{k=1}{\mathrm{\&Sigma;}}}}{b}_{t^{\&prime;}}^{\left(k\right)}{\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]}^T\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]\\ =\underset{k\&NotEqual;k^{\&prime;}}{\overset{K}{\underset{k=1}{\mathrm{\&Sigma;}}}}{b}_{t^{\&prime;}}^{\left(k\right)}\left[\begin{array}{cccc}{d}_{m,k^{\&prime;}}{a}_{1,t^{\&prime;}}& d_{m,k^{\&prime;}}{a}_{2,t^{\&prime;}}& ...& d_{m,k^{\&prime;}}\end{array},a_{N_t,t^{\&prime;}}\right]\left[\begin{array}{c}{d}_{m,k^{\&prime;}}{a}_{1,t^{\&prime;}}\\ d_{m,k^{\&prime;}}{a}_{2,t^{\&prime;}}\\ .\\ .\\ .\\ d_{m,k^{\&prime;}}{a}_{N_t,t^{\&prime;}}\end{array}\right]\\ =\underset{k\&NotEqual;k^{\&prime;}}{\overset{K}{\underset{k=1}{\mathrm{\&Sigma;}}}}{N}_t{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{d}_{m,k^{\&prime;}}{d}_{m,k}\end{array},---(4-26)$

According to formula (4-26) relation, separate stirring operation and draw:

Merging, judging process are:

Combined signal all carrier waves after obtain judgment variables

Orthogonality according to the vector of matrix D draws:

$\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{d}_{m,k^{\&prime;}}{d}_{m,k}=0,---(4-29)$

Judgement vector becomes:

Finally obtain signal

According to multi-user interference equation is turned to four parts and the energy of every bit transmission signal is E _b, Part I is desired signal, and desired signal is:

$g_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}={\mathrm{MN}}_t{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}={\mathrm{MN}}_t\sqrt{\frac{E_b}{{\mathrm{MN}}_t}}=\sqrt{{\mathrm{MN}}_t{E}_b},---(4-31)$

The average of desired signal is:

${\mathrm{\&mu;}}_g=E\left[g_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}\right]=\sqrt{{\mathrm{MN}}_t{E}_b},---(4-32)$

Desired signal is a constant, show that variance is zero, that is:

${\mathrm{\&delta;}}_g^{\left(k^{\&prime;}\right)}=0,---(4-33)$

Part II is multi-path jamming part, and multi-path jamming part is:

$I_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]}^T{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right],---(4-34)$

Average is:

${\mathrm{\&mu;}}_I^{\left(k\right)}=E\left[I_t^{\left(k\right)}\right]=0,---(4-35)$

Variance is:

$\begin{array}{c}{\left({\mathrm{\&delta;}}_I^{\left(k\right)}\right)}^2=\mathrm{var}\left[I_t^{\left(k\right)}\right|h_{i,n_r,m,t}^{\left(k\right)},{\mathrm{\&beta;}}_{n_t,n_r,m,l}^{\left(k\right)}]\\ =\frac{E_b}{2M{N}_t}\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}\underset{n_t=1}{\overset{N_t}{\mathrm{\&Sigma;}}}\underset{n_r=1}{\overset{N_r}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{N_t}{\mathrm{\&Sigma;}}}{\left(h_{i,n_r,m,t}^{\left(k\right)}\right)}^2{\left({\mathrm{\&beta;}}_{n_t,n_r,m,l}^{\left(k\right)}\right)}^2\end{array},---(4-36)$

Part III is the multi-access inference that multi-user causes, that is:

$J_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{k\&NotEqual;k^{\&prime;}}{\overset{K}{\underset{k=1}{\mathrm{\&Sigma;}}}}\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]}^T{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right],---(4-37)$

Average is:

${\mathrm{\&mu;}}_J^{\left(k\right)}=E\left[J_t^{\left(k\right)}\right]=0,---(4-38)$

Variance is:

$J_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{k\&NotEqual;k^{\&prime;}}{\overset{K}{\underset{k=1}{\mathrm{\&Sigma;}}}}\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]}^T{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ .\\ .\\ .\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right],---(4-39)$

Last part is noise, that is:

${\mathrm{\&eta;}}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ .\\ .\\ .\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}\left[\begin{array}{c}{n}_1\\ n_2\\ .\\ .\\ .\\ n_{N_r}\end{array}\right],---(4-40)$

Average is:

${\mathrm{\&mu;}}_{\mathrm{\&eta;}}^{\left(k\right)}=0,---(4-41)$

Variance is:

${\left({\mathrm{\&delta;}}_{\mathrm{\&eta;}}^{\left(k\right)}\right)}^2=\frac{N_0}{2}\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{n_t=1}{\overset{N_t}{\mathrm{\&Sigma;}}}\underset{n_r=1}{\overset{N_r}{\mathrm{\&Sigma;}}}{\left(h_{n_t,n_r,m,t}^{\left(k\right)}\right)}^2,---(4-42)$

The error rate is:

$P_b\left(x\right)=Q\left(\frac{\sqrt{{\mathrm{MN}}_t{E}_b}}{\sqrt{{\left({\mathrm{\&delta;}}_I^{\left(k\right)}\right)}^2+{\left({\mathrm{\&delta;}}_J^{\left(k\right)}\right)}^2+{\left({\mathrm{\&delta;}}_{\mathrm{\&eta;}}^{\left(k\right)}\right)}^2}}\right),----(4-43)$

The data obtained substitute into formula (4-43) and obtain:

E _bfor by N _tthe energy of a mark signal of individual transmitting antenna and M carrier wave transmission.

Claims (3)

1., based on the signal transmitting method of the complementation stirring code division multiple access system of multipath fading channels, it is characterized in that:

Described launching technique is:

Step one, by signal B to be sent ^(k)data Replica becomes N _tindividual, N _tfor being greater than the positive integer of zero, k=1,2 ... K;

Step 2, by each signal B ^(k)data are copied into M signal again, M be greater than zero positive integer;

By n-th _tm signal in M the signal that individual signal is corresponding and coding carry out stirring operation, obtain signal n _t=1,2 ... N _t, m is the positive integer being greater than zero and being less than M;

Step 3, to be outputed signal in step 2 with carry out product, after product, obtain signal by n-th _tby n-th after M the modulation signal that individual signal is corresponding superposes _tindividual transmission antennas transmit,

The method of stirring operation in step 2:

Initial transmit for $B^{\left(k\right)}=[b_1^{\left(k\right)},b_2^{\left(k\right)},\&CenterDot;\&CenterDot;\&CenterDot;,b_N^{\left(k\right)}],---(2-1)$

$b_t^{\left(k\right)}=b^{\left(k\right)}{p}_t,---(2-2)$

B ^(k)∈-1 ,+1} and

Coding

Signal $B^{\left(k\right)}={[b_1^{\left(k\right)},b_2^{\left(k\right)},\&CenterDot;\&CenterDot;\&CenterDot;,b_N^{\left(k\right)}]}_{1\&times;N}$ With coding $C_{n_t,m}^{\left(k\right)}={[c_{n_t,m,1}^{\left(k\right)},c_{n_t,m,2}^{\left(k\right)},\&CenterDot;\&CenterDot;\&CenterDot;,c_{n_t,m,N}^{\left(k\right)}]}_{1\&times;N}$ In corresponding element stir formed output signal e _bfor by N _tthe energy of a mark signal of individual transmitting antenna and M carrier wave transmission.

2., based on the signal acceptance method of the complementation stirring code division multiple access system of multipath fading channels, it is characterized in that:

The signal acceptance method of user k is:

The N of step 4, receiving terminal _rindividual reception antenna receives the signal that transmitting terminal is launched, N _rfor being greater than the positive integer of zero, and N _tbe less than or equal to N _r, n-th _rindividual reception antenna receives n-th _tsignal after the superposition of individual transmission antennas transmit, and by N _r× 1 dimensional signal merges formation vector Y _t, n _r=1,2 ... N _r, vector Y _tsignal U is obtained after superposing with N _t, N is coding degree;

Step 5, the signal U that will obtain _tdata Replica becomes N _rindividual;

Step 6, by each signal U _tat f _mcarrier frequency carries out demodulation operation, and the signal after demodulation operation by obtaining two signal datas after low pass filter filtering is respectively and P _m,t;

Signal signal is obtained by channel estimator by described signal carry out pseudo-inverse operation, obtain signal signal P _m,tsample in time t, obtain signal R _m,t; By signal with signal R _m,tcarry out product, after product, obtain signal

Step 7, the signal that will obtain with carry out solution and stir operation, obtain solution stir after signal by N _rindividual solution stir after signal data superpose after obtain signal then carry out adjudicating rear output final signal B ^(k),

The detailed process of corresponding step 7 is:

The solution process of stirring is:

Signal the input signal separating stirring operation, and signal will by relevant coding separate and stir, for:

$C_{m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}=[c_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)},c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)},\&CenterDot;\&CenterDot;\&CenterDot;,c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}],---(4-25)$

with coding $C_{m,t}^{\left(k^{\&prime;}\right)}={[c_{1,m,t}^{\left(k^{\&prime;}\right)},c_{2,m,t}^{\left(k^{\&prime;}\right)},\&CenterDot;\&CenterDot;\&CenterDot;,c_{N_t,m,t}^{\left(k^{\&prime;}\right)}]}_{1\&times;N_t}$ In corresponding element solution stir formed output signal $s_{m,t}^{\left(k^{\&prime;}\right)}=C_{m,t}^{\left(k^{\&prime;}\right)}\&times;{\tilde{R}}_{m,t}^{\left(k^{\&prime;}\right)},$

$\begin{array}{c}\underset{\underset{k\&NotEqual;k^{\&prime;}}{k=1}}{\overset{K}{\mathrm{\&Sigma;}}}{\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]}^T\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^k{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]=\underset{\underset{k\&NotEqual;k^{\&prime;}}{k=1}}{\overset{K}{\mathrm{\&Sigma;}}}{b}_{t^{\&prime;}}^{\left(k\right)}{\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]}^T\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]\\ =\underset{\underset{k\&NotEqual;k^{\&prime;}}{k=1}}{\overset{K}{\mathrm{\&Sigma;}}}{b}_{t^{\&prime;}}^{\left(k\right)}\left[\begin{array}{cccc}{d}_{m,k^{\&prime;}}{a}_{1,t^{\&prime;}}& d_{m,k^{\&prime;}}{a}_{2,t^{\&prime;}}& \&CenterDot;\&CenterDot;\&CenterDot;& d_{m,k^{\&prime;}}{a}_{N_t,t^{\&prime;}}\end{array}\right]\left[\begin{array}{c}{d}_{m,k^{\&prime;}}{a}_{1,t^{\&prime;}}\\ d_{m,k^{\&prime;}}{a}_{2,t^{\&prime;}}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ d_{m,k^{\&prime;}}{a}_{N_t,t^{\&prime;}}\end{array}\right]\\ =\underset{\underset{k\&NotEqual;k^{\&prime;}}{k=1}}{\overset{K}{\mathrm{\&Sigma;}}}{N}_t{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{d}_{m,k^{\&prime;}}{d}_{m,k}\end{array},---(4-26)$

According to formula (4-26) relation, separate stirring operation and draw:

Merging, judging process are:

Combined signal all carrier waves after obtain judgment variables

Orthogonality according to the vector of matrix D draws:

$\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{d}_{m,k^{\&prime;}}{d}_{m,k}=0,---(4-29)$

Judgement vector becomes:

Finally obtain signal

According to multi-user interference equation is turned to four parts, Part I is desired signal, and desired signal is:

$g_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}=M{N}_t{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}=M{N}_t\sqrt{\frac{E_b}{{\mathrm{MN}}_t}}=\sqrt{{\mathrm{MN}}_t{E}_b},---(4-31)$

The average of desired signal is:

${\mathrm{\&mu;}}_g=E\left[g_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}\right]=\sqrt{{\mathrm{MN}}_t{E}_b},---(4-32)$

Desired signal is a constant, show that variance is zero, that is:

${\mathrm{\&delta;}}_g^{\left(k^{\&prime;}\right)}=0,---(4-33)$

Part II is multi-path jamming part, and multi-path jamming part is:

$I_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]}^T{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right],---(4-34)$

Average is:

${\mathrm{\&mu;}}_I^{\left(k\right)}=E\left[I_t^{\left(k\right)}\right]=0,---(4-35)$

Variance is:

$\begin{array}{c}{\left({\mathrm{\&delta;}}_I^{\left(k\right)}\right)}^2=\mathrm{var}\left[I_t^{\left(k\right)}\right|h_{i,n_r,m,t}^{\left(k\right)},{\mathrm{\&beta;}}_{n_t,n_r,m,l}^{\left(k\right)}]\\ =\frac{E_b}{2{\mathrm{MN}}_t}\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}\underset{n_t=1}{\overset{N_t}{\mathrm{\&Sigma;}}}\underset{n_r=1}{\overset{N_r}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{N_t}{\mathrm{\&Sigma;}}}{\left(h_{i,n_r,m,t}^{\left(k\right)}\right)}^2{\left({\mathrm{\&beta;}}_{n_t,n_r,m,l}^{\left(k\right)}\right)}^2\end{array},---(4-36)$

Part III is the multi-access inference that multi-user causes, that is:

$J_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{\underset{k\&NotEqual;k^{\&prime;}}{k=1}}{\overset{K}{\mathrm{\&Sigma;}}}\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]}^T{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right],---(4-37)$

Average is:

${\mathrm{\&mu;}}_J^{\left(k\right)}=E\left[J_t^{\left(k\right)}\right]=0,---(4-38)$

Variance is:

$J_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{\underset{k\&NotEqual;k^{\&prime;}}{k=1}}{\overset{K}{\mathrm{\&Sigma;}}}\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]}^T{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right],---(4-39)$

Last part is noise, that is:

${\mathrm{\&eta;}}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\left[\begin{array}{c}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ c_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ c_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}\left[\begin{array}{c}{n}_1\\ n_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ n_{N_r}\end{array}\right],---(4-40)$

Average is:

${\mathrm{\&mu;}}_{\mathrm{\&eta;}}^{\left(k\right)}=0,---(4-41)$

Variance is:

${\left({\mathrm{\&delta;}}_{\mathrm{\&eta;}}^{\left(k\right)}\right)}^2=\frac{N_0}{2}\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{n_t=1}{\overset{N_t}{\mathrm{\&Sigma;}}}\underset{n_r=1}{\overset{N_r}{\mathrm{\&Sigma;}}}{\left(h_{n_t,n_r,m,t}^{\left(k\right)}\right)}^2,---(4-42)$

The error rate is:

$P_b\left(x\right)=Q\left(\frac{\sqrt{{\mathrm{MN}}_t{E}_b}}{\sqrt{{\left({\mathrm{\&delta;}}_I^{\left(k\right)}\right)}^2+{\left({\mathrm{\&delta;}}_J^{\left(k\right)}\right)}^2+{\left({\mathrm{\&delta;}}_{\mathrm{\&eta;}}^{\left(k\right)}\right)}^2}}\right),---(4-43)$

The data obtained substitute into formula (4-43) and obtain:

E _bfor by N _tthe energy of a mark signal of individual transmitting antenna and M carrier wave transmission.

3. the signal acceptance method of code division multiple access system is stirred in the complementation based on multipath fading channels according to claim 2, it is characterized in that: the detailed process of step 6 is:

The detailed process of corresponding step 6 is: signal U _tat carrier wave f _mbe in time t from transmitting antenna n _tto reception antenna n _rchannel gain be

${\tilde{H}}_{n_t,n_r,m,t}^{\left(k\right)}=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\tilde{h}}_{n_t,n_r,m,t-l}^{\left(k\right)}=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{n_t,n_r,m,t}^{\left(k\right)}{e}^{i{\mathrm{\&theta;}}_{n_t,n_r,m,t}^{\left(k\right)}}{\mathrm{\&delta;}}_{t-l},---(4-1)$

Channel postpones distribution by L and forms, and time of delay, t+1 to t+L was formed continuously, parameter represent l path, l=0,1,2 ..., L-1, obtains:

${\tilde{h}}_{n_t,n_r,m,t-l}^{\left(k\right)}={\mathrm{\&beta;}}_{n_t,n_r,m,t}^{\left(k\right)}{e}^{i{\mathrm{\&theta;}}_{n_t,n_r,m,t}^{\left(k\right)}}---(4-2)$

The overall attenuation factor depends on the complex Gaussian random variables of attenuation channel:

${\mathrm{\&beta;}}_{n_t,n_r,m,t}^{\left(k\right)}{e}^{i{\mathrm{\&theta;}}_{n_t,n_r,m,t}^{\left(k\right)}}---(4-3)$

The phase place of signal is: and rayleigh distributed;

Multipath time of delay of time in units of a symbol of what l represented is time t; L represents the channel quantity of multipath fading, N _t=L≤N _r;

L is in units of the delay of a symbol time and a total L path, postpones expansion L and is less than N;

real part be then:

$H_{n_t,n_r,m,t}^{\left(k\right)}=\mathrm{Re}\left[{\tilde{H}}_{n_t,n_r,m,t}^{\left(k\right)}\right]=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_{n_t,n_r,m,t}^{\left(k\right)}\cos \left({\mathrm{\&theta;}}_{n_t,n_r,m,t}^{\left(k\right)}\right){\mathrm{\&delta;}}_{n_t,n_r,m,t-l}$

Or $h_{n_t,n_r,m,t-l}^{\left(k\right)}=\mathrm{Re}\left[{\tilde{h}}_{n_t,n_r,m,t-l}^{\left(k\right)}\right]={\mathrm{\&beta;}}_{n_t,n_r,m,t}^{\left(k\right)}\cos \left({\mathrm{\&theta;}}_{n_t,n_r,m,t}^{\left(k\right)}\right){\mathrm{\&delta;}}_{t-l};---(4-4)$

The signal of user k is by transmitting antenna n _tlaunch, reception antenna n _rreceive, signal U _tby carrier wave f _mbe expressed as after demodulation after low pass filter be:

$p_{n_t,n_r,m,t}^{\left(k\right)}=H_{n_t,n_r,m,t}^{\left(k\right)}*t_{n_t,m,t}^{\left(k\right)}+n_{n_r,m,t}^{\left(k\right)},---(4-5)$

The signal that user k' receives comprises the signal that all users launch:

$p_{n_t,n_r,m,t}=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}(H_{n_t,n_r,m,t}^{\left(k\right)}*t_{n_t,m,t}^{\left(k\right)}+n_{n_r,m,t}^{\left(k\right)}),---(4-6)$

Multiple transmit antennas model, reception antenna n _rwhat receive is the signal launched of each transmitting antenna and is:

$p_{n_r,m,t}=\underset{n_t=1}{\overset{N_t}{\mathrm{\&Sigma;}}}{p}_{n_t,n_r,m,t}=\underset{n_t=1}{\overset{N_t}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}(H_{n_t,n_r,m,t}^{\left(k\right)}*t_{n_t,m,t}^{\left(k\right)}+n_{n_r,m,t}^k),---(4-7)$

What perform is demodulation operation, obtains:

By

$P_{m,t}={\left[\begin{array}{cccc}{p}_{1,m,t}& p_{2,m,t}& \&CenterDot;\&CenterDot;\&CenterDot;& p_{N_r,m,t}\end{array}\right]}^T,---(4-9)$

Obtain signal phasor P _m,t:

obey independent Gaussian distribution and itself and also Gaussian distributed:

$\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{n}_{n_r,m,t}^{\left(k\right)}=n_{n_r},---(4-11)$

Channel matrix be divided into different path:

Obtain:

represent at carrier wave f _mthe impulse response square of the baseband equivalence channel on l path, signal phasor P _m,tbecome:

$\begin{array}{c}{P}_{m,t}=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\{H_{m,t}^{\left(k\right)}*\left[\begin{array}{c}{b}_t^{\left(k\right)}{c}_{1,m,t}^{\left(k\right)}\\ b_t^{\left(k\right)}{c}_{2,m,t}^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_t^{\left(k\right)}{c}_{N_t,m,t}^{\left(k\right)}\end{array}\right]\}+\left[\begin{array}{c}{n}_1\\ n_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ n_{N_r}\end{array}\right]\\ =\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\{H_{m,t}^{(k,0)}*\left[\begin{array}{c}{b}_t^{\left(k\right)}{c}_{1,m,t}^{\left(k\right)}\\ b_t^{\left(k\right)}{c}_{2,m,t}^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_t^{\left(k\right)}{c}_{N_t,m,t}^{\left(k\right)}\end{array}\right]+\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_{m,t}^{(k,l)}*\left[\begin{array}{c}{b}_t^{\left(k\right)}{c}_{1,m,t}^{\left(k\right)}\\ b_t^{\left(k\right)}{c}_{2,m,t}^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_t^{\left(k\right)}{c}_{N_t,m,t}^{\left(k\right)}\end{array}\right]\}+\left[\begin{array}{c}{n}_1\\ n_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ n_{N_r}\end{array}\right]\end{array},---(4-14)$

To P _m,tsample at time t':

$\begin{array}{c}{R}_{m,t^{\&prime;}}=\underset{t=-\&infin;}{\overset{\&infin;}{\&Integral;}}{P}_{m,t}{\mathrm{\&delta;}}_{t-t^{\&prime;}}\mathrm{dt}\\ =\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\{H_{m,t^{\&prime;}}^{(k,0)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^k{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_{m,t^{\&prime;}}^{(k,l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]\}+\left[\begin{array}{c}{n}_1\\ n_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ n_{N_r}\end{array}\right]\end{array},---(4-15)$

Channel receiver is estimated at carrier wave f by the control signal receiving receiver known _mfor the impulse response matrix of the baseband equivalence channel of desired signal (l=0) on first path, matrix is:

Here l=0 represents first path of acknowledge(ment) signal:

$h_{n_t,n_r,m,t^{\&prime;}-l}^{\left(k\right)}={\mathrm{\&beta;}}_{n_t,n_r,m,t^{\&prime;}}^{\left(k\right)}{\mathrm{\&delta;}}_{n_t,n_r,m,t^{\&prime;}-l}^{\left(k\right)}\cos {\mathrm{\&theta;}}_{n_t,n_r,m,t^{\&prime;}}^{\left(k\right)},---(4-17)$

Channel estimator obtains gain and the phase data in Article 1 path, that is:

Launch data receive by user k', signal is broken down into:

$\begin{array}{c}{R}_{m,t^{\&prime;}}=H_{m,t^{\&prime;}}^{(k^{\&prime;},0)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]+\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]\\ +\underset{\underset{k\&NotEqual;k^{\&prime;}}{k=1}}{\overset{K}{\mathrm{\&Sigma;}}}\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_{m,t^{\&prime;}}^{(k,l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+\left[\begin{array}{c}{n}_1\\ n_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ n_{N_r}\end{array}\right]\end{array},---(4-19)$

The signal of different user will face identical channel, that is:

$H_{m,t^{\&prime;}}^{\left(\mathrm{1,0}\right)}=H_{m,t^{\&prime;}}^{\left(\mathrm{2,0}\right)}=\&CenterDot;\&CenterDot;\&CenterDot;=H_{m,t^{\&prime;}}^{(K,0)}=H_{m,t^{\&prime;}}^{(k^{\&prime;},0)},---(4-20)$

Substituting into formula (4-19) abbreviation is:

$\begin{array}{c}{R}_{m,t^{\&prime;}}=H_{m,t^{\&prime;}}^{(k^{\&prime;},0)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]+\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]\\ +\underset{\underset{k\&NotEqual;k^{\&prime;}}{k=1}}{\overset{K}{\mathrm{\&Sigma;}}}\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{H}_{m,t^{\&prime;}}^{(k,l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+\left[\begin{array}{c}{n}_1\\ n_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ n_{N_r}\end{array}\right]\end{array},---(4-21)$

Signal phasor R _{m, t'}with the N of user k' _t× N _rdimension pseudo inverse matrix is multiplied the signal being separated different antennae transmitting, N _t× N _rtie up pseudo-inverse channel-matrix for:

${\left({\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right)}^{+}={\left[{\left({\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right)}^H{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{-1}{\left({\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right)}^H,---(4-22)$

with signal R _m,tobtain after product:

$\begin{array}{c}{\tilde{R}}_{m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}={\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{R}_{m,t^{\&prime;}}\\ ={\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]+\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]\\ +\underset{\underset{k\&NotEqual;k^{\&prime;}}{k=1}}{\overset{K}{\mathrm{\&Sigma;}}}{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+\underset{\underset{k\&NotEqual;k^{\&prime;}}{k=1}}{\overset{K}{\mathrm{\&Sigma;}}}\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}\left[\begin{array}{c}{n}_1\\ n_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ n_{N_r}\end{array}\right]\end{array},---(4-23)$

Above formula is reduced to:

$\begin{array}{c}{\tilde{R}}_{m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}=\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]+\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{1,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{2,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k^{\&prime;}\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k^{\&prime;}\right)}\end{array}\right]\\ +\underset{\underset{k\&NotEqual;k^{\&prime;}}{k=1}}{\overset{K}{\mathrm{\&Sigma;}}}\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+\underset{\underset{k\&NotEqual;k^{\&prime;}}{k=1}}{\overset{K}{\mathrm{\&Sigma;}}}\underset{l=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}{H}_{m,t^{\&prime;}}^{(k^{\&prime;},l)}*\left[\begin{array}{c}{b}_{t^{\&prime;}}^{\left(k\right)}{c}_{1,m,t^{\&prime;}}^{\left(k\right)}\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{2,m,t^{\&prime;}}^{\left(k\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ b_{t^{\&prime;}}^{\left(k\right)}{c}_{N_t,m,t^{\&prime;}}^{\left(k\right)}\end{array}\right]+{\left[{\stackrel{\&OverBar;}{H}}_{m,t^{\&prime;}}^{(k^{\&prime;},0)}\right]}^{+}\left[\begin{array}{c}{n}_1\\ n_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ n_{N_r}\end{array}\right]\end{array},---(4-24).$