CN103781167A - Downlink multi-user energy-efficiency beam forming method based on duality property - Google Patents

Abstract

The invention discloses a beam forming method with energy efficiency optimization considered under a broadcast multi-antenna channel. The optimization goal of the method is maximization of the data transmission rate under constraint of given power and the signal interference noise ratio. Firstly, duality property of traditional uplink and downlink transmission is led into energy-efficiency optimization, a corresponding energy-efficiency optimization goal function is set, and a virtual uplink problem dual to downlink transmission is led in; then, the virtual uplink transmission problem is correspondingly converted to obtain a solvable GP optimization problem, the corresponding uplink optimization result is converted into a solve of an original downlink transmission problem after optimization, and accordingly a downlink multi-user energy-efficiency transmission problem is solved. Compared with an existing beam forming method with the energy efficiency considered, the method is low in computation complexity and easy to carry out, and can obtain higher energy efficiency than a traditional minimized transmitting power algorithm.

Description

Descending multi-user efficiency beam-forming method based on duality

Technical field

The invention belongs to wireless communication technology field, be specifically related to a kind of downlink wave beam manufacturing process of the maximum chemical combination speed of utilizing up-downgoing Dual properties under power constraint of considering efficiency.

Background technology

Along with the development of the communication technology and equipment, the data volume of wirelessly transmitting data increases severely, the remarkable increase that has also caused corresponding energy to consume.In the past, multi-antenna transmission had obtained utilizing widely as a kind of method that effectively improves system spectral efficiency, and the extensive antenna thereupon deriving can improve the efficiency of system.Efficiency is generally defined as the ratio of system and speed and total power loss, and recently, in descending multi-user multiaerial system, utilizing community beam forming and Poewr control method to suppress to solve efficiency problem becomes a large study hotspot of wireless communication field.Efficiency problem under power constraint is a non-protruding problem, solve more difficult, the at present design of beam forming and power distribution method mainly concentrates on by iteration and gets the methods such as boundary and changes into and be easy to accordingly the protruding problem that solves, does not consider the Dual properties of up-downgoing.For this reason, the multi-user beam-forming method under a kind of base station power constraints that the present invention is based on duality theory principle design.

Summary of the invention

Based on the problems referred to above, the invention provides a kind of computation complexity lower, the beam-forming method based on up-downgoing duality under the power constraint that effectively improves system energy efficiency.

For solving the problems of the technologies described above, the technical solution used in the present invention is: a kind of descending multi-user efficiency beam-forming method based on duality, and the method comprises the following steps:

1). initialization downlink transmission power p ⁽ⁿ⁾with beam vector W ⁽ⁿ⁾, guarantee to meet the constraint of Signal to Interference plus Noise Ratio and power.Then by downlink transmission power p ⁽ⁿ⁾with beam vector W ⁽ⁿ⁾calculate Signal to Interference plus Noise Ratio now

by the virtual up Signal to Interference plus Noise Ratio calculating

calculate respectively approximation parameters

with

virtual uplink transmit power q is now set ⁽ⁿ⁾=0, and initialization target function now ${\stackrel{\←}{g}}^{\left(n\right)}=0;$

it is the value of target function after the n time iteration; K is the quantity of base station; K is Customs Assigned Number;

N is algorithm iteration number of times, and initial value is 0;

W ⁽ⁿ⁾for

for the beam vector of base station to user k;

P ⁽ⁿ⁾for

for the transmitting power of base station to user k;

Q ⁽ⁿ⁾for

for the virtual ascending power of user k to base station;

for

for the virtual up Signal to Interference plus Noise Ratio of user k;

for

for the approximate auxiliary variable of speed of user k;

for

for the approximate auxiliary variable of speed of user k;

H _kfor base station is to the channel parameter between user k; σ is system thermal noise;

Wherein utilize p ⁽ⁿ⁾and W ⁽ⁿ⁾the computational methods that obtain Signal to Interference plus Noise Ratio are as follows:

${\widetilde{\mathrm{\γ}}}_k^{\left(n\right)}=\frac{p_k^{\left(n\right)}{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_k^{\left(n\right)}\left|\right|}^2}{\underset{m=1,m\≠k}{\overset{K}{\mathrm{\Σ}}}{p}_m^{\left(n\right)}{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_m^{\left(n\right)}\left|\right|}^2+1};{\stackrel{\‾}{h}}_k=\frac{h_k}{\mathrm{\σ}}$

Utilize calculate respectively approximation parameters

with

method as follows:

Wherein θ represents user rate weight.

2). make n=n+1, solve following GP optimization problem:

$s.t.{\stackrel{\←}{\mathrm{\γ}}}_k\≥{\widetilde{\mathrm{\γ}}}_k,{\stackrel{\←}{\mathrm{\γ}}}_k\≥{\mathrm{\γ}}_k,\∀k,\underset{m=1}{\overset{K}{\mathrm{\Σ}}}{q}_k\≤\mathrm{\αP},0\≤\mathrm{\α}\≤1.$

Wherein

what represent is the loss of base station power amplification, P _cwhat represent is the permanent circuit loss of every antenna, P ₀what represent is the fixed loss irrelevant with antenna, and what M represented is the quantity of antenna for base station, and P is transmission power limit.By solving above optimization problem, obtain virtual uplink transmit power q ⁽ⁿ⁾.

3). utilize the virtual uplink transmit power q after optimizing ⁽ⁿ⁾calculate corresponding beam vector W ⁽ⁿ⁾, computational methods are as follows:

$w_k=\frac{{(\underset{m=1}{\overset{K}{\mathrm{\Σ}}}{q}_m{\stackrel{\‾}{h}}_m{\stackrel{\‾}{h}}_m^H+1)}^{-1}{\stackrel{\‾}{h}}_k}{\left|\right|{(\underset{m=1}{\overset{K}{\mathrm{\Σ}}}{q}_m{\stackrel{\‾}{h}}_m{\stackrel{\‾}{h}}_m^H+1)}^{-1}{\stackrel{\‾}{h}}_k\left|\right|},\∀k$

If carry out step 4),

shown in being defined as follows:

If do not met, utilize the q after upgrading ⁽ⁿ⁾and W ⁽ⁿ⁾the virtual up Signal to Interference plus Noise Ratio that calculating makes new advances computational methods are as follows:

${\widetilde{\mathrm{\γ}}}_k^{\left(n\right)}=\frac{q_k^{\left(n\right)}{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_k^{\left(n\right)}\left|\right|}^2}{\underset{m=1,m\≠k}{\overset{K}{\mathrm{\Σ}}}{q}_m^{\left(n\right)}{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_m^{\left(n\right)}\left|\right|}^2+1};{\stackrel{\‾}{h}}_k=\frac{h_k}{\mathrm{\σ}}$

By upgrade after the approximation parameters that calculating makes new advances with

update method is identical with step 1), then returns to step 2), ζ is predefined required precision.

4). up optimum results is converted into descending, equates to obtain descending through-put power p according to the Signal to Interference plus Noise Ratio of up-downgoing ⁽ⁿ⁾.

The object of the inventive method application is single base stations and multiuser communication system, comprises K user, and there is M transmit antennas base station.

Adopt the beneficial effect after technique scheme to be, the inventive method is compared with minimum power algorithm in the past, and computation complexity is low, and arithmetic speed is fast, and the efficiency obtaining is higher.

Accompanying drawing explanation

Fig. 1 is the system model of the inventive method;

Fig. 2 is single base station power constraint multipoint coordinated beam forming and power distribution method flow chart;

Fig. 3 is the performance efficiency of algorithms of different;

Reference numeral:

1-base station, 2-user, 3-communication link

Embodiment

The concrete theoretical foundation explanation of technical scheme of the present invention:

Technical solution of the present invention is the multi-user downlink system for power constraint, and as shown in Figure 1, what Fig. 1 represented is the downlink communication network configuration of system to the concrete network configuration of this algorithm.In Fig. 1,1 represents base station, and 2 represent user, and 3 represent communication link.

As shown in Figure 1, in the communication system of this algorithm, comprise single base station, and multiple users are served in this base station, link between different base station and user is considered as disturbing, and corresponding base station power will be distributed on the corresponding communication link of each user, send to all users' the namely transmitting power of base station of signal power sum, meet corresponding constraint.Single base stations and multiuser communication system shown in Fig. 1 is the communication scenes that this algorithm is considered, comprises K user at corresponding communication network, and there is M transmit antennas base station.

Whole algorithm turns to optimization aim with Optimization Solution system and efficiency maximum, and the expression formula of definition efficiency is as follows:

（1）

the speed that represents user k, its unit is bps/hertz;

for the descending Signal to Interference plus Noise Ratio of user k, θ _krepresent user rate weight.K is the quantity of base station, and k is Customs Assigned Number, wherein

what represent is the loss of base station power amplification, P _cwhat represent is the permanent circuit loss of every antenna, and what P0 represented is the fixed loss irrelevant with antenna, and what M represented is the quantity of antenna for base station.

Descending Signal to Interference plus Noise Ratio is defined as follows:

${\stackrel{\→}{\mathrm{\γ}}}_k=\frac{p_k{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_k\left|\right|}^2}{\underset{m=1,m\≠k}{\overset{K}{\mathrm{\Σ}}}{p}_m{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_m\left|\right|}^2+2};{\stackrel{\‾}{h}}_k=\frac{h_k}{\mathrm{\σ}}$

Wherein W ⁽ⁿ⁾for

for the beam vector of base station to user k, h _kfor base station is to the channel parameter between user k, p ⁽ⁿ⁾for for the transmitting power of base station to user k, σ is system thermal noise.

Therefore corresponding optimization aim is defined as follows:

$\underset{W,p}{\max }f(W,p)$

（2）

$s.t.{\stackrel{\→}{\mathrm{\γ}}}_k\≥{\mathrm{\γ}}_k,\∀k,\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{p}_k\≤P,{\left|\right|w_k\left|\right|}^2=1,\∀k$

Wherein

for

for the virtual up Signal to Interference plus Noise Ratio of user k, γ _kfor the target Signal to Interference plus Noise Ratio of user k, i.e. desired minimum Signal to Interference plus Noise Ratio, is exactly in fact the minimum transmission rate that has defined each user, and P is transmission power limit.

First above optimization problem is transformed, can be converted into following form:

$\underset{W,p,\mathrm{\α}}{\max }\stackrel{\→}{g}(W,p,\mathrm{\α})---\left(3\right)$

$s.t.{\stackrel{\→}{\mathrm{\γ}}}_k\≥{\mathrm{\γ}}_k,{\left|\right|w_k\left|\right|}^2=1,\∀k,\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{p}_k\≤\mathrm{\αP},0\≤\mathrm{\α}\≤1$

Wherein α is a variable, and target function is defined as follows:

Be easy to judge restrictive condition be equal to the Power Limitation condition in optimization problem (2).Utilize the duality of channel up-downgoing, above-mentioned descending optimization problem can be converted to up problem solving, corresponding up optimization problem is as follows:

$\underset{W,p,\mathrm{\α}}{\max }\stackrel{\←}{g}(W,q,\mathrm{\α})---\left(5\right)$

$s.t.{\stackrel{\←}{\mathrm{\γ}}}_k\≥{\widetilde{\mathrm{\γ}}}_k,{\left|\right|w_k\left|\right|}^2=1,\∀k,\underset{m=1}{\overset{K}{\mathrm{\Σ}}}{q}_k\≤\mathrm{\αP},0\≤\mathrm{\α}\≤1$

Wherein up target function is defined as follows:

Up user rate in target function and corresponding Signal to Interference plus Noise Ratio are defined as follows:

${\stackrel{\←}{R}}_k={\log }_2(1+{\stackrel{\←}{\mathrm{\γ}}}_k)---\left(7\right)$

${\stackrel{\←}{\mathrm{\γ}}}_k=\frac{q_k{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_k\left|\right|}^2}{\underset{m=1,m\≠k}{\overset{K}{\mathrm{\Σ}}}{q}_m{\left|\right|{\stackrel{\‾}{h}}_m^H{w}_k\left|\right|}^2+1};{\stackrel{\‾}{h}}_k=\frac{h_k}{\mathrm{\σ}}$

According to the duality of up-downgoing, can learn that optimization problem (3) and optimization problem (5) have identical optimum results, so only need to obtain the result of optimization problem (5), just can be converted to descending optimum results.Carry out certain conversion for problem (5), the method that can adopt GP to optimize is solved.First set with minor function:

$\mathrm{\φ}\left(\widetilde{\mathrm{\γ}}\right)=\frac{2\mathrm{\κ}\widetilde{\mathrm{\γ}}}{2+\mathrm{\θ}\widetilde{\mathrm{\γ}}}$

it is rate function approximate function, meet

approximation parameters is wherein defined as follows:

By this approximation to function, optimization problem before can be converted into following form:

$s.t.{\stackrel{\←}{\mathrm{\γ}}}_k\≥{\widetilde{\mathrm{\γ}}}_k,{\stackrel{\←}{\mathrm{\γ}}}_k\≥{\mathrm{\γ}}_k,\∀k,\underset{m=1}{\overset{K}{\mathrm{\Σ}}}{q}_k\≤\mathrm{\αP},0\≤\mathrm{\α}\≤1.$

Like this, the GP optimization problem that problem just can be converted to a standard solves, and can obtain the optimal value of corresponding ascending power, constantly iteration, can obtain the ascending power of last optimum, then, by duality, be converted to the solution of corresponding descending optimization problem.

Specifically, a kind of descending multi-user efficiency beam-forming method based on duality of the present invention (can referring to Fig. 1-2), the method comprises the following steps:

1). initialization downlink transmission power p ⁽ⁿ⁾with beam vector W ⁽ⁿ⁾, guarantee to meet the constraint of Signal to Interference plus Noise Ratio and power.Then by downlink transmission power p ⁽ⁿ⁾with beam vector W ⁽ⁿ⁾calculate Signal to Interference plus Noise Ratio now

by the virtual up Signal to Interference plus Noise Ratio calculating

calculate respectively approximation parameters

with

virtual uplink transmit power q is now set ⁽ⁿ⁾=0, and initialization target function now

it is the value of target function after the n time iteration;

K is the quantity of base station;

N is algorithm iteration number of times, and initial value is 0;

K is Customs Assigned Number;

W ⁽ⁿ⁾for

for the beam vector of base station to user k;

P ⁽ⁿ⁾for

for the transmitting power of base station to user k;

Q ⁽ⁿ⁾for

for the virtual ascending power of user k to base station;

for

for the virtual up Signal to Interference plus Noise Ratio of user k;

for

for the approximate auxiliary variable of speed of user k;

for

for the approximate auxiliary variable of speed of user k;

H _kfor base station is to the channel parameter between user k; σ is system thermal noise

Wherein utilize p ⁽ⁿ⁾and W ⁽ⁿ⁾the computational methods that obtain Signal to Interference plus Noise Ratio are as follows:

${\widetilde{\mathrm{\γ}}}_k^{\left(n\right)}=\frac{p_k^{\left(n\right)}{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_k^{\left(n\right)}\left|\right|}^2}{\underset{m=1,m\≠k}{\overset{K}{\mathrm{\Σ}}}{p}_m^{\left(n\right)}{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_m^{\left(n\right)}\left|\right|}^2+1};{\stackrel{\‾}{h}}_k=\frac{h_k}{\mathrm{\σ}}$

Utilize

calculate respectively approximation parameters

with

method as follows:

Wherein θ represents user rate weight.

2). make n=n+1, solve following GP optimization problem:

$s.t.{\stackrel{\←}{\mathrm{\γ}}}_k\≥{\widetilde{\mathrm{\γ}}}_k,{\stackrel{\←}{\mathrm{\γ}}}_k\≥{\mathrm{\γ}}_k,\∀k,\underset{m=1}{\overset{K}{\mathrm{\Σ}}}{q}_k\≤\mathrm{\αP},0\≤\mathrm{\α}\≤1.$

Wherein

what represent is the loss of base station power amplification, P _cwhat represent is the permanent circuit loss of every antenna, P ₀what represent is the fixed loss irrelevant with antenna, and what M represented is the quantity of antenna for base station.By solving above optimization problem, obtain virtual uplink transmit power q ⁽ⁿ⁾;

3). utilize the virtual uplink transmit power q after optimizing ⁽ⁿ⁾calculate corresponding beam vector W ⁽ⁿ⁾, computational methods are as follows:

$w_k=\frac{{(\underset{m=1}{\overset{K}{\mathrm{\Σ}}}{q}_m{\stackrel{\‾}{h}}_m{\stackrel{\‾}{h}}_m^H+1)}^{-1}{\stackrel{\‾}{h}}_k}{\left|\right|{(\underset{m=1}{\overset{K}{\mathrm{\Σ}}}{q}_m{\stackrel{\‾}{h}}_m{\stackrel{\‾}{h}}_m^H+1)}^{-1}{\stackrel{\‾}{h}}_k\left|\right|},\∀k$

If carry out step 4),

shown in being defined as follows:

If do not met, utilize the q after upgrading ⁽ⁿ⁾and W ⁽ⁿ⁾the virtual up Signal to Interference plus Noise Ratio that calculating makes new advances

computational methods are as follows:

${\widetilde{\mathrm{\γ}}}_k^{\left(n\right)}=\frac{q_k^{\left(n\right)}{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_k^{\left(n\right)}\left|\right|}^2}{\underset{m=1,m\≠k}{\overset{K}{\mathrm{\Σ}}}{q}_m^{\left(n\right)}{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_m^{\left(n\right)}\left|\right|}^2+1};{\stackrel{\‾}{h}}_k=\frac{h_k}{\mathrm{\σ}}$

By upgrade after

the approximation parameters that calculating makes new advances

with

update method is identical with step 1), then returns to step 2), wherein ζ is predefined required precision.

4). up optimum results is converted into descending, equates to obtain descending through-put power p according to the Signal to Interference plus Noise Ratio of up-downgoing ⁽ⁿ⁾.

As shown in Figure 2, algorithm has four steps to above algorithm flow, comprising: (1) initialization downlink transmission power and beam vector, calculate Signal to Interference plus Noise Ratio now and relevant approximation parameters, and the virtual uplink transmit power of initialization, making target function is 0; (2) solve corresponding GP optimization problem, obtain uplink transmit power; (3) utilize uplink transmit power to calculate beam vector, judge whether target function end condition meets, if meet, carries out next step, if do not meet, calculates the up Signal to Interference plus Noise Ratio making new advances, and upgrades approximation parameters and returns to previous step; (4) up optimum results is converted to descending, equates to obtain downlink transmission power according to up-downgoing Signal to Interference plus Noise Ratio.

Below the performance comparison of the inventive method and additive method is made an explanation:

Fig. 3 be the present invention and other algorithms of different Performance Ratio, be the comparison analogous diagram of corresponding performance efficiency and system spectral efficiency performance.In analogous diagram, what PowerMinimization represented is traditional minimum power beam forming algorithm under rate requirement, what ProposedAlgorithm represented is the algorithm that the present invention carries, and what ManoshaAlgorithm represented is that a kind of efficiency flying under cellular environment at many antennas that K.Manosha proposes is optimized beam forming algorithm.Because the present invention is mainly the efficiency that need to improve system, therefore in emulation, compared the efficiency between algorithms of different, in addition, spectrum efficiency is also the very important standard of considering, only in improving efficiency, guarantee the spectrum efficiency of system, just can not have influence on user's use and service quality.

Meanwhile, Fig. 3 has also provided efficiency and the spectrum efficiency that the various algorithms under different transmission power obtain.Wherein efficiency unit is bit/Hz/Joule, and spectrum efficiency unit is bit/s/Hz, as can be seen from Figure 3, the method that the algorithm that the present invention carries is carried with Manosha is compared and can be obtained identical efficiency and spectrum efficiency, and in obtaining identical performance, algorithm complex of the present invention is lower, this is because corresponding problem solving has obtained great simplification after adopting approximate function, and this simplification does not bring the loss in performance, and the efficiency that traditional minimum power beam forming algorithm under rate requirement is obtained is lower, the algorithm of carrying lower than the present invention, therefore compared with other algorithms, the algorithm that the present invention carries has been realized effectively and having been improved in this target of efficiency.In addition, also can see, the spectrum efficiency of the algorithm of carrying is also higher than traditional minimum power beam forming algorithm under rate requirement, therefore the algorithm that the present invention carries does not cause a large amount of losses of system spectral efficiency in improving efficiency, just in reducing energy consumption, has guaranteed user's service quality yet.

Claims (1)

1. the descending multi-user efficiency beam-forming method based on duality, is characterized in that the method comprises the following steps:

1) initialization downlink transmission power p ⁽ⁿ⁾with beam vector W ⁽ⁿ⁾, guarantee to meet the constraint of Signal to Interference plus Noise Ratio and power, then by downlink transmission power p ⁽ⁿ⁾with beam vector W ⁽ⁿ⁾calculate Signal to Interference plus Noise Ratio now

by the virtual up Signal to Interference plus Noise Ratio calculating

calculate respectively approximation parameters

with

virtual uplink transmit power q is now set ⁽ⁿ⁾=0, and initialization target function now ${\stackrel{\←}{g}}^{\left(n\right)}=0;$

Wherein:

it is the value of target function after the n time iteration;

K is the quantity of base station;

K is Customs Assigned Number;

N is algorithm iteration number of times, and initial value is 0;

W ⁽ⁿ⁾for

for the beam vector of base station to user k;

P ⁽ⁿ⁾for

for the transmitting power of base station to user k;

Q ⁽ⁿ⁾for

for the virtual ascending power of user k to base station;

for

for the virtual up Signal to Interference plus Noise Ratio of user k;

for

for the approximate auxiliary variable of speed of user k;

for

for the approximate auxiliary variable of speed of user k;

H _kfor base station is to the channel parameter between user k; σ is system thermal noise;

Wherein utilize p ⁽ⁿ⁾and W ⁽ⁿ⁾the computational methods that obtain Signal to Interference plus Noise Ratio are as follows:

${\widetilde{\mathrm{\γ}}}_k^{\left(n\right)}=\frac{p_k^{\left(n\right)}{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_k^{\left(n\right)}\left|\right|}^2}{\underset{m=1,m\≠k}{\overset{K}{\mathrm{\Σ}}}{p}_m^{\left(n\right)}{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_m^{\left(n\right)}\left|\right|}^2+1};{\stackrel{\‾}{h}}_k=\frac{h_k}{\mathrm{\σ}}$

Utilize

calculate respectively approximation parameters

with

method as follows:

Wherein θ represents user rate weight;

2). make n=n+1, solve following GP optimization problem:

$s.t.{\stackrel{\←}{\mathrm{\γ}}}_k\≥{\widetilde{\mathrm{\γ}}}_k,{\stackrel{\←}{\mathrm{\γ}}}_k\≥{\mathrm{\γ}}_k,\∀k,\underset{m=1}{\overset{K}{\mathrm{\Σ}}}{q}_k\≤\mathrm{\αP},0\≤\mathrm{\α}\≤1.$

Wherein

what represent is the loss of base station power amplification, P _cwhat represent is the permanent circuit loss of every antenna, P ₀what represent is the fixed loss irrelevant with antenna, and what M represented is the quantity of antenna for base station, and P is transmission power limit; By solving above optimization problem, obtain virtual uplink transmit power q ⁽ⁿ⁾;

3). utilize the virtual uplink transmit power q after optimizing ⁽ⁿ⁾calculate corresponding beam vector W ⁽ⁿ⁾, computational methods are as follows:

$w_k=\frac{{(\underset{m=1}{\overset{K}{\mathrm{\Σ}}}{q}_m{\stackrel{\‾}{h}}_m{\stackrel{\‾}{h}}_m^H+1)}^{-1}{\stackrel{\‾}{h}}_k}{\left|\right|{(\underset{m=1}{\overset{K}{\mathrm{\Σ}}}{q}_m{\stackrel{\‾}{h}}_m{\stackrel{\‾}{h}}_m^H+1)}^{-1}{\stackrel{\‾}{h}}_k\left|\right|},\∀k$

If

carry out step 4),

shown in being defined as follows:

If do not met, utilize the q after upgrading ⁽ⁿ⁾and W ⁽ⁿ⁾the virtual up Signal to Interference plus Noise Ratio that calculating makes new advances

computational methods are as follows:

${\widetilde{\mathrm{\γ}}}_k^{\left(n\right)}=\frac{q_k^{\left(n\right)}{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_k^{\left(n\right)}\left|\right|}^2}{\underset{m=1,m\≠k}{\overset{K}{\mathrm{\Σ}}}{q}_m^{\left(n\right)}{\left|\right|{\stackrel{\‾}{h}}_k^H{w}_m^{\left(n\right)}\left|\right|}^2+1};{\stackrel{\‾}{h}}_k=\frac{h_k}{\mathrm{\σ}}$

By upgrade after

the approximation parameters that calculating makes new advances with

update method is identical with step 1), then returns to step 2), ζ is predefined required precision;

4). up optimum results is converted into descending, equates to obtain descending through-put power p according to the Signal to Interference plus Noise Ratio of up-downgoing ⁽ⁿ⁾.

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