CN102364973A - Sharing spectrum access-based carrier and power combined allocation method - Google Patents

Abstract

The invention discloses a sharing spectrum access-based carrier and power combined allocation method. By the method, the problem of spectrum allocation in cognitive radio is solved by combining a game correlation theory, a duality principle, a subgradient method and the like; when an overlay spectrum accesses, an iterative algorithm for power allocation is provided, the convergence and the availability of the iterative algorithm are verified, and the problem of carrier and power allocation is solved when an underlay spectrum accesses; and when the underlay spectrum accesses, due to the constraint of the interference tolerance, strategy spaces among users are mutually coupled, and a coupling strategy game is decomposed into an independent strategy non-cooperative game and an optimization problem by introducing the duality principle and the subgradient method, so that the problem of carrier and power allocation is solved when the underlay spectrum accesses.

Description

Based on sharing carrier wave and the power combined distributing method that frequency spectrum inserts

Technical field

The present invention relates to power water-filling algorithm in the cognitive radio system, carrier allocation method and power iterative algorithm; Shared frequency spectrum when being specially adapted to the authorized user existence or having the jamming margin constraint inserts; Purpose is reasonably to distribute the power of cognitive user and the frequency spectrum of authorized user, improves the utilance of frequency spectrum resource.

Background technology

Along with the appearance of 3-G (Generation Three mobile communication system) and high speed data network, particularly to the professional support of multi-medium data, advanced spectrum utilization technology and spectrum allocation may algorithm play crucial effects to the raising of systematic function.Cognitive radio technology becomes the research focus of industry and each spectrum management mechanism gradually owing to can make full use of the idle frequency spectrum of authorized user.Not only can accomplish the reasonable distribution of CR network intermediate frequency spectrum and power resource based on the spectrum allocation may strategy of cognitive radio, and the frequency spectrum resource utilization rate that improves the existing wireless communications system is also had important significance for theories.

Dynamic frequency spectrum deployment can be utilized the usable spectrum of authorized user, limits and reduce the possibility of conflict generation simultaneously effectively.In quadrature spectrum inserted, every the channel or a certain moment of carrier wave only allowed a cognitive user to insert, distribute finish after, the communication channel between the cognitive user is mutually orthogonal, does not promptly have interferences (or interference can be ignored) between the user.Because every channel has only a user to insert, when the operating state of authorized user changes or because environmental change when causing the jamming margin of authorized user to change, only needs one or the relevant transmission parameter of minority cognitive user adjustment to get final product.Therefore, quadrature formula frequency spectrum inserts to have lower system complexity and response time, the variation of external environment condition is little to the operating state influence of cognitive user, but is cost to sacrifice user's effectiveness.

In shared frequency spectrum inserted, cognitive user is insertion authority user's many channels or carrier wave simultaneously, and the user also need consider the interference from other user except that need are considered the jamming margin of authorized user.In this case; Cognitive user can be used whole available channels, through the form transmission information of similar " spread spectrum ", but when external environment condition changes; All users' transmission parameter all needs adjustment thereupon, and is very high to the dynamic and the real-time requirement of cognitive radio system.

Summary of the invention

The objective of the invention is to avoid the lower present situation of user's effectiveness in the quadrature spectrum access, provide a kind of based on sharing carrier wave and the power combined distributing method that frequency spectrum inserts.Carrier wave and power division problem when the present invention has solved shared frequency spectrum fully and inserts under filled type and the following cushion pattern have improved the utilance of frequency spectrum resource, for the spectrum allocation may in the cognitive radio provides new approaches.

The objective of the invention is to realize like this:

Based on sharing carrier wave and the power combined distributing method that frequency spectrum inserts; Through Carrier State information with frequency spectrum perception and channel estimating acquisition; The carrier wave suitable according to the different choice of access way distributes between cognitive user, it is characterized in that comprising that step is following:

(1) set up cognition wireless network, the cognitive user number and the authorized user number of channel are respectively N and M, and the jamming margin of authorized user on each bar channel is I _k, initialization jamming margin factor η _k(0)=0, wherein k is the k bar channel of authorized user, and k=1,2 ..., M;

(2) judging the network insertion pattern, if allow cognitive user to insert in running order authorization channel, then is that the cushion frequency spectrum inserts down, changes step (5) over to; Otherwise, for the filled type frequency spectrum inserts, order execution in step (3);

(3) according to the utility function and the Lagrangian advantest method of cognitive user; Try to achieve arbitrary cognitive user t through-put power

(k ∈ //) constantly on arbitrary idle channel; Wherein i is an i cognitive user, and i=1,2;, N;

(4) pass through iterative formula $p_i^k(t+1)=\mathrm{Max}(0,{\mathrm{\μ}}_i(t+1)-\frac{{\mathrm{\σ}}^2+\underset{j\≠i}{\mathrm{\Σ}}{p}_j^k\left(t\right){\left|H_{j,i}\right|}^2}{K{H_{i,i}|}^2})$ Try to achieve the power distribution result of each cognitive user, and then obtain each user's throughput, wherein μ _i(t+1) be t+1 water line constantly, Expression gain interference ratio is accomplished carrier wave and power division based on shared frequency spectrum access under the filled type;

(5) through-put power

of initialization t moment cognitive user on each bar channel

(6), call based on the power water-filling algorithm of cushion frequency spectrum access down and try to achieve t+1 water line μ constantly to cognitive user i _iAnd then try to achieve power antithesis factor lambda (t+1), _i(t+1) and power distribution result (k=1,2 ..., M);

(7) judge t+1 constantly with t constantly the absolute value of power difference whether satisfy error requirement, if more than or equal to ERROR CONTROL factor ε ₁Then return step (6); Otherwise, then according to formula ${\mathrm{\η}}_k(n+1)=\mathrm{Max}\{0,{\mathrm{\η}}_k\left(n\right)-{\mathrm{\α}}_n(I_k-\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{p}_j^k(n+1){\left|H_{j,0}^k\right|}^2)\}$ Try to achieve jamming margin antithesis factor η _k(n+1);

(8) judge n+1 constantly with n constantly the absolute value of jamming margin antithesis factor difference whether less than ERROR CONTROL factor ε ₂, if not, then return step (5); If then export the power distribution result of each cognitive user, and then obtain each user's throughput, carrier wave and power division under accomplishing under the cushion based on shared frequency spectrum access.

The present invention compared with prior art has following beneficial effect:

(1) carrier wave and the power division problem when sharing frequency spectrum in the cognitive radio and insert; Designed the power water-filling algorithm of a kind of suitable filled type and following cushion frequency spectrum access in this method; It is the function of variable with the water line that this algorithm has made up one; At first obtained the carrier number of actual use through the cognitive user interference ratio that on each bar channel, gains then, and then confirmed the interval of water line, last solved function has obtained user's water line.Compare with traditional water-filling algorithm, the water line of trying to achieve through this method is optimum, and convergence of algorithm speed is very fast.

Carrier wave and power division problem when (2) inserting to cushion under sharing in the frequency spectrum access; This method has designed a kind of two iterative algorithms based on the principle of duality and subgradient method of finding the solution the tactful game of coupling; This method has resolved into one to the tactful game of coupling and has retrained independently non-cooperative game and a parameter optimization problem; Thereby stable power distribution result, fast convergence rate in the limited time, have been obtained.

Description of drawings:

Fig. 1 is a process flow block diagram of the present invention.

Fig. 2 is the cognition wireless network sketch map.

Fig. 3 is a power water-filling algorithm flow chart.

Power water filling sketch map when Fig. 4 is the access of filled type frequency spectrum.

Fig. 5 is that the effectiveness of sharing following Underlay of frequency spectrum access and Overlay compares.

Embodiment:

Below, in conjunction with accompanying drawing the present invention is described further.

Based on sharing carrier wave and the power combined distributing method that frequency spectrum inserts; Through Carrier State information with frequency spectrum perception and channel estimating acquisition; The carrier wave suitable according to the different choice of access way distributes between cognitive user, it is characterized in that comprising that step is following:

(1) set up cognition wireless network, the cognitive user number and the authorized user number of channel are respectively N and M, and the jamming margin of authorized user on each bar channel is I _k, initialization jamming margin factor η _k(0)=0, wherein k is the k bar channel of authorized user, and k=1,2 ..., M.

(2) judging the network insertion pattern, if allow cognitive user to insert in running order authorization channel, then is that the cushion frequency spectrum inserts down, changes step (5) over to; Otherwise, for the filled type frequency spectrum inserts, order execution in step (3).

(3) according to the utility function and the Lagrangian advantest method of cognitive user; Try to achieve arbitrary cognitive user t through-put power

(k ∈ //) constantly on arbitrary idle channel; Wherein i is an i cognitive user, and i=1,2;, N.

At first, call cognitive user utility function under this pattern:

$s.t.\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{p}_i^k\≤P_i$

channel k is in the off state

channel k is in the on state

Wherein,

Be the through-put power of cognitive user i on channel k;

The channel gain of expression cognitive user i on channel k; σ ²Be the noise power level on the channel;

Be the transmitter of cognitive user j the channel gain of receiver on channel k to user i; P _iOverall transmission power for cognitive user i.

Then, definition gain interference ratio function

And according to Lagrange's equation $L_i(p_i,{\mathrm{\λ}}_i)=\underset{k=1}{\overset{M}{\mathrm{\Σ}}}b{\mathrm{Log}}_2(1+p_i^k{g}_i^k)+{\mathrm{\λ}}_i(P_i-\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{p}_i^k)$ And power water-filling algorithm (the interference-free tolerance constraints of idle channel) is tried to achieve cognitive user at t through-put power constantly, p in the formula _iThe power allocation vector of expression user i, and

λ _iBe the Lagrangian factor.

(4) pass through iterative formula $p_i^k(t+1)=\mathrm{Max}(0,{\mathrm{\μ}}_i(t+1)-\frac{{\mathrm{\σ}}^2+\underset{j\≠i}{\mathrm{\Σ}}{p}_j^k\left(t\right){\left|H_{j,i}\right|}^2}{K{\left|H_{i,i}\right|}^2})$ Try to achieve the power distribution result of each cognitive user, and then obtain each user's throughput, wherein μ _i(t+1) be t+1 water line constantly,

Expression gain interference ratio is accomplished carrier wave and power division based on shared frequency spectrum access under the filled type.

To user i (i ∈ //) arbitrarily, the power distribution strategies in its t+1 stage is relevant with t other all users' of stage power distribution result, and promptly the payoff of previous stage can influence user's decision-making of next stage.However, user's policy space is separately independently, is being no more than the power allocation vector that each user under the prerequisite of its power margin can independently choose self; Because selfishness, the rational faculty between the user, they all can choose final through-put power by this formula, thereby realize the optimization of self effectiveness.

(5) through-put power

of initialization t moment cognitive user on each bar channel

At this moment, cognitive user can insert in running order authorized user channel, but the constraint of the tolerance limit I that will be interfered, at this moment the effectiveness of cognitive user can be expressed as:

$\underset{p_j}{\max }U=\underset{j=1}{\overset{M}{\mathrm{\Σ}}}\frac{B}{M}{\log }_2(1+K{\mathrm{\γ}}_j)$

$s.t.\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{p}_j\≤P,p_j\≥0$

${\mathrm{\σ}}^2+p_j{\left|H_{j,0}\right|}^2\≤I_j\∀j\∈//$ And carrier wave j is not idle

Wherein, M is the carrier wave sum; B is the channel total bandwidth; p _jCognitive user transmitting power on the expression subcarrier j;

Be the noise power on the unit bandwidth; K representes user's error rate requirement; | H _{J, 0}| ²Channel gain for the monitoring point that transmits on subcarrier j of cognitive user.The frequency spectrum share problem of this moment finally can be summed up as cognitive user and on each subcarrier, reasonably distribute transmitting power in the hope of obtaining optimum transmission rate.The power division situation of cognitive user does $p_j=\mathrm{Min}(\frac{I_j-{\mathrm{\σ}}^2}{{\left|H_{j,0}\right|}^2},{(\mathrm{\μ}-g_j^{-1})}^{+}),$ In the formula

The jamming margin and (x) of expression authorized user ⁺=max (x, 0), μ be water line and λ is the Lagrangian factor, g _jExpression gain interference ratio, and

(6), call based on the power water-filling algorithm of cushion frequency spectrum access down and try to achieve t+1 water line μ constantly to cognitive user i _iAnd then try to achieve power antithesis factor lambda (t+1), _i(t+1) and power distribution result

(6.1) according to computes cognitive user effectiveness:

$\underset{p_j}{\max }U=\underset{j=1}{\overset{M}{\mathrm{\Σ}}}b{\log }_2(1+K{\mathrm{\γ}}_j)$

$s.t.\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{p}_j\≤P,p_j\≥0$

${\mathrm{\σ}}^2+p_j{\left|H_{j,0}\right|}^2\≤I_j\∀j\∈//$ And carrier wave j is not idle

Wherein, b is a channel width; p _jBe the cognitive user transmitting power on the subcarrier j; | H _{J, 0}| ²The channel gain of the monitoring point that transmits on subcarrier j of expression cognitive user; On idle channel, the constraint of the interference-free tolerance limit of power division of cognitive user.

(6.2) can get its power division situation by the utility function of cognitive user and Lagrangian advantest method is:

$p_j=\min (\frac{I_j-{\mathrm{\σ}}^2}{{\left|H_{j,0}\right|}^2},{(\mathrm{\μ}-g_j^{-1})}^{+})$

Wherein,

The jamming margin and (x) of expression authorized user ⁺=max (x, 0); μ is a water line, and

λ is the Lagrangian factor; g _jExpression gain interference ratio, and

Can know that by this formula the water line of only requiring promptly can obtain the result of power division.For realizing this target, the gain interference ratio is arranged by its ascending order reciprocal.

(6.3) when the optimal utility of cognitive user, should have

Formula by in the step (6.2) can be known power p _jBe the function of water line μ, therefore, constraints can be expressed as:

$f\left(\mathrm{\μ}\right)=\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{p}_j-P=\underset{j=1}{\overset{M}{\mathrm{\Σ}}}\min (\frac{I_j-{\mathrm{\σ}}^2}{{\left|H_{j,0}\right|}^2},{(\mathrm{\μ}-g_j^{-1})}^{+})-P_i$

Let

the value obtained function f

(6.4) whether discriminant function

is greater than 0; If then the power that distributes of expression is greater than the gross power of cognitive user, should puts M=M-1 and return step (6.3) and continue to find the solution water line; Otherwise then the gross power restriction is satisfied in expression, and order is carried out next step.

(6.5) the actual carrier number that uses of cognitive user is num=M; Try to achieve the value of water line according to function f (μ)=0 and water line interval

, and then try to achieve the result

of power division

(7) judge t+1 constantly with t constantly the absolute value of power difference whether satisfy error requirement, if more than or equal to ERROR CONTROL factor ε ₁Then return step (6); Otherwise, then according to formula Try to achieve jamming margin antithesis factor η _k(n+1);

At first, according to the t+1 that tries to achieve water line constantly, try to achieve the power antithesis factor and the power distribution result in this moment respectively by water line formula in the step (5) and power division formula.The power iterative formula that is obtained by step (6) can be expressed as:

Wherein, λ _i(t+1) the expression t+1 power antithesis factor constantly.

At this moment, when cognitive user t+1 constantly with t constantly the absolute value of the difference of power less than ε ₁The time, satisfying the ERROR CONTROL condition of this method, order is carried out next step; Otherwise the ERROR CONTROL condition does not satisfy, and algorithm should be got back to step (6), and to put t power constantly be t+1 power constantly, and continuation is carried out in proper order, till satisfying the ERROR CONTROL condition.

Then, according to formula ${\mathrm{\η}}_k(n+1)=\mathrm{Max}\{0,{\mathrm{\η}}_k\left(n\right)-{\mathrm{\α}}_n(I_k-\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{p}_j^k(n+1){\left|H_{j,0}^k\right|}^2)\}$ Try to achieve n+1 jamming margin antithesis factor η constantly _k(n+1), wherein k representes arbitrary working channel of authorized user.

(8) judge n+1 constantly with n constantly the absolute value of jamming margin antithesis factor difference whether less than ERROR CONTROL factor ε ₂, if not, then return step (5); If then export the power distribution result of each cognitive user, and then obtain each user's throughput, carrier wave and power division under accomplishing under the cushion based on shared frequency spectrum access.

In following cushion frequency spectrum share, cognitive user can insert the channel of in running order authorized user simultaneously.At this moment, the strategy of cognitive user also receives the constraint of authorized user jamming margin except that the overall transmission power restriction that receives self: on the channel of authorized user work, the interference power summation that adds up of all cognitive user can not surpass the jamming margin of this channel.Therefore, different with traditional non-cooperative game, the subscriber policy here intercouples.Power policy p as given other user _-iThe time, the policy space of the coupling of cognitive user i can be expressed as:

P wherein _iBe the power policy of cognitive user i, and

Ω _iThe power division space of expression cognitive user i, and

Its allocation space can be expressed as ${\mathrm{\&Omega;}}_i=\{({\mathrm{<figure-callout\; id="1"\; label="p\; i"\; filenames="HSA00000623099400011.png,HSA00000623099400021.png"\; state="\{\{state\}\}">p</figure-callout>}}_i^{},\&CenterDot;\&CenterDot;\&CenterDot;,p_i^M)\&Element;R^M|p_i^k\&GreaterEqual;0,\&ForAll;k\&Element;//\};$

Be cognitive user i gain on channel l to the monitoring point; I _lBe the jamming margin on the channel l; Represent in running order authorized user channel set.

This method is introduced the principle of duality and subgradient method, has solved the power division problem in this manifold type non-cooperative game through the Hiberarchy Decomposition model.In the game of the described manifold type strategy of step (1), each cognitive user all need be understood other users' strategy fully just can make final effective decision-making, and this can't realize in distributed cognition radio network.This method is considered to use based on the principle of duality of Lagrangian the manifold type jamming margin is decomposed.Because the manifold type jamming margin is protruding for the power policy of cognitive user, retrains independently non-cooperative game and a parameter optimization problem so the tactful game of this coupling can be decomposed into one.Can get Lagrangian by the utility function in the step (1) is:

$L_i(p,{\mathrm{\&lambda;}}_i,\mathrm{\&eta;})=U_i\left(p_i\right)+{\mathrm{\&lambda;}}_i(P_i-\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{p}_i^k)+\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{\&eta;}}_k(I_k-\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{p}_j^k{\left|H_{j,0}^k\right|}^2)$

Wherein, λ _iRepresent the antithesis factor (the Lagrangian factor) relevant with the power margin of cognitive user i; η is the antithesis factor relevant with the jamming margin of channel, and η=[η ¹..., η ^M]; Be user j gain on channel k to the monitoring point; I _kJamming margin on the expression channel k, when not having authorized user work on the k, I _kInfinitely great.

According to the principle of duality and subgradient method, the power iterative formula that promptly can obtain being adopted in this method and the jamming margin antithesis factor be new formula more.

Claims (2)

1. based on sharing carrier wave and the power combined distributing method that frequency spectrum inserts; Through Carrier State information with frequency spectrum perception and channel estimating acquisition; The carrier wave suitable according to the different choice of access way distributes between cognitive user, it is characterized in that comprising that step is following:

(1) set up cognition wireless network, the cognitive user number and the authorized user number of channel are respectively N and M, and the jamming margin of authorized user on each bar channel is I _k, initialization jamming margin factor η _k(0)=0, wherein k is the k bar channel of authorized user, and k=1,2 ..., M;

(2) judging the network insertion pattern, if allow cognitive user to insert in running order authorization channel, then is that the cushion frequency spectrum inserts down, changes step (5) over to; Otherwise, for the filled type frequency spectrum inserts, order execution in step (3);

(3) according to the utility function and the Lagrangian advantest method of cognitive user; Try to achieve arbitrary cognitive user t through-put power

(k ∈ //) constantly on arbitrary idle channel; Wherein i is an i cognitive user, and i=1,2;, N;

(4) pass through iterative formula $p_i^k(t+1)=\mathrm{Max}(0,{\mathrm{\&mu;}}_i(t+1)-\frac{{\mathrm{\&sigma;}}^2+\underset{j\&NotEqual;i}{\mathrm{\&Sigma;}}{p}_j^k\left(t\right){\left|H_{j,i}\right|}^2}{K{\left|H_{i,i}\right|}^2})$ Try to achieve the power distribution result of each cognitive user, and then obtain each user's throughput, wherein μ _i(t+1) be t+1 water line constantly, Expression gain interference ratio is accomplished carrier wave and power division based on shared frequency spectrum access under the filled type;

(5) through-put power

of initialization t moment cognitive user on each bar channel

(6), call based on the power water-filling algorithm of cushion frequency spectrum access down and try to achieve t+1 water line μ constantly to cognitive user i _iAnd then try to achieve power antithesis factor lambda (t+1), _i(t+1) and power distribution result

(k=1,2 ..., M);

(7) judge t+1 constantly with t constantly the absolute value of power difference whether satisfy error requirement, if more than or equal to ERROR CONTROL factor ε ₁Then return step (6); Otherwise, then according to formula ${\mathrm{\&eta;}}_k(n+1)=\mathrm{Max}\{0,{\mathrm{\&eta;}}_k\left(n\right)-{\mathrm{\&alpha;}}_n(I_k-\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{p}_j^k(n+1){\left|H_{j,0}^k\right|}^2)\}$ Try to achieve jamming margin antithesis factor η _k(n+1);

(8) judge n+1 constantly with n constantly the absolute value of jamming margin antithesis factor difference whether less than ERROR CONTROL factor ε ₂, if not, then return step (5); If then export the power distribution result of each cognitive user, and then obtain each user's throughput, carrier wave and power division under accomplishing under the cushion based on shared frequency spectrum access.

2. according to claim 1 based on sharing carrier wave and the power combined distributing method that frequency spectrum inserts, it is characterized in that: the power water-filling algorithm based on cushion frequency spectrum access down in the step (6) may further comprise the steps:

(6.1) according to computes cognitive user effectiveness:

$\underset{p_j}{\max }U=\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}b{\log }_2(1+K{\mathrm{\&gamma;}}_j)$

$s.t.\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{p}_j\&le;P,p_j\&GreaterEqual;0$

${\mathrm{\&sigma;}}^2+p_j{\left|H_{j,0}\right|}^2\&le;I_j\&ForAll;j\&Element;//$ And carrier wave j is not idle

Wherein, b is a channel width; p _jBe the cognitive user transmitting power on the subcarrier j; | H _{J, 0}| ²The channel gain of the monitoring point that transmits on subcarrier j of expression cognitive user; On idle channel, the constraint of the interference-free tolerance limit of power division of cognitive user;

(6.2) can get its power division situation by the utility function of cognitive user and Lagrangian advantest method is:

$p_j=\min (\frac{I_j-{\mathrm{\&sigma;}}^2}{{\left|H_{j,0}\right|}^2},{(\mathrm{\&mu;}-g_j^{-1})}^{+})$

Wherein,

The jamming margin and (x) of expression authorized user ^-=max (x, 0); μ is a water line, and λ is the Lagrangian factor; g _jExpression gain interference ratio, and Can know that by this formula the water line of only requiring promptly can obtain the result of power division; For realizing this target, the gain interference ratio is arranged by its ascending order reciprocal;

(6.3) when the optimal utility of cognitive user, should have

Formula by in the step (6.2) can be known power p _jBe the function of water line μ, therefore, constraints can be expressed as:

$f\left(\mathrm{\&mu;}\right)=\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{p}_j-P=\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}\min (\frac{I_j-{\mathrm{\&sigma;}}^2}{{\left|H_{j,0}\right|}^2},{(\mathrm{\&mu;}-g_j^{-1})}^{+})-P_i$

Let

calculated value of the function f

(6.4) whether discriminant function

is greater than 0; If then the power that distributes of expression is greater than the gross power of cognitive user, should puts M=M-1 and return step (6.3) and continue to find the solution water line; Otherwise then the gross power restriction is satisfied in expression, and order is carried out next step;

(6.5) the actual carrier number that uses of cognitive user is num=M, tries to achieve the value of water line according to function f (μ)=0 and water line interval

.

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