CN102149203B - Power allocation method in cognition orthogonal frequency division multiple access (OFDMA) system based on proportional fairness and interference constraints - Google Patents

Abstract

The invention discloses a power allocation method in a cognition orthogonal frequency division multiple access (OFDMA) system based on proportional fairness and interference constraints, comprising the following steps: firstly carrying out power allocation among cognitive users in accordance with proportional fairness factors, total power constraints and permanent speed values; then using a quick water injection method to carry out carrier power allocation by each cognitive user; if the carrier power of each cognitive user does not exceed a power constraint value, ending an algorithm, and otherwise, modifying allocated power of a carrier exceeding the power constraint to be the power constraint value; calculating the speed of the carrier and adding the speed to the permanent speed value of the user; eliminating the carrier from the carrier set of the user; and if the carrier set of each cognitive user is a null set, ending the algorithm, otherwise, subtracting the allocated power constraint value from a total power value, and repeating the above steps until the algorithm ends. The method is better in performances of the system capacity and the proportional fairness among the cognitive users, low in the algorithmic complexity and applied to engineering.

Description

Power distribution method based on proportional fairness and interference constraint in cognitive OFDMA system

Technical Field

The invention relates to the field of wireless communication, in particular to a power distribution method based on proportional fairness and interference constraint in a cognitive OFDMA system.

Background

The cognitive radio technology is a key technology for solving the problems of lack of spectrum resources and low spectrum utilization rate at present. In cognitive radio, a cognitive user uses an idle frequency band on the premise of not interfering an authorized user by dynamically adjusting parameters such as transmitting power, frequency, a modulation mode and the like, so that the utilization efficiency of a frequency spectrum is effectively improved. Orthogonal Frequency Division Multiplexing Access (OFDMA) technology is currently recognized as a transmission technology that facilitates spectrum resource control. OFDMA technology enables flexible allocation of system resources among users through spectrum combining and tailoring, which makes it well integrated with cognitive systems. In the cognitive OFDMA system, how to effectively and reasonably allocate resources (carriers, power, etc.) to each cognitive user on the premise of satisfying various constraint conditions (interference constraint, proportional fairness constraint, total power constraint, etc.) becomes a key for improving the performance of the cognitive OFDMA system.

The existing resource allocation methods are mainly divided into two categories: static resource Allocation (see "Multiuser OFDM," in IEEE International Symposium On Signal Processing and itsApplications, 1999) and dynamic resource Allocation (see "On the Use of line Programming for dynamic sub channel and Bit Allocation in Multiuser OFDM," in IEEE GLOBECOM, 2001). Static resource allocation methods, such as TDMA, FDMA, etc., although simple, have limited performance due to the inability to make reasonable use of the dynamically changing information of cognitive users and channels. On the contrary, the dynamic resource allocation rule can reasonably utilize the diversity gain among the cognitive users to greatly improve the performance compared with the static resource allocation method, thereby gaining great attention. At present, a plurality of dynamic resource allocation methods related to a cognitive OFDMA system exist, but two problems basically exist, namely, the algorithm is complex and is not suitable for engineering application; secondly, the constraint of proportional fairness is rarely considered, and much work is focused on the optimization of the whole capacity, but the fairness problem among the cognitive users is ignored. When fairness constraints among cognitive users are added to the resource allocation problem of the cognitive OFDMA system, the complexity of the problem may be greatly increased.

The cognitive OFDMA system power distribution problem considering the proportional fairness constraint is modeled and analyzed, and reasonable simplified derivation is performed by using structural characteristics of a nonlinear equation in a model, so that the power distribution problem among cognitive users is simplified into an equation solving process for solving a single variable, and the solution of the problem is greatly simplified. Meanwhile, for the carrier power distribution of a single user, in order to overcome the defect that the traditional water filling algorithm needs iterative computation to obtain a reasonable water filling threshold, a rapid water filling algorithm established on the basis of carrier signal-to-noise ratio sequencing is provided, and the water filling threshold can be obtained by the algorithm in one step. The complexity of the computation of the carrier signal-to-noise ratio sequencing (which can be realized in the carrier allocation process) is ignored, and the complexity of the fast water filling algorithm is o (n), which is only equivalent to the complexity of one iteration of the conventional water filling algorithm.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a power allocation method based on proportional fairness and interference constraint in a cognitive OFDMA system.

The power distribution method based on proportional fairness and interference constraint in the cognitive OFDMA system comprises the following steps:

1) the following variables are initialized as follows and,P_k，total＝0，R_k，fixed＝0，Ω_k，left＝Ω_k2, 3, K, wherein P is_totalA value representing the total power constraint is indicated,representing the current total power constraint value, P_k，totalRepresents the power, Ω, allocated to the kth cognitive user_kRepresents the set of carriers, Ω, allocated to the kth cognitive user_k，fixedRepresents a set of carriers of fixed rate, Ω, belonging to the kth cognitive user_k，leftRepresents omega_kRemoving omega_k，fixedThe elements left after the elements in the list are collected, and K is the number of the cognitive users;

2) proportional fairness factor gamma based on cognitive user rate₁∶γ₂...∶γ_K、Ω_k，leftCarrier to channel noise ratio, current fixed rate R_k，fixedAnd the current total powerCalculating power P distributed to each cognitive user_k，total；

3) Each cognitive user is according to the divided power value P_k，totalUsing rapid water injection method to adjust omega_k，leftCarrying out power distribution on the carrier waves in the group;

4) each cognitive user detects omega_k，leftWhether the carrier power in (1) all meets the interference constraint condition: p_k，n≤P_k，max，n∈Ω_k，leftIn which P is_k，nRepresents the power, P, allocated by the k cognitive user on the n carrier_k，maxRepresents the set omega_k，leftIf the power distribution of the carrier of all cognitive users meets the power constraint condition, the algorithm is ended, otherwise, P is detected_k，n＞P_k，maxThe k-th cognitive user divides the n-th carrier into a carrier set omega with a fixed rate_k，fixedAnd the nth carrier is selected from the set omega_k，leftDeleting and updating the fixed rate R of the kth cognitive user_k，fixedComprises the following steps: r_k，fixed＝R_k，fixed+log₂(1+P_k，maxH_k，n) In which H is_k，n＝|h_k，n|²/(N₀BN^-1)，h_k，nIs omega_k，leftCarrier gain of the nth carrier, N₀Updating the current total power constraint value for the channel noise power spectral density, B for the total bandwidth and N for the total number of carriersComprises the following steps:wherein N is_k，fixedIs a set omega_k，fixedAnd (4) the number of the medium carriers is transferred to the step 2) until the algorithm is finished.

Proportional fairness factor gamma according to cognitive user rate in step 2)₁∶γ₂...∶γ_K、Ω_k，leftCarrier to channel noise ratio, current fixed rate R_k，fixedAnd the current total powerCalculating power P distributed to each cognitive user_k，totalThe method comprises the following steps:

power P of cognitive user_k，totalThe calculation formula is as follows

<math> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>a</mi> <mi>k</mi> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mi>k</mi> </msub> </msup> <mo>-</mo> <msub> <mover> <mi>P</mi> <mo>~</mo> </mover> <mi>total</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </math>

$P_{k,\mathrm{total}}=a_k{\left(P_{1,\mathrm{total}}\right)}^{b_k}$

Wherein,

<math> <mrow> <msub> <mi>a</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>H</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>mid</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mrow> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> <msup> <mn>2</mn> <mfrac> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>fixed</mi> </mrow> </msub> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>_</mo> <mi>left</mi> </mrow> </msub> </mfrac> </msup> <mo>)</mo> </mrow> <mfrac> <mrow> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> <msub> <mi>&gamma;</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <msub> <mi>&gamma;</mi> <mn>1</mn> </msub> </mrow> </mfrac> </msup> <mo>&CenterDot;</mo> <mfrac> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <mrow> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>mid</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mrow> </mfrac> <msup> <mn>2</mn> <mfrac> <msub> <mi>R</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>fixed</mi> </mrow> </msub> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> </msup> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

<math> <mrow> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> <msub> <mi>&gamma;</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <msub> <mi>&gamma;</mi> <mn>1</mn> </msub> </mrow> </mfrac> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

a_kand b_kThe variables in (1) describe: h_k，mid＝|h_k，mid|²/(N₀BN^-1)，h_k，midIs omega_k，leftIntermediate value of intermediate carrier gain, N₀For the channel noise power spectral density, B is the total bandwidth and N is the total number of carriers.N_k，leftIs omega_k，leftThe number of medium carriers.

Each cognitive user in the step 3) according to the divided power value P_k，totalUsing rapid water injection method to adjust omega_k，leftThe power allocation step of the carrier wave in (1) is as follows:

(1) determining the interval [ alpha ]_n，α_n+1]WhereinThe interval satisfiesThereby obtaining a phi aggregate_k＝{i|i≤n，i∈Ω_k，leftIf it is aligned with Ω for the first time_k，leftThe carrier wave in (1) carries out rapid power water injection and omega_k，leftHas a carrier to channel noise ratio ofAccording to the left boundary value alpha of the interval_nAnd interval right boundary value alpha_n+1Is directly calculated to satisfy P_k，total∈[α_n，α_n+1]The required carrier number n is not the first time to Ω_k，leftThe carrier wave in the interval is subjected to rapid power water injection, and only the left boundary value alpha of the interval needs to be subjected to rapid power water injection on the basis of the previous time_nAnd interval right boundary value alpha_n+1Adjusting without recalculation, and assuming that the water injection power of the ith carrier exceeds the power constraint value in the last rapid water injection process, the ith carrier will be from the set omega_k，leftRemoving the middle part, not participating the fast water injection process of the round, and then carrying out the left boundary value alpha of the interval_nAnd interval right boundary value alpha_n+1And (3) adjusting: first, the left boundary value alpha of the interval is modified_nHas a value ofModified interval right boundary value alpha_n+1Has a value ofJudgment of conditionsIf the left boundary value alpha is still satisfied, if yes, the left boundary value alpha of the interval is determined_nAnd interval right boundary value alpha_n+1If not, ifThen add the n +1 th carrier to the set phi_kOf medium, i.e. phi_k＝{i|i≤n+1，i∈Ω_k，leftThe left boundary value alpha of the modification interval_nHas a value ofModified interval right boundary value alpha_n+1Has a value ofRepeating the above steps until the conditionsMeets the requirements;

(2) calculating a fast power water filling threshold:wherein M is_kAs a set of phi_kThe number of the elements in (B).

The method fully utilizes the model characteristics of power distribution among the cognitive users under the proportional fairness and the interference constraint, effectively simplifies the power distribution among the cognitive users into the equation solving process of a single variable, and greatly reduces the computational complexity of the problem. Meanwhile, the rapid water injection method for the carrier power distribution problem of the single user avoids the iterative process, and the water injection threshold can be determined through one-time calculation.

Drawings

Fig. 1 is a flow chart of a power allocation method based on proportional fairness and interference constraints in a cognitive OFDMA system;

FIG. 2 is a graph showing the change of proportional fairness among cognitive users with the total power constraint value, and the simulation graph compares the fairness performance of the algorithm of the present invention with ergodic solutions (optimal solutions obtained by traversing all the cases), TDMA algorithm and reference algorithm ("associating in Capacity of Multi user OFDM System Using dynamic basic Allocation", in Proc. IEEE VTC, 2000),

fig. 3 is a variation of the System Capacity gain of the cognitive user with the total power constraint value, and the simulation chart compares the Capacity gain of the TDMA algorithm with the Capacity gain of the algorithm of the present invention, which is obtained by dividing the System Capacity of each algorithm by the Capacity of the TDMA algorithm under the same condition, with the traversal solution (the optimal solution obtained by traversing all the cases), and the reference algorithm ("including in Capacity of multi-user OFDM System Using Dynamic sub channel allocation", in proc.

Detailed Description

The power distribution method based on proportional fairness and interference constraint in the cognitive OFDMA system comprises the following steps:

1) the following variables are initialized as follows and,P_k，total＝0，R_k，fixed＝0，Ω_k，left＝Ω_k2, 3.., K, wherein P is_totalA value representing the total power constraint is indicated,representing the current total power constraint value, P_k，totalRepresents the power, Ω, allocated to the kth cognitive user_kRepresents the set of carriers, Ω, allocated to the kth cognitive user_k，fixedRepresents a set of carriers of fixed rate, Ω, belonging to the kth cognitive user_k，leftRepresents omega_kRemoving omega_k，fixedThe elements left after the elements in the list are collected, and K is the number of the cognitive users;

2) proportional fairness factor gamma based on cognitive user rate₁∶γ₂...∶γ_K、Ω_k，leftCarrier to channel noise ratio, current fixed rate R_k，fixedAnd the current total powerCalculating power P distributed to each cognitive user_k，total；

3) Each cognitive user is according to the divided power value P_k，totalUsing rapid water injection method to adjust omega_k，leftCarrying out power distribution on the carrier waves in the group;

4) each cognitive user detects omega_k，leftWhether the carrier power in (1) all meets the interference constraint condition: p_k，n≤P_k，max，n∈Ω_k，leftIn which P is_k，nRepresents the power, P, allocated by the k cognitive user on the n carrier_k，maxRepresents the set omega_k，leftIf the power distribution of the carrier of all cognitive users meets the power constraint condition, the algorithm is ended, otherwise, P is detected_k，n＞P_k，maxThe k-th cognitive user divides the n-th carrier into a carrier set omega with a fixed rate_k，fixedAnd the nth carrier is selected from the set omega_k，leftDeleting and updating the fixed rate R of the kth cognitive user_k，fixedComprises the following steps: r_k，fixed＝R_k，fixed+log₂(1+P_k，maxH_k，n) In which H is_k，n＝|h_k，n|²/(N₀BN^-1)，h_k，nIs omega_k，leftThe carrier gain of the nth carrier of the plurality of carriers,N₀updating the current total power constraint value for the channel noise power spectral density, B for the total bandwidth and N for the total number of carriersComprises the following steps:wherein N is_k，fixedIs a set omega_k，fixedAnd (4) the number of the medium carriers is transferred to the step 2) until the algorithm is finished.

Proportional fairness factor gamma according to cognitive user rate in step 2)₁∶γ₂...∶γ_K、Ω_k，leftCarrier to channel noise ratio, current fixed rate R_k，fixedAnd the current total powerCalculating power P distributed to each cognitive user_k，totalThe method comprises the following steps:

power P of cognitive user_k，totalThe calculation formula is as follows

<math> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>a</mi> <mi>k</mi> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mi>k</mi> </msub> </msup> <mo>-</mo> <msub> <mover> <mi>P</mi> <mo>~</mo> </mover> <mi>total</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </math>

$P_{k,\mathrm{total}}=a_k{\left(P_{1,\mathrm{total}}\right)}^{b_k}$

Wherein,

<math> <mrow> <msub> <mi>a</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>H</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>mid</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mrow> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> <msup> <mn>2</mn> <mfrac> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>fixed</mi> </mrow> </msub> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>_</mo> <mi>left</mi> </mrow> </msub> </mfrac> </msup> <mo>)</mo> </mrow> <mfrac> <mrow> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> <msub> <mi>&gamma;</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <msub> <mi>&gamma;</mi> <mn>1</mn> </msub> </mrow> </mfrac> </msup> <mo>&CenterDot;</mo> <mfrac> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <mrow> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>mid</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mrow> </mfrac> <msup> <mn>2</mn> <mfrac> <msub> <mi>R</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>fixed</mi> </mrow> </msub> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> </msup> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

<math> <mrow> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> <msub> <mi>&gamma;</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <msub> <mi>&gamma;</mi> <mn>1</mn> </msub> </mrow> </mfrac> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

a_kand b_kThe variables in (1) describe: h_k，mid＝|h_k，mid|²/(N₀BN^-1)，h_k，midIs omega_k，leftIntermediate value of intermediate carrier gain, N₀For the channel noise power spectral density, B is the total bandwidth and N is the total number of carriers.N_k，leftIs omega_k，leftThe number of medium carriers.

Each cognitive user in the step 3) according to the divided power value P_k，totalUsing rapid water injection method to adjust omega_k，leftThe power allocation step of the carrier wave in (1) is as follows:

(1) determining the interval [ alpha ]_n，α_n+1]WhereinThe interval satisfiesThereby obtaining a set phi_k＝{i|i≤n，i∈Ω_k，leftIf it is aligned with Ω for the first time_k，leftThe carrier wave in (1) carries out rapid power water injection and omega_k，leftHas a carrier to channel noise ratio ofAccording to the left boundary value alpha of the interval_nAnd interval right boundary value alpha_n+1Is directly calculated to satisfy P_k，total∈[α_n，α_n+1]The required carrier number n is not the first time to Ω_k，leftThe carrier wave in the interval is subjected to rapid power water injection, and only the left boundary value alpha of the interval needs to be subjected to rapid power water injection on the basis of the previous time_nAnd interval right boundary value alpha_n+1Adjusting without recalculation, and assuming that the water injection power of the ith carrier exceeds the power constraint value in the last rapid water injection process, the ith carrier will be from the set omega_k，leftRemoving the middle part, not participating the fast water injection process of the round, and then carrying out the left boundary value alpha of the interval_nAnd interval right boundary value alpha_n+1And (3) adjusting: first, the left boundary value alpha of the interval is modified_nHas a value ofModified interval right boundary value alpha_n+1Has a value ofJudgment of conditionsIf the left boundary value alpha is still satisfied, if yes, the left boundary value alpha of the interval is determined_nAnd interval right boundary value alpha_n+1If not, ifThen add the n +1 th carrier to the set phi_kOf medium, i.e. phi_k＝{i|i≤n+1，i∈Ω_k，leftThe left boundary value alpha of the modification interval_nHas a value ofModified interval right boundary value alpha_n+1Has a value ofRepeating the above steps until the conditionsMeets the requirements;

(2) calculating a fast power water filling threshold:wherein M is_kIs a phi aggregate_kThe number of the elements in (B).

Examples

The carrier Allocation process in this embodiment does not belong to the research range of this algorithm, and a carrier Allocation manner in a reference algorithm ("associating in Capacity of multi-user OFDM System Using Dynamic sub-channel Allocation", in proc. ieee VTC, 2000) is adopted, but the average Allocation of the power on each carrier in the carrier Allocation process in the reference algorithm ("associating in Capacity of multi-user OFDM System Using Dynamic sub-channel Allocation", in proc. ieee VTC, 2000) is changed into the carrier power constraint value in this example. For ease of understanding, the carrier allocation in the modified reference ("associating in Capacity of multi-user OFDM System Using Dynamic subcarrier allocation", in proc. ieee VTC, 2000) is briefly described as follows:

(1) initializing carrier sets for individual cognitive usersInitializing rate R of each cognitive user_kK, Ω is a total available carrier set, where N is 14 available carriers, and the carrier gain h of the cognitive user 1 is_1，nIn the [0.84, 0.99 ]]Randomly generates and recognizes the carrier gain h of the user 2_2，nIn the [0.85, 1.04 ]]Generated randomly, noise power spectral density N of each carrier₀The value of the total bandwidth B is set to 1 mW;

(2) finding out the cognitive user k to satisfySelecting a carrier n by a cognitive user k to satisfy: h_k，n≥H_k，m，n∈Ω，H_k，n＝|h_k，n|²/(N₀BN^-1) Updating cognitive user k at rate R_k＝R_k+Blog₂(1+H_k，nP_k，max) Updating the carrier set omega of the cognitive user k_kIs omega_k＝Ω_k∪{n}；

(3) Carrier n is removed from the set omega. If it isFinishing the carrier allocation, otherwise returning to the step (2) until the carrier allocation is finished, and obtaining the carrier set omega of each cognitive user_k，k＝1，2，...K。

The power distribution method based on proportional fairness and interference constraint in the cognitive OFDMA system comprises the following steps:

1) initializing variables:P_k，total＝0，R_k，fixed＝0，Ω_k，left＝Ω_kfor K2, 3. Wherein P is_totalThe total power constraint value is expressed, the value is from 10mW to 15mW, the performance of the algorithm under different total power constraints is observed respectively,representing the current total power constraint value, P_k，totalRepresents the power, Ω, allocated to the kth cognitive user_kRepresents the set of carriers allocated to the kth cognitive user, obtained by the carrier allocation process described above, Ω_k，fixedRepresents a set of carriers of fixed rate, Ω, belonging to the kth cognitive user_k，leftRepresents omega_kRemoving omega_k，fixedThe number of the elements in the element set is K2, and the carrier power constraint value P of the cognitive user is_1，max＝P_2，max＝1mW；

2) Proportional fairness factor gamma based on cognitive user rate₁∶γ₂＝1∶1、Ω_k，leftCarrier to channel noise ratio, current fixed rate R_k，fixedAnd the current total powerCalculating power P distributed to each cognitive user_k，total；

3) Each cognitive user is according to the divided power value P_k，totalUsing rapid water injection method to adjust omega_k，leftCarrying out power distribution on the carrier waves in the group;

4) each cognitive user detects omega_k，leftWhether the allocated power of the carrier in (1) meets the interference constraint condition: p_k，n≤P_k，max，n∈Ω_k，leftIn which P is_k，nRepresents the power, P, allocated by the k cognitive user on the n carrier_k，maxRepresents the set omega_k，leftPower constraint value of the medium carrier. If the carrier power allocation of all the cognitive users meets the power constraint condition,the algorithm ends, otherwise P is detected_k，n＞P_k，maxThe k-th cognitive user divides the n-th carrier into a carrier set omega with a fixed rate_k，fixedAnd the nth carrier is selected from the set omega_k，leftDeleting and updating the fixed rate R of the kth cognitive user_k，fixedComprises the following steps: r_k，fixed＝R_k，fixed+log₂(1+P_k，maxH_k，n)，H_k，n＝|h_k，n|²/(N₀BV^-1)，h_k，nFor the carrier gain value of the nth carrier of the cognitive user k, the carrier gain h of the cognitive user 1_1，nIn the [0.84, 0.99 ]]Randomly generates and recognizes the carrier gain h of the user 2_2，nIn the [0.85, 1.04 ]]Are randomly generated. N is a radical of₀The channel noise power spectral density is 1mW, the total bandwidth is B, the value is assumed to be 1, and the total number of carriers is N14. Updating a current total power constraint valueComprises the following steps:wherein N is_k，fixedIs a set omega_k，fixedAnd (4) the number of the medium carriers is transferred to the step 2) until the algorithm is finished.

Proportional fairness factor gamma according to cognitive user rate in step 2)₁∶γ₂＝1、Ω_k，leftCarrier to channel noise ratio, current fixed rate R_k，fixedAnd the current total powerCalculating power P distributed to each cognitive user_k，totalThe method comprises the following steps: solution equation

<math> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>2</mn> </munderover> <msub> <mi>a</mi> <mi>k</mi> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mi>k</mi> </msub> </msup> <mo>-</mo> <msub> <mover> <mi>P</mi> <mo>~</mo> </mover> <mi>total</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </math>

$P_{2,\mathrm{total}}=a_2{\left(P_{1,\mathrm{total}}\right)}^{b_2}$

Wherein,

<math> <mrow> <msub> <mi>a</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>H</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>mid</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mrow> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> <msup> <mn>2</mn> <mfrac> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>fixed</mi> </mrow> </msub> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> </msup> <mo>)</mo> </mrow> <mfrac> <mrow> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> <mi></mi> </mrow> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> </msup> <mo>&CenterDot;</mo> <mfrac> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <mrow> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>mid</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mrow> </mfrac> <msup> <mn>2</mn> <mfrac> <msub> <mi>R</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>fixed</mi> </mrow> </msub> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> </msup> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>2</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

$b_k=\left\{\begin{array}{cc}1,& k=1\\ \frac{N_{1,\mathrm{left}}}{N_{k,\mathrm{left}}},& k=2\end{array}\right.,$

a_kand b_kThe variables in (1) describe: h_k，mid＝|h_k，mid|²/(N₀BN^-1)，h_k，midIs omega_k，leftThe intermediate value of the medium carrier gain, the carrier gain h of the cognitive user 1_1，nIn the [0.84, 0.99 ]]Randomly generates and recognizes the carrier gain h of the user 2_2，nIn the [0.85, 1.04 ]]Are randomly generated. N is a radical of₀The channel noise power spectral density is 1mW, the total bandwidth is B, the value is assumed to be 1, and the total number of carriers is N14.N_k，leftIs omega_k，leftThe number of medium carriers.

The equations in this step can be solved by Newton's method or trial method (see "Handbook of chemical Functions with formals, Graphs, and chemical Tables", 9)^thprinting.New York：Dover，1972.)

Each cognitive user in the step 3) according to the divided power value P_k，totalUsing rapid water injection method to adjust omega_k，leftThe power allocation step of the carrier wave in (1) is as follows:

(1) determining the interval [ alpha ]_n，α_n+1]WhereinThe interval satisfiesThereby obtaining a phi aggregate_k＝{i|i≤n，i∈Ω_k，leftIf it is aligned with Ω for the first time_k，leftThe carrier wave in (1) carries out rapid power water injection and omega_k，leftHas a carrier to channel noise ratio ofAccording to the left boundary value alpha of the interval_nAnd interval right boundary value alpha_n+1Is directly calculated to satisfy P_k，total∈[α_n，α_n+1]The required carrier number n. If not for the first time to Ω_k，leftThe carrier wave in the interval is subjected to rapid power water injection, and only the left boundary value alpha of the interval needs to be subjected to rapid power water injection on the basis of the previous time_nAnd interval right boundary value alpha_n+1Adjustments are made without recalculation. Assuming that the water filling power of the ith carrier exceeds the power constraint value in the last rapid water filling process, the ith carrier will be selected from the set omega_k，leftMiddle elimination without taking part in the fast water injection process of the wheel, so that the left boundary value alpha of the modification interval_nHas a value ofModified interval right boundary value alpha_n+1Has a value ofJudgment of conditionsIf it is still satisfied, if yes, the left boundary value of the interval is alpha_nAnd interval right boundary value alpha_n+1If not, ifThen add the n +1 th carrier to the set phi_kOf medium, i.e. phi_k＝{i|i≤n+1，i∈Ω_k，leftH, modify interval left boundary value α_nHas a value ofModified interval right boundary value alpha_n+1Has a value ofRepeating the above steps until the conditionsAnd (4) meeting the requirement.

(2) Calculating a water injection threshold of the rapid water injection method:wherein M is_kAs a set of phi_kThe number of the elements in (B).

Fig. 2 is a variation situation of proportional fairness among cognitive users along with total power, and a simulation diagram compares proportional fairness performance of the method of the present invention with traversal solutions (optimal solutions obtained by traversing all cases), a TDMA method, and a reference method ("associating in Capacity of multi user OFDM System Using Dynamic basic allocation", in proc. When the total power constraint value exceeds 14mW, all carrier power exceeds the carrier power constraint value, and the capacity of each cognitive user is determined by the carrier power constraint value, so that the curves of the traversal solution, the method and the reference method are overlapped. The TDMA method has a different carrier allocation mode from the former three, so that the proportional fairness performance of the cognitive user is different from the former three. In addition, when the total power constraint value is less than 12.5mW, it can be seen from the simulation result that the method of the present invention can well approximate the traversal solution, but the complexity is much higher than that of the method of the present invention because the solving process of the traversal solution is obtained by traversing all cases. When the total power constraint value is greater than 12.5mW and less than 14mW, the allocated power of the partial carriers exceeds the power constraint value of the carriers, and the partial approximate calculation adopted in the method process for simplifying the calculation leads to a result deviating from the traversal solution. Fig. 3 is a change situation of system Capacity gain of cognitive users with total power, and a simulation chart compares the Capacity gain of the TDMA method with the traversal solution (the optimal solution obtained by traversing all the cases), the reference method ("including in Capacity of multi user ofdm system Using Dynamic sub channel Allocation", in proc. ieee VTC, 2000), and the value is obtained by dividing the system Capacity of each method by the Capacity of the TDMA method under the same condition, and the curve has a descending trend because the Capacity difference value decreases with the increase of the total power constraint. It can be seen from the graph that the method of the present invention is superior to the TDMA method and the reference method in system capacity when the total power constraint value is lower than 14 mW. When the total power constraint value is higher than 14mW, all carrier power exceeds the power constraint value of the carrier, and the capacity of each cognitive user is determined by the carrier power constraint value, so that the curves of the traversal solution, the method and the reference method are overlapped. Although the system capacity of the method is reduced compared with that of the traversal solution, the complexity of the method is far lower than that of the traversal solution, and the method is more suitable for engineering application.

Claims (1)

1. A power distribution method based on proportional fairness and interference constraint in a cognitive OFDMA system is characterized by comprising the following steps:

1) the following variables are initialized as follows and,P_k，total=0，R_k，fixed=0，Ω_k，left=Ω_kk =2, 3, …, K, wherein P_totalA value representing the total power constraint is indicated,representing the current total power constraint value, P_k，totalRepresents the power, Ω, allocated to the kth cognitive user_kRepresents the set of carriers, Ω, allocated to the kth cognitive user_k，fixedRepresents a set of carriers of fixed rate, Ω, belonging to the kth cognitive user_k，leftRepresents omega_kRemoving omega_k，fixedThe elements left after the elements in the list are collected, and K is the number of the cognitive users;

2) proportional fairness factor gamma based on cognitive user rate₁∶γ₂…∶γ_K、Ω_k，leftCarrier to channel noise ratio, current fixed rate R_k，fixedAnd the current total powerCalculating power P distributed to each cognitive user_k，total；

3) Each cognitive user is according to the divided power value P_k，totalUsing rapid water injection method to adjust omega_k，leftCarrying out power distribution on the carrier waves in the group;

4) each cognitive user detects omega_k，leftWhether the carrier power in (1) all meets the interference constraint condition: o is_k，n≤P_k，max，n∈Ω_k，leftIn which P is_k，nRepresents the power, P, allocated by the k cognitive user on the n carrier_k，maxRepresents the set omega_k，leftIf the power distribution of the carrier of all cognitive users meets the power constraint condition, the algorithm is ended, otherwise, P is detected_k，n>P_k，maxThe k-th cognitive user divides the n-th carrier into a carrier set omega with a fixed rate_k，fixedAnd the nth carrier is selected from the set omega_k，leftDeleting and updating the fixed rate R of the kth cognitive user_k，fixedComprises the following steps: r_k，fixed=R_k，fixed+log₂(1+P_k，maxH_k，n) In which H is_k，n＝|h_k，n|²/(N₀BN^-1)，h_k，nIs omega_k，leftCarrier gain of the nth carrier, N₀Updating the current total power constraint value for the channel noise power spectral density, B for the total bandwidth and N for the total number of carriersComprises the following steps:wherein N is_k，fixedIs a set omega_k，fixedThe number of the medium carriers is transferred to the step 2) until the algorithm is finished;

proportional fairness factor gamma according to cognitive user rate in step 2)₁∶γ₂…∶γ_K、Ω_k，leftCarrier to channel noise ratio, current fixed rate R_k，fixedAnd the current total powerCalculating power P distributed to each cognitive user_k，totalThe method comprises the following steps:

power P of cognitive user_k，totalThe calculation formula is as follows

<math> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>a</mi> <mi>k</mi> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mi>k</mi> </msub> </msup> <mo>-</mo> <msub> <mover> <mi>P</mi> <mo>~</mo> </mover> <mi>total</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </math>

$P_{k,\mathrm{total}}=a_k{\left(P_{1,\mathrm{total}}\right)}^{b_k}$

Wherein,

<math> <mrow> <msub> <mi>a</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>H</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>mid</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mrow> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> <msup> <mn>2</mn> <mfrac> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>fixed</mi> </mrow> </msub> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> </msup> <mo>)</mo> </mrow> <mfrac> <mrow> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>fixed</mi> </mrow> </msub> <msub> <mi>&gamma;</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <msub> <mi>&gamma;</mi> <mn>1</mn> </msub> </mrow> </mfrac> </msup> <mo>&CenterDot;</mo> <mfrac> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <mrow> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>mid</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mrow> </mfrac> <msup> <mn>2</mn> <mfrac> <mrow> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>fixed</mi> </mrow> </msub> </mrow> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> </msup> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

<math> <mrow> <msub> <mi>b</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> <msub> <mi>&gamma;</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <msub> <mi>&gamma;</mi> <mn>1</mn> </msub> </mrow> </mfrac> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

a_kand b_kThe variables in (1) describe: h_k，mid=|h_k，mid|²／(N₀BN^-1)，h_k，midIs omega_k，leftIntermediate value of intermediate carrier gain, N₀For the channel noise power spectral density, B is the total bandwidth and N is the total number of carriers.N_k，leftIs omega_k，leftThe number of medium carriers, j is a carrier counting variable;

each cognitive user in the step 3) according to the divided power value P_k，tatolUsing rapid water injection method to adjust omega_k，leftThe power allocation step of the carrier wave in (1) is as follows:

(1) determining the interval [ alpha ]_n，α_n+1]Wherein <math> <mrow> <msub> <mi>&alpha;</mi> <mi>n</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>i</mi> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mfrac> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> </mtd> <mtd> <mi>n</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>&infin;</mo> <mo>,</mo> </mtd> <mtd> <mi>n</mi> <mo>=</mo> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math> The interval satisfiesThereby obtaining a set phi_k={i|i≤n，i∈Ω_k，leftIf it is aligned with Ω for the first time_k，leftThe carrier wave in (1) carries out rapid power water injection and omega_k，leftHas a carrier to channel noise ratio ofN_k，leftThe number of the carriers is determined according to the left boundary value alpha of the interval_nAnd interval right boundary value alpha_n+1Is directly calculated to satisfy P_k，total∈[α_n，α_n+1]The required carrier number n is not the first time to Ω_k，leftThe carrier wave in the interval is subjected to rapid power water injection, and only the left boundary value alpha of the interval needs to be subjected to rapid power water injection on the basis of the previous time_nAnd interval right boundary value alpha_n+1Adjusting without recalculation, and assuming that the water injection power of the ith carrier exceeds the power constraint value in the last rapid water injection process, the ith carrier will be from the set omega_k，leftRemoving the middle part, not participating the fast water injection process of the round, and then carrying out the left boundary value alpha of the interval_nAnd interval right boundary value alpha_n+1And (3) adjusting: first, the left boundary value alpha of the interval is modified_nHas a value ofModified interval right boundary value alpha_n+1Has a value of <math> <mrow> <msub> <mi>&alpha;</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>&alpha;</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> </mfrac> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math> Judgment of conditions <math> <mrow> <msub> <mover> <mi>P</mi> <mo>~</mo> </mover> <mrow> <mi>k</mi> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>&alpha;</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>&alpha;</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>]</mo> </mrow> </math> If it is still satisfied, if yes, the left boundary value of the interval is alpha_nAnd interval right boundary value alpha_n+1If not, ifThen add the n +1 th carrier to the set phi_kOf medium, i.e. phi_k={i|i≤n+1，i∈Ω_k，leftThe left boundary value alpha of the modification interval_nHas a value ofModified interval right boundary value alpha_n+1Has a value of <math> <mrow> <msub> <mi>&alpha;</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>&alpha;</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>&NotEqual;</mo> <mi>l</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </munderover> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>3</mn> </mrow> </msub> </mfrac> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> Repeating the above steps until the conditions <math> <mrow> <msub> <mover> <mi>P</mi> <mo>~</mo> </mover> <mrow> <mi>k</mi> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>&alpha;</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>&alpha;</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>]</mo> </mrow> </math> Meets the requirements;

(2) calculating a fast power water filling threshold:wherein M is_kAs a set of phi_kThe number of the elements in (B).