A resource allocation method for a symbiotic network of reciprocity combining active transmission and passive transmission

Abstract

The embodiment of the present disclosure relates to a resource allocation method of a symbiotic network combining active transmission and passive transmission. The method comprises the following steps: establishing a symbiotic network combining active transmission and passive transmission, wherein the symbiotic network comprises one primary user, a plurality of secondary users and one receiver; the secondary users in the symbiotic network perform passive communication and active communication in turn; obtaining variables in the passive communication and the active communication, obtaining a variable group, and establishing a non-convex resource allocation optimization problem model according to the variable group; converting the non-convex resource allocation optimization problem model into a convex optimization problem model; and obtaining the optimal resource allocation method in the symbiotic network according to the convex optimization problem model. The embodiment of the present disclosure improves the communication rate of the secondary user, guarantees the communication rate of the primary user transmitter, and can quickly converge to the optimal value.

Description

Technical Field

[0001] This disclosure relates to the field of wireless communication technology, and in particular to a resource allocation method for a mutually beneficial symbiotic network that integrates active and passive transmission. Background Technology

[0002] With the massive number of nodes connecting to the Internet of Things (IoT), spectrum shortage and node energy constraints have become bottlenecks restricting the development of IoT technology, urgently requiring a technology that can improve spectrum efficiency and reduce power consumption. Against this backdrop, symbiotic radio networks have emerged. In this network, secondary users modulate their own signals onto environmental radio frequency signals by adjusting antenna impedance for information transmission. The receiver uses serial interference cancellation technology to decode information from both the primary and secondary users sequentially. Depending on whether the period of the secondary user signal is greater than that of the primary user signal, symbiotic radio networks can be further divided into parasitic and reciprocal modes. In reciprocal mode, the signal from the secondary user can serve as a multipath for the primary user signal, bringing performance gains to the primary user. Therefore, reciprocal symbiotic radio has greater application prospects. However, in traditional reciprocal symbiotic communication networks, the data transmission rate of secondary users is relatively slow, making it difficult to meet the needs of application scenarios with certain data rate requirements.

[0003] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0004] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention

[0005] The purpose of this disclosure is to provide a resource allocation method for a mutually beneficial symbiotic network that integrates active and passive transmission, thereby overcoming, to at least some extent, one or more problems caused by the limitations and defects of related technologies.

[0006] According to embodiments of this disclosure, a resource allocation method for a mutually beneficial symbiotic network integrating active and passive transmission is provided, the method comprising:

[0007] Establish a mutually beneficial symbiotic network that integrates active and passive transmission, wherein the mutually beneficial symbiotic network includes a primary user, several secondary users, and a receiver;

[0008] The secondary users in the mutually beneficial symbiotic network sequentially perform passive communication and active communication.

[0009] Obtain the variables in the passive communication and the active communication to obtain a variable set, and establish a non-convex resource allocation optimization problem model based on the variable set;

[0010] Transform the non-convex resource allocation optimization problem model into a convex optimization problem model;

[0011] Based on the convex optimization problem model, the optimal resource allocation method in the mutually beneficial symbiotic network is obtained.

[0012] In one embodiment of this disclosure, the passive communication includes:

[0013] The secondary user performs passive communication and energy harvesting sequentially; wherein, after the passive communication is completed, the secondary user only performs energy harvesting.

[0014] In one embodiment of this disclosure, the active communication includes:

[0015] The secondary users sequentially perform active communication; wherein, after the active communication is completed, the secondary users perform the energy harvesting.

[0016] In one embodiment of this disclosure, the time of passive communication and the time of active communication are both divided into several time slots, and the number of time slots corresponds to the number of secondary users; wherein, the time of passive communication is a first preset value, and the time of active communication is a second preset value.

[0017] In one embodiment of this disclosure, the variable group includes:

[0018] The active communication time, the passive communication time, the primary user's transmit power, the secondary user's backscatter coefficient, the secondary user's transmit power, and the secondary user's maximum secondary user and rate.

[0019] In one embodiment of this disclosure, the primary user's transmit power is a third preset value, the secondary user's backscatter coefficient is a fourth preset value, the secondary user's transmit power is a fifth preset value, and the secondary user's maximum secondary user sum rate is a sixth preset value.

[0020] In one embodiment of this disclosure, the step of establishing a non-convex resource allocation optimization problem model based on the variable set includes:

[0021] With the maximum number of secondary users and the rate of the secondary users as the objective, a non-convex resource allocation optimization problem model is established based on the active communication time, the passive communication time, the primary user's transmit power, the secondary user's backscatter coefficient, and the secondary user's transmit power.

[0022] In one embodiment of this disclosure, the step of transforming the non-convex resource allocation optimization problem model into a convex optimization problem model includes:

[0023] The non-convex resource allocation optimization problem model is transformed into a convex optimization problem model using proof by contradiction, continuous convex approximation, and auxiliary variable method.

[0024] In one embodiment of this disclosure, the step of obtaining the optimal resource allocation method in the mutually beneficial symbiotic network based on the convex optimization problem model includes:

[0025] The optimization variables and the optimal objective value in the convex optimization problem model are updated using a preset iterative algorithm until convergence is obtained to obtain the maximum number of secondary users and the rate for all secondary users.

[0026] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects:

[0027] In the embodiments of this disclosure, the resource allocation method of the mutually beneficial symbiotic network that integrates active and passive transmission is used to improve the communication rate of secondary users, ensure the communication rate of primary user transmitters, and enable rapid convergence to the optimal value. Attached Figure Description

[0028] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0029] Figure 1 A flowchart illustrating the steps of a resource allocation method for a mutually beneficial symbiotic network integrating active and passive transmission in an exemplary embodiment of this disclosure;

[0030] Figure 2 A schematic diagram of a mutually beneficial symbiotic network integrating active and passive transmissions is shown in an exemplary embodiment of this disclosure;

[0031] Figure 3 This invention discloses a graph showing the relationship between the communication rate of a secondary user and the number of iterations in an exemplary embodiment of the present invention.

[0032] Figure 4 The diagram illustrates the secondary user communication rate and rate in an exemplary embodiment of this disclosure, compared with the secondary user communication rate and rate of a conventional reciprocal radio system as a function of the primary user transmit power.

[0033] Figure 5 The diagram illustrates the variation of the secondary user communication rate and the rate with the primary user minimum rate gain under different primary user transmit powers in an exemplary embodiment of this disclosure.

[0034] Figure 6 The diagram illustrates the variation of the primary user communication rate with the primary user transmit power under different primary user minimum rate gains in an exemplary embodiment of this disclosure. Detailed Implementation

[0035] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0036] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0037] This example implementation provides a resource allocation method for a mutually beneficial symbiotic network that integrates active and passive transmission. (See reference...) Figure 1 As shown, the resource allocation method of the mutually beneficial symbiotic network integrating active and passive transmission may include steps S101 to S105.

[0038] Step S101: Establish a mutually beneficial symbiotic network that integrates active and passive transmission, wherein the mutually beneficial symbiotic network includes a primary user, several secondary users, and a receiver;

[0039] Step S102: The sub-users in the mutually beneficial symbiotic network sequentially perform passive communication and active communication;

[0040] Step S103: Obtain the variables in the passive communication and the active communication to obtain a variable group, and establish a non-convex resource allocation optimization problem model based on the variable group;

[0041] Step S104: Transform the non-convex resource allocation optimization problem model into a convex optimization problem model;

[0042] Step S105: Based on the convex optimization problem model, obtain the optimal resource allocation method in the mutually beneficial symbiotic network.

[0043] Through the resource allocation method of the aforementioned mutually beneficial symbiotic network integrating active and passive transmission, each secondary user can sequentially perform passive and active communication. In addition to active and passive communication, each secondary user also harvests energy. During passive communication, a mutually beneficial transmission is formed between the secondary user and the primary user; that is, while the secondary user utilizes the primary user's signal to transmit its own information, the primary user's transmission performance is also improved. During active communication, the secondary user sequentially performs active communication, forming a two-way uplink NOMA transmission with the primary user's signal. The information receiver first decodes the received signal transmitted by the primary user using continuous interference cancellation technology, completely removing the signal from the primary user before decoding the received signal from the secondary user. This improves the communication rate of the secondary user, ensures the communication rate of the primary user's transmitter, and enables rapid convergence to the optimal value.

[0044] Below, we will refer to Figures 1 to 5 The steps of the resource allocation method for the above-described mutually beneficial symbiotic network that integrates active and passive transmission in this example embodiment will be described in more detail.

[0045] In steps S101, S102, and S103, establish as follows Figure 2 The illustrated mutually beneficial symbiotic network communication system integrating active and passive transmission includes one primary user, K secondary users, and one receiver; wherein, the channel coefficient between the primary user and the receiver is... Figure 2 g in PR The channel coefficient between primary user i and secondary user i is Figure 2 g in PS,i The channel coefficients from secondary user i to secondary user K are: Figure 2 g in SS,ik The channel coefficient between secondary user i and the receiver is Figure 2 g in SR The total transmission time T is divided into two stages, and time division multiple access (TDMA) technology is used to allocate the passive communication time T to all secondary users. b and active communication time T a The system is divided into K sub-time slots, each corresponding to one of the K secondary users. The time allocated to the i-th secondary user for passive communication and active communication is τ, respectively. i and t i .then, In passive communication T b During this period, secondary users perform passive communication and energy harvesting in their corresponding time slots, and only perform energy harvesting in non-corresponding time slots, taking into account energy harvesting from reflected signals from other secondary users and signals from the primary user. In active communication T... aDuring this period, secondary users actively communicate within their corresponding time slots and only collect energy in non-corresponding time slots, considering energy collection from signals from other secondary users' active communication and from primary user signals. A non-convex resource allocation optimization problem model is established, with the primary user's transmit power, the secondary user's backscatter coefficient, the secondary user's transmit power, and the secondary user's active / passive communication time as the objective, constrained by the primary link communication capacity and the causal constraints of the secondary user's energy. The non-convex resource allocation optimization problem is transformed into a convex optimization problem model using proof by contradiction, continuous convex approximation, and auxiliary variable methods. A preset iterative algorithm is used to update the optimization variables and the optimal objective value in the convex optimization problem model until convergence is obtained to obtain the optimal rate for all secondary users.

[0046] In the communication system, during the passive information transmission of the i-th secondary user, the signal received by the receiver is: The signal consists of two parts: the first part being the received signal transmitted by the primary user; the second part being the received backscattered signal from the i-th secondary user; and w(n) being the noise received by the receiver, which has a mean of 0 and a variance of σ. 2 Gaussian distribution, P p The primary user transmit power, β i : The backscattering coefficient of the i-th secondary user, s(n); : The transmitted signal of the primary user, c i The i-th secondary user backscattered signal, and s(n),c i All follow a standard circularly symmetric complex Gaussian distribution, g PR The channel coefficient between the primary user and the receiver, g PS,i : The channel coefficient between the primary user and the secondary user i, g SR,i : The channel coefficient between the secondary user i and the receiver, g SS,ij The channel coefficients between secondary user i and secondary user j are obtained by the receiver decoding the received signal to determine the primary user's channel coefficients in time slot τ. i communication capacity In the above formula,

[0047]

[0048] The proof of the second equation is given in Lemma 1, regarding the signal-to-noise ratio of the primary user. Assuming the primary user signal is perfectly removed, the i-th secondary user is obtained in time slot τ. i communication capacity Compared to the transmission rate of the primary user when there is no secondary user access in the traditional case In comparison, during the entire passive communication phase, the system's master user transmission rate increased. Δ1 is positive because when x > 0, Ei(-x) < 0. From the perspective of energy harvesting, each sub-user in T b Energy collected internally: The first part represents the energy collected by secondary user i during passive communication, and the second part represents the energy collected by secondary user i during passive communication with other users. i The third part represents the energy collected from the primary user's signal, and the energy collected by the secondary user from the backscattered signals of other secondary users.

[0049] In the communication system, during the active communication of the i-th secondary user, the signal received by the receiver is: Wherein, the first part represents the signal received from the primary user, the second part represents the signal received from the i-th secondary user, P tr,i : The transmit power of the i-th secondary user, x i (n): The signal sent by the i-th secondary user follows a standard circularly symmetric complex Gaussian distribution. The signal from the secondary user and the primary user signal form a two-way uplink NOMA transmission. When decoding the primary user signal, the signal from the secondary user will interfere with the primary user signal. The primary user signal in time slot t is obtained. i communication capacity Compared to the transmission rate of the primary user when there is no secondary user access in the traditional case In comparison, during the entire active communication phase, the system's primary user transmission rate was reduced. After perfectly removing the primary user signal from the received signal using serial interference cancellation technology, the i-th secondary user signal in time slot t is obtained. i The communication capacity is From an energy harvesting perspective, secondary user i in T a Energy collected internally: The first part represents the energy collected by secondary user i from primary user when other users actively communicate, and the second part represents the energy collected by secondary user i from signals of active communication from other secondary users.

[0050] Energy consumed by secondary user i during passive communication: Where, ε b This refers to the static power consumption of the passive communication circuit. The energy consumed by secondary user i during active communication includes transmission energy consumption and the static power consumption of the circuit. Where, ε a This refers to the power consumption of the static circuit for active communication.

[0051] The model for the non-convex resource allocation optimization problem is as follows:

[0052]

[0053] Here, Δ is a constant representing the minimum rate gain of the primary user. F1 ensures that the sum of the rate increase and decrease of the primary user is not less than Δ, meaning that in our proposed network, the communication capacity of the primary user can be improved, thus guaranteeing the reciprocal relationship between the primary and secondary users. F2 is the energy causal constraint for the secondary user, meaning that the energy collected by the secondary user must be greater than or equal to the energy consumed. F3 and F4 are constraints on the backscattering coefficient of the secondary user and the range of transmission power of the primary and secondary users. F6 and F7 represent that the sum of the passive and active communication times of all secondary users cannot exceed the allocated time. F8 constrains the sum of the total active communication time and the total passive communication time.

[0054] In steps S104 and S105, the non-convex resource allocation optimization problem is transformed into a convex optimization problem model through proof by contradiction, continuous convex approximation, and auxiliary variable method.

[0055] By proving Lemma 1, we know that the second equality holds in the following equation:

[0056]

[0057] Due to the objective function In this term, there are multiple coupled variables P in constraints F1 and F2. p τ i and β i In addition, the objective function Furthermore, there are coupled variables in constraints F1 and F2. To simplify the problem, Lemma 2 is introduced to show that the optimal transmit power of the primary user is its maximum transmit power, i.e., P. p =P max The optimization problem Q1 is obtained.

[0058] Although the optimization problem Q1 is easier to solve than Q0, there are still several coupled variables in the objective function and constraints F1 and F2, such as τ. i and β i , t i and P tr,i To further decouple the variables, the SCA technique was used to decouple the constraints. Perform a Taylor expansion and substitute the expansion into the optimization problem Q1 to obtain the optimization problem Q2.

[0059] Constructing auxiliary variable q i =τ i β i , z i =t i P tr,i Substituting this into optimization problem Q2 yields optimization problem Q3.

[0060] In a specific embodiment, the above method is as follows:

[0061] Lemma 1:

[0062]

[0063] The proof of Lemma 1 is as follows:

[0064]

[0065]

[0066] The third equation above is based on roll out.

[0067]

[0068] Therefore, the main user is in τ i The rate over a time period can be expressed as:

[0069]

[0070] Lemma 2: It can be proved by contradiction that the optimal transmit power of the primary user is its maximum transmit power, i.e., P. p =P max Substituting this into optimization problem Q0 yields optimization problem Q1.

[0071]

[0072] Proof of Lemma 2: Proof by contradiction. Assume the solution to the optimization problem is... and Construct another solution And satisfy Furthermore, the solution satisfies all constraints. By the original assumption, since... This is the optimal solution, therefore Established.

[0073] Due to the equation Established, and The objective function is about P p It is an increasing function, therefore we have This is true, which clearly contradicts the original assumption. Established.

[0074] The constraint F in the optimization model corresponding to the optimization problem Q1 1-1 In Taylor expansion yields:

[0075]

[0076] In the above formula, the equal sign only applies when... When it holds true, substituting the expansion into the constraint F... 1-1 The new constraint F is obtained. 1-2 , will F 1-2 Substituting into optimization problem Q1, we get optimization problem Q2. In optimization problem Q2, the coupling variable τ still exists. i and β i , t i and P tr,i To decouple the above variables, an auxiliary variable q is constructed. i =τ i β i , z i =t i P tr,i Substituting this into optimization problem Q2 yields optimization problem Q3.

[0077]

[0078] The objective function is a concave function in standard logarithmic form, and the constraint F 2-2 F 3-1 F 4-2 F5-F8 are all about the optimization variable τ. i t i q i z i T a and T b By introducing Lemma 3, it can be proved that the constraint F is a linear function. 1-3 middle, It's about q i and τ i The joint concave function, F 1-3 The remaining terms in the equation are linear functions.

[0079] Lemma 3: It's about q i and τ i The joint concave function.

[0080] The proof of Lemma 3 is as follows: The affine function, since the affine function has the property of preserving convexity, therefore and Having the same unevenness, in order to The form is more concise, making Therefore there is Only proof is needed The concavity or convexity of θ is sufficient. If θ follows a standard circularly symmetric complex Gaussian distribution, then... Therefore, it is only necessary to prove The concavity or convexity of the function is sufficient, since the expectation function is convex-preserving. and Having the same concavity and convexity, obviously, It's about q i The concave function, therefore It is a concave function, and therefore it can be proven that... It's about q i and τ i The joint concave function.

[0081] According to the mutually beneficial symbiotic network resource allocation method for the integrated active-passive hybrid energy-carrying communication, the method of updating the optimization variables and optimal objective values ​​in the convex optimization problem model using a preset iterative algorithm until convergence is obtained to obtain the optimal rate for the secondary user includes:

[0082] Initialize system parameters Define the maximum number of iterations L for the outermost layer. max and convergence accuracy ρ;

[0083] Given a feasible initial value Maximum number of iterations L max The objective value of Q3 is then solved using CVX.

[0084] If Q3 converges, then let... And output the optimal value;

[0085] Otherwise, let l = l + 1, and return to step 2 until Q3 converges or l = L. max ;

[0086] The optimal rate for the secondary user is calculated based on the optimal value.

[0087] CVX is a utility algorithm in simulation software.

[0088] In a specific embodiment, the simulation diagram obtained in the simulation experiment is as follows: Figure 3 , Figure 4 and Figure 5 As shown; where, Figure 3 The graph shows the communication rate of the secondary user and the relationship between the rate and the number of iterations. Figure 4 A graph showing the secondary user communication rate and its variation with the primary user's transmit power in a conventional reciprocal radio secondary user communication rate. Figure 5 The graph shows the changes in the secondary user communication rate and rate with the minimum communication rate gain of the primary user under different primary user transmit powers. Figure 6 This is a graph showing how the primary user communication rate varies with the primary user transmit power under different primary user minimum rate gains.

[0089] The resource allocation method of the above-mentioned mutually beneficial symbiotic network that integrates active and passive transmission improves the communication rate of secondary users compared with common mutually beneficial symbiotic networks. Compared with traditional communication systems without secondary system access, the communication rate of the primary user transmitter is guaranteed, and the iterative algorithm used in this method can quickly converge to the optimal value.

[0090] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of this disclosure, "a plurality of" means two or more, unless otherwise explicitly specified.

[0091] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0092] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A resource allocation method for a mutually beneficial symbiotic network integrating active and passive transmission, characterized in that, The method includes: Establish a mutually beneficial symbiotic network that integrates active and passive transmission, wherein the mutually beneficial symbiotic network includes a primary user, several secondary users, and a receiver; The secondary users in the mutually beneficial symbiotic network sequentially perform passive communication and active communication. The variables in the passive communication and the active communication are obtained to form a variable set, and a non-convex resource allocation optimization problem model is established based on the variable set. The non-convex resource allocation optimization problem model includes a primary user rate gain constraint, which is Δ1 + Δ2 ≥ Δ, where Δ1 is the increase in the primary user transmission rate during the passive communication stage, Δ2 is the decrease in the primary user transmission rate during the active communication stage, and Δ is the minimum rate gain constant for the primary user. Transforming the non-convex resource allocation optimization problem model into a convex optimization problem model includes: using proof by contradiction, continuous convex approximation, and auxiliary variable method to transform the non-convex resource allocation optimization problem model into a convex optimization problem model. Based on the convex optimization problem model, the optimal resource allocation method in the mutually beneficial symbiotic network is obtained; The passive communication includes: The secondary user performs passive communication and energy harvesting sequentially; wherein, after the passive communication is completed, the secondary user only performs energy harvesting. The active communication includes: The secondary users then initiate communication in turn. The time for both passive communication and active communication is divided into several time slots, and the number of time slots corresponds to the number of sub-users. The steps for establishing a non-convex resource allocation optimization problem model based on the set of variables include: With the maximum number of secondary users and the rate of the secondary users as the objective, a non-convex resource allocation optimization problem model is established based on the active communication time, the passive communication time, the primary user's transmit power, the secondary user's backscatter coefficient, and the secondary user's transmit power.

2. The resource allocation method for a mutually beneficial symbiotic network integrating active and passive transmission as described in claim 1, characterized in that, The secondary user performs the energy harvesting after the active communication is completed.

3. The resource allocation method for a mutually beneficial symbiotic network integrating active and passive transmission as described in claim 2, characterized in that, The duration of the passive communication is a first preset value, and the duration of the active communication is a second preset value.

4. The resource allocation method for a mutually beneficial symbiotic network integrating active and passive transmission as described in claim 3, characterized in that, The variable group includes: The active communication time, the passive communication time, the primary user's transmit power, the secondary user's backscatter coefficient, the secondary user's transmit power, and the secondary user's maximum secondary user and rate.

5. The resource allocation method for a mutually beneficial symbiotic network integrating active and passive transmission as described in claim 4, characterized in that, The primary user's transmit power is a third preset value, the secondary user's backscatter coefficient is a fourth preset value, the secondary user's transmit power is a fifth preset value, and the secondary user's maximum secondary user sum rate is a sixth preset value.

6. The resource allocation method for a mutually beneficial symbiotic network integrating active and passive transmission as described in claim 1, characterized in that, The step of obtaining the optimal resource allocation method in the mutually beneficial symbiotic network based on the convex optimization problem model includes: The optimization variables and the optimal objective value in the convex optimization problem model are updated using a preset iterative algorithm until convergence is obtained to obtain the maximum number of secondary users and the rate for all secondary users.

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