CN113795013A - Lyapunov optimization-based V2V communication resource allocation method in Internet of vehicles - Google Patents
Lyapunov optimization-based V2V communication resource allocation method in Internet of vehicles Download PDFInfo
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Abstract
A Lyapunov optimization-based V2V resource allocation method in the Internet of vehicles belongs to the technical field of wireless communication. A V2V communication system model for configuring a buffer queue is firstly constructed, and comprises a base station, a plurality of vehicle-to-vehicle links and vehicle-to-infrastructure links, wherein the V2V links realize information exchange between adjacent vehicles in a D2D communication mode by multiplexing resource blocks of the V2I links. Based on the system model, the optimization problem of resource allocation is planned by taking the maximized V2V link energy efficiency as an objective function, and simultaneously ensuring the requirements of V2V link queue delay and reliability and the requirement of V2I link minimum rate. Aiming at the optimization problem of planning, a Lyapunov optimization-based V2V resource allocation method is provided. The resource allocation method can effectively balance the energy efficiency of the V2V link and the queue delay and reliability, and has the characteristic of simple calculation.
Description
Technical Field
The invention relates to a Lyapunov optimization-based V2V communication resource allocation method in the Internet of vehicles, and belongs to the technical field of wireless communication.
Background
In recent years, private cars have entered a period of rapid growth, which has put tremendous pressure on traffic and the environment. In some developed and developing countries, traffic congestion and traffic accidents become increasingly serious, which not only reduces traffic efficiency and causes environmental pollution, but also causes serious loss of lives and property. In order to solve the problem, a more environment-friendly, safer and more intelligent safe trip method is created, and the car networking technology becomes the focus of attention of government agencies, academic circles and industrial circles. The V2V communication is one of key technologies of car networking technology, and can widely support road safety-related applications such as emergency brake warning, collision warning, and overtaking warning, which are related to road safety, and thus meet the requirements of having severe time-ductility and reliability to ensure safe driving.
In recent years, researchers have conducted extensive research on low latency and high reliability of V2V communication in the internet of vehicles. "Resource Allocation for Vehicular Communications With Low Latency and High Reliability" [ C.Guo, L.Liang, and G.Y.Li ], IEEE Transactions on Wireless Communications, vol.18, pp.3887-3902,2019 ] aims to maximize the throughput of V2N (Vehicular-to-Network) links, and addresses a Resource Allocation problem With the constraint of ensuring Low Latency and High Reliability of V2V links. The author obtains a constraint expression based on steady-state reliability and time delay based on queue analysis, and then provides a low-complexity algorithm for solving resource allocation and spectrum sharing matching based on an analysis result. "Dynamic Resource Allocation for Optimized Latency and Reliability in Vehicular Networks," [ m.i.ashraf, c.f.liu, m.bennis, w.saad, and c.s.hong, IEEE Access, vol.6, pp.63843-63858,2018 ] uses Lyapunov optimization technique to decouple the planned V2V link power minimization problem into Resource Allocation and power optimization sub-problems, and then proposes a semi-distributed Resource Allocation strategy to solve the optimal Resource Allocation. The above-described resource allocation does not fully consider the energy efficiency problem of the V2V communication system while studying latency and reliability. In the data looked up at present, there is no precedent for simultaneously optimizing the energy efficiency, the time delay and the reliability of the V2V communication system by using the Lyapunov optimization theory in the V2V resource allocation process.
Disclosure of Invention
In order to overcome the defects and shortcomings of the background art, the invention provides a Lyapunov optimization-based V2V communication resource allocation method in the Internet of vehicles.
The technical scheme of the invention is as follows:
a Lyapunov optimization-based V2V resource allocation method in the Internet of vehicles runs communication services in a system which comprises a base station, a plurality of V2V links and V2I links, wherein the V2I link is pre-allocated with a spectrum resource block, and the V2V link realizes communication between two adjacent vehicles in a D2D communication mode by multiplexing the spectrum resource block of the V2I downlink; the sets of V2V and V2I links are denoted as V2V and V2I, respectively
And
wherein K and M represent the total number of V2V links and V2I links, respectively; in order to analyze the time delay and reliability of the V2V link, a buffer queue for buffering data is configured at the transmission end of each V2V link, the communication system runs communication services according to time slots, and an interval [ t, t +1 ] which uses a time slot t e {1, 2. } to represent a period of time is defined; aiming at the V2V communication system model, an optimization problem is planned, and a resource allocation method is designed according to a Lyapunov optimization theory to solve the optimization problem, wherein the method comprises the following specific steps: 1) problem planning
In time slot t, the data transmission rate of the k-th V2V link is defined as
Wherein
The representation takes arbitrary symbols, B represents the bandwidth, δ represents the time slot duration, αk,m(t) is the resource block multiplexing factor, if the kth V2V link multiplexes the resource block of the mth V2I link at the time slot t, then αk,m(t) 1, otherwise αk,m(t)＝0，σ2Representing the interference work of Gaussian white noiseRate, Pk,m(t) represents transmission power when the frequency spectrum resource block of the mth V2I link is multiplexed by the kth V2V link in the time slot t, Pm(t) denotes the transmission power of the mth V2I link at time slot t, hk,m(t) denotes a channel gain when the k-th V2V link shares a resource block with the m-th V2I link at the slot t, sm,k(t) represents the interference channel gain of the mth V2I link transmission end to the k V2V link receiving ends at the time slot t; V2V link long-time average aggregate throughput
Is defined as
Wherein
τ denotes the τ -th slot of 0 to t-1 slots, Rk(τ) represents the throughput of the k-th V2V link at time slot τ,
represents the throughput of all V2V links at time slot tau, tau is less than or equal to t-1; V2V link long-time average total transmission power
Is composed of
Wherein P isk,m(τ) denotes a transmission power when the kth V2V link of the slot τ multiplexes the spectrum resource block of the mth V2I link,
indicates the total transmission power, alpha, of all V2V links in time slot tauk,m(τ) is the resource block multiplexing factor, if the k-th V2V link multiplexes the resource of the m-th V2I link in the time slot τBlock, then αk,m(τ) ═ 1, otherwise αk,m(t) ═ 0; in time slot t, the base station transmission rate of any V2I link m is defined as
Wherein h ism(t) denotes the channel gain of the mth V2I link at time slot t, gk,m(t) represents the interference channel gain of the kth V2V link transmission end to the mth V2I link receiving end at the time slot t; a task queue is configured at the transmission end of each V2V link, and any V2V link
Is defined as Qk(t) the update formula of which is defined as
Wherein A isk(t) denotes the task arrival rate at time slot t, obeying an average of λ at each time slotkThe distribution of the poisson's distribution of (c),
represents a to Ak(τ) expect, max represents the sign of the maximum;
applying a probability constraint to the queue length of each V2V link, the probability constraint to the queue length of the k-th V2V link being
Wherein Pr represents the probability, LkThe boundary that indicates the length of the queue,
indicating an arbitrary queue length Qk(t) exceeding LkA violation probability of; qk(τ) represents the queue length of link k at time slot τ V2VAnd (3) taking the maximum V2V link energy efficiency as an objective function and taking the delay and reliability requirements of the V2V link and the minimum speed requirement of the V2I link as constraints, planning the following optimization problem
Wherein s.t. represents a constraint symbol, C1, C2, C3, C4 and C5 represent constraint symbols, ηEERepresenting the energy efficiency, R, of the V2V linkCIndicating a minimum value for the V2I link transmission rate,
represents the maximum value of the transmission power of the V2V link;
2) optimization problem equivalence transformation
Constraint C1 may be relaxed to
When the kth V2V link shares a resource block with the mth V2I link, α is satisfied at this timek,mAt 1, the power optimum for the V2I link can be derived from the constraint C2 in problem (7)
Is composed of
Wherein
Optimizing the power of the V2I link
Substituting the optimization problem (7) can result in the following problem
Wherein
3) Lyapunov optimization theory
For the time-averaged constraint C1 in problem (11), a virtual queue is introduced:
Gk(t +1) and Gk(t) denotes any V2V link, respectively
In the virtual queue of the time slot t +1 and the time slot t, a secondary Lyapunov function is defined as
Wherein G (t) ═ G1(t),...,GK(t) }; during any time slot t, the Lyapunov drift and penalty based on the virtual queue G (t) are defined as
Wherein
Representing the desired value of x based on condition y,
representing the amount of change in the Lyapunov function value between two slots,
v > 0 represents a control parameter that trades off queue length against V2V link energy efficiency; under any queue state and control strategy during the time slot t, the Lyapunov drift and penalty based on the virtual queue condition can meet the following upper bound
Wherein [ a ]]+Max {0, a }; according to [ Q ]k(t)-Rk(t)+Ak(t)]+≤max{Qk(t)+Ak(t),Rk,max(t)}-Rk(t) wherein Rk,max(t) represents the maximum transmission rate of the k-th V2V link at time slot t, and it can be concluded that equation (15) satisfies the following equation
Wherein C is a constant, and C is a constant,
Γk(t)＝Qk(t)+Ak(t)+Gk(t); based on the Lyapunov optimization theory, the optimization problem (11) can be converted into an optimization problem of minimizing Lyapunov drift and punishing an upper bound of each time slot, namely
Wherein min represents the sign of the minimum value,
is represented by alpha and P1Is an objective function of the variable and is,
by optimizing alpha and P1The variable gets the minimum value of the objective function,
4) resource allocation method based on Lyapunov optimization
Aiming at the optimization problem (17), firstly, the binary variable relaxation interval is [0,1 ]]Then introducing the auxiliary variable muk,m(t)＝αk,m(t)Pk,m(t), a vector α and can be obtained
Is expressed as a combined convex function of
Using a convex optimization method to solve when the objective function of the optimization problem (18) is applied to the power variable Pk,m(t) calculating the partial derivative, and when the value of the partial derivative is equal to 0, obtaining the power optimal solution of the convex problem in the time slot t
Namely, it is
Wherein
At a known power optimum solution
Under the condition of (1), according to the 'winner takes all' principle, the optimal resource block allocation result in the time slot t can be obtained
Namely, it is
Wherein
Indicating that H can be taken when k' is k in the time slot tk′,m(ii) the maximum value of (t),
will be continuous T0> 1 time slots constitute a time frame, the base station only needs to execute the channel state acquisition task once at the beginning stage of each time frame, and each time slot needs to execute the resource allocation task; according to the convex optimization problem solving process, the resource allocation method based on the Lyapunov optimization is as follows:
i. at the beginning of a time frame, the initialization t-1,
in time slot t, the base station acquires channel state information Q (t) { Q) of the V2V link and the V2I link1(t),Q2(t),...,QK(t)}；
Based on current channel state information q (t), queue length g (t), and task arrival rate a (t) { a }1(t),A2(t),...,AK(t) } performing the V2V communication resource allocation task by formula (19) and formula (21);
updating the energy efficiency of the V2V communication system for the current time slot according to equation (12)
v. updating the queue length g (t) according to equation (5) and equation (13), and updating the time slot t ═ t + 1;
repeating steps iii to v until T > T0And then, jumping to step ii to recapture the channel state information of the V2V link and the V2I link.
The method has the advantages that a resource allocation method with low computation complexity can be designed by using a Lyapunov optimization theory, and the requirements on time delay and reliability of the V2V communication link are met; in addition, in order to avoid the problem of resource over-allocation in the process of pursuing delay and reliability requirements of resource allocation, the Lyapunov optimization theory is adopted to simultaneously optimize the energy efficiency and the delay and reliability requirements of the V2V communication system.
Drawings
Fig. 1 is a schematic structural diagram of a V2V communication system configured with a buffer queue in the car networking of the present invention.
Detailed Description
The invention is further described below, but not limited to, with reference to the following figures and examples.
Example (b):
a Lyapunov optimization-based V2V resource allocation method in an internet of vehicles, where a communication service is operated in a system, as shown in fig. 1, the system includes a base station, a plurality of V2V links and V2I links, where a spectrum resource block is pre-allocated to a V2I link, and the V2V link implements communication between two nearby vehicles in a D2D communication manner by multiplexing the spectrum resource block of a V2I downlink; the sets of V2V and V2I links are denoted as V2V and V2I, respectively
And
wherein K and M represent the total number of V2V links and V2I links, respectively; in order to analyze the time delay and reliability of the V2V link, a buffer queue for buffering data is configured at the transmission end of each V2V link, the communication system runs communication services according to time slots, and an interval [ t, t +1 ] which uses a time slot t e {1, 2. } to represent a period of time is defined; aiming at the V2V communication system model, an optimization problem is planned, and a resource allocation method is designed according to a Lyapunov optimization theory to solve the optimization problem, wherein the method comprises the following specific steps:
1) problem planning
In time slot t, the data transmission rate of the k-th V2V link is defined as
Wherein
The representation takes arbitrary symbols, B represents the bandwidth, δ represents the time slot duration, αk,m(t) is the resource block multiplexing factor, if the kth V2V link multiplexes the resource block of the mth V2I link at the time slot t, then αk,m(t) 1, otherwise αk,m(t)＝0，σ2Representing the power of Gaussian white noise interference, Pk,m(t) represents transmission power when the frequency spectrum resource block of the mth V2I link is multiplexed by the kth V2V link in the time slot t, Pm(t) denotes the transmission power of the mth V2I link at time slot t, hk,m(t) denotes a channel gain when the k-th V2V link shares a resource block with the m-th V2I link at the slot t, sm,k(t) represents the interference channel gain of the mth V2I link transmission end to the k V2V link receiving ends at the time slot t; V2V link long-time average aggregate throughput
Is defined as
Wherein
τ denotes the τ -th slot of 0 to t-1 slots, Rk(τ) represents the throughput of the k-th V2V link at time slot τ,
represents the throughput of all V2V links at time slot tau, tau is less than or equal to t-1; V2V link long-time average total transmission power
Is composed of
Wherein P isk,m(τ) denotes a transmission power when the kth V2V link of the slot τ multiplexes the spectrum resource block of the mth V2I link,
indicates the total transmission power, alpha, of all V2V links in time slot tauk,m(τ) is the resource block multiplexing factor, if the kth V2V link multiplexes the resource block of the mth V2I link at the time slot τ, then αk,m(τ) ═ 1, otherwise αk,m(t) ═ 0; in time slot t, the base station transmission rate of any V2I link m is defined as
Wherein h ism(t) denotes the channel gain of the mth V2I link at time slot t, gk,m(t) represents the interference channel gain of the kth V2V link transmission end to the mth V2I link receiving end at the time slot t; each V2VThe transmission end of the link is configured with a task queue, namely any V2V link
Is defined as Qk(t) the update formula of which is defined as
Wherein A isk(t) denotes the task arrival rate at time slot t, obeying an average of λ at each time slotkThe distribution of the poisson's distribution of (c),
represents a to Ak(τ) expect, max represents the sign of the maximum;
applying a probability constraint to the queue length of each V2V link, the probability constraint to the queue length of the k-th V2V link being
Wherein Pr represents the probability, LkDenotes the boundary of the queue length, theta denotes an arbitrary queue length Qk(t) exceeding LkA violation probability of; qk(τ) represents the queue length of link k at time slot τ V2V, with the objective function of maximizing the energy efficiency of the V2V link, and with the constraints of delay and reliability requirements of the V2V link and minimum rate requirements of the V2I link, the following optimization problem is formulated
Wherein s.t. represents a constraint symbol, C1, C2, C3, C4 and C5 represent constraint symbols, ηEERepresenting the energy efficiency, R, of the V2V linkCIndicating a minimum value for the V2I link transmission rate,
represents the maximum value of the transmission power of the V2V link;
2) optimization problem equivalence transformation
Constraint C1 may be relaxed to
When the kth V2V link shares a resource block with the mth V2I link, α is satisfied at this timek,mAt 1, the power optimum for the V2I link can be derived from the constraint C2 in problem (7)
Is composed of
Wherein
Optimizing the power of the V2I link
Substituting the optimization problem (7) can result in the following problem
Wherein
3) Lyapunov optimization theory
For the time-averaged constraint C1 in problem (11), a virtual queue is introduced:
Gk(t +1) and Gk(t) denotes any V2V link, respectively
In the virtual queue of the time slot t +1 and the time slot t, a secondary Lyapunov function is defined as
Wherein G (t) ═ G1(t),...,GK(t) }; during any time slot t, the Lyapunov drift and penalty based on the virtual queue G (t) are defined as
Wherein
Representing the desired value of x based on condition y,
representing the amount of change in the Lyapunov function value between two slots,
v > 0 represents a control parameter that trades off queue length against V2V link energy efficiency; under any queue state and control strategy during the time slot t, the Lyapunov drift and penalty based on the virtual queue condition can meet the following upper bound
Wherein [ a ]]+Max {0, a }; according to [ Q ]k(t)-Rk(t)+Ak(t)]+≤max{Qk(t)+Ak(t),Rk,max(t)}-Rk(t) wherein Rk,max(t) represents the maximum transmission rate of the k-th V2V link at time slot t, and it can be concluded that equation (15) satisfies the following equation
Wherein C is a constant, and C is a constant,
Γk(t)＝Qk(t)+Ak(t)+Gk(t); based on the Lyapunov optimization theory, the optimization problem (11) can be converted into an optimization problem of minimizing Lyapunov drift and punishing an upper bound of each time slot, namely
Wherein min represents the sign of the minimum value,
is represented by alpha and P1Is an objective function of the variable and is,
by optimizing alpha and P1The variable gets the minimum value of the objective function,
4) resource allocation method based on Lyapunov optimization
Aiming at the optimization problem (17), firstly, the binary variable relaxation interval is [0,1 ]]Then introducing the auxiliary variable muk,m(t)＝αk,m(t)Pk,m(t), a vector α and can be obtained
Is expressed as a combined convex function of
Using a convex optimization method to solve when the objective function of the optimization problem (18) is applied to the power variable Pk,m(t) calculating the partial derivative, and when the value of the partial derivative is equal to 0, obtaining the power optimal solution of the convex problem in the time slot t
Namely, it is
Wherein
At a known power optimum solution
Under the condition of (1), according to the 'winner takes all' principle, the optimal resource block allocation result in the time slot t can be obtained
Namely, it is
Wherein
Indicating that H can be taken when k' is k in the time slot tk′,m(ii) the maximum value of (t),
will be continuous T0> 1 time slots constitute a time frame, the base station only needs to execute the channel state acquisition task once at the beginning stage of each time frame, and each time slot needs to execute the resource allocation task; according to the convex optimization problem solving process, the resource allocation method based on the Lyapunov optimization is as follows:
i. at the beginning of a time frame, the initialization t-1,
at time slot t, the base station acquires channel state information of the V2V link and the V2I link
Q(t)＝{Q1(t),Q2(t),...,QK(t)}；
According to the current channel state information Q (t), the queue length G (t) and the task arrival rate
A(t)＝{A1(t),A2(t),...,AK(t) } performing the V2V communication resource allocation task by formula (19) and formula (21);
updating the energy efficiency of the V2V communication system for the current time slot according to equation (12)
v. updating the queue length g (t) according to equation (5) and equation (13), and updating the time slot t ═ t + 1;
repeating steps iii to v until T > T0And then, jumping to step ii to recapture the channel state information of the V2V link and the V2I link.
Claims (1)
1. A Lyapunov optimization-based V2V resource allocation method in the Internet of vehicles runs communication services in a system which comprises a base station, a plurality of V2V links and V2I links, wherein the V2I link is pre-allocated with a spectrum resource block, and the V2V link realizes communication between two adjacent vehicles in a D2D communication mode by multiplexing the spectrum resource block of the V2I downlink; the sets of V2V and V2I links are denoted as V2V and V2I, respectively
And
wherein K and M represent the total number of V2V links and V2I links, respectively; in order to analyze the time delay and reliability of the V2V link, a buffer queue for buffering data is configured at the transmission end of each V2V link, the communication system runs communication services according to time slots, and an interval [ t, t +1 ] which uses a time slot t e {1, 2. } to represent a period of time is defined; aiming at the V2V communication system model, an optimization problem is planned, and a resource allocation method is designed according to a Lyapunov optimization theory to solve the optimization problem, wherein the method comprises the following specific steps:
1) problem planning
In time slot t, the data transmission rate of the k-th V2V link is defined as
Wherein
The representation takes arbitrary symbols, B represents the bandwidth, δ represents the time slot duration, αk,m(t) is the resource block multiplexing factor, if it is the second in time slot tThe k V2V links reuse the resource block of the mth V2I link, then αk,m(t) 1, otherwise αk,m(t)＝0，σ2Representing the power of Gaussian white noise interference, Pk,m(t) represents transmission power when the frequency spectrum resource block of the mth V2I link is multiplexed by the kth V2V link in the time slot t, Pm(t) denotes the transmission power of the mth V2I link at time slot t, hk,m(t) denotes a channel gain when the k-th V2V link shares a resource block with the m-th V2I link at the slot t, sm,k(t) represents the interference channel gain of the mth V2I link transmission end to the k V2V link receiving ends at the time slot t; V2V link long-time average aggregate throughput
Is defined as
Wherein
τ denotes the τ -th slot of 0 to t-1 slots, Rk(τ) represents the throughput of the k-th V2V link at time slot τ,
represents the throughput of all V2V links at time slot tau, tau is less than or equal to t-1; V2V link long-time average total transmission power
Is composed of
Wherein P isk,m(τ) denotes a transmission power when the kth V2V link of the slot τ multiplexes the spectrum resource block of the mth V2I link,
indicates the total transmission power, alpha, of all V2V links in time slot tauk,m(τ) is the resource block multiplexing factor, if the kth V2V link multiplexes the resource block of the mth V2I link at the time slot τ, then αk,m(τ) ═ 1, otherwise αk,m(t) ═ 0; in time slot t, the base station transmission rate of any V2I link m is defined as
Wherein h ism(t) denotes the channel gain of the mth V2I link at time slot t, gk,m(t) represents the interference channel gain of the kth V2V link transmission end to the mth V2I link receiving end at the time slot t; a task queue is configured at the transmission end of each V2V link, and any V2V link
Is defined as Qk(t) the update formula of which is defined as
Wherein A isk(t) denotes the task arrival rate at time slot t, obeying an average of λ at each time slotkThe distribution of the poisson's distribution of (c),
represents a to Ak(τ) expect, max represents the sign of the maximum;
applying a probability constraint to the queue length of each V2V link, the probability constraint to the queue length of the k-th V2V link being
Wherein Pr represents the probability, LkDenotes the boundary of the queue length, theta denotes an arbitrary queue length Qk(t) exceeding LkA violation probability of; qk(τ) represents the queue length of link k at time slot τ V2V, with the objective function of maximizing the energy efficiency of the V2V link, and with the constraints of delay and reliability requirements of the V2V link and minimum rate requirements of the V2I link, the following optimization problem is formulated
Wherein s.t. represents a constraint symbol, C1, C2, C3, C4 and C5 represent constraint symbols, ηEERepresenting the energy efficiency, R, of the V2V linkCIndicating a minimum value for the V2I link transmission rate,
represents the maximum value of the transmission power of the V2V link;
2) optimization problem equivalence transformation
Constraint C1 may be relaxed to
When the kth V2V link shares a resource block with the mth V2I link, α is satisfied at this timek,mAt 1, the power optimum for the V2I link can be derived from the constraint C2 in problem (7)
Is composed of
Wherein
Optimizing the power of the V2I link
Substituting the optimization problem (7) can result in the following problem
Wherein
3) Lyapunov optimization theory
For the time-averaged constraint C1 in problem (11), a virtual queue is introduced:
Gk(t +1) and Gk(t) represents an arbitrary V2V chainRoad surface
In the virtual queue of the time slot t +1 and the time slot t, a secondary Lyapunov function is defined as
Wherein G (t) ═ G1(t),...,GK(t) }; during any time slot t, the Lyapunov drift and penalty based on the virtual queue G (t) are defined as
Wherein
Representing the desired value of x based on condition y,
representing the amount of change in the Lyapunov function value between two slots,
v > 0 represents a control parameter that trades off queue length against V2V link energy efficiency; under any queue state and control strategy during the time slot t, the Lyapunov drift and penalty based on the virtual queue condition can meet the following upper bound
Wherein [ a ]]+Max {0, a }; according to [ Q ]k(t)-Rk(t)+Ak(t)]+≤max{Qk(t)+Ak(t),Rk,max(t)}-Rk(t) wherein Rk,max(t) represents the maximum transmission rate of the k-th V2V link at time slot t, and it can be concluded that equation (15) satisfies the following equation
Wherein C is a constant, and C is a constant,
Γk(t)＝Qk(t)+Ak(t)+Gk(t); based on the Lyapunov optimization theory, the optimization problem (11) can be converted into an optimization problem of minimizing Lyapunov drift and punishing an upper bound of each time slot, namely
Wherein min represents the sign of the minimum value,
is represented by alpha and P1Is an objective function of the variable and is,
by optimizing alpha and P1The variable gets the minimum value of the objective function,
4) resource allocation method based on Lyapunov optimization
Aiming at the optimization problem (17), firstly, the binary variable relaxation interval is [0,1 ]]Then introducing the auxiliary variable muk,m(t)＝αk,m(t)Pk,m(t), a vector α and can be obtained
Is expressed as a combined convex function of
Using a convex optimization method to solve when the objective function of the optimization problem (18) is applied to the power variable Pk,m(t) calculating the partial derivative, and when the value of the partial derivative is equal to 0, obtaining the power optimal solution of the convex problem in the time slot t
Namely, it is
Wherein
At a known power optimum solution
Under the condition of (1), according to the 'winner takes all' principle, the optimal resource block allocation result in the time slot t can be obtained
Namely, it is
Wherein
Indicating that H can be taken when k' is k in the time slot tk′,m(ii) the maximum value of (t),
will be continuous T0> 1 time slots constitute a time frame, the base station only needs to execute the channel state acquisition task once at the beginning stage of each time frame, and each time slot needs to execute the resource allocation task; according to the convex optimization problem solving process, the resource allocation method based on the Lyapunov optimization is as follows:
i. at the beginning of a time frame, the initialization t-1,
in time slot t, the base station acquires channel state information Q (t) { Q) of the V2V link and the V2I link1(t),Q2(t),...,QK(t)}；
Based on current channel state information q (t), queue length g (t), and task arrival rate a (t) { a }1(t),A2(t),...,AK(t) } performing the V2V communication resource allocation task by formula (19) and formula (21);
updating the energy efficiency of the V2V communication system for the current time slot according to equation (12)
v. updating the queue length g (t) according to equation (5) and equation (13), and updating the time slot t ═ t + 1;
repeating steps iii to v until T > T0And then, jumping to step ii to recapture the channel state information of the V2V link and the V2I link.
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