CN105916206B - Multi-hop cellular network resource allocation method and system based on game theory - Google Patents

Multi-hop cellular network resource allocation method and system based on game theory Download PDF

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CN105916206B
CN105916206B CN201510810366.XA CN201510810366A CN105916206B CN 105916206 B CN105916206 B CN 105916206B CN 201510810366 A CN201510810366 A CN 201510810366A CN 105916206 B CN105916206 B CN 105916206B
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cellular network
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张钦宇
王野
孔庆磊
杨艺
于佳
董唯一
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Shenzhen Graduate School Harbin Institute of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/50—Allocation or scheduling criteria for wireless resources
    • H04W72/54—Allocation or scheduling criteria for wireless resources based on quality criteria
    • H04W72/541—Allocation or scheduling criteria for wireless resources based on quality criteria using the level of interference
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/38—TPC being performed in particular situations
    • H04W52/46—TPC being performed in particular situations in multi hop networks, e.g. wireless relay networks
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/50—Allocation or scheduling criteria for wireless resources
    • H04W72/54—Allocation or scheduling criteria for wireless resources based on quality criteria
    • H04W72/542—Allocation or scheduling criteria for wireless resources based on quality criteria using measured or perceived quality

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Abstract

The invention provides a multi-hop cellular network resource allocation method and a system based on a game theory, wherein the multi-hop cellular network resource allocation method comprises the steps that in a two-stage master-slave model, in the first stage, an upper-layer relay firstly releases an excited numerical value; in the second phase, the lower layer relay adjusts its transmit power according to the upper layer relay. The invention has the beneficial effects that: the invention designs a transmission excitation mechanism in a multi-hop cellular network based on cooperative crowdsourcing, and by designing the excitation mechanism between a base station and a relay and between the relay and the relay, the base station can improve the spectrum utilization rate and reduce the deployment and management cost of equipment, and the relay can also obtain part of profit by participating in cooperative transmission.

Description

Multi-hop cellular network resource allocation method and system based on game theory
Technical Field
The invention relates to the technical field of communication, in particular to a multi-hop cellular network resource allocation method and system based on game theory.
Background
Multi-hop cellular networks are considered by the academia and industry as a heterogeneous network technology that can be used to effectively improve network throughput and extend network coverage. The multi-hop cellular network not only has the characteristics of the traditional network, namely, the fixed base station equipment of the traditional cellular network is utilized, but also fully utilizes the characteristics of high energy efficiency, high flexibility and the like of the multi-hop relay network. However, widespread deployment of multi-hop cellular networks will face several challenges: the first challenge is high deployment and high maintenance costs at wireless access points; the second challenge is the high difficulty and complexity of managing a large number of diverse access points.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a multi-hop cellular network resource allocation method based on a game theory.
The invention provides a game theory-based game playerA method for distributing resources of cellular network by hop includes receiving data sent by its recruiter at (n +1) th time slot by relay, representing information received at receiving end of relay as channel parameter between (n-1) th layer relay and s (n) th layer relay containing path loss and frequency selective fading, interference at receiving end of relay, n(n)Is additive white Gaussian noise with variance of σ2In the amplify-and-forward mode, the amplify-and-forward coefficient of the relay isLayer (n) relay forwards received signal as A(n)，h(n)，p(n)The input and output expressions of the transmission link of the N-hop relay network are respectively expressed as
Figure BDA0000853548180000027
The received SNR of the link at the receiving end, i.e. at the user end, through the layer (N) relay is the instantaneous SNR of the time slot N, i.e. the layer (N-1) relay RN(n-1)And (n) th layer relay RN(n)The signal-to-noise ratio of the link between, for the base station, is the utility function
Figure BDA00008535481800000211
I.e. gain minus incentive, alpha being gain per spectral efficiency, R0The base station is given the sum of the excitations of the first tier relays.
As a further improvement of the invention, the utility function for the (n) th layer relay is
Figure BDA00008535481800000213
I.e. the revenue is first to energy consumption and the incentive to give to the next layer of relays, where c is the price per unit power consumption, where the sum represents the signal-to-noise ratio through the (n) th layer relay and through the (n-1) th layer relay, respectively.
As a further improvement of the present invention, in the two-stage master-slave model, in the first stage, the upper layer relay firstly releases its excited value; in the second phase, the lower layer relay adjusts its transmit power according to the upper layer relay.
As a further improvement of the present invention, in the game between the (n) th layer and the (n +1) th layer, the optimization problem of the (n) th layer relay is:
Figure BDA0000853548180000031
as a further improvement of the present invention, in the game between the (n-1) th layer relay and the (n) th layer relay, the optimization problem of the (n) th layer relay is:
Figure BDA0000853548180000032
wherein T is(n)The minimum signal-to-noise ratio limit for the (n) th relay.
The invention also provides a multi-hop cellular network resource allocation system based on the game theory, which is characterized in that the relay receives the data sent by the recruiter in the (n +1) th time slot, and the information received at the receiving end of the relay is represented as the channel parameter between the (n-1) th layer relay and the(s) th layer relay, including path loss and frequency selective fading, and is the interference of the receiving end of the relay, n is the channel parameter between the n-1 th layer relay and the s (n) th layer relay(n)Is additive white Gaussian noise with variance of σ2In the amplify-and-forward mode, the amplify-and-forward coefficient of the relay is that the (n) th layer relay forwards the received signal as A(n)，h(n)，p(n)The input and output expressions of the transmission link of the N-hop relay network are respectively expressed as
Figure BDA0000853548180000041
The received SNR of the link at the receiving end, i.e. at the user end, through the layer (N) relay is the instantaneous SNR of the time slot N, i.e. the layer (N-1) relay RN(n-1)And (n) th layer relay RN(n)The signal-to-noise ratio of the link between, for the base station, is the utility function
Figure BDA0000853548180000045
I.e. gain minus incentive, alpha being gain per spectral efficiency, R0Giving a base station a first layerThe sum of the excitations of the relays.
As a further improvement of the invention, the utility function for the (n) th layer relay is
Figure BDA0000853548180000047
I.e. the revenue is first to energy consumption and the incentive to give to the next layer of relays, where c is the price per unit power consumption, where the sum represents the signal-to-noise ratio through the (n) th layer relay and through the (n-1) th layer relay, respectively.
As a further improvement of the present invention, in the two-stage master-slave model, in the first stage, the upper layer relay firstly releases its excited value; in the second phase, the lower layer relay adjusts its transmit power according to the upper layer relay.
As a further improvement of the present invention, in the game between the (n) th layer and the (n +1) th layer, the optimization problem of the (n) th layer relay is:
Figure BDA00008535481800000412
Figure BDA00008535481800000413
as a further improvement of the present invention, in the game between the (n-1) th layer relay and the (n) th layer relay, the optimization problem of the (n) th layer relay is:
Figure BDA0000853548180000051
wherein T is(n)The minimum signal-to-noise ratio limit for the (n) th relay.
The invention has the beneficial effects that: in summary, the present invention designs a transmission incentive mechanism in a multi-hop cellular network based on cooperative crowdsourcing, and by designing an incentive mechanism between a base station and a relay, and between the relay and the relay, the base station can not only improve the spectrum utilization rate, but also reduce the deployment and management cost of the device, and the relay can also obtain a part of profit by participating in cooperative transmission.
Drawings
FIG. 1 is a system model diagram.
Fig. 2 is a simulation diagram of a network architecture.
Fig. 3 is a diagram of PT relay policy versus PU capacity.
Fig. 4 is a graph of utility function values for 6 relays in the case of one and two layer relays.
Fig. 5 is a graph comparing the utility function of the base station with the price at two levels of relaying and direct transmission.
Fig. 6 is a graph of first tier relays versus spectrum utility price.
Detailed Description
The invention discloses a multi-hop cellular network resource allocation method and system based on a game theory.
With the advent of a series of portable low power wireless access points, such as LightRadio developed by alcatel lucent, a new era of base station deployment is promised, i.e. operators and owners of low power base stations are going to cooperate in transmission. By fully utilizing the low-power wireless access points within the coverage area, operators can reduce the investment in equipment deployment and equipment management, and can relieve the pressure of managing various kinds of equipment. By participating in cooperative transmissions, relays participating in cooperative transmissions may be rewarded with cooperative crowd-sourced transmissions. In order to fully utilize the multi-hop cellular network resources, a new transmission strategy is proposed, namely, a base station recruits a plurality of first-layer relays or an upper-layer relay recruits a lower-layer relay to participate in cooperative transmission.
However, several problems still exist with this new transmission mechanism. The first issue is how the base station recruits relays in such a multihop relay network. The second problem is how to motivate the relay to participate in cooperative transmission, on the one hand because the owner of the relay is not the operator, and on the other hand the relay needs reasonable motivation to make up for the computational and transmission energy it consumes. For relays, the purpose of relaying is to maximize their benefit in cooperative transmission. In order to solve the above problems, the present invention aims to design a transmission incentive mechanism for motivating relays to participate in the multi-hop cellular network transmission of cooperative crowdsourcing.
The present invention considers that in a single cell Orthogonal Frequency Division Multiple Access (OFDMA) network there is one user, one base station and a series of half-duplex relays, i.e. the base station communicates with the users through an N-hop relay network, as shown in fig. 1. It is assumed that in an N-hop relay network, the transmission time of each hop is the same, i.e. each frame is divided into (N +1) identical subframes. We use relaying at layer (n)
Figure BDA0000853548180000061
Representation relayed by layer (n-1)
Figure BDA0000853548180000062
Recruited
Figure BDA0000853548180000063
The s-th relay of the relays. For ease of analysis, we take a link instance, Relay
Figure BDA0000853548180000064
At the (n +1) th time slot, its recruiter is received
Figure BDA0000853548180000065
The data to be transmitted. In the relay
Figure BDA0000853548180000066
The information received by the receiving end of (1),
Figure BDA0000853548180000067
can be expressed as
Figure BDA0000853548180000068
Wherein
Figure BDA0000853548180000071
For layer (n-1) relaying
Figure BDA0000853548180000072
And s (n) th layer relay
Figure BDA0000853548180000073
The channel parameters between them include large scale (path loss) and small scale (frequency selective) fading.
Figure BDA0000853548180000074
Is a relay
Figure BDA0000853548180000075
Interference at the receiving end, n(n)Is additive white Gaussian noise with variance of σ2. In amplify-and-forward mode, relaying
Figure BDA0000853548180000076
Has an amplification forwarding coefficient of
Figure BDA0000853548180000077
Layer (n) relay
Figure BDA0000853548180000078
Forwarding the received signal as
Figure BDA0000853548180000079
For convenience, we use A(n)，h(n)，p(n)Respectively represent
Figure BDA00008535481800000710
Then, the input and output expressions of a transmission link of an N-hop relay network are
Figure BDA00008535481800000711
The received SNR at the receiving end, i.e. at the user end, of the link is as follows through the (N) th layer relay
Wherein
Figure BDA00008535481800000714
Instantaneous signal-to-noise ratio for time slot n, i.e. layer (n-1) relay RN(n-1)And (n) th layer relay RN(n)The signal to noise ratio of the link between. When the instantaneous signal-to-noise ratio of each link is large, the signal-to-noise ratio of the link can be approximated to be larger for calculation
Figure BDA00008535481800000715
For a base station, its utility function can be written as
Figure BDA00008535481800000716
I.e. gain minus incentive, alpha being gain per spectral efficiency, R0The base station is given the sum of the excitations of the first tier relays.
So its optimization problem can be written as
Figure BDA0000853548180000081
s.t.U0>0,R0>0
For layer (n) relayIts utility function can be written as
Figure BDA0000853548180000083
I.e. the revenue is first to the energy consumption and the incentive to give the next layer of relays, where c is the price per unit power consumption. Wherein
Figure BDA0000853548180000084
And
Figure BDA0000853548180000085
respectively represent the passage in the (n) th layerRelay (S)
Figure BDA0000853548180000086
And relaying through (n-1) th layer
Figure BDA0000853548180000087
Signal to noise ratio of (c). Each intermediate level of relaying will be associated with two stancoberg games, i.e. the (n) th level of relaying will participate in both stancoberg games, the game between the (n) th level and the (n +1) th level, and the game between the (n-1) th level and the (n) th level. In a game between the (n) th layer and the (n +1) th layer, the relay of the (n) th layer is used as a master, namely, the party giving excitation, and the relay of the (n +1) th layer is used as a slave; in the game between the (n) th layer and the (n-1) th layer, the relay of the (n-1) th layer is the master, and the relay of the (n) th layer is the slave, that is, the party for adjusting the transmission power. In the two-stage master-slave model, in the first stage, the upper-layer relay firstly releases the excited value; in the second phase, the lower layer relay adjusts its transmit power according to the upper layer relay. In the game between the (n) th layer and the (n +1) th layer, the optimization problem of the (n) th layer relay is
Figure BDA0000853548180000088
Figure BDA0000853548180000089
In the game between the (n-1) layer relay and the (n) layer relay, the optimization problem of the (n) layer relay is
Figure BDA0000853548180000091
Figure BDA0000853548180000092
Figure BDA0000853548180000093
Wherein T is(n)The minimum signal-to-noise ratio limit for the (n) th relay.
2. Game analysis
Given the above-described excitation mechanism, we need to solve several problems as follows. The first problem we are concerned with is whether there is a stable set of policies between the lower relays given the stimulus, so that the relays all maintain a steady set of policies, i.e. no relays have the incentive to change their policies. The second question is whether this stabilization strategy is unique. A third problem is how to compute the optimal excitation of the base station and the upper layer relays. To solve the first and second problems, we introduce here the concept of nash equalization.
Definition 1: for a given transmission power vector
Figure BDA0000853548180000094
If the condition is satisfied
Figure BDA0000853548180000095
It is called nash equalization.
Here we shall demonstrate the existence and uniqueness of nash equilibrium between relays of cooperative transmission. FromIn view of the above, the existence of nash equilibrium can ensure that each relay can achieve a stable strategy in a satisfactory state, i.e., each relay has no motivation to change its strategy. The uniqueness of nash equalization allows the base station or upper layer relay to fully predict the strategy of lower layer relays to optimize its utility function. For ease of illustration, relays
Figure BDA0000853548180000097
And its transmission power
Figure BDA0000853548180000098
Can use
Figure BDA0000853548180000099
And
Figure BDA00008535481800000910
and (4) showing.
Theorem 1: relayRecruited (n +1) layer relays
Figure BDA00008535481800000912
There is at least one nash equilibrium between.
To demonstrate theorem 1, we first introduce theorem 1
Introduction 1: for (n +1) layer relay
Figure BDA0000853548180000101
If the following conditions are satisfied
(a)P(n+1)Policy set is a non-empty compact convex set
(b)
Figure BDA0000853548180000102
Is continuous and relates toIs concave. Then there is at least one nash balance in the power transmission strategy.
Due to the fact that
Figure BDA0000853548180000104
We can reach the conclusion P(n+1)Is a non-empty compact convex set. As can be seen from (8), P(n+1)Is continuous. To prove that
Figure BDA0000853548180000105
Is concave, to
Figure BDA0000853548180000106
The second derivative is calculated and the second derivative is calculated,
Figure BDA0000853548180000107
due to the fact that
Figure BDA0000853548180000108
To pair
Figure BDA0000853548180000109
Is concave and the above equation is always negative, so it can be shown that
Figure BDA00008535481800001010
To pair
Figure BDA00008535481800001011
Is concave. Next we demonstrate the uniqueness of Nash equilibrium.
Theorem 2: in non-cooperative power distribution gaming
Figure BDA00008535481800001012
There is a unique nash equalization.
To demonstrate theorem 2 we give the concept of an optimal response function.
Definition 2: given a transmission power vectorIf all possible values are taken such that
Figure BDA00008535481800001014
Maximum, then strategy
Figure BDA00008535481800001015
May be referred to as an optimal reaction strategy.
According to definition 1, the strategy of each user in nash equilibrium is the optimal reaction strategy. To find a relay
Figure BDA00008535481800001016
For the optimal reaction strategy of
Figure BDA00008535481800001017
The first derivative is calculated. If not taken into consideration
Figure BDA00008535481800001018
The upper and lower bounds of (a) are,
Figure BDA00008535481800001019
satisfies the condition
Figure BDA00008535481800001020
Due to the fact thatTo pair
Figure BDA0000853548180000112
Is a concave function, thenTo pairIs a strictly decreasing function. There is a unique numerical value
Figure BDA0000853548180000115
So that
Figure BDA0000853548180000118
If the upper and lower bounds are considered,
Figure BDA0000853548180000119
of transmitted powerOptimum reaction valueCan be written as
Figure BDA00008535481800001111
Figure BDA00008535481800001112
The only nash equilibrium still exists because
Figure BDA00008535481800001113
Is a concave function, we can get a relay using the Jackson inequality
Figure BDA00008535481800001114
Lower bound of SNR, SNR of other than (n +1) th hop in a link can be written as
Figure BDA00008535481800001115
The sum of the signal-to-noise ratios of other relays of the same layer can be written as
Figure BDA00008535481800001116
Figure BDA00008535481800001117
Is and relay
Figure BDA00008535481800001118
The number of links involved. Then
Figure BDA00008535481800001119
Has a lower bound of
Figure BDA00008535481800001120
Theorem 3 there is a unique Steiner between the (n) th relay and the (n +1) th relayLattice equalization, i.e. the presence of an optimum excitation value (R)(n))*So that the utility function u (R) of the (n) th layer(n)) And max.
To prove theorem 3, we first pair u (R)(n)) Taking the second derivative so that its utility function is R(n)By the strict concave function we can ensure that the value of the optimal excitation is unique. The optimal excitation value can be determined by an iterative algorithm.
Figure BDA00008535481800001121
Similarly, we can also demonstrate that there is Steckelberg equalization between the base station and the first tier relays, the utility function of the base station versus R0And (4) solving a second derivative, and solving an excitation value of the second derivative through an iterative algorithm.
Figure BDA0000853548180000121
3. Simulation and experimental result analysis
To verify the effectiveness of the proposed excitation mechanism, we performed several numerical simulations. We perform the simulation in the network structure as shown in fig. 2 above. In the simulated network, there are layer 2 relays, i.e., each first layer relay recruits two second layer relays. Figure 3 compares the values of the utility function for the two-tier relay, one-tier relay, and direct-propagation cases. Here we assume a price per spectrum utilization of 150, i.e. a-150. The utility function value of the two-layer relay adopting the excitation mechanism is larger than that of the one-layer relay, and the utility function of the one-layer relay is larger than that of the direct transmission. We compare the utility function values for base stations with transmit powers of 1W and 0.5W, respectively.
Figure 4 gives the utility function values for 6 relays in the case of one and two layer relays. Simulation data shows that for a first layer of relays, namely relays closer to the base station, the benefit in two hops is greater than the benefit in one hop, and for a second layer of relays, namely relays closer to the user, the opposite is true.
Next, we shall verify the curve of the utility function value of the base station and the relay as a function of the spectrum utilization rate price α, which ranges from 50 to 250. In fig. 5, the utility function versus price for the base station at 1W and 0.5W power respectively is shown compared between two levels of relaying and direct transmission. As the price of spectrum utilization rises, the number of incentives grows and the incentives received by the relay increases. For further verification, in fig. 6, we present the first tier relay versus spectrum utility price.
As is apparent from fig. 2, the value of the safe capacity in the SU cooperation is significantly higher than that in the primary user direct transmission mode. And, when P isA1＝676mw，PA2At 324mw, the sum of the primary user safe rate and the secondary user throughput reaches a maximum
Figure BDA0000853548180000131
At this point the safe capacity of PR reaches CS6.89bps/Hz instead of the secure capacity of less than 1bps/Hz in the cooperative mode.
To verify the impact on all user throughput when the primary user transmitter broadcasts information using different powers in the first phase, we will again refer to PPThe range of (1 mw) to (1000 mw) is set, other parameters are unchanged, simulation is performed, and the simulation result is shown in fig. 3:
in fig. 3, the black curve represents the safe capacity of the primary user in the cooperative mode, the red curve represents the SUB throughput, the blue curve represents the SUA throughput, the dotted black solid line represents the safe capacity of the PR in the non-cooperative mode, and we can see that the value is constant at 1.14bps/Hz, while the total throughput of the primary user and the secondary user in the cooperative mode is PPAt 339mw, the optimum value is reachedWherein the safe capacity of the primary user reaches CS7.82bps/Hz, the performance is obviously improved compared with the single-link direct transmission mode.
In summary, the present invention designs a transmission incentive mechanism in a multi-hop cellular network based on cooperative crowdsourcing. By designing an excitation mechanism between the base station and the relay and between the relay and the relay, the base station can improve the spectrum utilization rate and reduce the deployment and management cost of equipment, and the relay can also obtain part of profit by participating in cooperative transmission.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (10)

1. A multi-hop cellular network resource allocation method based on game theory is characterized in that a relay
Figure FDA0002152267500000011
At the (n +1) th time slot, its recruiter is received
Figure FDA0002152267500000012
The transmitted data being relayed
Figure FDA0002152267500000013
The receiving end of the network receives the information
Figure FDA0002152267500000014
Is shown as
Figure FDA0002152267500000015
Wherein
Figure FDA0002152267500000016
For layer (n-1) relaying
Figure FDA0002152267500000017
And s (n) th layer relay
Figure FDA0002152267500000018
The channel parameters between, including path loss and frequency selective fading,
Figure FDA0002152267500000019
is a relay
Figure FDA00021522675000000110
Interference at the receiving end, n(n)Is additive white Gaussian noise with variance of σ2In amplify-and-forward mode, relaying
Figure FDA00021522675000000111
Has an amplification forwarding coefficient of
Figure FDA00021522675000000112
P(n) i,j,…,r,sIndicating the forwarding power of the (n) th layer relay
Figure FDA00021522675000000113
Forwarding the received signal as
Figure FDA00021522675000000114
With A(n)，h(n)，p(n)Respectively represent
Figure FDA00021522675000000115
Then the signal input and output expression of the transmission link of the N-hop relay network is as follows
Figure FDA00021522675000000116
By means of (N) -th layer relays
Figure FDA00021522675000000117
g(N)The independent same-distribution small-scale fading coefficient of the (N) th layer is shown, and the receiving signal-noise of the link at the receiving end, namely at the user endRatio of
Figure FDA00021522675000000118
Wherein
Figure FDA00021522675000000119
Instantaneous signal-to-noise ratio for time slot n, i.e. layer (n-1) relay RN(n-1)And (n) th layer relay RN(n)The signal-to-noise ratio of the link between, for the base station, is the utility function
Figure FDA0002152267500000021
I.e. gain minus incentive, alpha being gain per spectral efficiency, R0The base station is given the sum of the excitations of the first tier relays.
2. The multi-hop cellular network resource allocation method according to claim 1, characterized in that for layer (n) relays
Figure FDA0002152267500000022
Having a utility function of
Figure FDA0002152267500000023
I.e. revenue energy consumption and incentive given to the next layer of relays, where c is the price per unit power consumption, where
Figure FDA0002152267500000024
And
Figure FDA0002152267500000025
respectively representing relaying by the (n) th layer
Figure FDA0002152267500000026
And relaying through (n-1) th layer
Figure FDA0002152267500000027
Signal to noise ratio of (c).
3. The method of claim 1, wherein in the two-stage master-slave model, in the first stage, the upper layer relay first reports its excited value; in the second phase, the lower layer relay adjusts its transmit power according to the upper layer relay.
4. The multi-hop cellular network resource allocation method according to claim 3, wherein in the game between the (n) th layer and the (n +1) th layer, the optimization problem of the (n) th layer relay is:
Figure FDA0002152267500000031
Figure FDA0002152267500000032
5. the multi-hop cellular network resource allocation method according to claim 4, wherein in the game between the layer (n-1) relay and the layer (n) relay, the optimization problem of the layer (n) relay is:
Figure DEST_PATH_FDA0000853548170000046
wherein T is(n)The minimum signal-to-noise ratio limit for the (n) th relay.
6. A multi-hop cellular network resource allocation system based on game theory is characterized in that relays
Figure FDA0002152267500000034
At the (n +1) th time slot, its recruiter is received
Figure FDA0002152267500000035
The transmitted data being relayed
Figure FDA0002152267500000036
The receiving end of the network receives the informationIs shown as
Figure FDA0002152267500000038
Wherein
Figure FDA0002152267500000039
For layer (n-1) relaying
Figure FDA00021522675000000310
And s (n) th layer relay
Figure FDA00021522675000000311
The channel parameters between, including path loss and frequency selective fading,
Figure FDA00021522675000000312
is a relay
Figure FDA00021522675000000313
Interference at the receiving end, n(n)Is additive white Gaussian noise with variance of σ2In amplify-and-forward mode, relaying
Figure FDA00021522675000000314
Has an amplification forwarding coefficient of
Figure FDA00021522675000000315
P(n) i,j,…,r,sIndicating the forwarding power of the (n) th layer relay
Figure FDA00021522675000000316
Forwarding the received signal as
Figure FDA00021522675000000317
With A(n)，h(n)，p(n)Respectively represent
Figure FDA00021522675000000318
Then the signal input and output expression of the transmission link of the N-hop relay network is as follows
Figure FDA0002152267500000041
By means of (N) -th layer relays
Figure FDA0002152267500000042
g(N)The independent same-distribution small-scale fading coefficient of the (N) th layer is shown, and the receiving signal-to-noise ratio of the link at the receiving end, namely at the user end is
Figure FDA0002152267500000043
Wherein
Figure FDA0002152267500000044
Instantaneous signal-to-noise ratio for time slot n, i.e. layer (n-1) relay RN(n-1)And (n) th layer relay RN(n)The signal-to-noise ratio of the link between, for the base station, is the utility functionI.e. gain minus incentive, alpha being gain per spectral efficiency, R0The base station is given the sum of the excitations of the first tier relays.
7. The multi-hop cellular network resource allocation system according to claim 6, wherein for layer (n) relays
Figure FDA0002152267500000046
Having a utility function of
Figure FDA0002152267500000047
I.e. revenue energy consumption and incentive to relay to the next layer, where c is unit workPrice of specific consumption, wherein
Figure FDA0002152267500000048
And
Figure FDA0002152267500000049
respectively representing relaying by the (n) th layer
Figure FDA00021522675000000410
And relaying through (n-1) th layer
Figure FDA00021522675000000411
Signal to noise ratio of (c).
8. The system according to claim 6, wherein in the two-stage master-slave model, in the first stage, the upper layer relay first reports its excited value; in the second phase, the lower layer relay adjusts its transmit power according to the upper layer relay.
9. The multi-hop cellular network resource allocation system according to claim 8, wherein in the game between layer (n) and layer (n +1), the optimization problem of the layer (n) relay is:
Figure FDA0002152267500000052
10. the multi-hop cellular network resource allocation system according to claim 9, wherein in the game between the layer (n-1) relay and the layer (n) relay, the optimization problem of the layer (n) relay is:
Figure 867764DEST_PATH_FDA0000853548170000046
wherein T is(n)The minimum signal-to-noise ratio limit for the (n) th relay.
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