CN106413074A - Optimal power allocation method of untrusted relay network under perfect CSI - Google Patents

Abstract

The invention provides an optimal power allocation method of an untrusted relay network under perfect CSI. The method comprises the following steps: firstly, describing a communication scheme of a two-hop half-duplex relay network, then providing an optimal power allocation scheme, and finally analyzing channel ESR to acquire a reachable safety rate. According to the optimal power allocation method provided by the invention, an optimal power allocation formula in a transmission process is provided to maximize the safety rate, and the ESR under high SNR is further analyzed for evaluating the reachable average safety rate. The approximate optimal power allocation can bring a higher safety rate than equal power allocation.

Description

Optimal power distribution method for untrusted relay network under imperfect CSI

Technical Field

The invention relates to an optimal power allocation scheme of an untrusted relay network under the condition of non-ideal Channel State Information (CSI).

Background

The multi-hop relay is considered as an energy-efficient transmission scheme and is the optimal approach for solving the wireless communication safety. The method for the physical layer secure transmission has the advantages of low computational complexity and resource saving. In recent years, cooperative diversity techniques have attracted the attention of many scholars because they can improve the security of the physical layer against eavesdropping.

In the physical layer there is a gaming problem of power distribution between users and interference sources. The interferer wants to transmit an interfering signal with sufficient power to avoid eavesdroppers from eavesdropping on the user's transmitted information, and the user also wants the transmitted signal to have sufficient power to guarantee the rate of signal transmission. Under the condition of a certain total power, many scholars have made corresponding researches on how to find an optimal power allocation scheme to maximize the safe rate.

Document 1, "originating He, affinity based with an undirected relay [ J ]. IEEE trans. inf. theory,2010,56(8): 3807-.

Document 2 "Li Sun, Taiyi Zhang, Yubo Li and Hao niu. performance student-and-forward systems with untreatment process nodes [ J ]. ieee trans. veh.technol.,2012,61(8):3801 3807" obtains the lower bound of the traversal security Capacity (ESC) of a single untrusted relay by Destination-based interference techniques (DBJ), and expands it to a plurality of untrusted relay scenarios, proposing a security relay selection scheme that can maximize the system security Capacity that can be reached, realizes the secure communication of an untrusted amplified forward (amplitude formed, AF) relay system, but does not consider the optimized power allocation, and document 2 is a perfect based on the CSI and the actual communication environment that can not be obtained.

Document 3 "life Wang, large Elkashlan, king Huang, Nghi h. tan, et al. secure transmission with optimal power allocation in undiusted delaynetworks [ J ]. ieee commun. let, 2014,3(3): 289-292" expands the study of document 2 to a two-hop amplified repeater network and tests the effects of large-scale antenna arrays. When the large-scale antenna array is at the source node, the ESC only depends on the channel state information between the relay and the destination node; when the large-scale antenna array is at the destination node, the ESC depends only on the channel state information between the relay and source nodes. However, document 3 only considers maximizing the safe capacity and does not consider the energy efficiency, and the same research is performed under the assumption that the state information is perfect.

The above documents all develop research under the assumption of perfect CSI, but perfect CSI is basically impossible to achieve in a real communication environment.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides an optimal power allocation scheme improved under the condition of imperfect CSI on the basis of document 3, a cooperative interference relay communication scheme is researched, the conditions that a relay node is not credible and the total power is limited are considered, and an optimal power allocation factor α is extracted under the condition that the statistical information of channel estimation errors can be obtained_optAnd further analyzing a channel-realizable traversal security Rate (ESR) to obtainThe average safe rate that can be achieved.

The technical scheme adopted by the invention for solving the technical problem comprises the following steps:

step one, in a two-hop half-duplex relay network, in a first time slot, a source node Alice transmits information x to an untrusted relay node R_AWhile the destination node Bob transmits the information x to the untrusted relay node R_BSignals received by the relay node RWherein, P_AAnd P_BRespectively representing the transmission power, h, of nodes Alice and Bob_A-RAnd h_B-RComplex channel gains, h, from nodes Alice and Bob to the Relay node R, respectively_B-R＝h_R-B，n_RRepresenting additive white Gaussian noise at the relay node R, and the total power transmitted by the nodes Alice and Bob is P, α∈ [0, 1 ]]Representing the power distribution factor, the node Alice sends the encrypted information power P_Aα P, the power P transmitted by the node Bob_B(1- α) P, instantaneous signal to interference plus noise ratio received at relay node RWherein, the ratio mu of the equivalent signal-to-noise ratios of the nodes Alice and Bob is gamma_A-R/γ_B-RAnd equivalent signal-to-noise ratios of the nodes Alice and Bob to the relay node R are respectively expressed as gamma_A-R＝||h_A-R||²P/N₀And gamma_B-R＝||h_B-R||²P/N₀，N₀＝1；

Step two, in a second time slot, the relay node R amplifies the received signal and sends the amplified signal to the destination node Bob, wherein the amplification factor is beta; the signal sent from the relay node R to the node Bob is denoted as

Both time slots transmit signals with the same power P, y_RNormalized to y_R||²Get the amplification factor P

The node Bob receives a signal sent from the untrusted relay node R as

Wherein n is_BIs additive white gaussian noise received by node Bob, is the estimated channel gain, h, between the untrusted relay node R and the node Bob_eIs a channel estimation error and obeys a complex Gaussian distributionh_B-RAnd h_eSatisfy the requirement ofE(h_e)＝0；

After self-interference elimination, the node Bob receives the signal of

Suppose thatThen for a given channel gain h_A-RAnd h_B-RThe equivalent SINR obtained at node Bob is

Step three, defining the instantaneous safe rateWherein, [ t ]]⁺＝max[t，0](ii) a Firstly, toMaking a derivative with respect to α to obtain

Wherein Δ ═ 2 γ_B-R-αγ_B-R+γ_e ²+αμγ_B-R-αγ_e ²+1；

Calculating two roots of the denominatorConsider α∈ [0, 1 ]]The optimized power division factor α is obtained by solving the root of the numerator to find the solution of equation (12)_opt。

The invention has the beneficial effects that: an Optimized Power Allocation (OPA) formula during transmission is given to maximize the safe rate. To address the complexity of the optimization problem, the ESR at high SNR was further analyzed to evaluate the average safe rate that can be achieved. The approximate optimized power distribution can bring higher safety rate than equal power distribution, and the simulation result proves the effectiveness of the algorithm.

Drawings

Fig. 1 is a schematic diagram of two-hop relay network cooperative interference and secure transmission;

FIG. 2 shows different μ values and channel estimation errorsLower exact and approximate power optimized division factor α_optA schematic diagram;

FIG. 3 is a graph of the relative error between the exact and approximate optimum power factors;

FIG. 4 shows the difference γ_B-RComparing the optimal power distribution and the safe rate corresponding to the average power distribution when mu is 0.5;

FIG. 5 shows the difference γ_B-RComparing the optimal power distribution and the safe rate corresponding to the average power distribution when mu is 2;

fig. 6 is a schematic diagram of ESR distributions at 0.5 μ and different channel estimation errors;

fig. 7 is a diagram of ESR distributions at 2 and different channel estimation errors.

Detailed Description

The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.

The system model used by the present invention is a relay network with three nodes, the principle of which is shown in fig. 1. The model consists of a source node (Alice), an untrusted amplify-and-forward relay node (R) and a destination node (Bob)), each node uses a single antenna configuration, and one transmission process needs 2 time slots to complete. Assuming that there is no direct communication link between Alice and Bob due to shadow fading or too far distance, communication can only be performed through one untrusted relay node R. In the first placeOne time slot, Alice transmits information x to an untrusted relay node R_AWhile Bob transmits information x to the untrusted relay node R_RIn the second time slot, the relay node R amplifies the received signal by an amplifier and retransmits the amplified signal to Bob, wherein the amplification factor is β. further, assuming that all the wireless channels are time-varying rayleigh fading channels, the noise received by each node is 0 on average, and the power spectral density is N₀Additive White Gaussian Noise (AWGN).

The invention firstly describes a communication scheme of a two-hop half-duplex relay network, then gives an optimal power distribution scheme, and finally analyzes channel ESR to obtain the reachable safe rate.

As can be seen from fig. 1, the communication process of the half-duplex relay network needs to be completed by two time slots, and in the first time slot, the signal received by the relay node R can be represented as

Wherein, P_AAnd P_BRespectively representing the transmission power, h, of nodes Alice and Bob_A-RAnd h_B-RThe complex channel gains to the relay node R for Alice and Bob, respectively, are assumed to be mean 0 and variance σ²Complex gaussian variable of (a). The channel satisfies the reciprocity theorem, i.e., h_B-R＝h_R-BAnd is andn_Rassuming that the total power transmitted by nodes Alice and Bob is P, α∈ [0, 1 ]]Representing the power distribution factor, the power of the encrypted information sent by Alice is P_Aα P, Bob transmits power P_BP. (1- α) thus, the instantaneous signal to interference and noise ratio (SINR) γ received at the relay node R_RCan be expressed as:

wherein, | | h_B-R||²(1- α) P represents the interference signal sent by Bob and received at R in the transmission process of Alice, and the equivalent signal-to-noise ratios (SNR) from the nodes Alice and Bob to the relay node R can be respectively represented as gamma_A-R＝||h_A-R||²P/N₀，γ_B-R＝||h_B-R||²P/N₀μ is defined as the ratio of the equivalent signal-to-noise ratios of the nodes Alice and Bob, i.e.: mu-gamma_A-R/γ_B-R. Without loss of generality, we assume N₀The SNR can be adjusted by the transmit power, 1. Based on the above definition, the SINR received at the relay node R shown in equation (2) can be simplified as:

in the second time slot, the relay node R amplifies the received signal by beta times and then retransmits the amplified signal to Bob, and the signal transmitted from the relay node R to the node Bob can be represented as

Will y_RNormalized to y_R||²P, resulting in an amplification factor β

The node Bob receives the signal sent from the untrusted relay node R as follows:

wherein n is_BIs node Bob additive white gaussian noise received. Due to x_BIs the interference signal sent by Bob in the last time slot, and under the condition that Bob has perfect CSI, the self-interference term in the formula (6)

An accurate estimate can be obtained. Here we consider a more practical application scenario where the state information (CSI) of the channel is not perfect for node Bob, but statistical information about channel estimation errors is available. In the present invention, imperfect channel state information is consideredIs known, then

Wherein,is the estimated channel gain, h, between the untrusted relay node R and the node Bob_eIs a channel estimation error and obeys a complex Gaussian distributionh_B-RAnd h_eSatisfy the requirement ofE(h_e) 0. After self-interference elimination, the node Bob receives the signal of

Suppose thatThen for a given channel gain h_A-RAnd h_B-RThe equivalent SINR can be obtained at the node Bob as

Based on the above analysis, optimization of the power allocation factor is next sought.

First, based on equation (3) and equation (9), an instantaneous safety rate is defined

Wherein the preceding factorsBecause a transmission requires 2 time slots to complete, [ t ]]⁺＝max[t，0]。

The invention aims to maximize the safe rate by optimizing the power distribution of the nodes Alice and Bob under imperfect CSI. Based on equation (10), the maximum power allocation problem is expressed mathematically as

s.t.：α∈[0，1]) (11)

Wherein,is monotonically increasing, sinceA maximum value of ζ (α) is present.

Typically, to get the maximum, the optimal power division factor α is found_optThe present invention obtains by making a derivative operation on ζ (α) with respect to α and equaling it to 0

Wherein Δ ═ 2 γ_B-R-αγ_B-R+γ_e ²+αμγ_B-R-αγ_e ²+1. It can be seen from equation (12) that finding its root is somewhat difficult, but in the case where the denominator is not equal to 0, the present invention can use the numerator to obtain the solution of equation (12). First, two roots of the denominator are calculated asIt can be easily found that the method can be easily found out,thus consider α∈ [0, 1 ]]The present invention can find the solution of equation (12) by solving the root of the numerator, thereby resulting in the optimized power division factor α_opt：

In the formula (13), the first and second groups,

k₁＝s-μ+1， k₂＝s²-3μ+4s-sμ-1，

k₃＝s²-2μ+2s-sμ-1，k₄＝k₃-2μs+2μ²+1，

whereinΔ_s＝μ-s+γ_B-R(1+ μ). In the interference signal gamma_B-ROptimized power division factor α of equation (13) with high signal-to-noise ratio_optCan be approximated as

Wherein, Delta_opt＝μ(s+2)(1+μ)，Δ_d＝μ²+μ-s-2。

At perfect CSI, i.e., s-0, the approximate optimized power division factor α_optIs composed of

The Ergodic Security Rate (ESR) characterizes the maximum security Rate that can be achieved on average. In the present invention, ESR is defined as being γ_B-RAll mathematical expectations for achieving a maximum safe rate in implementation, i.e.

Wherein R is_s(α) achievable safe Rate, α, expressed in equation (10)_optFor the optimized power division factor calculated by equation (15), R is shown in equation (10)_s(α) and γ_B(α) and γ_R(α) accordingly, when α is α_optWe first consider γ_B(α) and γ_R(α) substituting equation (15) into equations (3) and (9) yields the optimized SNR for the untrusted relay node R and the node Bob:

when gamma is_B-R> 1 andγ in equation (19)_R(α_opt) Can be simplified as follows:

similarly, γ in simplified formula (19)_B(α_opt) Obtaining:

further, substituting equation (20) and equation (21) into equation (10), and finally substituting the result into equation (18), the general equation for ESR is as follows:

wherein,andis gamma_B-RAnd is defined as follows:

due to the fact thatWhereinThus, the ESR in equation (22) can be further written as:

wherein,

in particular, in the case of Equal Power Allocation (EPA), that is,

α＝0.5，when further considering gamma_B-R> andwhen, gamma_RAnd gamma_BCan be approximated as

γ_R≈μ，

Calculating the ESR in the same manner, one can obtain:

wherein,

fig. 1 shows a system model and a transmission method of a cooperative interference relay network according to the present invention. The system consists of nodes Alice, a point adding Bob and an untrusted relay node Alice which plays a role in amplification and forwarding. Each node is configured with a single antenna.

FIG. 2 shows the difference between the mu value and the channel estimation errorLower exact and approximate power optimized division factor α_optBy comparison, as can be seen in FIG. 2, α_optIt can be seen from equation (3) that for larger values of μ, to avoid the relay intercepting the trusted message sent from the node Alice, we should reduce the power allocation to the node Alice, i.e. reduce α. with the value of μ unchanged, α_optError with channel estimationIncreases because node Alice needs to allocate more power to compensate for the effects introduced due to channel estimation errors. From the figure, we can also find that whenThe estimated value has relatively small error, and the error is followedIs increased.

In order to further carry out quantitative analysis on the error, a relative error variable R is introduced_eAnd is defined as follows:

wherein d andrepresenting the exact and approximate power division factors, respectively. The relative error between the exact and near optimal power allocation factors under different scenarios is shown in fig. 3.

As can be seen from fig. 3, the relative error varies with the value of μ and the channel estimation errorIs increased. And, the relative error R_eRelatively small at perfect CSI and, at large channel estimation errors, relative error R_eIs relatively large, e.g. whenWhen mu is 3, relative error R_e12% by weight. In the following simulations, we consider two scenarios for different μ: μ ═ 0.5 and μ ═ 2, demonstrated for γ_A-R＞γ_B-RAnd gamma_B-R＞γ_A-RThe estimated value is valid.

In fig. 4 and 5, the safe rate at α ═ 0.5 and the error in different channel estimates are comparedAnd the maximum power allocation factor at μ ═ 0.5 or μ ═ 2. Considering different channel estimation errorsWe conclude that: an approximately optimal power allocation may result in a higher security rate than an equal power allocation. This conclusion is feasible even in the worst scenario (μ > 1) and large channel estimation errors. The presence of channel estimation errors both for maximum power allocation and equal power allocation reduces the achievable safe rate.

FIGS. 6 and 7 are differentBelow, forAnd μ ═ 0.5 or μ ═ 2, the realizations and the dashed lines represent the achievable ESRs at the optimum power allocation and at the equal power allocation, respectively. As can be seen from the figure, the optimized power allocation scheme can achieve a higher security rate than the equal power allocation. With signal to noise ratio gamma_B-RThe channel estimation error decreases the impact on the achievable ESR.

Claims (1)

1. An optimal power distribution method of an untrusted relay network under imperfect CSI is characterized by comprising the following steps:

step one, in a two-hop half-duplex relay network, in a first time slot, a source node Alice transmits information x to an untrusted relay node R_AWhile the destination node Bob transmits the information x to the untrusted relay node R_BSignals received by the relay node RWherein, P_AAnd P_BRespectively representing the transmission power, h, of nodes Alice and Bob_A-RAnd h_B-RComplex channel gains, h, from nodes Alice and Bob to the Relay node R, respectively_B-R＝H_R-B，n_RRepresenting additive white Gaussian noise at the relay node R, and the total power transmitted by the nodes Alice and Bob is P, α∈ [0, 1 ]]Representing the power distribution factor, the node Alice sends the encrypted information power P_Aα P, the power P transmitted by the node Bob_B(1- α) P, instantaneous signal to interference plus noise ratio received at relay node RWherein, the ratio mu of the equivalent signal-to-noise ratios of the nodes Alice and Bob is gamma_A-R/γ_B-RAnd equivalent signal-to-noise ratios of the nodes Alice and Bob to the relay node R are respectively expressed as gamma_A-R＝||h_A-R||²P/N₀And gamma_B-R＝||h_B-R||²P/N₀，N₀＝1；

Step two, in a second time slot, the relay node R amplifies the received signal and sends the amplified signal to the destination node Bob, wherein the amplification factor is beta; the signal sent from the relay node R to the node Bob is denoted as

$y_R=\mathrm{\β}(\sqrt{\mathrm{\α}P}{h}_{A-R}{x}_A+\sqrt{(1-\mathrm{\α})P}{h}_{B-R}{x}_B+n_R);$

Both time slots transmit signals with the same power P, y_RNormalized to y_R||²Get the amplification factor P

$\mathrm{\β}=\sqrt{\frac{P}{\mathrm{\α}P\left|\right|h_{A-R}|{|}^2+(1-\mathrm{\α})P|\left|h_{B-R}\right|{|}^2+1}};$

The node Bob receives a signal sent from the untrusted relay node R as

$z_B=\mathrm{\β}\sqrt{\mathrm{\α}P}{h}_{A-R}{x}_A{h}_{R-B}+\mathrm{\β}\sqrt{(1-\mathrm{\α})P}{h}_{B-R}{x}_B{h}_{R-B}+{\mathrm{\βn}}_R{h}_{R-B}+n_B;$

Wherein n is_BIs additive white gaussian noise received by node Bob, is the estimated channel gain, h, between the untrusted relay node R and the node Bob_eIs a channel estimation error and obeys a complex Gaussian distributionh_B-RAnd h_eSatisfy the requirement ofE(h_e)＝0；

After self-interference elimination, the node Bob receives the signal of

$z_B^{*}=\mathrm{\β}\sqrt{\mathrm{\α}P}{h}_{A-R}{x}_A{h}_{R-B}+\mathrm{\β}\sqrt{(1-\mathrm{\α})P}{h}_e{x}_B{h}_e+{\mathrm{\βn}}_R{h}_{R-B}+n_B;$

Suppose thatThen for a given channel gain h_A-RAnd h_B-RThe equivalent SINR obtained at node Bob is

$\begin{array}{c}{\mathrm{\γ}}_B\left(\mathrm{\α}\right)=\frac{{\mathrm{\β}}^2\mathrm{\α}P\left|\right|h_{A-R}\left|{|}^2\right|\left|h_{B-R}\right|{|}^2}{{\mathrm{\β}}^2\left|\right|h_{B-R}|{|}^2+{\mathrm{\β}}^2\left(1-\mathrm{\α}\right)P{\left({\mathrm{\σ}}_e^2\right)}^2+1}\\ =\frac{{\mathrm{\α\γ}}_{A-R}{\mathrm{\γ}}_{B-R}}{{\mathrm{\γ}}_{B-R}+{\mathrm{\α\γ}}_{A-R}+\left(1-\mathrm{\α}\right)\left({\left({\mathrm{P\σ}}_e^2\right)}^2+{\mathrm{\γ}}_{B-R}\right)+1}\\ =\frac{{\mathrm{\α\μ\γ}}_{B-R}}{2-\mathrm{\α}+\mathrm{\α}\mathrm{\μ}+\left(1-\mathrm{\α}\right)\left(\frac{{\left({\mathrm{\γ}}_e\right)}^2}{\left({\mathrm{\γ}}_{B-R}\right)}\right)+\frac{1}{{\mathrm{\γ}}_{B-R}}}\end{array};$

Step three, defining the instantaneous safe rateWherein, [ t ]]⁺＝max[t，0](ii) a Firstly, toMaking a derivative with respect to α to obtain

$\begin{array}{c}\frac{d\mathrm{\ζ}}{d\mathrm{\α}}=\frac{{\mathrm{\μ\γ}}_{B-R}^2({\mathrm{\γ}}_{B-R}-{\mathrm{\α\γ}}_{B-R}+1)(2{\mathrm{\γ}}_{B-R}+{{\mathrm{\γ}}_e}^2+1)}{({\mathrm{\γ}}_{B-R}-{\mathrm{\α\γ}}_{B-R}+{\mathrm{\α\γ}}_{B-R}\mathrm{\μ}+1){\mathrm{\Δ}}^2}\\ -\frac{{\mathrm{\μ\γ}}_{B-R}(\frac{{\mathrm{\α\γ}}_{B-R}\mathrm{\μ}}{\mathrm{\Δ}}+1)({\mathrm{\γ}}_{B-R}+1)}{{({\mathrm{\γ}}_{B-R}-{\mathrm{\α\γ}}_{B-R}+{\mathrm{\α\γ}}_{B-R}\mathrm{\μ}+1)}^2}=0\end{array}$

Wherein Δ ═ 2 γ_B-R-αγ_B-R+γ_e ²+αμγ_B-R-αγ_e ²+1；

Calculating two roots of the denominatorConsider α∈ [0, 1 ]]The optimized power division factor α is obtained by solving the root of the numerator to find the solution of equation (12)_opt。