CN107071886B - An Optimal Power Allocation Method for Untrusted Relay Networks with Bounded CSI - Google Patents

Abstract

The present invention provides an optimal power allocation method for an untrusted relay network under bounded CSI, firstly describing the communication scheme of the two-hop half-duplex relay network, giving the optimal power allocation scheme, and then obtaining the lower bound of the security rate , and finally analyze the channel ESR to obtain the attainable safe rate. The present invention provides the optimal power allocation formula in the transmission process to maximize the safe rate, and further analyzes the ESR under high SNR to evaluate the attainable average safe rate. Approximate optimal power allocation can lead to higher security rates than equal power allocation.

Description

An Optimal Power Allocation Method for Untrusted Relay Networks with Bounded CSI

technical field

The invention relates to an optimal power allocation scheme of an untrustworthy relay network under the condition that the channel estimation error is bounded.

Background technique

Multi-hop relay is identified as an energy-efficient transmission scheme, which is the optimal way to solve wireless communication security. The method of physical layer secure transmission has the advantages of low computational complexity and resource saving. In recent years, cooperative diversity technology has attracted the attention of many scholars because it can improve the security of the physical layer against eavesdropping.

In the physical layer, there is a game problem of power allocation between users and interference sources. The interference source hopes to transmit an interference signal with sufficient power to prevent eavesdroppers from eavesdropping on the user's transmission information, and the user also hopes that the transmitted signal has sufficient power to ensure the rate of signal transmission. Under the condition of a certain total power, how to find the optimal power allocation scheme to maximize the security rate, many scholars have made corresponding research.

Document 1 "Xiang He, Aylin Yener. Cooperation with an untrusted relay: Asecrecy perspective [J]. IEEE Trans. Inf. Theory, 2010, 56(8): 3807-3827" proposes that the relay node is untrusted, it may It will eavesdrop and interfere with the forwarded information. However, compared with not using such relay nodes, using untrusted relay nodes for cooperative communication can improve the security capacity of the system.

Document 2 "Li Sun, Taiyi Zhang, Yubo Li and Hao Niu. Performance study of two-hop amplify-and-forward systems with untrustworthy relay nodes[J]. IEEETrans.Veh.Technol.,2012,61(8):3801- 3807" Obtain the lower bound of Ergodic Secrecy Capacity (ESC) of a single untrusted relay through Destination-based Jamming (DBJ), and extend it to multiple untrusted relay scenarios , a secure relay selection scheme is proposed, which can maximize the reachable system security capacity and realize the secure communication of untrustworthy Amplify Forwaed (AF) relay system, but it does not consider the optimal power allocation, and Document 2 is based on the perfect channel state information (Channel State Information, CSI) condition, but the actual communication environment cannot obtain perfect CSI.

Literature 3 "Lifeng Wang, Maged Elkashlan, Jing Huang, Nghi H.Tan, et al.Securetransmission with optimal power allocation in untrusted relaynetworks[J].IEEECommun.Lett.,2014,3(3):289-292" The study of 2 extends the two-hop amplify-and-forward relay network and tests the impact of large-scale antenna arrays. When the large-scale antenna array is at the source node, 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, ESC only depends on the channel state information between the relay and the source node. However, Document 3 only considers the maximization of the safety capacity, and does not consider the energy efficiency. The same research is carried out under the assumption that the state information is perfect.

The above literatures are all researched under the assumption of perfect CSI, but in a real communication environment, perfect CSI is basically impossible to achieve. The invention considers the actual communication model, and studies the cooperative interference relay communication scheme under the condition that the channel estimation error is bounded. In the case that the statistical information of the channel estimation error is available, the optimal power allocation factor that maximizes the security rate R _s is extracted, and the lower bound of the security rate and the achievable ergodic security rate (Ergodic Secrecy Rate, ESR) of the channel are further analyzed to obtain the optimal power allocation factor that maximizes both.

Contents of the invention

In order to overcome the deficiencies of the prior art, the present invention proposes an improved optimal power allocation scheme under bounded channel estimation error on the basis of Document 3, considering the condition that the relay node is untrustworthy and the total power is limited, in When the statistical information of the channel estimation error is available, the optimal power allocation factor α _opt is extracted, and the lower bound of the security rate and the achievable ergodic security rate (Ergodic Secrecy Rate, ESR) of the channel are further analyzed.

The technical solution adopted by the present invention to solve its technical problems comprises the following steps:

Step 1. In a two-hop half-duplex relay network, in the first time slot, the source node Alice transmits information x _A to the untrusted relay node R, and at the same time, the destination node Bob sends information x A to the untrusted relay node R Transmit message x _B , signal received by relay node R Among them, PA and _{P B represent} the transmit power of nodes Alice and Bob respectively, h _AR and h _BR are the complex channel gains from nodes Alice and Bob to relay node R respectively, h _BR =h _RB , n _R represents the additive white Gaussian noise at the relay node R; the total power sent by nodes Alice and Bob is P, α∈[0,1] represents the power allocation factor, then the power of encrypted information sent by node Alice P _A = αP , the encrypted information power P _B sent by node Bob = (1-α)P, the instantaneous signal-to-interference-noise ratio received at relay node R Among them, the ratio of the equivalent signal-to-noise ratio of nodes Alice and Bob μ=γ _AR /γ _BR , and the equivalent signal-to-noise ratios from nodes Alice and Bob to the relay node R are respectively expressed as γ _AR ＝||h _AR || ² P /N ₀ and γ _BR =||h _BR || ² P/N ₀ , N ₀ =1;

Step 2, in the second time slot, the relay node R amplifies the received signal and sends it to the destination node Bob, the amplification factor is β; the signal sent from the relay node R to the node Bob

Considering that both time slots transmit signals with the same power P, normalize y _R to ||y _R || ² =P to obtain the amplification factor

Node Bob receives a signal from an untrusted relay node R

Among them, n _B is the additive Gaussian white noise received by node Bob, is the estimated channel gain between untrusted relay node R and node Bob, he is the channel estimation error, h _BR and _{he satisfy} E[h _e ]=0;

Assuming that the channel estimation error obeys the uniform distribution on [0, δ], after self-interference cancellation, the signal received by node Bob

Therefore, for given channel gains h _AR and h _BR , the equivalent SINR obtained at node Bob is

When γ _BR ≥ 20dB, the equivalent SINR of node Bob is approximately

Step 3, define the instantaneous safe rate Among them, [t] ⁺ = max[t, 0]; first to Do the derivation about α to get the optimal power allocation factor that maximizes the safe rate R _s (α);

Step 4, define the lower bound of the safe rate

Among them, Δ ₁ =αμ-α+2;

Substitute the exact power allocation factor and the approximate power allocation factor under high SNR into In , the accurate maximum safe rate lower bound and the approximate maximum safe rate lower bound under high SNR are obtained;

Step five, define ESR as the mathematical expectation of the maximum safe rate attainable on all realizations of ||h _e || ² , namely right Regarding the derivative of α, we get .

Under the condition of γ _BR ≥ 20dB, the Approximately expressed as

Under the condition of 0≤γ _AR ≤2γ _BR , we get The largest approximate optimal power allocation factor is

The beneficial effect of the present invention is: under the condition that the channel estimation error is bounded, in order to reduce the complexity, an approximate optimal power allocation (OPA) formula in the transmission process is given to maximize the safe rate. The lower bound of the security rate and the ESR at high SNR are further analyzed to evaluate the attainable average security rate. The simulation results confirm the effectiveness of the proposed scheme.

Description of drawings

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

Figure 2 is a schematic diagram of the ESR distribution under different α and γ _BRs when μ=1;

Fig. 3 is the change trend diagram of the ergodic security rate, the upper bound and the lower bound of the safe rate with γ _BR under the optimal power allocation factor.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and embodiments, and the present invention includes but not limited to the following embodiments.

The system model used in 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 a transmission process requires 2 time slots to complete. Assuming that there is no direct communication link between Alice and Bob due to shadow fading or too far away, they can only communicate through an untrusted relay node R. In the first time slot, Alice transmits information x _A to untrusted relay node R, while Bob transmits information x _B to untrusted relay node R. In the second time slot, the relay node R re-sends the received signal to Bob after being amplified by an amplifier, where the amplification factor is β. Further, assuming that all wireless channels are time-varying Rayleigh fading channels, the noise received by each node is additive white Gaussian noise (AWGN) with a mean value of 0 and a power spectral density of N ₀ .

The invention firstly describes the communication scheme of the two-hop half-duplex relay network, provides the optimal power distribution scheme, then obtains the lower bound of the safe rate, and finally analyzes the channel ESR to obtain the attainable safe rate.

It can be seen from Figure 1 that the communication process of the half-duplex relay network needs two time slots to complete. In the first time slot, the signal received by the relay node R can be expressed as

Among them, PA and _{P B represent} the transmit power of nodes Alice and Bob respectively, h _AR and h _BR represent the complex channel gain from Alice and Bob to relay node R respectively, assuming that it is a complex channel with mean value 0 and variance σ ² Gaussian variable. The channel satisfies the reciprocity theorem, that is, h _BR =h _RB , and n _R denotes additive white Gaussian noise at relay R. Assuming that the total power sent by nodes Alice and Bob is P, and α∈[0,1] represents the power allocation factor, then the power of encrypted information sent by Alice is P _A = αP, and the power sent by Bob is P _B = (1-α) p. Therefore, the instantaneous signal-to-interference-noise ratio (SINR) γ _R received at the relay node R can be expressed as:

Among them, ||h _BR || ² (1-α)P indicates that the interference signal sent by Bob is received at R during Alice’s transmission, and the equivalent signal-to-noise ratio (SNR) from node Alice and Bob to relay node R can be respectively Expressed as: γ _AR ＝||h _AR || ² P/N ₀ , γ _BR ＝||h _BR || ² P/N ₀ , μ is defined as the ratio of the equivalent signal-to-noise ratio between nodes Alice and Bob, namely: μ = γ _AR /γ _BR . Without loss of generality, we assume that N ₀ =1, and the SNR can be adjusted by transmitting power. Based on the above definition, the SINR received at the relay node R shown in formula (2) can be simplified as:

In the second time slot, the relay node R amplifies the received signal by β times and resends it to Bob. The signal sent from the relay node R to node Bob can be expressed as

Normalize y _R to ||y _R || ² = P to get the amplification factor β

Node Bob receives the signal from the untrusted relay node R as:

Among them, n _B is the additive white Gaussian noise received by node Bob. Since x _B is the interference signal sent by Bob in the previous slot, under the condition that node Bob has perfect CSI, the self-interference term in formula (6) accurate estimates can be obtained. Here we consider a more practical application scenario. For node Bob, the channel state information (CSI) is not perfect, but statistical information about channel estimation errors is available. In the present invention, considering the imperfect channel state information is known, then

in, is the estimated channel gain between untrusted relay node R and node Bob, he is the channel estimation error, h _BR and _{he satisfy} E[h _e ]=0.

In the present invention, it is assumed that the channel estimation error obeys the uniform distribution on [0, δ], then

||h _e || ² ＝ε:ε～unif(0,δ) (8)

After self-interference cancellation, the signal received by node Bob is

For given channel gains h _AR and h _BR , the equivalent SINR at node Bob can be obtained as

When γ _BR ≥ 20dB, the equivalent SINR at Node B can be approximated as

Based on the above analysis, the next step is to seek to optimize the power allocation factor.

First, based on formula (3) and formula (11), define the instantaneous safety rate

Among them, the previous factors It is because a transmission needs 2 time slots to complete, [t] ⁺ =max[t, 0].

The purpose of the present invention is to maximize the safe rate by optimizing the power allocation of nodes Alice and Bob under imperfect CSI. Based on formula (12), the problem of maximizing power allocation is expressed mathematically as

s.t.: α ∈ [0, 1]) (13)

in, is monotonically increasing, since So the maximum value of ζ(α) exists.

Generally, in order to obtain the maximum value and find the optimal power allocation factor α _opt , the present invention performs a derivation operation on ζ(α) with respect to α, and makes it equal to 0. can get

Where Δ _L =γ _BR Δ ₁ +ε ² (1−α)+1, Δ ₁ =αμ−α+2.

Solving formula (14), the optimal power allocation factor α _opt can be obtained:

in,

In the case of interference signal γ _BR ≥ 20dB, the optimal power allocation factor α _opt of formula (15) can be approximated as

It can be seen from formula (16) that when the interference signal γ _BR ≥ 20dB, the optimal power allocation factor α _opt is only determined by μ, that is, the channel estimation error has no influence on the optimal power allocation factor α _opt .

It can be known from formula (10) that γ _B (α) decreases monotonously with ||h _e || ² , therefore, when ||h _e || ² =ε=δ, the lower bound of the safe rate can be defined as

When α=α _opt , the formula (15) is brought into (17), and ε=δ, the lower bound of the safe rate can be maximized. In particular, when γ _BR ≥ 20dB, substituting formula (16) into (17), the lower bound of the approximate safe rate can be obtained as

in, In addition, when the node has perfect CSI, the upper bound of the security rate can be obtained, which is described in detail in Document 3.

Ergodic Secrecy Rate (ESR) represents the average achievable maximum security rate. In the present invention, ESR is defined as the mathematical expectation of the maximum safe rate attainable on all realizations of ||h _e || ² , namely

Put formulas (3), (11) and (12) into formula (19), we can get

Among them, f(ε) is the probability density function (Probability Density Function, PDF) of ||h _e || ² , which is defined as Therefore, formula (20) can be further expressed as

Among them, Δ1=αμ-α+2. by right Regarding the derivative of α, we can get . However, directly solving Difficulty, when γ _BR ≥ 20dB, the Approximately expressed as

Under the condition of 0≤γ _AR ≤2γ _BR , by solving formula (22), we can get

FIG. 1 shows the system model of the present invention and the transmission mode of the cooperative interference relay network. The system consists of the node Alice, the point-added Bob, and the untrusted relay node Alice that plays the role of amplification and forwarding. Each node is configured with a single antenna.

Fig. 2 is a schematic diagram of ESR distribution under different α and γ _BR when μ=1. It can be seen from Figure 2 that the ESR first increases and then decreases with the increase of α. When γ _BR =5dB, the optimal power allocation factor that maximizes the ESR When γ _BR is 20, 25, 30dB respectively, the optimal power allocation factors in these three cases are almost equal, as

Fig. 3 is the change trend diagram of the ergodic security rate, the upper bound and the lower bound of the safe rate with γ _BR under the optimal power allocation factor. The lower bound in Fig. 3 is obtained by substituting α _opt and δ=10 ⁻³ into formula (17), and the approximate lower bound is obtained by substituting α _opt and δ=10 ⁻³ into formula (17). It can be seen from Fig. 3 that when γ _BR is large, the exact lower bound and the approximate lower bound are almost the same. Furthermore, the upper bound is the safe rate under exact CSI. By substituting ||h _e || ² ＝0 into formula (15), we can get This is defined in literature 3 as the optimal power allocation factor under perfect CSI. Substituting formula (23) into formula (21), the average achievable maximum safe rate under different γ _BR can be obtained. It can be seen from Fig. 3 that under the condition of low signal-to-noise ratio, the channel estimation error has a significant impact on ESR, but when γ _BR ≥ 20dB, the change of ESR and the upper bound of the safe rate are consistent. It can be seen from Fig. 3 that under the condition of high signal-to-noise ratio, the approximate power allocation factor is valid for both the lower bound of the safe rate and the average achievable safe rate. Moreover, the achievable safe rate is always greater than the lower bound of the safe rate. Under the condition of high signal-to-noise ratio, the influence of the channel estimation error is negligible, so at this time, the achievable safe rate and the upper bound of the safe rate are almost identical.

Claims (2)

1. an optimal power distribution method of untrusted relay network under bounded CSI, it is characterized in that comprising the following steps: Step 1: In a two-hop half-duplex relay network, in the first time slot, the source node Alice transmits information x _A to the untrusted relay node R, and at the same time, the destination node Bob sends information x A to the untrusted relay node R Transmit message x _B , signal received by relay node R Among them, PA and _{P B represent} the encrypted information power sent by nodes Alice and Bob respectively, h _AR and h _BR are the complex channel gains from nodes Alice and Bob to relay node R respectively, h _BR =h _RB , in Indicates that the mean is 0 and the variance is The complex Gaussian process of n _R represents the additive white Gaussian noise at the relay node R; the total power sent by nodes Alice and Bob is P, and α∈[0,1] represents the power allocation factor, then the encrypted information sent by node Alice Power P _A = αP, the encrypted information power P _B sent by node Bob = (1-α)P, the instantaneous signal-to-interference-noise ratio received at relay node R Among them, the ratio of the equivalent signal-to-noise ratio of nodes Alice and Bob μ=γ _AR /γ _BR , and the equivalent signal-to-noise ratios from nodes Alice and Bob to the relay node R are respectively expressed as γ _AR ＝||h _AR || ² P /N ₀ and γ _BR =||h _BR || ² P/N ₀ , N ₀ =1; Step 2, in the second time slot, the relay node R amplifies the received signal and sends it to the destination node Bob, the amplification factor is β; the signal sent from the relay node R to the node Bob Considering that both time slots transmit signals with the same power P, normalize y _R to ||y _R || ² =P to obtain the amplification factor Node Bob receives a signal from an untrusted relay node R Among them, n _B is the additive Gaussian white noise received by node Bob, is the estimated channel gain between untrusted relay node R and node Bob, he is the channel estimation error, h _BR and _{he satisfy} E[h _e ]=0; Assuming that the channel estimation error obeys the uniform distribution on [0, δ], after self-interference cancellation, the signal received by node Bob Therefore, for given channel gains h _AR and h _BR , the equivalent SINR obtained at node Bob is When γ _BR ≥ 20dB, the equivalent SINR of node Bob is approximately Step 3, define the instantaneous safe rate Among them, [t] ⁺ = max[t, 0]; first to Do the derivation about α to get the optimal power allocation factor that maximizes the safe rate R _s (α); Step 4, define the lower bound of the safe rate Among them, Δ ₁ =αμ-α+2; Substitute the exact power allocation factor and the approximate power allocation factor under high SNR into In , the accurate maximum safe rate lower bound and the approximate maximum safe rate lower bound under high SNR are obtained; Step five, define ESR as the mathematical expectation of the maximum safe rate attainable on all realizations of ||h _e || ² , namely right Regarding the derivative of α, we get 2. The optimal power allocation method for an untrusted relay network under bounded CSI according to claim 1, characterized in that: in the step five, under the condition of γ _BR ≥ 20dB, the Approximately expressed as Under the condition of 0≤γ _AR ≤2γ _BR , we get The largest approximate optimal power allocation factor is