CN107071886A - A kind of optimal power allocation method of insincere junction network under bounded CSI - Google Patents

Abstract

The invention provides a kind of optimal power allocation method of insincere junction network under bounded CSI, the communication plan of double bounce half-duplex relay network is described first, optimal power allocation scheme is provided, and then obtains the lower bound of safe rate, ultimate analysis channel ESR, obtains reachable safe rate.Distribute formula to maximize safe rate The present invention gives the optimized power in transmitting procedure, the ESR under high SNR is further analyzed, for assessing reachable average security speed.Approximate optimized power distribution, which can be brought, distributes higher safe rate than constant power.

Description

Optimal power distribution method for untrusted relay network under bounded CSI

Technical Field

The invention relates to an optimal power distribution scheme of an untrusted relay network under the condition of bounded channel estimation errors.

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 study ofwo-hop amplification-and-forward systems with untrue process release nodes [ J ]. ieee trans. 3801-, the scheme can maximize the achievable system safety capacity, realize the safety communication of an untrusted Amplified Forward (AF) relay system, but does not consider the optimized power distribution, furthermore, document 2 is studied based on a perfect Channel State Information (CSI) condition, and a perfect CSI cannot be obtained in an actual communication environment.

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 studies under the assumption of perfect CSI,however, in a real communication environment, perfect CSI is substantially impossible to achieve. The invention considers the actual communication model and researches the cooperative interference relay communication scheme under the condition of bounded channel estimation error. Extracting a maximum safe rate R under the condition that the statistical information of the channel estimation error can be obtained_sAnd further analyzing a lower bound of the safe Rate and a channel achievable traversal safe Rate (ESR) to obtain an optimal power allocation factor that maximizes both.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides an improved optimal power distribution scheme under bounded channel estimation errors on the basis of document 3, and under the condition that a relay node is not credible and the total power is limited, an optimal power distribution factor α is extracted under the condition that the statistical information of the channel estimation errors is available_optAnd further analyzing the lower bound of the security Rate and the traversal security Rate achievable by the channel (ESR).

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 of the encrypted information sent 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; signals sent from the relay node R to the node Bob

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

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

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 the channel estimation error, h_B-RAnd h_eSatisfy the requirement ofE[h_e]＝0；

Assuming that the channel estimation error obeys 0,]is uniformly distributed, and the signal received by the node Bob is eliminated by self-interference

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

When gamma is_B-RWhen the equivalent SINR of the node Bob is more than or equal to 20dB, the equivalent SINR of the node Bob is approximately

Step three, defining the instantaneous safe rateWherein, [ t ]]⁺＝max[t，0](ii) a Firstly, toMaking a derivative with respect to α to obtain a resulting safe rate R_s(α) a maximum optimal power allocation factor;

step four, defining a lower bound of the safety rate

Wherein, Delta₁＝αμ-α+2；

Substituting the accurate power allocation factor and the approximate power allocation factor at high SNR into each otherObtaining an accurate lower bound of the maximum safe speed and an approximate lower bound of the maximum safe speed under high SNR;

step five, defining ESR as | | | h_e||²Mathematical expectations for the maximum safe rate achievable over all implementations, i.e.To pairDerived by α derivation。

At gamma_B-RUnder the condition of more than or equal to 20dB, theIs approximately expressed as

Gamma is more than or equal to 0_A-R≤2γ_B-RUnder the conditions of (1), obtainingThe maximum approximately optimal power allocation factor is

The invention has the beneficial effects that: under the condition that the channel estimation error is bounded, in order to reduce complexity, an approximately Optimized Power Allocation (OPA) formula in the transmission process is given to maximize a safe rate. And further analyzing the lower bound of the safety rate and the ESR under high SNR to evaluate the achievable average safety rate, and the simulation result proves the effectiveness of the scheme.

Drawings

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

fig. 2 shows that when μ ═ 1, α and γ are different_B-RSchematic diagram of ESR distribution under;

FIG. 3 is a graph of traversal safety rate, upper and lower bounds of safety rate with gamma for an optimal power allocation factor_B-RA trend graph of the change.

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 time slot, Alice transmits information x to the untrusted relay node R_AWhile Bob transmits information x to the untrusted relay node R_BIn 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, gives an optimal power distribution scheme, then obtains a lower bound of a safe speed, and finally analyzes a channel ESR to obtain a reachable safe speed.

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 that the node Bob receives additivity highWhite noise. 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 the channel estimation error, h_B-RAnd h_eSatisfy the requirement ofE[h_e]＝0。

In the present invention, assuming that the channel estimation error follows a uniform distribution over [0, ], then

||h_e||²＝∶～unif(0，) (8)

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

For a given letterChannel gain h_A-RAnd h_B-RAn equivalent SINR of Bob may be obtained at node Bob

When gamma is_B-RThe equivalent SINR at the node B may be approximated as ≧ 20dB

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

First, an instantaneous safety rate is defined based on formula (3) and formula (11)

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 (12), the maximum power allocation problem is mathematically expressed as

s.t.：α∈[0，1]) (13)

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_L＝γ_B-RΔ₁+²(1-α)+1，Δ₁＝αμ-α+2。

Solving equation (14) yields the optimized power division factor α_opt：

Wherein,

in the interference signal gamma_B-RThe optimized power division factor α of equation (15) for ≧ 20dB_optCan be approximated as

As can be seen from equation (16), the interference signal γ_B-RThe optimal power allocation factor α when being equal to or more than 20dB_optDetermined only by mu, i.e. channel estimation error versus optimum power allocation factor α_optThere is no effect.

As can be seen from the formula (10), γ_B(α) with | | | h_e||²Monotonically decreasing, therefore, at | | h_e||²When, the lower bound of safe rates can be defined as

When α is α ═ b_optWhen, the formula (15) is taken into (17), and let us say, the safe lower rate bound can be maximized. Particularly, when γ_B-RWhen the speed is more than or equal to 20dB, the lower limit of the obtained approximate safe speed is that the formula (16) is brought into the formula (17)

Wherein,furthermore, an upper bound on the safe rate is obtained when the node has perfect CSI, as described in detail in document 3.

The safety Rate is traversed (Ergodic security Rate,ESR) characterizes the maximum safe rate that can be achieved on average. In the present invention, ESR is defined as being in | | | h_e||²Mathematical expectations for the maximum safe rate achievable over all implementations, i.e.

Substituting the equations (3), (11) and (12) into the equation (19) can obtain

Wherein f () is | | h_e||²Is defined as the Probability Density Function (PDF)Therefore, equation (20) can be further expressed as

Wherein, Delta 1 is α mu- α +2For the derivation of α, it can be found. However, direct solvingWith difficulty, when gamma_B-RWhen the power is more than or equal to 20dB, the power can be adjustedIs approximately expressed as

Gamma is more than or equal to 0_A-R≤2γ_B-RBy solving the equation (22) under the conditions (2), the

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 that when μ ═ 1, α and γ are different_B-RFIG. 2 shows that the ESR increases and then decreases with increasing α, when γ is_B-RWhen 5dB, make maximum ESR optimum power distribution factorWhen gamma is_B-RAt 20, 25, and 30dB, the optimal power allocation factors for these three cases are almost equal to

FIG. 3 is a graph of traversal safety rate, upper and lower bounds of safety rate with gamma for an optimal power allocation factor_B-RThe lower bound in fig. 3 is by α_optAnd 10^-3Obtained by substituting equation (17), the approximate lower bound is α_optAnd 10^-3Obtained by substituting into formula (17). As can be seen from FIG. 3, when γ is_B-RLarger, the exact lower bound and the approximate lower bound are nearly identical. Furthermore, the upper bound is the safe rate under accurate CSI. By mixing h_e||²Substituting 0 into the formula(15) Is obtained byThis is defined in document 3 as the optimal power allocation factor under perfect CSI. By substituting equation (23) into equation (21), the difference in γ can be obtained_B-RThe average of (c) can reach the maximum safe rate. As can be seen from fig. 3, under the condition of low snr, the channel estimation error has a significant effect on ESR, but when γ is equal to_B-RWhen the ESR is more than or equal to 20dB, the ESR is consistent with the upper bound of the safe speed. As can be seen from fig. 3, the approximate power allocation factor is effective for both the safe rate lower bound and the average achievable safe rate under high snr conditions. Moreover, the achievable safe rate is always greater than the safe rate lower bound. Under high snr conditions, the effect of channel estimation errors is negligible, and thus, the achievable safe rate and the upper bound of the safe rate are almost matched at this time.

Claims (2)

1. An optimal power allocation method for an untrusted relay network under bounded 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 of the encrypted information sent 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; signals sent from the relay node R to the node Bob

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

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

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 the channel estimation error, h_B-RAnd h_eSatisfy the requirement ofE[h_e]＝0；

Assuming that the channel estimation error obeys 0,]is uniformly distributed, and the signal received by the node Bob is eliminated by self-interference

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

When gamma is_B-RWhen the equivalent SINR of the node Bob is more than or equal to 20dB, the equivalent SINR of the node Bob is approximately

Step three, defining the instantaneous safe rateWherein, [ t ]]⁺＝max[t，0](ii) a Firstly, toMaking a derivative with respect to α to obtain a resulting safe rate R_s(α) a maximum optimal power allocation factor;

step four, defining a lower bound of the safety rate

Wherein, Delta 1_＝αμ-α+2；

Substituting the accurate power allocation factor and the approximate power allocation factor at high SNR into each otherObtaining an accurate lower bound of the maximum safe speed and an approximate lower bound of the maximum safe speed under high SNR;

step five, defining ESR as | | | h_e||²Mathematical expectations for the maximum safe rate achievable over all implementations, i.e.To pairDerived by α derivation

2. The method for optimal power allocation for an untrusted relay network under bounded CSI as claimed in claim 1, wherein: in the fifth step, the alpha is_B-RUnder the condition of more than or equal to 20dB, theIs approximately expressed as

Gamma is more than or equal to 0_A-R≤2γ_B-RUnder the conditions of (1), obtainingThe maximum approximately optimal power allocation factor is