Wireless communication system, method and optimization method of mixed IRS and DF relay

Abstract

The invention provides a wireless communication system, method and optimization method for mixed IRS and DF relay, and belongs to the technical field of wireless communication, and the wireless communication system comprises a transmitter, a receiver, a decoding and forwarding relay node and an active IRS configured with an active reflection unit. The active IRS is deployed in a space between a transmitter and a receiver, and an active unit of the active IRS performs joint adjustment of amplitude and phase of an incident signal and introduces amplification. By dynamically adjusting the transmitting power of the transmitter and the DF relay, the end-to-end achievable rate of the system is maximized on the premise that the total power constraint is met. According to the method, the tight upper bound of the achievable rate of the system under the Rayleigh fading channel and the mixed Rayleigh-Rice fading channel is deduced, and a tool is provided for theoretical performance analysis; the performance bottleneck of a traditional passive IRS system is overcome, and the signal amplification capacity of the active IRS and the signal regeneration capacity of the DF relay are fully utilized; and an effective and promising scheme is provided for improving the rate, efficiency and reliability of a future wireless communication network.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication technologies, and particularly relates to a wireless communication system, method and optimization method combining an intelligent reflecting surface (IRS) and a decode-and-forward (DF) relay, which enhance signal transmission by using the IRS and relay technologies. In particular, it relates to a wireless communication system combining an active IRS and a decode-and-forward (DF) relay for enhancing wireless communication performance and its performance optimization method. Background Art

[0002] With the exponential growth of the number of connected devices and data traffic, wireless communication systems are facing unprecedented challenges. To meet the requirements of high data rate and high spectral efficiency, researchers have proposed various technologies, including multiple-input multiple-output (MIMO), relay-assisted communication, and intelligent reflecting surface (IRS), etc. Among them, as an emerging technology, the IRS can reconstruct the propagation environment of wireless signals by dynamically adjusting the phase and amplitude of reflection units, thereby significantly improving communication performance without increasing the cost of radio frequency chains.

[0003] Traditional IRS technologies are mainly divided into two categories: passive IRS and active IRS. The passive IRS consists of a large number of low-cost passive reflection units and can optimize the signal propagation direction through phase adjustment. However, the passive IRS has significant limitations, the most prominent of which is the "multiplicative fading effect". This effect stems from the fact that the equivalent path loss from the transmitter to the IRS and then to the receiver is the product of the link losses of the transmitter-IRS and IRS-receiver segments, resulting in severe limitations on signal gain in scenarios where the direct link is strong or the path loss is large. In addition, the passive IRS cannot amplify signals, which further limits its applicability in high-fading or complex interference environments.

[0004] On the other hand, the decode-and-forward (DF) relay technology plays an important role in expanding the signal coverage and improving communication reliability by receiving, decoding, and forwarding signals. Traditional DF relay systems make up for the deficiencies of the direct link to a certain extent, but their performance is limited by the channel conditions between the relay node and the Tx and Rx, and they cannot fully utilize the signal regulation ability of the IRS. Using only DF relays or only active IRS may not achieve optimal performance and efficiency in all scenarios. Therefore, researchers have begun to explore hybrid architectures that combine the IRS and DF relays in order to further improve system performance through their synergistic effects.

[0005] Compared with AF relaying, DF relaying has stronger noise suppression ability. By decoding and re-encoding the regenerated signal, the noise propagation path is cut off, thus avoiding the noise accumulation problem of AF relaying. At the same time, it supports error checking and retransmission, reducing the bit error rate, especially performing better in low signal-to-noise ratio scenarios and having higher transmission reliability. On the other hand, DF relaying can dynamically balance the signal-to-noise ratio of the two-hop link, improving the power utilization efficiency, and thus the power allocation is more flexible.

[0006] In the prior art, certain progress has been made in the research on hybrid passive IRS and DF relaying systems. For example, by optimizing the reflection coefficient of IRS and the resource allocation of the relay, the system throughput and bit error rate have been improved. However, due to the limitations of passive IRS, the performance bottleneck of traditional passive IRS-assisted DF relaying systems caused by the multiplicative fading effect results in large path loss and limited performance improvement under the conditions of a limited number of reflection units or medium signal-to-noise ratio. In addition, multi-IRS deployment, power allocation optimization, and performance analysis under different fading channels have also been studied, but the hybrid system combining active IRS and DF relaying still belongs to a blank field, lacking a hybrid system architecture that can effectively combine the signal amplification ability of active IRS and the signal regeneration ability of DF relaying and its performance optimization method.

[0007] The thermal noise introduced when the active IRS amplifies the signal will cause the decoding failure of the DF relay, and the reflection coefficients of the two-hop link need to be jointly optimized in stages. At the same time, the non-linear relationship between active amplification and noise, and the mixed fading channel modeling increase the complexity of power allocation. The cost of obtaining the channel state information of the two-hop link is high, the hardware design of the active IRS is complex (requiring dynamic adjustment of amplitude and phase), and the computational pressure of the real-time optimization algorithm is large. Existing solutions have not fully addressed the trade-off between the thermal noise introduced by the active IRS and signal amplification, and also lack a comprehensive optimization strategy for different propagation environments. An effective resource allocation strategy (especially power allocation) is needed to maximize the end-to-end communication performance (such as achievable rate) of the proposed hybrid active IRS and DF relaying network.

[0008] The patent document "Wireless Communication Method, Device and Equipment Based on IRS-Assisted AF Relaying" (CN114726418A) discloses that by optimizing the configurable parameters of the wireless communication system and controlling the operation of the transmitter, AF relay, IRS, and receiver through the transmission power of the optimized transmitter, the transmission power of the AF relay, and the N reflection coefficients in the first and second half transmission periods of the IRS, the communication transmission efficiency and channel capacity between the transmitter and the receiver can be enhanced, and the robustness of wireless communication can be enhanced. However, due to the use of AF relaying, it is impossible to replace it with DF in terms of noise, performance, optimized power allocation, etc., and it also lacks the advantages of DF relaying.

[0009] Based on the above background, there is an urgent need for a hybrid system that can combine the signal amplification ability of active IRS and the reliable forwarding function of DF relay to significantly improve the achievable rate and system efficiency of wireless communication in complex propagation environments, while providing comprehensive support for theoretical analysis and optimization methods. Summary of the Invention

[0010] Aiming at the defects in the prior art, the purpose of the present invention is to provide a wireless communication system, method and optimization method that hybridize IRS and DF relay.

[0011] According to a wireless communication system that hybridizes IRS and DF relay provided by the present invention, it includes: a transmitter Tx, a receiver Rx, a DF relay, and an active IRS;

[0012] Both the transmitter and the receiver are equipped with single antennas or MIMO antennas. The active IRS is deployed in the half-space area between the transmitter and the receiver, and the DF relay is deployed between the transmitter and the receiver;

[0013] The DF relay is equipped with a single antenna, and the active IRS includes L active reflection units, where L≥1;

[0014] The active reflection unit integrates active devices.

[0015] Preferably, the additive Gaussian white noises ω(n) and ω(n+1) of the active IRS are added to the received signal in different time slots n and n+1 respectively, which are zero-mean random variables with variances of And introduce the total noise vector thermal noise

[0016] The two-stage reflection coefficient matrix of the active IRS is independently controlled. The first-stage reflection coefficient matrix Θ:

[0017]

[0018] The second-stage reflection coefficient matrix Φ:

[0019]

[0020] ξ l 、η l ∈[1,∞)

[0021] θ l 、φ l ∈[0,2π]

[0022] l = 1, 2,..., L

[0023] where 0 L represents an L-dimensional vector;

[0024] I L represents the \(L\times L\) identity matrix;

[0025] represents the thermal noise power of each cell;

[0026] represents a complex Gaussian distribution with an expectation of 0 L and a variance of ;

[0027] \(\xi\) l and \(\eta\) l respectively represent the amplification factors of the \(l\)th active reflection unit in the first stage and the second stage;

[0028] \(\theta\) l and \(\varphi\) l respectively represent the phase shifts applied to the \(l\)th unit in the first stage and the second stage.

[0029] Preferably, the links between the transmitter Tx, the receiver Rx, the DF relay, and the active IRS are simultaneously affected by large-scale fading and small-scale fading, defined as

[0030] the path loss of the large-scale fading is \(d\) -α .

[0031] where \(h\) TI represents the channel vector from Tx to the active IRS;

[0032] \(h\) ID represents the channel vector from the active IRS to the DF relay;

[0033] \(h\) DI represents the equivalent channel gain from the channel vector from the DF relay to the active IRS to the receiver;

[0034] \(h\) IR represents the channel vector from the active IRS to Rx;

[0035] \(h\) TD represents the direct link channel gain coefficient from Tx to the DF relay;

[0036] \(h\) DR represents the direct link channel gain coefficient from the DF relay to Rx;

[0037] represents a complex matrix of dimension \(M\times N\);

[0038] \(d\) represents the distance;

[0039] \(\alpha\) represents the path loss exponent.

[0040] Small-scale fading uses time-division duplexing or frequency-division duplexing methods, and an end-to-end transmission is completed in two equal-length time slots. At the same time, a channel model is constructed considering Rayleigh fading and mixed Rayleigh-Rician fading.

[0041] Preferably, the links between Tx, DF relay, Rx, and the links between the IRS without line-of-sight are constructed as Rayleigh fading channels, and the channel gain is:

[0042]

[0043] where X represents the link identifier, X ∈ {TI, ID, DI, IR};

[0044] d X represents the distance corresponding to the link;

[0045] represents the path loss exponent of the Rayleigh fading channel;

[0046] represents a complex Gaussian distribution with an expected value of 0 and a variance of ;

[0047] represents the l-th channel element of the X link, which is a complex Gaussian variable with a mean of zero and a variance of ;

[0048] For the channel vector related to the IRS X ∈ {TI, ID, DI, IR}, the Rician fading channel is modeled as:

[0049]

[0050] where κ X represents the Rician factor;

[0051] represents the path loss exponent of the line-of-sight link under the Rician fading channel

[0052] represents the determined LoS component, which is the array response vector;

[0053] represents the phase of the l-th reflection unit in the Rician channel.

[0054] According to a wireless communication method combining an IRS and a DF relay provided by the present invention, it is implemented by using the wireless communication system combining the IRS and the DF relay, including:

[0055] Step 1: The transmitter Tx sends a signal x(n) with power P1. After transmission through the link, the DF relay receives the signal y D(n);

[0056] Step 2: The DF relay transmits the decoded and re-encoded signal x(n + 1) with power P2. After transmission through the link, the receiver Rx receives the signal y R (n + 1).

[0057] Preferably, the signal x(n) is transmitted through the direct link from Tx to the DF relay and / or the reflected link via Tx - active IRS - DF relay, satisfying the power constraint

[0058] The signal y D (n) received by the DF includes the signal of the direct link the signal of the Tx - IRS - relay reflected link the noise introduced by the active IRS additive white Gaussian noise Expressed as:

[0059]

[0060] where P1 represents the transmit power of Tx;

[0061] Θ represents the first - stage reflection coefficient matrix of the active IRS;

[0062] n represents the time index;

[0063] E[] represents the expectation operation;

[0064] v represents the active IRS noise;

[0065] ω represents the additive white Gaussian noise;

[0066] represents the additive white Gaussian noise power;

[0067] represents a complex Gaussian distribution with an expectation of 0 and a variance of ;

[0068] h TI represents the channel vector from Tx to the active IRS;

[0069] h ID represents the channel vector from the active IRS to the DF relay;

[0070] h TD represents the direct - link channel gain coefficient from Tx to the DF relay.

[0071] Preferably, the received signal - to - noise ratio at the DF relay includes the signal power and the noise power is γD :

[0072]

[0073] Optimize and adjust the phase shift θ of the first - stage reflection coefficient matrix of the active IRS l , add in - phase or ignore the direct path:

[0074]

[0075] The optimal phase - shift selection is:

[0076] θ l = arg(h TD ) + arg([h ID ) l [h TI ) l )

[0077] Or:

[0078] θ l = arg([h ID ) l [h TI ) l )

[0079] The signal power is approximately:

[0080]

[0081] The received noise - to - ratio SNR of the optimized DF relay is expressed as:

[0082]

[0083] where ξ l represents the amplification factor of the l - th active reflection unit in the first stage;

[0084] represents the thermal noise power of each unit;

[0085] L represents the total number of active reflection units;

[0086] X represents the link identifier;

[0087] d X represents the distance corresponding to the link;

[0088] α represents the path - loss exponent.

[0089] Preferably, the signal x(n + 1) is transmitted through the direct link from the DF relay to Rx and / or via the reflected link of DF relay - active IRS - Rx.

[0090] The signal y received by the receiver R (n + 1) includes the signal of the direct link The signal of the relay-IRS-Rx reflection link The noise introduced by the active IRS Additive white Gaussian noise Is expressed as:

[0091]

[0092] where v represents the active IRS noise;

[0093] ω represents the additive white Gaussian noise;

[0094] Represents the equivalent channel vector related to the system topology and channel characteristics;

[0095] γ R Represents the SNR at the receiver;

[0096] h IR Represents the channel vector from the active IRS to the Rx;

[0097] h DR Represents the direct link channel gain coefficient from the DF relay to the Rx;

[0098] Represents the additive white Gaussian noise power;

[0099] Represents a complex Gaussian distribution with an expectation of 0 and a variance of ;

[0100] h ID Represents the channel vector from the active IRS to the DF relay;

[0101] Φ represents the second-stage reflection coefficient matrix;

[0102] n represents the time index.

[0103] Preferably, the SNR at the receiver, γ R Is expressed as:

[0104]

[0105] η l ∈[1, ∞)

[0106] Optimize and adjust the phase shift φ of the second-stage reflection coefficient matrix of the active IRS l :

[0107] φ l = arg(h DR)+arg([h IR l [h DI l )

[0108] φ l ∈[0,2π]

[0109] ηl=η

[0110] The SNR at the optimized receiver is:

[0111]

[0112] where η l represents the amplitude of the l-th reflecting element in the first stage;

[0113] represents the thermal noise power of each element;

[0114] L represents the total number of active reflecting elements;

[0115] X represents the link identifier;

[0116] d X represents the distance corresponding to the link;

[0117] α represents the path loss exponent.

[0118] According to an optimization method for a hybrid IRS and DF relay wireless communication system provided by the present invention, it is carried out in the hybrid IRS and DF relay wireless communication system, including:

[0119] The total power constraint is P1 + P2 = P:

[0120] P1P2 ≥ 0

[0121]

[0122] Under the Rayleigh fading channel:

[0123]

[0124] where X represents the link identifier, X ∈ {TI, ID, DI, IR};

[0125] d X represents the distance corresponding to the link;

[0126] represents the path loss exponent of the Rayleigh fading channel;

[0127] ξ represents the amplification factor of the active reflecting element in the first stage;

[0128] ​​ Represents the thermal noise power of each unit;

[0129] L represents the total number of active reflection units;

[0130] P1 represents the transmission power of Tx;

[0131] P2 represents the transmission power of the DF relay;

[0132] Represents the additive white Gaussian noise power;

[0133] A, B, C, and D all represent the equivalent gain and noise figure under the current channel state and IRS parameter configuration; Represents the square of the channel amplitude from Tx to the DF relay;

[0134] Represents the square of the channel amplitude from the DF relay to Rx;

[0135] Represents the square of the channel amplitude from Tx to the DF relay after reflection by the IRS; Represents the square of the channel amplitude from the DF relay to Rx after reflection by the IRS; h TI Represents the channel vector from Tx to the active IRS;

[0136] h ID Represents the channel vector from the active IRS to the DF relay;

[0137] h DI Represents the equivalent channel gain from the channel vector from the DF relay to the active IRS to the receiver; h IR Represents the channel vector from the active IRS to Rx;

[0138] h TD Represents the direct link channel gain coefficient from Tx to the DF relay;

[0139] h DR Represents the direct link channel gain coefficient from the DF relay to Rx;

[0140] γ D Represents the received noise ratio SNR of the DF relay;

[0141] γ R Represents the SNR at the receiver.

[0142] Substitute the constraint P2 = P - P1 into:

[0143] EP12 + FP1 + G = 0

[0144] γ D = [γ R

[0145] E = -AD + CB

[0146]

[0147] Among them, E, F, and G all represent coefficients.

[0148] If E = 0, then the optimal value of P1 is

[0149] FP1 + G = 0

[0150] P1 = -G / F

[0151] Verify whether the solution is within the valid interval of 0 < P1 < P. If it is satisfied, then P 1opt = -G / F. If not, then discard it;

[0152] If E ≠ 0, then calculate the discriminant Δ = F 2 - 4EG;

[0153] If Δ < 0, then it is considered that there is no solution. If Δ ≥ 0, then the real solution is Select the solution that satisfies the physical constraint 0 < P1 < P as the optimal transmitter power P 1opt .

[0154] Calculate the optimal DF relay power:

[0155] P 2opt = P - P 1opt

[0156] Substitute P 1opt into γ D or P 2opt into γ R , and obtain the optimal single - hop SNR:

[0157]

[0158] The maximum rate is:

[0159]

[0160] Under the Rice channel, introduce the parameters related to the Rice channel and others into the equation, calculate the coefficients A, B, C, and D, obtain the power - allocation optimization equation applicable to the Rice channel, and solve for the optimal DF relay power and the corresponding maximum rate.

[0161] The achievable rate of the system

[0162]

[0163] ​Compared with the prior art, the present invention has the following beneficial effects:

[0164] 1. By means of the optimal power allocation strategy, the present invention dynamically allocates the transmission power between the transmitter and the decode-and-forward relay, balances the signal-to-noise ratios of the two hops, further improves the overall achievable rate and power utilization efficiency of the system, and maximizes the end-to-end achievable rate of the system.

[0165] 2. By combining the signal amplification ability of the active IRS and the signal regeneration ability of the DF relay, the active IRS assists in the signal transmission from the transmitter to the relay and from the relay to the receiver. The active unit can jointly adjust the amplitude and phase of the incident signal and introduce amplification to overcome the multiplicative fading effect of the traditional passive IRS.

[0166] 3. By combining the amplification effect of the active IRS and the coverage extension ability of the DF relay, the present invention improves the signal quality, especially improves the reliability of the communication link in the scenarios with obstacles or long-distance transmission.

[0167] 4. Through simulation, the present invention reveals the influence rules of key parameters (such as SNR, IRS position, number of reflection units) on the system performance, and derives the tight upper bound of the achievable rate in the Rayleigh and Rician fading channels, providing a theoretical basis for system performance evaluation and parameter design. BRIEF DESCRIPTION OF THE DRAWINGS

[0168] Other features, objects and advantages of the present invention will become more apparent by reading the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0169] Figure 1 It is a schematic diagram of a wireless communication system with hybrid IRS and DF relay.

[0170] Figure 2 It is a schematic diagram of a simulation curve of the relationship between the achievable rate and the signal-to-noise ratio of a wireless communication system with hybrid IRS and DF relay and a comparison scheme in a Rayleigh fading channel.

[0171] Figure 3 It is a simulation curve graph of the relationship between the achievable rate and the position of the active IRS of a wireless communication system with hybrid IRS and DF relay and a comparison scheme in a Rayleigh fading channel. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0172] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that those of ordinary skill in the art can make several changes and improvements without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0173] According to a wireless communication system with a hybrid active IRS and DF relay provided by the present invention, the communication performance from a transmitter (Tx) to a receiver (Rx) is improved, especially in a scenario where the distance between the Tx and the Rx is relatively long and the direct link can be ignored due to severe path loss or obstacle blockage. Figure 1 For example, it includes: a transmitter, a receiver, a decode-and-forward relay node, and an active IRS configured with active reflection units.

[0174] The active IRS is deployed in the space between the transmitter and the receiver to assist the signal transmission from the transmitter to the relay and from the relay to the receiver. Its active unit can jointly adjust the amplitude and phase of the incident signal and introduce amplification to overcome the multiplicative fading effect of the traditional passive IRS.

[0175] Transmitter (Tx): The source node of the signal, equipped with a single antenna or a MIMO antenna.

[0176] Receiver (Rx): The destination node of the signal, equipped with a single antenna or a MIMO antenna.

[0177] Decode-and-forward (DF) relay: Non-linearly regenerates the signal, and the noise risk is concentrated on the link noise before relay decoding. It is necessary to optimize both the transmitter-IRS-receiver and transmitter-IRS-relay-receiver links simultaneously. Additionally, performance metrics such as decoding failure rate and two-hop rate bottleneck are introduced.

[0178] Active IRS: Strategically deployed in the environment, such as the half-space area between the Tx and the Rx, and its position is used to enhance the link signal transmission quality between the transmitter and the decode-and-forward relay node and between the decode-and-forward relay node and the receiver to assist the communication signal transmission of the Tx-relay link (the first stage) and / or the relay-Rx link (the second stage).

[0179] In more preferred examples, the active IRS is composed of L (L≥1) active reflection units with adjustable reflection coefficients. Each unit integrates active devices (such as amplifiers), and each node is equipped with a single antenna and operates in equal-length time slots, capable of independently adjusting the phase (θ l or φ l ) and amplitude (controlled by the amplification factor ξ l ≥1 or η l ≥1) of the incident signal, and is capable of amplifying the adjusted signal.

[0180] When the active IRS is working, additional thermal noise will be introduced due to active devices. That is to say, during the signal transmission process, there is additive Gaussian white noise and the thermal noise introduced by the active IRS itself. The noise introduced by each unit is independent and identically distributed complex Gaussian noise. The additive Gaussian white noise ω(n) and ω(n + 1) are added to the received signal in different time slots n and n + 1 respectively, and both are zero-mean random variables with a variance of The total noise vector thermal noise introduced by the active IRS where 0 L represents an L-dimensional vector, and I L represents the L×L identity matrix, and the parameter represents the thermal noise power of each unit. represents being subject to complex Gaussian distribution. The thermal noise will cause the DF relay decoding to fail and affect the signal quality of the signal reflected by the IRS. Therefore, the reflection coefficients of the two-hop link need to be jointly optimized in stages.

[0181] The first-stage reflection coefficient matrix Θ of the reflection unit of the active IRS:

[0182]

[0183] The second-stage reflection coefficient matrix Φ:

[0184]

[0185] Both reflection coefficient matrices can be independently controlled. Among them, l = 1, 2,..., L, and their reflection amplitudes satisfy ξ l , η l ∈[1, ∞), which are the amplification factors of the l-th active reflection unit in the first stage and the second stage. ξ > 1 or η > 1 reflects the amplification ability of the active IRS. In some preferred examples, it is assumed that all units have the same amplification factor, that is and

[0186] The phase shifts satisfy θ l , φ l ∈[0, 2π], which are the phase shifts applied by the l-th unit in the first stage and the second stage, and are adjusted continuously or discretely. And the reflection coefficient matrix is dynamically adjusted according to the channel state information of the system to optimize the signal transmission performance.

[0187] DF relay node: Located between the Tx and the Rx, it is also equipped with a single antenna. Since the distance between the transmitter and the receiver is relatively far, the path loss of the direct link is too large to be negligible. At this time, the DF relay node is responsible for decoding and forwarding the signals received from the transmitter. Its function is to receive and decode the signals from the Tx in the first transmission stage, and then re-encode and forward the decoded signals to the Rx in the second transmission stage.

[0188] By combining the signal amplification ability of the active IRS and the signal regeneration ability of the DF relay, the multiplicative fading limitation of the passive IRS is effectively overcome. Compared with the traditional passive IRS-assisted DF relay scheme and the independent (relay-free) active IRS scheme, it can achieve a higher end-to-end achievable rate in a wider range of scenarios. Especially in the case of a limited number of reflection elements or a medium signal-to-noise ratio range, the achievable rate can be significantly improved. At the same time, the combination of the amplification effect of the active IRS and the coverage extension ability of the DF relay can improve the signal quality, enhance the signal coverage, and improve the reliability of the communication link, especially in scenarios with obstacles or long-distance transmissions.

[0189] Define the channel coefficients or vectors / matrices according to the antenna configuration. Take the single-antenna node as an example:

[0190] Channel vector from the Tx to the active IRS.

[0191] Channel vector from the active IRS to the DF relay.

[0192] Equivalent channel gain from the channel vector from the DF relay to the active IRS to the receiver (in TDD, if channel reciprocity is considered, ).

[0193] Channel vector from the active IRS to the Rx.

[0194] Direct link channel gain coefficient from the Tx to the DF relay.

[0195] Direct link channel gain coefficient from the DF relay to the Rx.

[0196] Among them, represents a complex matrix of M×N dimensions. Each link is affected by both large-scale fading (path loss and shadow) and small-scale fading.

[0197] Large-scale fading: The path loss is d -α , where d is the distance and α is the path loss exponent.

[0198] Small-scale fading: For the links between the transmitter, decode-and-forward relay node, and receiver, i.e., the links between Tx, DF relay, and Rx (h TD , h DR ), and the links between these nodes and the IRS that may lack line-of-sight, considering that they are usually at relatively low heights and there are abundant scatterers around, they are modeled as Rayleigh fading channels. Considering the elements of the Rayleigh fading channel vectors related to the IRS, the channel gain:

[0199]

[0200] where, denotes being subject to complex Gaussian distribution, X represents the link identifier (such as TI, ID, TD, DI, IR), X ∈ {TI, ID, DI, IR}, d X is the distance of the corresponding link, is the path loss exponent of the Rayleigh fading channel. represents the l-th channel element of the X link and is a complex Gaussian variable with mean zero and variance .

[0201] For the links involving the IRS (h TI , h ID , h DI , h ID ), considering that the IRS is usually deployed at a relatively high position (such as the outer wall of a building) and there may be a strong line-of-sight path, a hybrid Rayleigh and Rician channel model is adopted. More specifically, for the IRS-related channel vector X ∈ {TI, ID, DI, IR}, the Rician channel is modeled as:

[0202]

[0203] where, κ X is the Rician factor, represents the path loss exponent of the line-of-sight link under Rician fading, and for these links, there is also a phase characteristic vector representing the determined LoS component (usually related to the array response), is represented as the array response vector, represents the phase of the l-th reflection element under the Rician channel, describing the phase characteristics of each reflection element of the active IRS in the Rician channel. At the same time, two scenarios of Rayleigh fading and hybrid Rayleigh-Rician fading (for example, the IRS-related links are Rician fading and the others are Rayleigh fading) are considered for analysis.

[0204] In more preferred examples, all nodes operate in a quasi-static flat fading channel, and the system adopts time-division duplex or frequency-division duplex. Taking the end-to-end transmission completed in two equal-length time slots as an example, a channel model is constructed.

[0205] A wireless communication method combining a hybrid active IRS and DF relay according to the present invention specifically includes:

[0206] Step 1: In the Tx-relay link (the first stage), the transmitter sends a signal x(n) with power P1.

[0207] The signal x(n) satisfies the power constraint The signal passes through the direct link from Tx to DF relay (channel h TD ) and / or the reflected link via Tx-active IRS-DF relay (involving channels h TI and h ID , and the first active reflection coefficient matrix Θ of the active IRS) for transmission.

[0208] The signal received by the DF relay includes the signal from the direct link The signal from the Tx-IRS-relay reflected link The noise introduced by the active IRS and transmitted through the IRS-relay channel The additive white Gaussian noise (AWGN) at the receiver The received signal y D (n) is expressed as:

[0209]

[0210] where P1 represents the transmission power of Tx, Θ is the reflection coefficient matrix of the active IRS, n represents the time index, the transmitted signal x(n) satisfies the power constraint E[|x(n)|²] = 1, E[] represents the expectation operation, v(n) is the active IRS noise, and ω(n) is the additive white Gaussian noise (AWGN). The received signal-to-noise ratio at the DF relay is γ D , including the signal power and the noise power Assuming that v(n) is independent of x(n) and ω(n), thus:

[0211]

[0212] To maximize the signal power part, the reflection coefficient matrix of the active IRS is optimized to adjust the phase shift θ l . Assuming that all channel state information is known, the optimal phase shift strategy is to perform co-phase addition, that is, to make have the same phase as the direct path h TD or, if the direct path is negligible, to maximize

[0213] Specifically, let and h ID = [[h ID 1,...,[h ID L , then:

[0214]

[0215] If the direct path cannot be ignored, the optimal phase shift selection is:

[0216] θ l = arg(h TD ) + arg([h ID ) l [h TI ) l )

[0217] If only maximizing the reflected path is considered, the optimal phase shift selection is:

[0218] θ l = arg([h ID ) l [h TI ) l )

[0219] To make the term in phase with h TD , assuming that all element amplification factors are the same ξ l = ξ, the signal power is approximately:

[0220]

[0221] In the noise power Assuming that the channel powers of each element are approximately equal, further approximation:

[0222]

[0223] Therefore, the received noise ratio of the optimized DF relay is expressed as:

[0224]

[0225] Step 2: In the relay-Rx link (the second phase), the DF relay transmits the decoded and re-encoded signal x(n + 1) with power P2.

[0226] The signal passes through the direct link (channel h DR ) from the DF relay to the Rx and / or the reflected link via the DF relay-active IRS-Rx (involving channels h DI and h​IR , and is transmitted by the second reflection coefficient matrix Φ of the active IRS. The signal received by the receiver includes the signal from the direct link The signal from the relay-IRS-Rx reflection link The noise introduced by the active IRS and transmitted through the IRS-Rx channel At the receiver

[0227] Therefore, y R (n + 1) is expressed as:

[0228]

[0229] where v(n + 1) is the active IRS noise, ω(n + 1) is the AWGN, is the equivalent channel vector related to the system topology and channel characteristics, and x(n + 1) is the signal forwarded by the decode-and-forward relay node. The SNR at the receiver is γ R . For each reflection unit amplitude η l ∈[1, ∞), γ R is expressed as:

[0230]

[0231] By optimizing the phase shift φ l , φ l ∈[0, 2π], and assuming η l = η, it is expressed as:

[0232] φ l = arg(h DR ) + arg([h IR l [h DI l )

[0233]

[0234] According to an optimization method for a hybrid IRS and DF relay wireless communication system provided by the present invention, through an optimal power allocation strategy, the limited total power resources are dynamically allocated between the transmitter and the DF relay. By balancing the signal-to-noise ratios of the two hops, the overall achievable rate and power utilization efficiency of the system are further improved, providing an effective and promising solution for improving the rate, efficiency, and reliability of future wireless communication networks, especially in terms of the interaction between signal amplification, noise control, and relay assistance.

[0235] ​​Under the condition of satisfying the total transmit power constraint \(P_1 + P_2\leq P\), find the optimal transmitter power \(P_1\) and DF relay power \(P_2\) to make the two-hop signal-to-noise ratio equal, so as to maximize the achievable rate of the system. Optimize the system efficiency. The specific steps are as follows:

[0236] Maximize is equivalent to maximizing \(\min\{\gamma\) D , \(\gamma\) R}\), with the total power constraint \(P_1 + P_2 = P\). The optimal power allocation strategy should make the SNR of the two hops equal, that is, the optimal solution usually reaches when \(\gamma\) D =\(\gamma\) R . Let \(\gamma\) D =\(\gamma\) R :

[0237] \(P_1P_2\geq0\)

[0238]

[0239] In a Rayleigh fading channel, assume:

[0240]

[0241] where \(A\), \(B\), \(C\), \(D\) all represent the equivalent gains and noise coefficients under the current channel state (\(h\) TD , \(h\) ID , \(h\) TI , \(h\) DR , \(h\) IR , \(h\) DI ) and IRS parameter configuration (\(L\), \(\xi\), \(\eta\), \(\theta\) l , \(\varphi\) l ), which are calculated according to the instantaneous channel for real-time power allocation and represent the equivalent channel gain and active noise impact. represents the square of the channel amplitude from the Tx to the DF relay; represents the square of the channel amplitude from the DF relay to the Rx; represents the square of the channel amplitude from the Tx to the DF relay after reflection by the IRS; represents the square of the channel amplitude from the DF relay to the Rx after reflection by the IRS.

[0242] Let \(\gamma\) D =[\(\gamma\) R , substitute the constraint \(P_2 = P - P_1\) into it, and after arrangement, a standard quadratic equation about \(P_1\) is obtained:

[0243] \(EP_1\) 2 + \(FP_1 + G = 0\)

[0244] where:

[0245] E = -AD + CB

[0246]

[0247] E, F, and G are all coefficients. Solve the quadratic equation to obtain a closed-form solution or an efficient numerical solution:

[0248]

[0249] If E = 0, the optimal value of P1 is Then the equation degenerates into a linear equation:

[0250] FP1 + G = 0

[0251] The solution is P1 = -G / F. It is necessary to verify whether the solution is within the valid interval: 0 < P1 < P. If it is satisfied, then P1opt = -G / F; if not, it is discarded.

[0252] If E ≠ 0, then calculate the discriminant Δ = F 2 -4EG;

[0253] If Δ < 0, there is theoretically no real solution (usually there is a solution in an actual physical system). If Δ ≥ 0, the real solutions are

[0254] From the obtained real solutions, select the solution that satisfies the physical constraint 0 < P1 < P as the optimal transmitter power P 1opt . Combine the system's signal-to-noise ratio formula and achievable rate formula to calculate the optimal DF relay power:

[0255] P 2opt = P - P 1opt

[0256] Substitute P 1opt and P 2opt into the transmitter and DF relay respectively. Substitute P 1opt into γ D (or substitute P 2opt into γ R ), and obtain the optimal single-hop SNR:

[0257]

[0258] Then the maximum achievable rate is:

[0259]

[0260] Systems employing DF relays need to consider more complex hybrid fading scenarios, such as Rice fading when the IRS is deployed at a relatively high position. Under the Rice channel, the optimization process of power allocation is exactly the same. By means of a similar variable substitution and equation-solving process, parameters related to the Rice channel are introduced into the equation to calculate the coefficients A, B, C, and D, obtaining an optimized power allocation equation applicable to the Rice channel and solving for the optimal power allocation of the decode-and-forward relay and the corresponding maximum rate calculation method.

[0261] In more preferred examples, in each transmission stage, the phase shifts of the active IRS units are adjusted to compensate for the channel phase and align the signals of each path, thereby maximizing the received signal amplitude at the DF relay or the receiver (achieving in-phase addition).

[0262] At this time, due to the characteristics of the DF relay, the end-to-end achievable rate of the entire system is limited by the worse hop in the two stages. Therefore, the achievable rate of the system

[0263]

[0264] Among them, is due to the adoption of two equal-duration time slots for operation, or in other words, two time slots are occupied.

[0265] In more preferred examples, when the signal directly reaches the receiver from the transmitter through the reflection of the active IRS without passing through the decode-and-forward relay node, the received signal:

[0266]

[0267] Among them, P t is the transmission power of the transmitter, h IR is the equivalent channel gain from the transmitter to the receiver via the active IRS, h TI is the channel gain from the transmitter to the active IRS, x is the signal sent by the transmitter, v is the thermal noise introduced by the active IRS, and ω is the additive Gaussian white noise. The reflection coefficient matrix of the active IRS:

[0268]

[0269] Among them, for each reflection unit, the amplitude satisfies ζ l ∈(1, ∞) and the phase shift satisfies ψ l ∈[0, 2π]; let Received signal-to-noise ratio:

[0270]

[0271] By adjusting the phase shift ψ l = arg([hIR l [h TI l ), which is further simplified to:

[0272]

[0273] The corresponding achievable rate of the active IRS

[0274] In more preferred examples, the tight upper bounds of the achievable rate of the system under Rayleigh fading and Rician fading channels are derived, that is, the closed-form upper bound expressions, which provide a theoretical basis for system performance evaluation and parameter design.

[0275] The upper bound of the achievable rate is established by using Jensen's inequality. For the hybrid active IRS and decode-and-forward relay system, its capacity upper bound

[0276]

[0277] where respectively represent the expectations of the decode-and-forward relay and the receiver-side SNR.

[0278] Under the Rayleigh fading channel, all channel coefficients follow a zero-mean complex Gaussian distribution. The SNR at the relay side is redefined as:

[0279]

[0280] By taking the expectation operation on γ D the expression of is obtained, which is substituted into the capacity upper bound formula to obtain the theoretical upper bound under the Rayleigh fading channel; for the calculation of , according to the channel model and corresponding parameters of the system, a similar expectation operation and variable substitution are used to obtain its expectation expression, and then it is substituted into the capacity upper bound formula to obtain a more accurate upper bound of the system performance.

[0281] In the hybrid Rayleigh and Rician channel environment, for the link X ∈ {TI, ID, DI, IR}, combined with the Rician factor K X , the path loss exponent of the line-of-sight link, and the path loss exponent of the Rayleigh fading channel and other parameters, the channel gains of different types are comprehensively processed. By statistically analyzing the channel gains and noises under different channel characteristics, using the relevant random variable expectation formula and the probability distribution characteristics of the channel parameters, calculate and Substitute into:

[0282]

[0283] ​​Obtain the theoretical upper bound in the hybrid Rayleigh and Rician channels.

[0284] In more preferred examples, through simulation, it is verified that the proposed hybrid system and power optimization method have significant performance advantages compared with the passive IRS-assisted decode-and-forward relay system and the standalone active IRS system under the conditions of limited reflection elements or medium signal-to-noise ratio, and the influence laws of key parameters (such as SNR, IRS position, number of reflection elements) on the system performance are revealed, providing guidance for practical deployment.

[0285] Specifically, Monte Carlo simulation is carried out, considering a two-dimensional coordinate system. The Tx is located at (0m, 0m), and the Rx is located at (120m, 0m). The active IRS is deployed at (x i , 10m), where x i is variable, and the reference position is (60m, 10m). The DF relay node is located at (60m, 0m).

[0286] Path loss exponent: Rayleigh fading channel Rician fading channel Rician factor κ = 10 dB.

[0287] Active IRS parameters: Amplification factors ξ = η = ζ = 2 (i.e., 3 dB amplification). The number of reflection elements L = 256. The active IRS noise power σ v 2 = -40 dBm.

[0288] Passive IRS of the comparison system: The magnitude of the reflection coefficient considers an energy loss of 0.8. The total transmit power P is defined by SNR:

[0289] All results are the ergodic achievable rates obtained by averaging over a large number of channels.

[0290] The achievable rate and SNR (Rayleigh fading channel) are compared, and the performance of the ergodic achievable rate varying with is presented. According to the hybrid active IRS and relay provided by the present invention, the system using optimal power allocation is compared with the hybrid passive IRS and DF relay (amplification factor 0.8, with optimal power allocation) and the standalone active IRS (without relay, total power P, L = 256, ζ = 2).

[0291] As Figure 2 shown, the hybrid active IRS and DF relay system is always significantly superior to the other two comparison systems throughout the investigated SNR range. For example, at SNR = 30 dB, the achievable rate is approximately 0.85 bps / Hz, while the passive IRS and DF relay system is approximately 0.3 bps / Hz, and the standalone active IRS system is only approximately 0.05 bps / Hz.

[0292] The amplification ability of the active IRS effectively overcomes multiplicative fading and provides stronger signal enhancement than the passive IRS. Meanwhile, the presence of the DF relay ensures reliable signal regeneration and avoids the sharp performance degradation that may occur in a system with only an active IRS due to poor channel conditions. Optimal power allocation further ensures the balance between the two hops and maximizes the end-to-end rate.

[0293] The performance of the passive IRS and DF relay system is limited, especially with slow growth in the medium and high SNR regions, verifying the limitation of multiplicative fading. The system with only an active IRS performs the worst in this setting (when the Tx-Rx distance is far and there may be no strong direct path), highlighting the importance of the relay in long-distance communication.

[0294] As Figure 3 shown, when the active IRS moves along the parallel line (y = 10m) between the Tx and Rx, the achievable rates of different systems change (fixed SNR, e.g., 20 dB). The abscissa x of the IRS i moves from a position close to the Tx to a position close to the Rx.

[0295] The optimal IRS position of the hybrid active IRS and relay system provided by the present invention is slightly biased towards the transmitter Tx side, rather than being strictly located at the geometric center between the Tx and the relay (or Rx). For example, the optimal performance may occur at x i ≈ 58 m instead of the midpoint 60 m. This is the result of the trade-off between the signal amplification gain of the active IRS and the thermal noise it introduces. Moving the IRS slightly closer to the source (Tx or relay) can reduce the propagation loss of the signal before it is amplified, thus alleviating the impact of the amplified noise at the IRS to a certain extent. Being too close to the source or too close to the destination will result in an overly long distance for a certain IRS-related link (Tx-IRS or IRS-relay / relay-IRS or IRS-Rx), increasing the path loss, and it is difficult to compensate even with amplification. The optimal position is to strike a balance between the signal enhancement effect and noise control.

[0296] The passive IRS and DF relay system usually performs best when the IRS is located at the midpoint of the Tx-relay or relay-Rx link because it does not introduce additional noise, and the goal is to minimize the total loss of the two reflected paths. The system with only an active IRS is more sensitive to the IRS position and its performance degrades more severely at non-ideal positions, again demonstrating the contribution of the DF relay to robustness.

[0297] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A wireless communication system integrating IRS and DF relay, characterized in that, It includes: A transmitter Tx, a receiver Rx, a DF relay, and an active IRS; Both the transmitter and the receiver are equipped with single antennas or MIMO antennas. The active IRS is deployed in the half-space region between the transmitter and the receiver, and the DF relay is deployed between the transmitter and the receiver; The DF relay is equipped with a single antenna, and the active IRS includes L active reflection units, where L≥1; The active reflection unit integrates active devices.

2. The hybrid IRS and DF relay wireless communication system according to claim 1, wherein The additive white Gaussian noise ω(n) and ω(n + 1) of the active IRS are added to the received signal in different time slots n and n + 1 respectively, and are zero-mean random variables with a variance of and introduce the total noise vector thermal noise The two-stage reflection coefficient matrix of the active IRS is independently controlled. The first-stage reflection coefficient matrix Θ: The second-stage reflection coefficient matrix Φ: ξ l 、η l ∈[1, ∞) θ l , φ l ∈ [0, 2π] l＝1、2、…、L Among them, 0 L represents an L-dimensional vector; I L represents an L×L identity matrix; Indicates the thermal noise power of each unit; Denotes a complex Gaussian distribution with an expectation of 0 L and a variance of ; ξ l 、η l respectively represent the amplification factors of the l-th active reflection unit in the first stage and the second stage; θ l and φ l respectively represent the phase shifts applied to the l-th unit in the first stage and the second stage.

3. The wireless communication system integrating IRS and DF relay according to claim 1, wherein The links between the transmitter Tx, receiver Rx, DF relay, and active IRS are affected by both large-scale fading and small-scale fading simultaneously, defined as The path loss of the large-scale fading is d -α ; where h TI represents the channel vector from Tx to the active IRS; h ID represents the channel vector from the active IRS to the DF relay; h DI represents the equivalent channel gain from the channel vector relayed from the DF to the active IRS to the receiver; h IR represents the channel vector from the active IRS to the Rx; h TD represents the direct link channel gain coefficient from Tx to the DF relay; h DR represents the direct link channel gain coefficient from the DF relay to the Rx; represents a complex matrix of M×N dimensions; d represents distance; α represents the path loss exponent; The small-scale fading adopts time-division duplex or frequency-division duplex mode, and an end-to-end transmission is completed in two equal-length time slots. At the same time, a channel model is constructed considering Rayleigh fading and mixed Rayleigh-Rician fading.

4. The hybrid IRS and DF relay wireless communication system according to claim 3, wherein The links between Tx, the DF relay, and Rx, as well as the links between them and the IRS without line-of-sight are constructed as Rayleigh fading channels, and the channel gain is: where X represents the link identifier, and X∈{TI, ID, DI, IR}; d X represents the distance corresponding to the link; represents the path loss exponent of the Rayleigh fading channel; Denotes a complex Gaussian distribution with an expectation of 0 and a variance of ; Denote the l-th channel element of the X-link, which is a complex Gaussian variable with zero mean and variance of ; For the IRS-related channel vectors For \(X\in\{TI, ID, DI, IR\}\), the Rice fading channel is modeled as: where κ X represents the Rice factor; Indicates the path loss exponent of the line-of-sight link in a Rice fading channel Indicates the determined LoS component, which is the array response vector; Denote the phase of the l-th reflection unit in the Rice channel.

5. A wireless communication method combining IRS and DF relay, implemented using any one of the wireless communication systems combining IRS and DF relay as claimed in claims 1 - 4, characterized in that, It includes: Step 1: The transmitter Tx sends the signal x(n) with power P1. After transmission through the link, the DF relay receives the signal y D (n); Step 2: The DF relay transmits the decoded and re-encoded signal x(n + 1) with power P2. After transmission through the link, the receiver Rx receives the signal y R (n + 1).

6. The wireless communication method combining IRS and DF relay according to claim 5, wherein The signal x(n) is transmitted through the direct link from Tx to the DF relay and / or the reflected link via Tx-active IRS-DF relay, satisfying the power constraint The signal y received by the DF D (n) includes the signal of the direct link The signal of the Tx-IRS-relay reflection link The noise introduced by the active IRS Additive white Gaussian noise Expressed as: where P1 represents the transmission power of Tx; Θ represents the first-stage reflection coefficient matrix of the active IRS; n represents the time index; E[] represents the expectation operation; v represents the active IRS noise; ω represents the additive white Gaussian noise; represents the power of additive white Gaussian noise; denotes a complex Gaussian distribution with an expectation of 0 and a variance of ; h TI represents the channel vector from Tx to the active IRS; h ID represents the channel vector from the active IRS to the DF relay; h TD Denotes the direct link channel gain coefficient from Tx to the DF relay.

7. The wireless communication method combining IRS and DF relay according to claim 6, characterized in that The received signal-to-noise ratio at the DF relay includes the signal power and the noise power which is γ D : Optimize and adjust the phase shift θ of the first-stage reflection coefficient matrix of the active IRS l , add in-phase or ignore the direct path: The optimal phase shift selection is: θ l = arg(h TD ) + arg([h ID l [h TI l )​​ or: θ l = arg([h ID l [h TI l )​​ The signal power is approximately: The received noise ratio SNR of the optimized DF relay is expressed as: Among them, ξ l represents the amplification factor of the l-th active reflection unit in the first stage; Represents the thermal noise power of each unit; L represents the total number of active reflection units; X represents the link identifier; d X represents the distance corresponding to the link; α represents the path loss exponent.

8. The wireless communication method combining IRS and DF relay according to claim 5, wherein The signal x(n + 1) is transmitted through the direct link from the DF relay to Rx and / or the reflected link via the DF relay - active IRS - Rx; The signal y received by the receiver R (n + 1) includes the signal of the direct link The signal of the relay-IRS-Rx reflection link The noise introduced by the active IRS Additive white Gaussian noise Expressed as: where v represents the active IRS noise; ω represents the additive white Gaussian noise; represent an equivalent channel vector related to system topology and channel characteristics; γ R represents the SNR at the receiver; h IR represents the channel vector from the active IRS to the Rx; h DR represents the direct link channel gain coefficient from the DF relay to the Rx; Indicates the additive white Gaussian noise power; Denotes a complex Gaussian distribution with an expectation of 0 and a variance of ; h ID represents the channel vector from the active IRS to the DF relay; Φ represents the second-stage reflection coefficient matrix; n represents the time index.

9. The wireless communication method combining IRS and DF relay according to claim 8, characterized in that, The SNR, γ, at the receiver R is expressed as: η l ∈ [1, ∞) Optimize and adjust the phase shift φ of the second-stage reflection coefficient matrix of the active IRS l : φ l = arg(h DR ) + arg([h IR l [h DI l )​​ φ l ∈ [0, 2π] ηl = η The SNR at the optimized receiver is: Among them, η l represents the amplitude of the l-th reflection unit in the first stage; Represents the thermal noise power of each unit; L represents the total number of active reflection units; X represents the link identifier; d X represents the distance corresponding to the link; α represents the path loss exponent.

10. An optimization method for a wireless communication system integrating IRS and DF relay, which is carried out in any one of the wireless communication systems integrating IRS and DF relay as claimed in claims 1-4, characterized in that It includes: The total power constraint is P1 + P2 = P: P1P2≥0 Under the Rayleigh fading channel: where X represents the link identifier, and X∈{TI, ID, DI, IR}; d X represents the distance corresponding to the link; represents the path loss exponent of the Rayleigh fading channel; ξ represents the amplification coefficient of the active reflection unit in the first stage; Indicates the thermal noise power of each unit; L represents the total number of active reflection units; P1 represents the transmission power of Tx; P2 represents the transmission power of the DF relay; Indicates the additive white Gaussian noise power; A, B, C, and D all represent the equivalent gain and noise figure under the current channel state and IRS parameter configuration; represents the square of the channel amplitude from Tx to the DF relay; Denote the square of the channel amplitude from the DF relay to the Rx; Denote the square of the channel amplitude from Tx to the DF relay after reflection by the IRS; Denote the square of the channel amplitude from the DF relay to Rx after reflection by the IRS; h TI represents the channel vector from Tx to the active IRS; h ID represents the channel vector from the active IRS to the DF relay; h DI represents the equivalent channel gain from the channel vector relayed by the DF to the active IRS to the receiver; h IR represents the channel vector from the active IRS to the Rx; h TD represents the direct link channel gain coefficient from Tx to the DF relay; h DR represents the direct link channel gain coefficient from the DF relay to the Rx; γ D represents the received noise ratio SNR of the DF relay; γ R represents the SNR at the receiver; Substitute the constraint P2 = P - P1 into: EP12 + FP1 + G = 0 γ D = [γ R ​ E = -AD + CB where E, F, and G all represent coefficients; If E = 0, then the optimal value of P1 is FP1 + G = 0 P1 = -G / F Verify whether the solution is within the valid range of 0 < P1 < P. If it is satisfied, then P 1opt = -G / F. If it is not satisfied, then discard it; If E≠0, then calculate the discriminant Δ = F2 - 4EG; If Δ < 0, it is considered that there is no solution. If Δ ≥ 0, the real solution is Select the solution that satisfies the physical constraint 0 < P1 < P as the optimal transmitter power P 1opt ; Calculate the optimal DF relay power: P 2opt = P - P 1opt Substitute P 1opt into γ D or substitute P 2opt into γ R , and the optimal single-hop SNR can be obtained: The maximum rate is: Under the Rician channel, introduce the parameters related to the Rician channel into the equation, calculate the coefficients A, B, C, and D, obtain the power allocation optimization equation applicable to the Rician channel, and solve for the optimal DF relay power and the corresponding maximum rate; Achievable rate of the system

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