CN115412141B - Phase shift optimization method of IRS-assisted space shift keying modulation system - Google Patents
Phase shift optimization method of IRS-assisted space shift keying modulation system Download PDFInfo
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Abstract
The invention belongs to the technical field of wireless communication, and particularly relates to a phase shift optimization method of an IRS (IRS-assisted space shift keying) modulation system. The scheme of the invention is that the communication system comprises a plurality of communication channels with N t The transmitting end of each transmitting antenna is an intelligent reflecting surface formed by N reflecting elements and is provided with a receiving end of one antenna, and the transmitting end selects and activates a single transmitting antenna at one moment to send the transferred index information to the receiving end through the IRS. In the invention, an IRS phase shift optimization model is constructed by taking the upper limit of the minimum joint error probability as a target, and in the process of optimizing the model, a continuous convex approximation method is adopted to convert a non-convex problem into a convex problem through first-order Taylor expansion for solving. Compared with the traditional scheme, the invention reduces the transmission error probability, can obtain higher diversity gain and greatly reduces the optimization complexity.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a phase shift optimization method of an IRS (IRS-assisted space shift keying) modulation system.
Background
With the vigorous development of emerging services such as the internet of things and the mobile internet and the proliferation of wireless devices, the wireless network has higher spectrum efficiency, faster transmission rate and larger system capacity in the future, so as to adapt to continuously changing environmental conditions and application types, and the future communication system has certain self-optimizing capability and is more environment-friendly, energy-saving and reliable. To achieve these goals, intelligent Reflective Surfaces (IRSs) are considered a promising green, cost-effective, energy-saving, and spectrally efficient technology. Meanwhile, the space shift keying modulation system is another important subject, is a preferred scheme for fusing the current large antenna technology and the green communication technology, can flexibly cooperate with other emerging communication systems, and plays a key role in realizing reliable communication and reducing path loss. Because IRS and space shift keying modulation systems have attractive advantages in terms of frequency spectrum and energy efficiency, combining IRS with space shift keying modulation, all of these advantages make IRS-assisted space shift keying modulation systems a promising practical research area for reliable energy-saving communication in the future.
IRS is an artificial surface composed of electromagnetic materials that can intelligently adjust the wireless propagation environment by integrating a large number of low cost passive reflective elements on the surface. The space shift keying technique activates only a single transmit antenna and uses the index of the active antenna for information transmission. Meanwhile, the IRS auxiliary space shift keying modulation system has higher energy efficiency and lower receiving and transmitting complexity because the traditional signal modulation is avoided. The existing IRS-assisted phase shift optimization algorithm of the space shift keying modulation system mostly adopts a semi-positive relaxation technology, and the algorithm can maximize the system throughput, but has high algorithm implementation complexity. In order to reduce the complexity, we convert the non-convex problem into the convex problem to solve by a continuous convex approximation method through first-order taylor expansion, so that the transmission error probability can be reduced under the condition of lower computational complexity.
Disclosure of Invention
The technical scheme is as follows: aiming at the performance problem of an IRS-assisted space shift keying modulation system, the invention optimizes the phase of an IRS array element, and provides a phase shift optimization method of the IRS-assisted space shift keying modulation system, which specifically comprises the following steps:
step 1, establishing an IRS-assisted space shift keying modulation system model, so as to obtain a receiving end baseband signal, decoding the receiving end baseband signal through maximum likelihood detection to obtain a condition pair error probability, and finally obtaining a joint error probability formula through a joint delimitation formula;
step 2, searching a variable formula affecting the joint error probability in the joint error probability formula by taking the upper limit of the minimum joint error probability as a target, so as to construct an IRS phase shift optimization model;
and step 3, finding that the optimization problem is not convex after the IRS phase shift optimization model is obtained, introducing auxiliary variables into the optimization problem, and converting the auxiliary variables into a convex problem through a first-order Taylor expansion method to solve the convex problem, so as to obtain the optimal phase shift.
Preferably, the step 1 includes the steps of:
consider an IRS-assisted space shift keying modulation system. The transmitting end (S) has N t A transmitting antenna and a receiving end (D) having a receiving antenna. Since the direct transmission path is blocked by the obstacle, the transmitting end and the receiving end can only communicate with each other through the IRS with N reflecting elements. Channel matrixes from transmitting end antenna to IRS and IRS to receiving end are respectively usedAndand (3) representing. Assuming that the fading channels are distributed independently and identically, the channel fading coefficients are subject to +.>The amplitude coefficient of the IRS reflective element is 1.
The total information is divided into length log 2 N t Is a block of (c). Each block is mapped to a transmit antenna index for data sequence transmission while the remaining antennas remain silent. Let m bits of information (m=log 2 N t ) Is mapped to symbol x l ，l∈{1,...,N t And transmitted from the first antenna, vector x l Can be expressed as
IRS inverseThe reflection phase of the emitter isThe baseband signal at the receiving end is therefore:
y＝H T ΦGx l +n＝H T ΦG l +n
wherein, the liquid crystal display device comprises a liquid crystal display device,is the ith reflector element, θ i Is the phase shift of the ith reflection element, l is e 1, N t The first transmitting end antenna, G l Is the channel matrix from the first transmitting antenna to IRS, H T Represents the transpose of H, N represents the variance N 0 Is defined as the transmission signal-to-noise ratio snr=1/N 0 。
The receiving end adopts maximum likelihood detection to decode,for the receiving end to estimate the antenna, the conditional pair error probability can be obtained as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,is the channel matrix from the estimated antenna to the IRS, and the Q (·) function is the right tail function of the standard normal distribution.
The upper limit of the error probability according to the joint delimitation formula is expressed as:
preferably, the step 2 includes the steps of:
the number of antennas N at the transmitting end is aimed at minimizing the probability of error t Optimizing Φ when determiningThe upper limit of the error probability is reduced, and an IRS phase shift optimization model is further constructed to be expressed as follows:
s.t.θ i ∈[0,2π),i＝1,...,N
wherein H is T Representing the transpose of the IRS to the channel matrix at the receiving end, Φ is the diagonal matrix of the reflection phase of the IRS reflector element, G l Is the channel matrix of the first transmit antenna to the IRS,is a channel matrix of estimated antenna to IRS, θ i Is the phase shift of the ith reflection element.
Preferably, the step 3 includes the steps of:
constructing a phase shift optimization objective function as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,is the IRS reflected phase shift collection vector.
Because the optimization model in the step 2 is not convex, after the auxiliary variable z is introduced, the auxiliary variable z is converted into a convex problem through a first-order Taylor expansion method, and the convex problem is expressed as follows:
θ i ∈[0,2π),i＝1,...,N
wherein z is a scalar quantity,k is the index of the iteration and,is the IRS reflection phase shift collection vector at the kth iteration, f (Θ (k) ) Optimizing the objective function for the phase shift at the kth iteration, v is a derivation of the vector,<a,b>represents the inner product, θ, of the two matrices i Is the phase shift of the ith reflection element.
Further, the solving algorithm for the optimization problem is as follows:
s1, initializing, and collecting vectors by IRS reflection phase shift. Initial value Θ @ 1 ) Auxiliary variable z (0) Iteration index k=1, maximum number of iterations K max Ending the error err, the channel matrix H from the IRS to the antenna of the receiving end, and the channel matrix G from all the transmitting antennas to the IRS;
s2, solving a convex optimization problem by adopting an existing convex optimization solver CVX:find a set of suboptimal solutions, Θ (k+1) Is a suboptimal solution vector of the IRS reflection phase shift collection vector, and obtains an auxiliary variable z after the kth iteration (k) ；
S3, judging |z (k) -z (k-1) The I is not less than err or the K is not less than K max If yes, updating the iteration index k=k+1, returning to the step 2, and continuing to solve the convex optimization problem to find the next suboptimal solution; if not, stopping the solving process to obtain the IRS local optimal phase shift theta opt ＝Θ (k+1) Which serves as an element of the IRS phase shift matrix Φ, thereby yielding an upper limit on the minimum joint error probability.
The beneficial effects are that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
(1) The transmission error probability is reduced compared to the conventional IRS-assisted space shift keying modulation system, and a higher diversity gain can be obtained.
(2) In contrast to the semi-positive relaxation technique,the continuous convex approximation method is adopted to convert the non-convex problem into the convex problem, so that the optimization complexity of the IRS-assisted space shift keying modulation system is greatly reduced, and the complexity is O (kN) 4 ) (k is the number of iterations) and the semi-positive relaxation technique complexity is O (N 6 )。
Drawings
FIG. 1 is a flow chart of a phase shift optimization method of an IRS-assisted space shift keying modulation system in the present invention;
FIG. 2 is a flow chart of an IRS-assisted air shift keying modulation system model optimization algorithm in the present invention;
fig. 3 is a diagram of an IRS-assisted space shift keying modulation system model in accordance with the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail below with reference to the accompanying drawings in the embodiments of the present invention.
Fig. 1 is a flowchart of a phase shift optimization method of an IRS-assisted space shift keying modulation system according to the present invention, which is an overall procedure of an embodiment of the present invention. Fig. 2 is a flow chart of an IRS-assisted space shift keying modulation system model optimization algorithm in the present invention.
Consider an IRS-assisted space shift keying modulation system. As shown in fig. 3, the present invention proposes a phase shift optimization method of an IRS-assisted space shift keying modulation system, which specifically includes the following steps:
step 1, establishing an IRS-assisted space shift keying modulation system model, so as to obtain a receiving end baseband signal, decoding the receiving end baseband signal through maximum likelihood detection to obtain a condition pair error probability, and finally obtaining a joint error probability formula through a joint delimitation formula;
step 2, searching a variable formula affecting the joint error probability in the joint error probability formula by taking the upper limit of the minimum joint error probability as a target, so as to construct an IRS phase shift optimization model;
and step 3, finding that the optimization problem is not convex after the IRS phase shift optimization model is obtained, introducing auxiliary variables into the optimization problem, and converting the auxiliary variables into a convex problem through a first-order Taylor expansion method to solve the convex problem, so as to obtain the optimal phase shift.
The step 1 comprises the following steps:
consider an IRS-assisted space shift keying modulation system. The transmitting end (S) has N t A transmitting antenna and a receiving end (D) having a receiving antenna. Since the direct transmission path is blocked by the obstacle, the transmitting end and the receiving end can only communicate with each other through the IRS with N reflecting elements. Channel matrixes from transmitting end antenna to IRS and IRS to receiving end are respectively usedAndand (3) representing. Assuming that the fading channels are distributed independently and identically, the channel fading coefficients are subject to +.>The amplitude coefficient of the IRS reflective element is 1.
The total information is divided into length log 2 N t Is a block of (c). Each block is mapped to a transmit antenna index for data sequence transmission while the remaining antennas remain silent. Let m bits of information (m=log 2 N t ) Is mapped to symbol x l ，l∈{1,...,N t And transmitted from the first antenna, vector x l Can be expressed as
The reflection phase of the IRS reflector isThe baseband signal at the receiving end is therefore:
y＝H T ΦGx l +n＝H T ΦG l +n
wherein, the liquid crystal display device comprises a liquid crystal display device,is the ith inverseShooting element, theta i Is the phase shift of the ith reflection element, l is e 1, N t The first transmitting end antenna, G l Is the channel matrix from the first transmitting antenna to IRS, H T Represents the transpose of H, N represents the variance N 0 Is defined as the transmission signal-to-noise ratio snr=1/N 0 。
The receiving end adopts maximum likelihood detection to decode,for the receiving end to estimate the antenna, the conditional pair error probability can be obtained as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,is the channel matrix from the estimated antenna to the IRS, and the Q (·) function is the right tail function of the standard normal distribution.
The upper limit of the error probability according to the joint delimitation formula is expressed as:
the step 2 comprises the following steps:
the number of antennas N at the transmitting end is aimed at minimizing the probability of error t When determining, optimizing phi can reduce the upper limit of error probability, and further constructing an IRS phase shift optimization model to be expressed as:
s.t.θ i ∈[0,2π),i＝1,...,N
wherein H is T Transpose of channel matrix representing IRS to receiving end, Φ is diagonal matrix of reflection phase of IRS reflection element，G l Is the channel matrix of the first transmit antenna to the IRS,is a channel matrix of estimated antenna to IRS, θ i Is the phase shift of the ith reflection element.
The step 3 comprises the following steps:
constructing a phase shift optimization objective function as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,is the IRS reflected phase shift collection vector.
Because the optimization model in the step 2 is not convex, after the auxiliary variable z is introduced, the auxiliary variable z is converted into a convex problem through a first-order Taylor expansion method, and the convex problem is expressed as follows:
θ i ∈[0,2π),i＝1,...,N
wherein z is a scalar quantity,k is the index of the iteration and,is the IRS reflection phase shift collection vector at the kth iteration, f (Θ (k) ) Optimizing the objective function for the phase shift at the kth iteration, v is a derivation of the vector,<a,b>represents the inner product, θ, of the two matrices i Is the phase shift of the ith reflection element.
The solving algorithm for the optimization problem is as follows:
s1, initializing, and collecting vectors by IRS reflection phase shift. Initial value theta (1) Auxiliary variable z (0) Iteration index k=1, maximum number of iterations K max Ending the error err, the channel matrix H from the IRS to the antenna of the receiving end, and the channel matrix G from all the transmitting antennas to the IRS;
s2, solving a convex optimization problem by adopting an existing convex optimization solver CVX:find a set of suboptimal solutions, Θ (k+1) Is a suboptimal solution vector of the IRS reflection phase shift collection vector, and obtains an auxiliary variable z after the kth iteration (k) ；
S3, judging |z (k) -z (k-1) The I is not less than err or the K is not less than K max If yes, updating the iteration index k=k+1, returning to the step 2, and continuing to solve the convex optimization problem to find the next suboptimal solution; if not, stopping the solving process to obtain the IRS local optimal phase shift theta opt ＝Θ (k+1) Which serves as an element of the IRS phase shift matrix Φ, thereby yielding an upper limit on the minimum joint error probability.
Through simulation tests, the IRS-assisted space shift keying modulation system in the technical scheme does not need to adjust the phase during each transmission, compared with the traditional scheme, the IRS-assisted space shift keying modulation system reduces the transmission error probability, can obtain higher diversity gain, and reduces the complexity.
The foregoing is one embodiment of the present invention and it should be noted that variations, modifications and adaptations of the invention herein described may occur to one skilled in the art without departing from the principle of the present invention.
Claims (3)
1. The phase shift optimization method of the intelligent reflection surface IRS-assisted space shift keying modulation system is characterized by comprising the following steps of:
step 1, establishing an intelligent reflection surface IRS-assisted space shift keying modulation system model, obtaining a receiving end baseband signal, obtaining a condition pair error probability through maximum likelihood detection decoding, and finally obtaining a joint error probability formula through a joint delimitation formula;
step 2, searching a variable equation affecting the joint error probability in the joint error probability equation by taking the upper limit of the minimum joint error probability as a target, so as to construct an intelligent reflection surface IRS phase shift optimization model;
step 3, after an intelligent reflection surface IRS phase shift optimization model is obtained, finding that the optimization problem is not convex, introducing auxiliary variables into the optimization problem, and converting the auxiliary variables into a convex problem through a first-order Taylor expansion method to solve the convex problem so as to obtain an optimal phase shift;
the step 1 comprises the following steps:
step 1.1, constructing an intelligent reflection surface IRS-assisted space shift keying modulation system, wherein a transmitting end (S) is provided with N t A transmitting antenna, a receiving end (D) is provided with a receiving antenna, the transmitting end and the receiving end can only communicate with each other through an intelligent reflection surface IRS with N reflection elements, and channel matrixes from the transmitting end antenna to the intelligent reflection surface IRS and from the intelligent reflection surface IRS to the receiving end are respectively usedAnd->The representation assumes that the fading channels are independently co-distributed and that the channel fading coefficients are subject to +.>The amplitude coefficient of the IRS reflecting element of the intelligent reflecting surface is 1;
the total information is divided into length log 2 N t Each block is mapped to a transmit antenna index for data sequence transmission while remaining antennas remain silent, allowing m bits of information to be mapped to symbol x l ，m＝log 2 N t ，l∈{1,...,N t And transmitted from the first antenna, vector x l Expressed as:
the reflection phase of the IRS reflection element of the intelligent reflection surface isThe baseband signal of the receiving end is:
y＝H T ΦGx l +n＝H T ΦG l +n
wherein, the liquid crystal display device comprises a liquid crystal display device,θ i is the phase shift of the ith reflection element, i e 1, N, N is the total number of reflective elements, l is e 1, N t }，N t Total number of transmitting end antennas, G l Is the channel matrix from the first transmitting antenna to the intelligent reflecting surface IRS, H T Represents the transpose of H, N represents the variance N 0 Is defined as the transmission signal-to-noise ratio snr=1/N 0 ；
Step 1.2, the receiving end adopts maximum likelihood detection to decode,the antenna is estimated for the receiving end, and the conditional pair error probability is obtained as follows:
wherein G is l Is the channel matrix of the first transmitting antenna to the intelligent reflective surface IRS,is a channel matrix from the estimated antenna to the IRS of the intelligent reflecting surface, the Q (·) function is a right tail function of standard normal distribution, and the I represents absolute valuePerforming value comparison operation;
the upper limit of the error probability according to the joint delimitation formula is expressed as:
2. a method for phase shift optimization of an intelligent reflective surface IRS assisted space shift keying modulation system according to claim 1, wherein said step 2 comprises the steps of: the number of antennas N at the transmitting end is aimed at minimizing the probability of error t When determining, optimizing phi to reduce the upper limit of error probability, and further constructing an intelligent reflection surface IRS phase shift optimization model to be expressed as:
s.t.θ i ∈[0,2π),i＝1,...,N
wherein H is T Representing the transpose of the channel matrix of the intelligent reflective surface IRS to the receiving end, Φ is the diagonal matrix of the reflection phases of the reflective elements of the intelligent reflective surface IRS, G l Is the channel matrix of the first transmitting antenna to the intelligent reflective surface IRS,is a channel matrix of the estimated antenna to the intelligent reflection surface IRS, theta i Is the phase shift of the ith reflection element.
3. A method for phase shift optimization of an intelligent reflective surface IRS assisted space shift keying modulation system according to claim 1, wherein said step 3 comprises the steps of:
step 3.1, after an intelligent reflection surface IRS phase shift optimization model is obtained, the optimization problem is found to be non-convex, and an auxiliary variable optimization model is introduced to be expressed as:
θ i ∈[0,2π),i＝1,...,N
wherein:
z is an introduced auxiliary variable, which is a scalar,H T representing the transpose of the channel matrix of the intelligent reflective surface IRS to the receiving end, Φ is the diagonal matrix of the reflection phases of the reflective elements of the intelligent reflective surface IRS, G l Is the channel matrix of the first transmitting antenna to the intelligent reflective surface IRS, < >>Is a channel matrix of the estimated antenna to the intelligent reflection surface IRS, theta i Is the phase shift of the ith reflection element;
step 3.2, constructing a phase shift optimization objective function as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,is an intelligent reflective surface IRS reflective phase shift collection vector;
the transformation into convex problem by the first-order taylor expansion method is expressed as:
θ i ∈[0,2π),i＝1,...,N
where k is the iteration index,is the smart reflective surface IRS reflection phase shift collection vector at the kth iteration, f (Θ) (k) ) Optimizing the objective function for the phase shift at the kth iteration,/->The method is to determine the deviation of the vector,<a,b>representing the inner product of the two matrices;
step 3.3, the convex optimization problem is realized through simulation by using the Matlab program by using the following algorithm:
step 3.3.1, initializing, collecting vector of IRS reflection phase shift of intelligent reflection surface, and initial value Θ (1) Auxiliary variable z (0) Iteration index k=1, maximum number of iterations K max Ending error err, and transmitting the channel matrix H from the intelligent reflection surface IRS to the receiving end antenna, and transmitting the channel matrix G from all the transmitting antennas to the intelligent reflection surface IRS;
step 3.3.2, solving a convex optimization problem by adopting an existing convex optimization solver CVX:find a set of suboptimal solutions, Θ (k+1) Is a suboptimal solution vector of the IRS reflection phase shift collection vector of the intelligent reflection surface, and obtains an auxiliary variable z after the kth iteration (k) ；
Step 3.3.3, judging |z (k) -z (k-1) The I is not less than err or the K is not less than K max If yes, updating the iteration index k=k+1, returning to the step 3.3.2, and continuing to solve the convex optimization problem to find the next suboptimal solution; if not, stopping the solving process to obtain the local optimal phase shift theta of the IRS of the intelligent reflecting surface opt ＝Θ (k+1) Which is an element of the intelligent reflective surface IRS phase shift matrix phi, thereby yielding a minimum upper bound on joint error probability, said K max Is the maximum number of iterations.
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| 获得天线选择分集的空移键控调制算法;李晓峰;王磊;张晓阳;;西安交通大学学报(08);全文 * |
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