CN116016074B - Intelligent reflecting surface phase shift design method based on cosine similarity - Google Patents
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Abstract
The invention provides an intelligent reflecting surface phase shift design method based on cosine similarity. When the transmitting end carries out space shift keying modulation, the phase shift is designed with the aim of maximizing Euclidean distance between ideal receiving signals corresponding to different transmitting vectors, the probability of detecting errors of the transmitting antenna index is reduced, and the error rate performance of a communication system is improved. In addition, when the transmitting end is provided with a plurality of antennas, the invention designs an algorithm based on cosine similarity aiming at the proposed phase shift design method, the algorithm can maximize Euclidean distance between ideal receiving signals corresponding to different transmitting vectors, improve the error rate performance of a communication system, calculate the phase shift of the reflecting unit of the intelligent reflecting surface with lower complexity, and ensure reliable communication.
Description
Technical Field
The invention belongs to the field of wireless communication, and particularly relates to an intelligent reflecting surface phase shift design method of a multi-input single-output wireless communication system during transmission end space shift keying modulation.
Background
Smart reflective surfaces are considered to be a very potential wireless communication technology that can reconfigure wireless propagation environments with a large number of low cost passive reflective units integrated on a flat surface. Specifically, the intelligent reflecting surface is provided with a large number of small and low-cost passive reflecting units, and the reflecting units reflect the incident signals only through adjustable phase shift without using special energy sources for radio frequency processing, decoding, encoding and other operations. The reflective elements of the smart reflective surface only passively reflect signals without any need for transmitting radio frequency chains, and thus the smart reflective surface can be implemented and operated with lower hardware, energy costs than conventional active antenna arrays or recently proposed active surfaces. By intelligently adjusting the phase shift of all the reflection units to adapt to the dynamic wireless channel, the signal reflected by the intelligent reflection surface can be overlapped or counteracted with the non-reflected signal on the user receiver so as to improve the required signal power or inhibit the channel interference, thereby greatly improving the wireless network performance.
Basar et al studied the problem of reflective element phase shift design in smart reflector assisted Space Shift Keying (SSK) modulation, and the article optimized the smart reflector phase shift by maximizing the instantaneous received signal-to-noise ratio (SNR) at the receiving end. However, since Bit Error Rate (BER) performance of transmitting-side SSK modulation is highly dependent on index detection of transmitting-side antennas, optimizing the phase shift of the intelligent reflecting surface by maximizing the receiving-side SNR may not achieve good bit error rate performance. QIANG LI et al propose a high performance method for intelligent reflection surface phase shift design, which aims at maximizing minimum euclidean distance between ideal receiving signals corresponding to different transmitting vectors in a communication system during SSK modulation of a transmitting end, so as to design intelligent reflection surface phase shift, reduce detection error probability of an antenna index of the transmitting end, and further improve error rate performance of the communication system. However, the method proposed by QIANG LI et al in the article to design the phase shift by traversing the reflection element phase shift set is only less complex when the number of transmit-side antennas is small. Specifically, the number of elements of the phase shift set and the number of antennas of the transmitting end are in positive correlation, so that the method is low in complexity when the number of the antennas of the transmitting end is small, but the complexity of traversing the phase shift set is high when the number of the antennas of the transmitting end is large.
Disclosure of Invention
The purpose of the invention is that: the method solves the problem that the error rate of a MISO system modulated by a transmitting end SSK is high due to the traditional method for designing the phase shift of the reflecting unit of the intelligent reflecting surface aiming at maximizing the signal-to-noise ratio of a receiving end, and designs the phase shift design method of the reflecting unit of the intelligent reflecting surface with low complexity when the transmitting end of the MISO system is provided with a plurality of antennas.
In order to achieve the above purpose, an intelligent reflecting surface phase shift design method based on cosine similarity comprises the following steps:
(1) Establishing an intelligent reflecting surface MISO wireless communication system model: the direct communication link between the transmitting end and the receiving end is blocked by the barrier, so the transmitting end can only communicate with the receiving end through the reflecting link with the assistance of the intelligent reflecting surface; the transmitting end is provided with N t antennas, SSK modulation is carried out, an unmodulated carrier signal is sent from the transmitting antenna with index of l to the intelligent reflecting surface, the intelligent reflecting surface with N reflecting units reflects the incident unmodulated signal with specific phase shift, and the receiving end is provided with 1 receiving antenna, and receives the signal reflected from the intelligent reflecting surface;
(2) And the phase shift of the intelligent reflecting surface reflecting unit is designed by taking the Euclidean distance between different transmitting vectors corresponding to ideal receiving signals when the SSK modulation of the transmitting end is maximized as a target.
Preferably, the reflection coefficient vector of the intelligent reflecting surface of the invention is expressed asWherein/>Beta i and theta i respectively represent the reflection amplitude and the reflection phase of the intelligent reflection surface reflection unit, wherein beta i∈[0,1],θi epsilon [0,2 pi ]; i is {1,2, …, N }, the i-th reflection unit representing the intelligent reflection surface, j is an imaginary unit,/> Is an exponential form of complex number, the formula is Euler formula, let beta i =1 under the condition of considering the maximum reflection of the reflecting unit of the intelligent reflecting surface, thus/>Then the reflection coefficient vector is further rewritten as/>W is a diagonalized matrix of reflection coefficient vectors Φ, w=diag { Φ };
Sub-channel between intelligent reflecting surface and transmitting end Let g il denote the channel between the ith reflecting element and the first transmitting element, the sub-channel/>, between the receiving end and the intelligent reflecting surfaceLet f i denote the channel between the receiving antenna and the ith reflecting element, i e {1,2, …, N }, l e {1,2, …, N t }; when the transmitting end performs SSK modulation and activates the first antenna, the received signal of the receiving end is expressed as follows:
y＝FWGel+n＝FWgl+n (1)
wherein e l is a transmitting end SSK signal, G l represents a first column of a channel G, namely a channel between a first transmitting antenna and an intelligent reflecting surface, N represents Gaussian white noise of a receiving end, and is subject to distribution with a mean value of 0 and a variance of N 0; at the signal receiving end, the maximum likelihood detection algorithm based on exhaustive search is used for demodulation.
Preferably, the specific process of the step (2) of the invention is as follows: according to the received signal formula (1), the euclidean distance between different transmitted vectors corresponding to the ideal received signal is expressed as:
is an estimate of the transmit antenna index l,/> Represents the/>, of channel GColumns, i.e./>The problem of the channel between the root transmit antenna and the smart reflective surface is described as follows:
s.t.θi∈[0，2π) (4)
When the transmitting end is provided with a plurality of antennas, d min is difficult to directly determine, and the phase shift is designed by maximizing Euclidean distance between ideal receiving signals corresponding to different transmitting vectors as far as possible; specifically, the optimal reflection phase is calculated as follows:
Wherein g il is the channel between the first transmit antenna and the i-th reflecting element, wherein Is/>A channel between the root transmit antenna and the ith reflecting element; from equation (5)/>An optimal reflection phase θ i must be present so that the equation is true, the calculation of which is determined by means of cosine similarity; specific:
To maximize the Euclidean distance between the ideal received signals corresponding to different transmitting vectors, the channel vectors are made Let the magnitude vector of u i/> According to/>The method comprises the following steps: when the cosine similarity is 1, the included angle between the two channel vectors is 0, and the two vectors u i and/>Is most similar; computing a channel vector u i and its magnitude vector/>Included angle v i between, and/>
Similarly, if the order isCalculate channel vector mu i and its magnitude vector/>Included angle omega i between them, andBased on θ i＝-(ωi+vi) sets the phase shift of the reflective element.
Preferably, the maximum likelihood detection algorithm of the present invention is expressed as follows:
Wherein, Is the estimated value of the index l of the transmitting antenna, and the signal receiving end is from/>B s bits of data information are recovered, and b s＝log2Nt,Nt is an integer power of 2.
Therefore, the invention designs a phase shift design method based on cosine similarity aiming at a Multiple-Input Single-Out (MISO) communication system assisted by an intelligent reflecting surface, wherein the transmitting end carries Out SSK modulation, and the transmitting end is provided with a plurality of antennas, so that the aim of maximizing Euclidean distance between ideal receiving signals corresponding to different transmitting vectors is fulfilled, and the complexity of the system is reduced while the error rate performance of the communication system is improved.
Drawings
FIG. 1 is a schematic diagram of an intelligent reflector assisted MISO communication system;
FIG. 2 is a flow chart of a cosine similarity based algorithm;
fig. 3 is a diagram of a comparative simulation of the inventive phase shift design with a conventional phase shift design with N t = 2;
Fig. 4 is a diagram of a comparative simulation of the inventive phase shift design with a conventional phase shift design with N t = 8.
Detailed Description
The application will be further illustrated with reference to specific examples. It is to be understood that these examples are illustrative of the present application and are not intended to limit the scope of the present application. Furthermore, it should be understood that various changes and modifications can be made by one skilled in the art after reading the teachings of the present application, and such equivalents are intended to fall within the scope of the application as defined in the appended claims.
The invention provides a reflection unit phase shift design method based on cosine similarity aiming at an intelligent reflection surface assisted transmitting end SSK modulation MISO system. Specifically, through the established MISO system model, the phase shift design of the intelligent reflecting surface reflecting unit is carried out on the basis of SSK modulation at the transmitting end. Through simulation result analysis, the intelligent reflection surface phase shift design method and performance advantages provided by the invention are proved, and the method specifically comprises the following steps:
Step one: the intelligent reflecting surface MISO system model shown in figure 1 is built, and the direct communication link between the transmitting end and the receiving end is blocked by an obstacle, so that the transmitting end can only communicate with the receiving end through the reflecting link with the aid of the intelligent reflecting surface. The transmitting end is provided with N t antennas, SSK modulation is carried out, an unmodulated carrier signal is sent from the transmitting antenna with index of l to the intelligent reflecting surface, the intelligent reflecting surface with N reflecting units reflects the incident unmodulated signal with specific phase shift, and the receiving end is provided with 1 receiving antenna, and receives the signal reflected from the intelligent reflecting surface.
The reflection coefficient vector of the intelligent reflection surface is expressed asWherein,And β i and θ i represent the reflection amplitude and reflection phase of the smart reflective surface reflection unit, respectively, where β i∈[0,1],θi ε [0,2π ]. i e {1,2, …, N }, representing the ith reflection element of the intelligent reflector, the invention makes β i =1, and therefore/>, taking into account the maximum reflection of the intelligent reflector reflection elementThe reflection coefficient vector can be further rewritten as/>W is a diagonalized matrix of reflection coefficient vectors Φ, w=diag { Φ }.
Sub-channel between intelligent reflecting surface and transmitting endLet g il denote the channel between the ith reflecting element and the first transmitting element, the sub-channel/>, between the receiving end and the intelligent reflecting surfaceLet f i denote the channel between the receiving antenna and the ith reflecting element, i e {1,2, …, N }, l e {1,2, …, N t }. When the transmitting end performs SSK modulation and activates the first antenna, the received signal of the receiving end is expressed as follows:
y＝FWGel+n＝FWgl+n (1)
Wherein G l represents the first column of the channel G, i.e. the channel between the first transmitting antenna and the intelligent reflecting surface, the transmitting side SSK signal can be expressed as N represents gaussian white noise at the receiving end and obeys a distribution with a mean of 0 and a variance of N 0. At the signal receiving end, the maximum likelihood detection algorithm based on exhaustive search is used for demodulation, and the method is specifically expressed as follows:
Wherein, Is the estimated value of l, and the signal receiving end is from/>And recovering the b s bits of data information. b s＝log2Nt, and N t is assumed to be an integer power of 2.
Step two: and the phase shift of the intelligent reflecting surface reflecting unit is designed by taking the Euclidean distance between different transmitting vectors corresponding to ideal receiving signals when the SSK modulation of the transmitting end is maximized as a target. According to the received signal equation (1), the euclidean distance between different transmitted vectors corresponding to the ideal received signal can be expressed as:
The optimization problem of the present invention is to design the reflection unit phase shift by maximizing d min to reduce the false detection of the transmit antenna index l as the index To improve the performance of MISO systems, the problem can be described as follows:
s.t.θi∈[0，2π) (4)
When there are multiple antennas at the transmitting end, d min is difficult to determine directly, and if an algorithm for traversing the phase shift set of the reflection unit is adopted, the algorithm has higher complexity. The present invention therefore proposes a high performance low complexity algorithm to solve this problem.
Step two: the reflective phase shift design problem is solved based on cosine similarity. The present invention designs the reflection unit phase shift by maximizing the euclidean distance between different transmit vectors corresponding to the ideal received signal. Specifically, the optimal phase shift is calculated as follows:
Wherein g il is the channel between the first transmit antenna and the i-th reflecting element, wherein Is/>A channel between the root transmit antenna and the ith reflecting element; from equation (5)/>In summary, there must be an optimal reflection phase θ i to make the equal sign hold, the calculation of the reflection phase can be obtained by means of cosine similarity, the cosine similarity is briefly described below, and the cosine similarity theorem can calculate the angle between two vectors by using the inner product and the amplitude of the two vectors, and the angle is represented by the cosine value of the angle, which is the cosine similarity. The concrete introduction is as follows:
In the present invention, in order to maximize the Euclidean distance between the different transmit vectors corresponding to the ideal received signal, the channel vectors are made to be Let the magnitude vector of u i/> From equation (6), it can be readily obtained: when the cosine similarity is 1, the included angle between the two channel vectors is 0, and the two vectors u i and/>Is most similar. Based on the description of cosine similarity, the channel vector u i and its magnitude vector/>, can be calculatedIncluded angle v i between, and/>
Similarly, if mu i＝fi is given,Channel vector mu i and its magnitude vector/>, can be calculatedIncluded angle omega i between, and/>The phase shift of the reflection unit can thus be set as follows:
θi＝-(ωi+vi) (7)
the specific algorithm flow based on cosine similarity is shown in algorithm 1 and fig. 2:
Fig. 3 and 4 simulate the bit error rate performance of the present invention. The SSK-Phase curve represents the bit error rate performance of the Phase shift design method, and the method is based on cosine similarity and aims at the Phase shift design of the intelligent reflecting surface reflecting unit of the MISO system modulated by the SSK of the transmitting end; the SNR-Phase curve represents the bit error rate performance of the Phase shift design approach targeting maximizing the receiver SNR. Fig. 3 and fig. 4 simulate the case where there are 2 antennas and 8 antennas at the transmitting end, respectively, and the number of reflection units of the intelligent reflection surface is set to be 32 and 64. As apparent from the simulation diagram, the phase shift design method provided by the invention has lower error rate than the traditional phase shift design method for maximizing the signal-to-noise ratio of the receiving end. In addition, the algorithm based on cosine similarity provided by the invention can design the phase shift of the reflecting unit with lower complexity when the number of the antennas at the transmitting end is more, so that the invention improves the error rate performance of a communication system and reduces the complexity of the system, and the design method of the invention has the advantage of ensuring reliable communication.
Claims (4)
1. The intelligent reflecting surface phase shift design method based on cosine similarity is characterized by comprising the following steps of:
(1) Establishing an intelligent reflecting surface MISO wireless communication system model: the direct communication link between the transmitting end and the receiving end is blocked by the barrier, so the transmitting end can only communicate with the receiving end through the reflecting link with the assistance of the intelligent reflecting surface; the transmitting end is provided with N t antennas, SSK modulation is carried out, an unmodulated carrier signal is sent from the transmitting antenna with index of l to the intelligent reflecting surface, the intelligent reflecting surface with N reflecting units reflects the incident unmodulated signal with specific phase shift, and the receiving end is provided with 1 receiving antenna, and receives the signal reflected from the intelligent reflecting surface;
(2) And the phase shift of the intelligent reflecting surface reflecting unit is designed by taking the Euclidean distance between different transmitting vectors corresponding to ideal receiving signals when the SSK modulation of the transmitting end is maximized as a target.
2. The intelligent reflector phase shift design method of claim 1, wherein the reflection coefficient vector of the intelligent reflector is expressed asWherein/>Beta i and theta i respectively represent the reflection amplitude and the reflection phase of the intelligent reflection surface reflection unit, wherein beta i∈[0,1],θi epsilon [0,2 pi ]; i e {1,2, …, N }, represents the ith reflection element of the intelligent reflector, let β i =1 in consideration of the maximum reflection of the intelligent reflector reflection element, thereforeThen the reflection coefficient vector is further rewritten as/>W is a diagonalized matrix of reflection coefficient vectors Φ, w=diag { Φ };
Sub-channel between intelligent reflecting surface and transmitting end Let g il denote the channel between the ith reflecting element and the first transmitting element, the sub-channel/>, between the receiving end and the intelligent reflecting surfaceLet f i denote the channel between the receiving antenna and the ith reflecting element, i e {1,2, …, N }, l e {1,2, …, N t }; when the transmitting end performs SSK modulation and activates the first antenna, the received signal of the receiving end is expressed as follows:
y＝FWGel+n＝FWgl+n (1)
wherein e l is a transmitting end SSK signal, G l represents a first column of a channel G, namely a channel between a first transmitting antenna and an intelligent reflecting surface, N represents Gaussian white noise of a receiving end, and is subject to distribution with a mean value of 0 and a variance of N 0; at the signal receiving end, the maximum likelihood detection algorithm based on exhaustive search is used for demodulation.
3. The intelligent reflecting surface phase shift design method according to claim 2, wherein the specific process of step (2) is as follows: according to the received signal formula (1), the euclidean distance between different transmitted vectors corresponding to the ideal received signal is expressed as:
is an estimate of the transmit antenna index l,/> Represents the/>, of channel GColumns, i.e./>The channel problem between the root transmit antenna and the smart reflective surface is described as follows:
When the transmitting end is provided with a plurality of antennas, d min is difficult to directly determine, and the phase shift is designed by maximizing Euclidean distance between ideal receiving signals corresponding to different transmitting vectors as far as possible; specifically, the optimal reflection phase is calculated as follows:
Wherein g il is the channel between the first transmit antenna and the i-th reflecting element, wherein Is/>A channel between the root transmit antenna and the ith reflecting element; from equation (5)/>An optimal reflection phase θ i must be present so that the equation is true, the calculation of which is determined by means of cosine similarity; specific:
To maximize the Euclidean distance between the ideal received signals corresponding to different transmitting vectors, the channel vectors are made Let the magnitude vector of u i/> According to/>The method comprises the following steps: when the cosine similarity is 1, the included angle between the two channel vectors is 0, and the two vectors u i and/>Is most similar; computing a channel vector u i and its magnitude vector/>Included angle v i between, and/>
Similarly, if mu i＝fi is given,Calculate channel vector mu i and its magnitude vector/>Included angle omega i between them, andBased on θ i＝-(ωi+vi) sets the phase shift of the reflective element.
4. The intelligent reflection surface phase shift design method according to claim 2, wherein the maximum likelihood detection algorithm is expressed as follows:
Wherein, Is the estimated value of the index l of the transmitting antenna, and the signal receiving end is from/>B s bits of data information are recovered, and b s＝log2Nt,Nt is an integer power of 2.
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