Space-time coding in backscatter communication: time-domain zero-plugging design method and application

Abstract

This invention belongs to the field of backscatter communication technology and discloses a time-domain nulling design method and application of space-time coding in backscatter communication. The nulling space-time coding simultaneously considers the circuit complexity, duty cycle, and reliability of backscatter tags, solving the problem that existing backscatter space-time coding does not fully consider the characteristics of backscatter communication. By designing the space-time coding in the time domain using nulling, an encoding scheme for nulling space-time coding in backscatter communication is proposed, and a joint design scheme with various query methods and corresponding decoding schemes are given. The proposed nulling space-time coding is analyzed and compared with the classic Alamouti coding in terms of circuit complexity, duty cycle, and bit error rate performance. This invention proposes a time-varying query antenna selection method at the query end and derives an asymptotic closed-form expression for the bit error rate of the joint design of nulling space-time coding and the time-varying query antenna selection method.

Description

Technical Field

[0001] This invention belongs to the field of backscatter communication technology, and particularly relates to a time-domain zero-plugging design method and application of space-time coding in backscatter communication. Background Technology

[0002] Backscatter communication has attracted increasing attention due to its near-zero maintenance advantage and has been studied in various IoT scenarios, such as smart homes, smart healthcare, vehicle networks, and sensor networks. Compared to traditional communication where the transmitter directly generates radio frequency signals, backscatter communication devices utilize radio frequency signals from other devices or the environment for signal modulation and reflect the modulated signal back to the receiver to achieve data transmission. Because it does not require actively generating radio frequency signals, its circuit design is simple, inexpensive, and has extremely low energy requirements. Backscatter communication technology has shown promising application prospects in many passive IoT fields such as agriculture, industry, warehousing and logistics, and healthcare. Although backscatter communication has shown great application potential in these passive IoT application areas, due to the bidirectional nature of the backscatter channel, it suffers from deeper fading than traditional channels, which severely affects its error rate performance, transmission rate, and transmission distance. Therefore, multi-antenna technology, which has been successful in traditional communication, has been introduced into backscatter communication to improve system performance. Using multi-antenna technology at the tag end not only provides transmit diversity gain to improve system reliability but also enhances the tag's energy harvesting capability. Therefore, employing multi-antenna technology at the tag end is an effective way to improve the performance of backscatter communication. Compared to other multi-antenna technologies such as beamforming and antenna selection, space-time coding is considered a primary multi-antenna technology at the tag end because it does not require the transmitter to know the channel state information.

[0003] While existing literature has investigated space-time coding techniques in backscatter communication, most studies simply transplant space-time coding from traditional channels to backscatter channels. For example, Goudeli E, Psomas C, and Krikidis I, as well as Niu Z, Wang W, and Jiang T, investigated the application of spatial modulation in MIMO backscatter communication in their papers "Spatial-modulation-based techniques for backscatter communication systems" and "Spatial modulation for ambient backscatter communications: Modeling and analysis," respectively. Liu H-C, Lin W-C, and Lin MY designed and implemented classical Alamouti coding for dual-antenna backscatter tags in their paper "Passive UHF RFID tag with backscatter diversity," and experimentally verified its feasibility. Du ZC, Xiong H, and Wang D proposed high data rate space-time coding in their paper "Signaling scheme design based on HDR Alamouti code for RFID tags using two antennas," demonstrating that this coding has better error performance at the same data rate. However, Boyer C and Roy S pointed out in their paper "Space-time coding for backscatter RFID" that the diversity gain achievable by backscatter space-time coding depends only on the number of tag antennas; that is, increasing the number of antennas at the query and receiver ends cannot further improve the diversity performance of backscatter space-time coding. To address this, He C, Wang ZJ, and Leung VC proposed a unitary query technique in their paper "Unitary query for the M×L×N MIMO backscatter RFID channel." This technique enables space-time coding to overcome the bottleneck of being limited by the number of tag antennas in MIMO backscatter channels, thus improving the diversity gain achievable in these channels.Based on unitary query technology, He C and Wang ZJ further proposed a method called block-level unitary query in their paper "Block-level unitary query: Enabling orthogonal-like space-time code with query diversity for MIMO backscatter RFID". This method enables space-time coding to fully exploit the diversity potential of the MIMO backscatter channel.

[0004] It is evident from the current research status that there is relatively little research on backscatter space-time coding, and most of it is based on or extends the space-time coding theory of traditional channels. However, due to significant differences between backscatter communication and traditional communication in channel structure (backscatter channels have a three-terminal topology), working mechanism (backscatter communication has a duty cycle mechanism), and application scenarios (backscatter tags have a miniaturization requirement), the design of backscatter space-time coding requires consideration of more dimensions compared to traditional space-time coding. Therefore, the optimal space-time coding in traditional channels may not be optimal in backscatter channels.

[0005] Based on the above analysis, the problems and shortcomings of existing technologies are as follows: the optimal space-time coding in traditional channels may not be optimal in backscatter channels. Therefore, traditional space-time coding cannot fully develop and utilize the diversity and coding potential in backscatter channels. Furthermore, backscatter communication has a special mechanism called duty cycle, which has a significant impact on communication transmission performance. Traditional communication lacks this mechanism. Therefore, traditional space-time coding cannot guarantee improved transmission performance in backscatter communication. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a time-domain zero-plugging design method and application of space-time coding in backscatter communication.

[0007] This invention is implemented as follows: a time-domain nulling design method for space-time coding in backscatter communication. The method includes: modeling the backscatter communication channel to obtain the modulation principle of the reflected signal and the working mechanism of the backscatter tag; performing nulling design on the space-time coding in the time domain to obtain a nulling space-time coding scheme; obtaining a joint design scheme of the nulling space-time coding and multiple query methods, and a corresponding decoding scheme; obtaining the circuit complexity, energy efficiency, and bit error rate performance of the nulling space-time coding, and comparing it with the classic Alamouti coding; proposing a time-varying query antenna selection method, and analyzing the bit error rate of the joint design of the nulling space-time coding and the time-varying query antenna selection method.

[0008] Furthermore, the space-time coding in the time-domain zero-placing design of backscatter communication specifically includes the following steps:

[0009] Step 1: Define an M×N×L backscatter channel consisting of M query antennas, L tag antennas, and N receive antennas. The M×N×L backscatter channel is modeled as follows:

[0010]

[0011] Where Q is a query matrix of size T×M, representing the query signals transmitted from M query antennas in time slot T; H is a forward channel matrix of size M×L, representing the path between the query antenna and the tag antenna; G is a reverse channel matrix of size L×N, representing the path between the tag antenna and the receiver; C is a coding matrix of size T×L, representing the signals transmitted from L tag antennas in time slot T; W is a noise matrix of size T×N; R is a received signal matrix of size T×N; ° represents the Hadamard product;

[0012] Step two involves zero-padding into the space-time code. By simultaneously considering tag circuit complexity, energy harvesting efficiency, and error rate performance, a zero-padding space-time code (ZSTBC) is proposed for backscatter communication. For two consecutive codewords c1 and c2, the structure of ZSTBC is as follows:

[0013]

[0014] Where vector c1 = (c1, c2) T Vector c2 = (c2, c1) T Vector i1 = (1,0) T Vector i2 = (0,1) T ,(·) T This is the transpose operator. Since ZSTBC extends the space-time coding in the time domain, the corresponding lookup matrix also needs to be extended in the time domain. The corresponding lookup matrix is ​​represented as follows:

[0015]

[0016] Where Q is the query matrix corresponding to the UFQ or BUTQ method, and vector 12 = (1,1) T ;

[0017] Step 3: Joint design using ZSTBC under the UFQ and BUTQ methods;

[0018] Step four: For any joint design pair {Q,C}, the maximum likelihood ML decoder is used to achieve optimal decoding performance. The ML decoder corresponding to ZSTBC is represented as:

[0019]

[0020] in This is the signal estimated by the receiver after ML detection, where min(·) represents taking the minimum value, ||·|| F Given the Frobenius norm and the receiver having perfect channel state information, ZSTBC can be decoded using a linear decoder after a channel structure equivalence transformation.

[0021] Step 5, the circuit complexity analysis is as follows: the reflection coefficient of the backscatter tag antenna is... Z L Z represents the load impedance. A This represents the impedance of the tag antenna, (·) * Let the complex conjugate operator be represented; consider the following mapping relationship between information bits and reflection coefficients:

[0022]

[0023] Step six, duty cycle analysis is as follows: For ZSTBC, since only one antenna is activated and the other is dormant in any time slot, under the linear energy harvesting model, the energy harvested when using ZSTBC on a tag is:

[0024]

[0025] Where η con It is the power conversion efficiency constant and 0 < η con ≤1, Γ a It is the reflection coefficient of the activated tag antenna, and satisfies 0 < |Γ|. B | 2 ≤1, Γ m It is the reflection coefficient of the tag antenna in dormant state, which satisfies |Γ m | 2 =0, P in It is the incident energy of the energy harvester; the energy collected by the tag during Alamouti encoding is... Further, there are:

[0026]

[0027] The above equation shows that, under a linear energy harvesting model, the ZSTBC method, when used for labeling, outperforms Alamouti coding in energy harvesting performance, resulting in higher energy collection efficiency. The energy P input to the energy harvester in The relationship between them is non-linear, i.e., the energy conversion efficiency η con Instead of being a constant, it is a nonlinear function, and the nonlinear energy harvesting model is expressed as:

[0028] η con (P in )=α1(P in )+α2(P in )+α3;

[0029] Where α1, α2, and α3 are model parameters, and under the linear energy harvesting model, the duty cycle of the backscattered tag can be expressed as:

[0030]

[0031] Where P M P represents the energy collected by the tag antenna in its dormant state, i.e., the energy collected when the tag antenna's reflection coefficient is 0. back P represents the energy collected by the tag antenna in the active state. C P represents the energy consumed by the tag antenna in the active state. M The size is related to the circuit hardware design, and there is P back ≤P M ;

[0032] Step 7, the bit error rate analysis is as follows: The symbol error rate (SER) is calculated using the Gaussian Q function, and it is proportional to the square root of the instantaneous signal-to-noise ratio (SNR) of the received signal. That is, under fading channel conditions, SER is calculated using the following formula:

[0033]

[0034] Where E x (·) represents the expectation with respect to x. Let f be the average signal-to-noise ratio, g be a modulation-related constant, and f be the signal-to-noise ratio. Z (z) is the probability density function corresponding to the system channel gain Z. Where exp(·) is an exponential function, and when performing M-ary phase shift keying modulation (MPSK), substituting Q(x) into... get:

[0035]

[0036] Where g psk =sin 2 (π / M), G Z (·) is the moment generating function corresponding to the channel gain Z;

[0037] Step 8, the time-varying query antenna selection scheme is designed as follows: The BUTQ method essentially performs tensor expansion on the query matrix and the encoding matrix in the time domain. The symbol rate that ZSTBC can achieve in an M×2×N backscatter channel under the BUTQ method is only... Based on the algebraic structure characteristics of the proposed ZSTBC, a time-varying query antenna selection (TQAS) method is proposed at the query end. Unlike BUTQ, the TQAS method enables the ZSTBC to achieve maximum diversity gain in the backscatter channel by improving the quality of the forward link.

[0038] Step 9: In an M×2×N backscatter channel, when using BPSK modulation, the asymptotic closed-form expression for the SER of ZSTBC in the backscatter channel under the TQAS method is calculated as follows:

[0039] For channel gain It can be broken down into:

[0040]

[0041] Where the definition And m opt,l ∈{1,2,…,M}, l∈{1,2} and n∈{1,2,…,N}, and They are mutually independent and follow the same distribution, and their moment generating functions are:

[0042]

[0043] in Ψ2(M,N)=N, and 2F1(;;) represents the Gaussian hypergeometric function, Γ(·) represents the gamma function, and the moment generating function of the channel gain implemented by ZSTBC using the TQAS method is:

[0044]

[0045] When using BPSK modulation, g psk =1, Will and Substituting into step seven, we can obtain the asymptotic closed-form expression for the bit error rate of ZSTBC in the backscattering channel under TQAS:

[0046]

[0047] The diversity gain achieved by ZSTBC under the TQAS method is derived as follows:

[0048]

[0049] This shows that ZSTBC can also fully exploit the inherent diversity gain of the backscatter channel under the TQAS method.

[0050] Furthermore, step three specifically includes:

[0051] (3a) When using ZSTBC in the UFQ method, the joint design pair is represented as:

[0052]

[0053] Where E is a matrix of dimension T×M with all internal elements being 1;

[0054] The joint design of ZSTBC and UFQ methods is specifically represented as follows:

[0055]

[0056] (3b) When using ZSTBC under the BUTQ method, the joint design pair is represented as:

[0057]

[0058] Where U is a unitary matrix, with a 2×2×2 backscattering channel and considering The joint design of ZSTBC and BUTQ methods is then specifically represented as follows:

[0059]

[0060]

[0061] Furthermore, step four specifically includes:

[0062] (4a) Under the UFQ method, ZSTBC has the following algebraic structure transformation:

[0063]

[0064] in Representing the query matrix The i-th row, h1 is the l-th column of the forward channel matrix H, e k Represents the k-th row of matrix E and And there are At this time, the signal received by the receiver can be expressed as

[0065]

[0066] Where vector Represents the received signal matrix The nth row. Because... Having a structure similar to traditional channels, and because the two columns of the ZSTBC are mutually orthogonal, it can be decoded using a linear decoding scheme. Its corresponding linear decoder is represented as follows:

[0067]

[0068] Among them, the decoding operator The specific form is g l,n This represents the reverse channel between the l-th tag antenna and the n-th receiving antenna;

[0069] (4b) Under the BUTQ method, ZSTBC has the following algebraic structure transformation:

[0070]

[0071] Where vector Representation matrix The i-th row, vector u k The k-th row of the unitary matrix U, k∈{1,2,…,M}. Therefore, the signal received by the receiver can be equivalently represented as

[0072]

[0073] Receiver matrix It can be further expressed as in Matrix W k It consists of rows (k-3) to (4k) of matrix W, where k ∈ {1, 2, ..., M}. Therefore, the linear decoding scheme of ZSTBC under the BUTQ method can be expressed as:

[0074]

[0075] Where the matrix Represents the received signal matrix The nth line, the decoding operator Matrix (H) k G) l,n Representation matrix (H) k The l-th row and n-th column of G), where l∈{1,2}, n∈{1,2,…,N};

[0076] Furthermore, step five specifically includes:

[0077] (5a) Using binary phase shift keying (BPSK) modulation, the mapping relationship between information and reflection coefficient is as follows:

[0078]

[0079] Where |Γ0|=|Γ1|, θ1=θ0+π, and 0<|Γ0|, |Γ1|≤1, 0<θ0, θ1≤2π. For BPSK modulation, the reflection coefficient required for the backscatter tag to achieve ZSTBC is:

[0080] (5b) When using binary amplitude shift keying (BASK) modulation, the mapping relationship is as follows:

[0081]

[0082] Where 0 <|Γ B |≤1,0<θ B ≤2π. For BASK modulation, the reflection coefficient required for the backscatter tag to achieve ZSTBC is {|Γ B |e jθ}

[0083] Furthermore, step seven specifically includes:

[0084] (7a) In the M×2×N backscatter channel under the UFQ method, the proposed ZSTBC has the same SER performance as the Alamouti coding, that is:

[0085]

[0086] The specific proof is as follows: In an M×2×N backscatter channel under the UFQ method, the signals received by the receiver when the tag is encoded using ZSTBC and Alamouti are as follows:

[0087] and

[0088] Therefore, when using maximum ratio combining reception, due to the orthogonal structure of ZSTBC and Alamouti coding, the achievable channel gains are expressed as follows:

[0089]

[0090]

[0091] Will and Substitute them separately From

[0092] (7b) In the M×2×N backscatter channel under the BUTQ method, the proposed ZSTBC has the same SER performance as the Alamouti coding, that is:

[0093]

[0094] The specific proof is as follows: In an M×2×N backscatter channel using the BUTQ method, the signals received by the receiver when the tag is encoded using ZSTBC and Alamouti are as follows:

[0095] and

[0096] in Therefore, when the receiver uses maximum ratio combining reception, the channel gains achievable by ZSTBC and Alamouti coding can be expressed as follows:

[0097]

[0098]

[0099] Will and Substitute them separately From which can be obtained

[0100] Furthermore, step eight specifically includes:

[0101] (8a) First, define the optimal query antenna. For an M×2×N backscatter channel, there exists an exponential m opt,l For any m ∈ {1,2,…,M}, the following condition is satisfied: Then m opt,l The corresponding query antenna is defined as the optimal query antenna corresponding to the l-th tag antenna, where l∈{1,2}; in an M×2×n backscatter channel, the selection rule for the optimal query antenna corresponding to each tag antenna is as follows:

[0102]

[0103] in The estimated channel after channel estimation for the receiver. The index of the optimal query antenna corresponding to the l-th tag antenna estimated by the receiver through the estimation channel;

[0104] (8b) Taking a 3×2×2 backscatter channel as an example, this illustrates how the proposed TQAS acts on the ZSTBC. That is, |h 2,1 | 2 and |h 3,2 | 2 They are {|h 1,1 | 2 ,|h 2,1 | 2 ,|h 3,1 | 2} and {|h 3,1 | 2 ,|h 3,2 |2 ,|h 3,3 | 2 The element with the largest median value is then the joint design pair of ZSTBC and TQAS:

[0105]

[0106] For this joint design pair, the signal received by the nth receiving antenna of the receiver is:

[0107]

[0108]

[0109]

[0110]

[0111] in w represents the signal received by the nth receiving antenna in the tth time slot. t,n The corresponding noise;

[0112] (8c) For any l∈{1,2}, we have Therefore, the signal received by the nth receiving antenna is represented as:

[0113]

[0114]

[0115] Then, when using maximum ratio combining reception, the channel gain is expressed as... Ultimately, a maximum likelihood decoder was used for decoding.

[0116] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the space-time coding time-domain zero-plugging design method in backscatter communication.

[0117] Another object of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the space-time coding time-domain zero-plugging design method in backscatter communication.

[0118] Another objective of this invention is to provide an application of the time-domain zero-plugging design method of the aforementioned space-time coding in backscatter communication in multi-antenna backscatter communication.

[0119] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0120] First, addressing the technical problems existing in the prior art and the difficulty in solving them, this paper closely analyzes, in conjunction with the technical solution to be protected by this invention and the results and data obtained during the research and development process, how the technical solution of this invention solves the technical problems, and the inventive technical effects brought about by solving these problems. The specific description is as follows:

[0121] This invention employs a zero-placing design in the time domain for space-time coding, proposing a zero-placing space-time coding scheme for backscatter communication. This scheme simultaneously considers the circuit complexity, duty cycle, and bit error rate of backscatter tags, thereby improving system performance while reducing tag circuit complexity. Ultimately, it provides gains in hardware design and energy harvesting of backscatter tags while ensuring high reliability. Therefore, based on the topology, random characteristics, and working mechanism and principle of backscatter tag circuits, this invention systematically studies the design of space-time coding in backscatter communication from multiple dimensions, providing theoretical basis and technical support for reducing the complexity of multi-antenna tag circuits and improving the duty cycle and reliability of backscatter communication.

[0122] This invention proposes a null-placing space-time coding for backscatter communication. The null-placing design of the space-time coding enables the multiplexing of load impedance on the tag, thereby effectively reducing the circuit complexity of the space-time coding on the tag. Regarding duty cycle, the existence of idle time slots in the null-placing space-time coding ensures that there is a matched tag antenna in each time slot, allowing tags using null-placing space-time coding to collect more energy, thus effectively improving the communication duty cycle. In terms of bit error rate (BER), considering the same modulation strategy, null-placing space-time coding exhibits the same performance as Alamouti coding under UFQ and BUTQ methods. Furthermore, to improve the BER of null-placing space-time coding in the backscatter channel, a time-varying query antenna selection scheme is proposed at the query end by combining the special structure of null-placing space-time coding. An asymptotic closed-form expression for the BER of null-placing space-time coding under the time-varying query antenna selection scheme is derived to illustrate its specific implementation performance. This invention provides a theoretical basis for improving the duty cycle and reliability of backscatter communication.

[0123] Secondly, considering the technical solution as a whole or from a product perspective, the technical effects and advantages of the technical solution protected by this invention are specifically described as follows: This invention provides a zero-placing space-time coding scheme for backscatter communication, which simultaneously considers the circuit complexity, duty cycle, and reliability of backscatter tags, mainly addressing the problem that existing backscatter space-time coding schemes do not fully consider the characteristics of backscatter communication. The implementation process is as follows: By designing the space-time coding with zero-placing in the time domain, an encoding scheme for zero-placing space-time coding for backscatter communication is proposed, and a joint design scheme with various query methods and corresponding decoding schemes are given. Based on this, the proposed zero-placing space-time coding is analyzed and compared with the classic Alamouti coding in terms of circuit complexity, duty cycle, and bit error rate performance. To further improve the bit error rate performance of the zero-placing space-time coding in the backscatter channel, this invention proposes a time-varying query antenna selection method at the query end and derives an asymptotic closed-form expression for the bit error rate of the joint design of the zero-placing space-time coding and the time-varying query antenna selection method.

[0124] Third, as supplementary evidence of the inventive step of the claims of this invention, it is also reflected in the following important aspects:

[0125] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0126] Designing space-time coding by combining the structural characteristics of backscatter channels and the hardware features of backscatter tags can enable backscatter communication to be more widely used and generate great value in many cutting-edge fields, such as industrial IoT, monitoring / warehouse applications, smart agriculture, smart healthcare and many other passive IoT fields. This has important scientific significance and application value.

[0127] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally:

[0128] Currently, research on backscatter space-time coding is relatively limited both domestically and internationally, and most studies simply transplant space-time coding from traditional channels to backscatter channels. However, backscatter communication differs significantly from traditional communication in channel structure (backscatter channels have a three-terminal topology), operating mechanism (backscatter communication has a duty cycle mechanism), and application scenarios (backscatter tags have a miniaturization requirement). Therefore, the design of backscatter space-time coding requires consideration of more performance dimensions compared to traditional space-time coding. This invention, for the first time, studies the design of space-time coding in backscatter communication from multiple dimensions based on the topology, random characteristics, and operating mechanism of backscatter tag circuits. This provides a theoretical basis and technical support for reducing the complexity of multi-antenna tag circuits and improving the duty cycle and reliability of backscatter communication. Attached Figure Description

[0129] Figure 1 This is a flowchart of the time-domain zero-plugging design method for space-time coding in backscatter communication provided by an embodiment of the present invention;

[0130] Figure 2 This is a model diagram of an M×N×L backscatter communication channel as considered in an embodiment of the present invention;

[0131] Figure 3 This is a signal flow graph of the joint design of ZSTBC and UFQ method in a 2×2×2 backscatter channel provided in the embodiments of the present invention;

[0132] Figure 4 This is a circuit diagram of ZSTBC implemented on a tag under (a) BPSK modulation and (b) BASK modulation, provided in an embodiment of the present invention;

[0133] Figure 5 This is a schematic diagram of the energy collected under the linear energy harvesting model (left figure) and the nonlinear energy harvesting model (right figure) respectively using ZSTBC and Alamouti encoding, as provided in the embodiments of the present invention;

[0134] Figure 6 This is a schematic diagram of the duty cycle when tags are encoded using ZSTBC and Alamouti in a linear energy harvesting model, provided by an embodiment of the present invention.

[0135] Figure 7 This is a schematic diagram illustrating the bit error rate performance of ZSTBC and Alamouti coding in 2×2×1, 2×2×2, and 2×2×3 backscatter channels under the UFQ method, provided in the embodiments of the present invention.

[0136] Figure 8 This is a schematic diagram illustrating the bit error rate performance of ZSTBC and Alamouti coding in 2×2×1, 2×2×2, and 2×2×3 backscatter channels under the BUTQ method, provided in an embodiment of the present invention.

[0137] Figure 9 This is a schematic diagram showing the theoretical analysis results and simulation results of the bit error rate of ZSTBC in 2×2×1, 2×2×2, and 2×2×3 backscattering channels under TQAS provided in the embodiments of the present invention. Detailed Implementation

[0138] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0139] I. Explanatory and Illustrative Embodiments. To enable those skilled in the art to fully understand how the present invention is specifically implemented, this section provides an explanatory and illustrative description of the embodiments described in the claims.

[0140] like Figure 1 As shown, the time-domain zero-plugging design method for space-time coding in backscatter communication provided by this embodiment of the invention includes the following steps:

[0141] The channel of backscatter communication is modeled to obtain the modulation principle of reflected signals and the working mechanism of backscatter tags;

[0142] In the time domain, zero-insertion design is applied to the space-time coding to obtain a zero-insertion space-time coding scheme;

[0143] Obtain the joint design scheme of zero-insertion spacetime encoding and multiple query methods, and the corresponding decoding scheme;

[0144] The circuit complexity, energy efficiency, and error rate performance of zero-placing spacetime coding are obtained and compared with those of classic Alamouti coding.

[0145] A time-varying query antenna selection method is proposed, and the bit error rate of the joint design of zero-insertion space-time coding and time-varying query antenna selection method is analyzed.

[0146] like Figure 2 As shown, the time-domain zero-plugging design of the space-time coding proposed in this invention for backscatter communication includes the following steps:

[0147] Step 1: Define an M×N×L backscatter channel consisting of M query antennas (carrier transmitter antennas), L tag antennas, and N receive antennas. The M×N×L backscatter channel can be modeled as follows:

[0148]

[0149] Where Q is a query matrix of size T×M, representing the query signals transmitted from M query antennas within time slot T; H is a forward channel matrix of size M×L, representing the path between the query antenna and the tag antenna; G is a reverse channel matrix of size L×N, representing the path between the tag antenna and the receiver; C is a coding matrix of size T×L, representing the signals transmitted by L tag antennas within time slot T; W is a noise matrix of size T×N; R is a received signal matrix of size T×N; and ° represents the Hadamard product. The above channel model shows that the performance of the backscatter channel depends not only on itself but also on the query matrix Q. Therefore, the performance of the backscatter communication system is determined by the joint design of {Q, C}. For the Uniform Query (UFQ) method, the joint design is represented as... Where E is a matrix of dimension T×M with all elements equal to 1; for the Block Unitary Query (BUTQ) method, the joint design is represented as Where U is a unitary matrix. For the Kronecker product, 1 M Let {Q} represent a vector of length M in which all elements are 1; for the Query Antenna Selection (QAS) method, the joint design is represented as {Q} QAS =S,C QAS =C}, where each row of S contains only one element that is 1 and the rest are 0, and the specific position of the 1 in each row is determined by the index m. opt It is determined that for any m∈{1,2,…,M}, the following condition is satisfied. l∈{1,2,…,L},h m,l This represents the forward channel between the m-th query antenna and the l-th tag antenna.

[0150] Step two: Since the tag can acquire more energy when the tag antenna is idle, this invention fills the space-time code with zeros to increase the idle time slots of the tag antenna. By simultaneously considering the tag circuit complexity, energy harvesting efficiency, and error rate performance, this invention proposes a zero-padding space-time block code (ZSTBC) for backscatter communication. For two consecutive codewords c1 and c2, the structure of ZSTBC is represented as follows:

[0151]

[0152] Where vector c1 = (c1, c2) T Vector c2 = (c2, c1) T Vector i1 = (1,0) T Vector i2 = (0,1) T ,in(·) T `<transpose>` is the transpose operator. Since ZSTBC extends the space-time encoding in the time domain, the corresponding query matrix also needs to be extended in the time domain to correctly preserve the dimensionality. The corresponding query matrix is ​​represented as follows:

[0153]

[0154] Where Q is the query matrix corresponding to the UFQ or BUTQ method, and vector 12 = (1,1) T .

[0155] Step 3, the co-design pair using ZSTBC under the UFQ and BUTQ methods can be expressed as follows:

[0156] (3a) When using ZSTBC in the UFQ method, the co-design pair can be expressed as:

[0157]

[0158] To better illustrate and present the joint design of ZSTBC and UFQ methods, taking a 2×2×2 backscatter channel as an example, the joint design of ZSTBC and UFQ methods is specifically represented as follows:

[0159]

[0160] Figure 2 The signal flow diagram of the joint design of ZSTBC and UFQ in a 2×2×2 backscatter channel is shown;

[0161] (3b) When using ZSTBC under the BUTQ method, the co-design pair can be expressed as:

[0162]

[0163] Where U is a unitary matrix, taking a 2×2×2 backscattering channel as an example and considering At this point, the joint design of ZSTBC and BUTQ methods is specifically represented as follows:

[0164]

[0165]

[0166] Step four: For any joint design pair {Q, C}, the maximum likelihood (ML) decoder can be used to achieve optimal decoding performance. The ML decoder corresponding to ZSTBC can be expressed as:

[0167]

[0168] in This is the signal estimated by the receiver after ML detection, where min(·) represents taking the minimum value, ||·|| F The Frobenius norm is used, and this invention assumes that the receiver has perfect channel state information. Furthermore, since the proposed ZSTBC has an orthogonal structure, it can be decoded using a linear decoder after an equivalent channel structure transformation.

[0169] (4a) Under the UFQ method, ZSTBC has the following algebraic structure transformation:

[0170]

[0171] in Representing the query matrix The i-th row, h1 is the l-th column of the forward channel matrix H, e kRepresents the k-th row of matrix E and And there are At this time, the signal received by the receiver can be expressed as

[0172]

[0173] Where vector Represents the received signal matrix The nth row. Because... Having a structure similar to traditional channels, and because the two columns of the ZSTBC are mutually orthogonal, it can be decoded using a linear decoding scheme. Its corresponding linear decoder is represented as follows:

[0174]

[0175] Among them, the decoding operator The specific form is g l,n This represents the reverse channel between the l-th tag antenna and the n-th receiving antenna;

[0176] (4b) Under the BUTQ method, ZSTBC has the following algebraic structure transformation:

[0177]

[0178] Where vector Representation matrix The i-th row, vector u k The k-th row of the unitary matrix U, k∈{1,2,…,M}. Therefore, the signal received by the receiver can be equivalently represented as

[0179]

[0180] Receiver matrix It can be further expressed as in Matrix W k It consists of rows (k-3) to (4k) of matrix W, where k ∈ {1, 2, ..., M}. Therefore, the linear decoding scheme of ZSTBC under the BUTQ method can be expressed as:

[0181]

[0182] Where the matrix Represents the received signal matrix The nth line, the decoding operator Matrix (H) k G) l,n Representation matrix (H) kLet G be the l-th row and n-th column of G, where l∈{1,2} and n∈{1,2,…,N}.

[0183] Step 5, the circuit complexity analysis is as follows: the reflection coefficient of the backscatter tag antenna is... Z L Z represents the load impedance. A This represents the impedance of the tag antenna, (·) * Let the complex conjugate operator be represented; consider the following mapping relationship between information bits and reflection coefficients:

[0184]

[0185] (5a) Using binary phase shift keying (BPSK) modulation, the mapping relationship between information and reflection coefficient is as follows:

[0186]

[0187] Where |Γ0|=|Γ1|, θ1=θ0+π, and 0<|Γ0|, |Γ1|≤1, 0<θ0, θ1≤2π. For BPSK modulation, the reflection coefficient required for the backscatter tag to achieve ZSTBC is: The zero-placing structure of ZSTBC allows only one antenna to operate in any given time slot, which further simplifies the complexity of ZSTBC tag circuitry. Figure 3 The diagram shows a schematic of the ZSTBC implementation on a tag under BPSK modulation. As can be seen from the figure, since only one tag antenna is activated in each time slot, the same set of reflection coefficients... Different tag antennas can be served within different time slots. Therefore, the complexity of tag circuitry can be further reduced by multiplexing the load impedance across different time slots.

[0188] (5b) When using binary amplitude shift keying (BASK) modulation, the mapping relationship is as follows:

[0189]

[0190] Where 0 <|Γ B |≤1,0<θ B ≤2π. For BASK modulation, the reflection coefficient required for the backscatter tag to achieve ZSTBC is {|Γ B |e jθ Similarly, due to the zero-placing structure of ZSTBC, only one tag antenna is activated in each time slot, allowing the tag to reuse its reflection coefficient (load impedance). Figure 3 The circuit diagram of ZSTBC implemented on a tag under BASK modulation is shown.

[0191] Step six, duty cycle analysis is as follows: For ZSTBC, since only one antenna is active while the other is dormant in any given time slot, the energy collected when using ZSTBC on a tag under the linear energy harvesting model is:

[0192]

[0193] Where η con It is the power conversion efficiency constant and 0 < η con ≤1, Γ a It is the reflection coefficient of the activated tag antenna, and satisfies 0 < |Γ|. B | 2 ≤1, Γ m It is the reflection coefficient of the tag antenna in dormant state, which satisfies |Γ m | 2 =0, P in This is the incident energy of the energy harvester. Because the energy collected by the tag during Alamouti encoding is... Therefore, we can further conclude:

[0194]

[0195] The above equation shows that, under a linear energy harvesting model, using ZSTBC for labeling results in better performance than using Alamouti coding. However, in reality, the energy harvester collects... The energy P input to the energy harvester in The relationship between them is non-linear, i.e., the energy conversion efficiency η con It is no longer a constant but a nonlinear function. Therefore, a nonlinear energy harvesting model will also be considered, which is expressed as:

[0196] η con (P in )=α1(P in )+α2(P in )+α3,

[0197] Where α1, α2, and α3 are model parameters. Since linear models are easier to analyze, a linear model is used below to analyze the tag's duty cycle. Under the linear energy harvesting model, the duty cycle of the backscattering tag can be expressed as:

[0198]

[0199] Where P M P represents the energy collected by the tag antenna in its dormant state, i.e., the energy collected when the tag antenna's reflection coefficient is 0. back P represents the energy collected by the tag antenna in the active state.C This represents the energy consumed by the tag antenna in the active state, where P M The size is related to the tag circuit hardware design, and there is P back ≤P M .

[0200] In summary, tags using ZSTBC exhibit better energy harvesting performance compared to those using Alamouti coding. Simultaneously observing the structures of ZSTBC and Alamouti encoding, we find that the energy consumption of the tag using ZSTBC is half that of the tag using Alamouti encoding. Therefore, we can obtain... In other words, using ZSTBC for tags results in a better duty cycle compared to using Alamouti encoding.

[0201] Step 7, Bit Error Rate Analysis: The Symbol Error Rate (SER) is generally calculated using the Gaussian Q function. It is proportional to the square root of the instantaneous signal-to-noise ratio of the received signal. That is, under fading channels, SER can be calculated using the following formula:

[0202]

[0203] Where E x (·) represents the expectation with respect to x. Let f be the average signal-to-noise ratio, g be a modulation-related constant, and f be the signal-to-noise ratio. Z (z) is the probability density function corresponding to the system channel gain Z. Where exp(·) is an exponential function, and when considering M-ary phase shift keying modulation (MPSK), substituting Q(x) into... Further results can be obtained:

[0204]

[0205] Where g psk =sin 2 (π / M), G Z (·) represents the moment generating function corresponding to the channel gain Z. For the proposed ZSTBC, the following results can be obtained regarding its error performance:

[0206] (7a) In the M×2×N backscatter channel under the UFQ method, the proposed ZSTBC has the same SER performance as the Alamouti coding, i.e.

[0207]

[0208] The specific proof is as follows: According to step (4a), in the M×2×N backscatter channel under the UFQ method, the signals received by the receiver when the tag is encoded using ZSTBC and Alamouti are as follows:

[0209] and

[0210] Therefore, when using maximum ratio combining reception, due to the orthogonal structure of ZSTBC and Alamouti coding, the achievable channel gains are expressed as follows:

[0211]

[0212]

[0213] Will and Substitute them separately From which can be obtained

[0214] (7b) In the M×2×N backscatter channel under the BUTQ method, the proposed ZSTBC has the same SER performance as the Alamouti coding, that is:

[0215]

[0216] The specific proof is as follows: According to step (4b), in the M×2×N backscatter channel under the BUTQ method, the signals received by the receiver when the tag is encoded using ZSTBC and Alamouti are as follows:

[0217] and

[0218] in Therefore, when the receiver uses maximum ratio combining reception, the channel gains achievable by ZSTBC and Alamouti coding can be expressed as follows:

[0219]

[0220]

[0221] Will and Substitute them separately From which can be obtained

[0222] Step 8, the time-varying query antenna selection scheme is designed as follows: The BUTQ method essentially performs tensor expansion on the query matrix and the encoding matrix in the time domain. Therefore, the symbol rate that ZSTBC can achieve in an M×2×N backscatter channel under the BUTQ method is only [missing information]. Based on the algebraic structure characteristics of the proposed ZSTBC, a Time-Varying Query Antenna Selection (TQAS) method is proposed at the query end. Unlike BUTQ, the TQAS method enables the ZSTBC to achieve maximum diversity gain in the backscatter channel by improving the quality of the forward link.

[0223] (8a) First, define the optimal query antenna. For an M×2×N backscatter channel, assume there exists an exponent m. opt,l For any m ∈ {1,2,…,M}, the following condition is satisfied: Then m opt,l The corresponding query antenna is defined as the optimal query antenna corresponding to the l-th tag antenna, where l∈{1,2}. Since ZSTBC activates different tag antennas in different time slots, m... opt,l The value of the query antenna is likely to differ across different time slots, meaning the query terminal is likely to activate different query antennas in different time slots; hence, this is called time-varying query antenna selection. From the definition of TQAS, it's clear that the TQAS scheme needs to compare the forward channel |h| in the backscatter channel when selecting the active query antenna. m,l | 2 The quality of the tag is important, but since the tag is a device with limited computing power, it is difficult to directly obtain the channel state information of the forward channel from the tag. Therefore, by comparing |h m,l g l,n | 2 To indirectly compare the forward channel |h m,l | 2 The quality. In an M×2×N backscatter channel, the selection rule for the optimal query antenna corresponding to each tag antenna can be expressed as:

[0224]

[0225] in The estimated channel after channel estimation for the receiver. The index of the optimal query antenna corresponding to the l-th tag antenna estimated by the receiver through the estimation channel;

[0226] (8b) Using a 3×2×2 backscatter channel as an example, illustrate how the proposed TQAS acts on the ZSTBC, assuming... That is, |h 2,1 |2 and |h 3,2 | 2 They are {|h 1,1 | 2 ,|h 2,1 | 2 ,|h 3,1 | 2} and {|h 3,1 | 2 ,|h 3,2 | 2 ,|h 3,3 | 2 The element with the largest median value is then the joint design pair of ZSTBC and TQAS:

[0227]

[0228] For this joint design pair, the signal received by the nth receiving antenna of the receiver is:

[0229]

[0230]

[0231]

[0232]

[0233] in w represents the signal received by the nth receiving antenna in the tth time slot. t,n The corresponding noise;

[0234] (8c) Since this invention assumes that the receiver has perfect channel information, for any l∈{1,2}, we have Therefore, the signal received by the nth receiving antenna can also be represented as:

[0235]

[0236]

[0237] Then, when using maximum ratio combining reception, the channel gain can be expressed as: Ultimately, a maximum likelihood decoder was used for decoding.

[0238] Step 9: In an M×2×N backscatter channel, when using BPSK modulation, the asymptotic closed-form expression for the SER of ZSTBC in the backscatter channel under the TQAS method is calculated as follows:

[0239] Step (8c) gives the channel gain of ZSTBC in the backscatter channel under the TQAS method. Furthermore, regarding channel gain It can be broken down into:

[0240]

[0241] Where the definition And for any m opt,l ∈{1,2,…,M}, l∈{1,2} and n∈{1,2,…,N}, since this invention does not consider the correlation between channels. and They are mutually independent and follow the same distribution, and their moment generating functions are:

[0242]

[0243] in Ψ2(M,N)=N, and 2F1(;;) represents the Gaussian hypergeometric function, and Γ(·) represents the gamma function. Therefore, the moment generating function of the channel gain implemented by ZSTBC using the TQAS method is:

[0244]

[0245] When using BPSK modulation, g psk =1, Will and Substituting into step seven, we can obtain the asymptotic closed-form expression for the bit error rate of ZSTBC in the backscattering channel under the TQAS method:

[0246]

[0247] Furthermore, the diversity gain achieved by ZSTBC under the TQAS method can be derived as follows:

[0248]

[0249] This indicates that ZSTBC can fully exploit the inherent diversity gain of the backscatter channel using the TQAS method.

[0250] II. Application Examples. To demonstrate the inventiveness and technical value of the technical solution of this invention, this section provides application examples of the technical solution of the claims on specific products or related technologies.

[0251] This invention proposes a space-time coding scheme for backscatter communication. For M×N×L backscatter channels, the proposed coding scheme for encoding and modulating transmitted information can significantly reduce the circuit complexity of tags and improve their energy harvesting efficiency. We provide rigorous mathematical analysis to illustrate the performance improvements and tag complexity reduction brought about by the proposed space-time coding scheme.

[0252] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0253] III. Evidence of the Relevant Effects of the Embodiments. The embodiments of the present invention have achieved some positive effects during research and development or use, and indeed possess significant advantages compared to existing technologies. The following description, in conjunction with data, charts, and other materials from the experimental process, illustrates these advantages.

[0254] A. Simulation conditions

[0255] A1) Assume the channel is a quasi-static Rayleigh flat fading channel, and assume the receiver has perfect channel state information;

[0256] A2) Assume the data rate is the bit rate (BitRate), where the bit rate R b With symbol rate R s The relationship between them is R b =R s log2M, where M represents the modulation order used for the symbol;

[0257] B. Simulation Content:

[0258] B1) in |Γ a | 2 =0.4, η con =0.2 and |Γ a | 2 =0.4, ηcon When the energy is 0.4, the energy collected by the method of this invention for ZSTBC and Alamouti encoding is compared, and the results are as follows: Figure 5 As shown;

[0259] B2) in |Γ a | 2 =0.4, η con =0.2 and |Γ a | 2 =0.4, η con When the value is 0.4, the duty cycle of ZSTBC and Alamouti encoding obtained by the method of this invention is compared, and the results are as follows: Figure 6 As shown;

[0260] B3) In 2×2×1, 2×2×2, and 2×2×3 backscattering channels, the error rate performance of ZSTBC and Alamouti coding obtained by the method of this invention under the UFQ method is compared, and the results are as follows: Figure 7 As shown;

[0261] B4) In 2×2×1, 2×2×2, and 2×2×3 backscattering channels, the error rate performance of ZSTBC and Alamouti coding obtained by the method of this invention under the BUTQ method is compared, and the results are as follows: Figure 8 As shown;

[0262] B5) In 2×2×1, 2×2×2, and 2×2×3 backscattering channels, the theoretical analysis results of the bit error rate of ZSTBC under TQAS obtained by the method of this invention are compared with the simulation results. The results are as follows: Figure 9 As shown;

[0263] C. Simulation results:

[0264] Figure 5 The figures represent the energy collected using ZSTBC and Alamouti encoding under linear energy harvesting models (left figure) and nonlinear energy harvesting models (right figure), respectively, where |Γ| is considered. a | 2 =0.4, η con =0.2 and |Γ a | 2 =0.4, η con =0.4. The simulation results show that the tag using ZSTBC can collect more energy compared to using Alamouti encoding;

[0265] Figure 6 This is a comparison of the duty cycles of ZSTBC and Alamouti encoding under a linear energy harvesting model, where |Γ| is considered respectively. a | 2=0.4, η con =0.2 and |Γ a | 2 =0.4, η con =0.4. The simulation shows that the label using ZSTBC has a better duty cycle than the label using Alamouti encoding.

[0266] Figure 7 This describes the bit error rate performance of ZSTBC and Alamouti coding in 2×2×1, 2×2×2, and 2×2×3 backscatter channels under the UFQ method, based on... Figure 7 (Left) As can be seen, similar to the traditional MIMO channel, the error curves of ZSTBC and Alamouti coding still coincide in the MIMO backscatter channel under the UFQ method. That is, Alamouti coding and ZSTBC have the same error performance. However, when both Alamouti coding and ZSTBC use BPSK modulation, although the error curves of the two codes coincide, the data rate of ZSTBC is half that of Alamouti coding. Figure 7 (As shown on the right);

[0267] Figure 8 This describes the bit error rate performance of ZSTBC and Alamouti coding in 2×2×1, 2×2×2, and 2×2×3 backscatter channels under the BUTQ method, based on... Figure 8 (Left) As can be seen, in the MIMO backscatter channel under the BUTQ method, when using the same modulation scheme, the bit error rate curves of ZSTBC and Alamouti completely overlap, indicating that they have the same bit error rate performance. However, the data rate of ZSTBC is only half that of Alamouti coding. For a fair comparison, both should maintain the same data rate; therefore, a higher-order modulation should be used in ZSTBC. Figure 8 (Right) It can be seen that, at the same data rate, the error rate performance of ZSTBC is weaker than that of Alamouti coding. Furthermore, in comparison... Figure 6 and Figure 7 It can be seen that the bit error rate curve of ZSTBC under the BUTQ method is steeper than that under the UFQ method. This indicates that compared with the UFQ method, the BUTQ method enables ZSTBC to make fuller use of the diversity gain of the MIMO backscatter channel.

[0268] Figure 9This presents the theoretical and simulation results of the bit error rate (BER) of ZSTBC in 2×2×1, 2×2×2, and 2×2×3 backscatter channels under TQAS. It can be seen that at high SNR, the theoretical BER curve of ZSTBC under the TQAS method closely matches the simulated BER curve, demonstrating the accuracy of the theoretical derivation of the asymptotic closed-form expression for the SER of ZSTBC under the TQAS method. Furthermore, the simulated SER curve in the 2×2×2 channel is approximately parallel to the SER curve in the 2×2×3 channel, and is steeper than the SER curve in the 2×2×1 channel. This indicates that under the TQAS method, ZSTBC achieves the same diversity gain in 2×2×2 and 2×2×3 channels, and outperforms it in the 2×2×1 channel, which is consistent with the expected results.

[0269] In summary, this invention proposes a null-placing space-time coding method for backscatter communication. Compared with conventional space-time coding methods, this invention simultaneously considers the circuit complexity, duty cycle, and reliability of backscattering tags. Specifically, this invention combines the principle of reflected signal modulation with the working mechanism of backscattering tags to perform null-placing design on the space-time coding in the time domain. The null-placing operation not only enables impedance multiplexing on the backscattering tag, thereby effectively reducing the tag's circuit complexity, but also ensures that the backscattering tag has a dormant antenna in any time slot, thus improving its energy harvesting capability and increasing the duty cycle. To further improve the bit error rate performance of the null-placing space-time coding, this invention also proposes a time-varying query antenna selection method and derives an asymptotic closed-form expression for the bit error rate of the null-placing space-time coding under the time-varying query antenna selection method to illustrate its performance.

[0270] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A time-domain zero-plugging design method for space-time coding in backscatter communication, characterized in that, The time-domain nulling design method for space-time coding in backscatter communication includes: modeling the backscatter communication channel to obtain the modulation principle of the reflected signal and the working mechanism of the backscatter tag; performing nulling design on the space-time coding in the time domain to obtain the coding scheme of the nulling space-time coding; obtaining the joint design scheme of the nulling space-time coding and multiple query methods and the corresponding decoding scheme; obtaining the circuit complexity, energy efficiency and bit error rate performance of the nulling space-time coding and comparing it with the classic Alamouti coding; proposing a time-varying query antenna selection method and analyzing the bit error rate of the joint design of the nulling space-time coding and the time-varying query antenna selection method. The time-domain zero-plugging design method for space-time coding in backscatter communication specifically includes the following steps: Step 1, Setting The backscatter channel is composed of One query antenna, L tag antennas and It consists of a receiving antenna. The backscatter channel is modeled as follows: ， in It is the size of The query matrix represents the time slots. From the inside The query signal is transmitted by each query antenna; It is the size of The forward channel matrix represents the path between the query antenna and the tag antenna; It is the size of The reverse channel matrix represents the path between the tag antenna and the receiver; It is the size of The encoding matrix represents the encoding matrix in the time slot. Inside The signal transmitted by the root tag antenna; It is the size of The noise matrix of N; It is the size of The received signal matrix of N; It represents the Hadamardi (or Hadama) stack; Step two involves zero-padding into the space-time code. By simultaneously considering tag circuit complexity, energy harvesting efficiency, and error rate performance, a zero-padding space-time code (ZSTBC) is proposed for backscatter communication. For two consecutive codewords... and The structure of ZSTBC is represented as follows: ， Where vector ,vector ,vector ,vector ,in This is the transpose operator; since ZSTBC extends the space-time encoding in the time domain, the corresponding query matrix also needs to be extended in the time domain to correctly preserve the dimension. The corresponding query matrix is ​​represented as follows: ， in The query matrix and vector corresponding to the UFQ or BUTQ method. ; Step 3: Joint design using ZSTBC under the UFQ and BUTQ methods; Step four, for any joint design pair Both employ a maximum likelihood ML decoder to achieve optimal decoding performance. The ML decoder corresponding to ZSTBC is represented as follows: ， in It is the signal estimated by the receiver after ML detection, min( () indicates taking the minimum value. The Frobenius norm is used, and the receiver has perfect channel state information. After channel structure equivalence transformation, a linear decoder is used to decode the ZSTBC. Step 5, the circuit complexity analysis is as follows: the reflection coefficient of the backscatter tag antenna is... ,in Indicates the load impedance. This indicates the impedance of the tag antenna. Let the complex conjugate operator be represented; consider the following mapping relationship between information bits and reflection coefficients: ， Step six, duty cycle analysis is as follows: For ZSTBC, since only one antenna is activated and the other is dormant in any time slot, under the linear energy harvesting model, the energy harvested when using ZSTBC on a tag is: ， in It is the power conversion efficiency constant and It is the reflection coefficient of the activated tag antenna, and satisfies... , It is the reflection coefficient of the tag antenna in dormant state, which satisfies , It is the incident energy of the energy harvester; the energy collected by the tag during Alamouti encoding is... 2 Furthermore: ， The above equation shows that, under the linear energy harvesting model, using ZSTBC for labeling results in better performance than using Alamouti coding, and the energy harvester collects more energy. Energy input to the energy harvester The relationship between them is non-linear, i.e., energy conversion efficiency. Instead of being a constant, it is a nonlinear function, and the nonlinear energy harvesting model is expressed as: ， in , and As model parameters, under the linear energy harvesting model, the duty cycle of the backscattered tag can be expressed as: ， in This represents the energy collected by the tag antenna in its dormant state, i.e., the energy collected when the tag antenna's reflection coefficient is 0. This represents the energy collected by the tag antenna when it is in the active state. This represents the energy consumed by the tag antenna in the active state, where The size is related to the tag circuit hardware design, and has ; Step 7, the bit error rate analysis is as follows: The symbol error rate (SER) is calculated using the Gaussian Q function, and it is proportional to the square root of the instantaneous signal-to-noise ratio (SNR) of the received signal. That is, under fading channel conditions, SER is calculated using the following formula: ， in Indicates about Take the expected value. The average signal-to-noise ratio. A constant related to modulation. Let Z be the probability density function corresponding to the system channel gain. ;in It is an exponential function, and when M-ary phase shift keying modulation (MPSK) is applied, it will... Substitution get: ， in , For channel gain The corresponding moment generating function; for the proposed ZSTBC; Step 8, the time-varying query antenna selection scheme is designed as follows: The BUTQ method is essentially a tensor expansion of the query matrix and the encoding matrix in the time domain. ZSTBC under the BUTQ method The achievable symbol rate in the backscatter channel is only Based on the algebraic structure characteristics of the proposed ZSTBC, a time-varying query antenna selection (TQAS) method is proposed at the query end. Unlike BUTQ, the TQAS method enables the ZSTBC to achieve maximum diversity gain in the backscatter channel by improving the quality of the forward link. Step nine, in In the backscatter channel, when using BPSK modulation, the asymptotic closed-form expression for the SER of ZSTBC in the backscatter channel under the TQAS method is calculated as follows: For channel gain It can be broken down into: ， Where the definition = And for any , and , and They are mutually independent and follow the same distribution, and their moment generating functions are: ， in ,and , Represents the Gaussian hypergeometry function. The moment generating function for the channel gain implemented by ZSTBC using the TQAS method, representing the gamma function, is: ， When using BPSK modulation ,Will Substituting into step seven, we can obtain the asymptotic closed-form expression for the bit error rate of ZSTBC in the backscattering channel under the TQAS method: ， The diversity gain achieved by ZSTBC under the TQAS method is derived as follows: ， This shows that ZSTBC can also fully exploit the inherent diversity gain of the backscatter channel under the TQAS method; Step three specifically includes: (3a) When using ZSTBC in the UFQ method, the joint design pair is represented as: } ， The joint design of ZSTBC and UFQ methods is specifically represented as follows: ， (3b) When using ZSTBC under the BUTQ method, the joint design pair is represented as: } ， in For a unitary matrix, with Taking the backscatter channel as an example and considering At this point, the joint design of ZSTBC and BUTQ methods is specifically represented as follows: 。 2. The time-domain zero-plugging design method for space-time coding in backscatter communication as described in claim 1, characterized in that, Step four specifically includes: (4a) Under the UFQ method, ZSTBC has the following algebraic structure transformation: ， in Representing the query matrix The i-th row, It is the forward channel matrix The lth column, Describe the k-th row of matrix E and = And there are = At this time, the signal received by the receiver can be represented as ， Where vector Represents the received signal matrix The nth row; because Having a structure similar to traditional channels, and because the two columns of a ZSTBC are mutually orthogonal, it can be decoded using a linear decoding scheme; its corresponding linear decoder is represented as follows: ， Among them, the decoding operator The specific form is , This represents the reverse channel between the l-th tag antenna and the n-th receiving antenna; (4b) Under the BUTQ method, ZSTBC has the following algebraic structure transformation: ， Where vector Representation matrix The i-th row, vector The k-th row of the unitary matrix U, k Therefore, the signal received by the receiver can be equivalently represented as ， Receiver matrix It can be further expressed as ,in ,matrix It is a matrix It consists of rows k-3 to 4k, and has k Therefore, the linear decoding scheme of ZSTBC under the BUTQ method can be expressed as: ， Where the matrix Represents the received signal matrix The nth line, the decoding operator ,matrix Representation matrix The l-th row and n-th column, and , .

3. The time-domain zero-plugging design method for space-time coding in backscatter communication as described in claim 1, characterized in that, Step five specifically includes: (5a) Using binary phase shift keying (BPSK) modulation, the mapping relationship between information and reflection coefficient is as follows: ； in , = ,and , , , For BPSK modulation, the reflection coefficient required for the backscatter tag to achieve ZSTBC is: ; (5b) When using binary amplitude shift keying (BASK) modulation, the mapping relationship is as follows: ； in For BASK modulation, the reflection coefficient required for the backscatter tag to achieve ZSTBC is: .

4. The time-domain zero-plugging design method for space-time coding in backscatter communication as described in claim 1, characterized in that, Step seven specifically includes: (7a) Under the UFQ method In the backscatter channel, the proposed ZSTBC exhibits the same SER performance as the Alamouti coding, namely: ， The specific proof is as follows: Under the UFQ method In the backscatter channel, the signals received by the receiver when the tag uses ZSTBC and Alamouti coding are as follows: ， The channel gains achieved by the orthogonal structures of ZSTBC and Alamouti coding are expressed as follows: ； ； Will and Substitute them separately From ; (7b) Under the BUTQ method In the backscatter channel, the proposed ZSTBC exhibits the same SER performance as the Alamouti coding, namely: ， The specific proof is as follows: Under the BUTQ method In the backscatter channel, the signals received by the receiver when the tag uses ZSTBC and Alamouti coding are as follows: ， in , Therefore, when the receiver uses maximum ratio combining reception, the channel gains achievable by ZSTBC and Alamouti coding are expressed as follows: ， ， Will and Substitute them separately From .

5. The time-domain zero-plugging design method for space-time coding in backscatter communication as described in claim 1, characterized in that, Step eight specifically includes: (8a) First, the optimal query antenna is defined. Backscattering channel, with exponential For any m All meet Then The corresponding query antenna is defined as the optimal query antenna corresponding to the l-th tag antenna, where l ;exist In the backscatter channel, the selection rule for the optimal query antenna corresponding to each tag antenna is expressed as follows: ， in The estimated channel after channel estimation for the receiver. The index of the optimal query antenna corresponding to the l-th tag antenna estimated by the receiver through the estimation channel; (8b) with 2. Taking the backscatter channel as an example, this illustrates how the proposed TQAS acts on the ZSTBC. ,Right now and They are respectively The element with the largest median is then represented as the joint design pair of the ZSTBC and TQAS methods: ， For this joint design pair, the signal received by the nth receiving antenna of the receiver is: ， in This represents the signal received by the nth receiving antenna in the tth time slot under the TQAS method. The corresponding noise; (8c) For any l All Therefore, the signal received by the nth receiving antenna is represented as: ， Then, when using maximum ratio combining reception, the channel gain is expressed as... Finally, a maximum likelihood decoder is used for decoding.

6. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor causes the processor to perform the time-domain zero-plugging design method for space-time coding in backscatter communication as described in any one of claims 1 to 5.

7. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the time-domain zero-plugging design method for space-time coding in backscatter communication according to any one of claims 1 to 5.

8. An application of the time-domain zero-plugging design method of space-time coding as described in any one of claims 1 to 5 in multi-antenna backscatter communication.

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