An optimization method for time-modulated array space division multiple access based on finite character input

Abstract

The application discloses a time modulation array space division multiple access optimization method based on limited character input, belongs to the field of space division multiple access technology in wireless communication systems, and constructs a space division multiple access uplink transmission model based on a time modulation array, including a base station end and a user end; the base station end is provided with a uniform linear time modulation array TMA composed of N elements; the time modulation array TMA is in a receiving state when working, and simultaneously performs space division multiple access communication with K mobile users equipped with single antennas at the user end; the base station end of the time modulation array receives signals with K user data, and performs time modulation at a radio frequency front end; a single-pole single-throw SPST radio frequency switch is adopted for the time modulation module, and is controlled uniformly by an FPGA.

Description

Technical Field

[0001] This invention belongs to the field of spatial division multiple access technology in wireless communication systems, and specifically relates to an optimization method for spatial division multiple access based on time modulation array with finite character input. Background Technology

[0002] Space Division Multiple Access (SDMA) technology leverages the spatial diversity of wireless channels to allow multiple users to share the same frequency band for parallel transmission, thereby improving spectral efficiency and system capacity. However, as 6G / B5G networks evolve towards ultra-dense deployments, the number of terminal devices will increase exponentially, increasing the complexity of communication system design and scaling. Therefore, it is necessary to adopt more advanced and efficient methods to maintain performance and reliability. However, traditional MIMO-based SDMA communication systems often require multiple radio frequency chains, leading to a sharp increase in hardware complexity, cost, and power consumption with the surge in the number of devices. This characteristic severely restricts its large-scale deployment capability in ultra-dense scenarios.

[0003] Time-Modulated Arrays (TMAs) dynamically control the operating modes of antenna elements through periodic state modulation of RF switches, generating fundamental and harmonic components with different radiation patterns, providing a low-complexity solution for SDMA. Its core advantage lies in introducing a time dimension as an additional design parameter, requiring only a single RF link to generate a beam containing both fundamental and harmonic components, and flexibly adapting to multi-user channel environments by optimizing switching timing parameters (such as duty cycle and conduction midpoint position). Existing research has verified the feasibility of TMAs in SDMA. For example, a novel multi-user communication system based on a Time-Modulated Ring Array (TMCA) has been proposed in existing technologies, and its effectiveness has been experimentally verified. Existing technologies introduce TMA-based SDMA systems and further enhance the system through comprehensive spectrum analysis and harmonic selection. Furthermore, existing technologies have studied the basic principles and performance of TMA-based MIMO transceivers in multi-user multipath propagation scenarios.

[0004] However, in existing Time-Modulated Array-based Space Division Multiple Access (TMA-SDMA) systems, the technical solutions typically rely on the Gaussian input signal assumption to achieve the theoretical capacity limit, while practical communication systems widely employ modulation schemes with finite character inputs (such as QAM and PSK). Given the distribution difference between Gaussian and finite character signals, there is a significant performance gap between communication systems designed under the Gaussian input assumption and those designed under the finite character input assumption, leading to a disconnect between theory and practice. Traditional methods optimize the RF switching timing of the TMA based on the Gaussian input assumption to maximize the theoretical rate; however, the discrete distribution characteristics of finite character input signals result in a significant rate difference between the practical system and the theoretical capacity limit. Furthermore, for TMA-SDMA systems with finite character inputs, the achievable rate expression is difficult to optimize directly due to its non-closed-form. Existing methods rely on high-dimensional numerical searches or heuristic algorithms, resulting in huge computational overhead and unreliable convergence. Meanwhile, existing optimization algorithms (such as traditional convex optimization or genetic algorithms) are inefficient at solving non-convex coupled problems, making it difficult to meet the requirements for fast beam reconfiguration in real-time communication scenarios, further exacerbating the contradiction between system performance and complexity. These problems collectively limit the application potential of TMA-SDMA technology in practical digital modulation communication scenarios. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide an optimization method for time-modulated array space division multiple access based on finite character input. With the system achievable rate under finite character input constraints as the optimization objective, the modulation timing of the TMA is jointly optimized, thereby further improving the transmission rate of the system.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] An optimization method for time-modulated array space division multiple access based on finite character input.

[0008] Construct a space division multiple access uplink transmission model based on a time modulation array, including a base station and a user terminal. The base station is equipped with a uniform linear time modulation array (TMA) consisting of N array elements. When the time modulation array (TMA) is working, it is in receiving mode and simultaneously communicates with K mobile users equipped with single antennas at the user terminal via space division multiple access.

[0009] The base station of the time modulation array receives a signal with K user data and performs time modulation at the radio frequency front end. The time modulation module uses a single-pole single-throw (SPST) radio frequency switch and is controlled by a single FPGA.

[0010] As a further preferred embodiment of the present invention, assuming that the base station TMA-BS of the time modulation array has channel state information for all users, and the channel from the k-th user to the n-th element of the time modulation array TMA is represented by h. n,k This indicates that the k-th user uses the center frequency f. c Send complex baseband signal s k (t); therefore, the received signal on the nth array element is represented as

[0011]

[0012] Furthermore, the TMA antenna element has an SPST switch at its front end, and each SPST switch is used for square wave modulation via timing control. During each modulation period T... p (for integers) ), switch at t n,on +mT p Always open, in t n,off +mT p It is always turned off; otherwise, it remains disconnected. Therefore, the nth element has a period of T. p The time switching function is

[0013]

[0014] Since the time-switching function is a periodic function, therefore for U n (t) Perform Fourier series expansion

[0015]

[0016] in, Indicates the time modulation frequency. β represents the order of the harmonic frequency components. n,q The coefficients of the q-th order Fourier series on the n-th array element are expressed as follows:

[0017]

[0018] in, Indicates the normalized on-time. Represented as the normalized turn-on intermediate time;

[0019] After passing through the SPST switch, the received signal will be combined into a single RF chain signal by the power divider. Therefore, the modulated single-channel signal in the TMA-based RF front-end is represented as follows:

[0020]

[0021] The modulated single-channel signal is down-converted to complex baseband by the receiver, and then further down-converted to zero frequency by the mixer, and sampled by the analog-to-digital converter (ADC).

[0022] Increase sampling rate f s The receiver obtains the entire signal and then performs a Fourier transform, separating the -Q to Q-order digital harmonic signals. Vector notation is used to represent these digital harmonic signals, and the received signal model is as follows:

[0023] y = BHs + n (6)

[0024] Where s represents the signal vector transmitted by K single-antenna users, it can be expressed as s=[s1,s2,…,s K ] T Matrix H represents the channel matrix from the user to the TMA-BS, defined by H = [h1, h2, ..., h...]. K The following is given: h. k =[h 1,k ,h 2,k ,…,h N,k ] T This represents the channel from the k-th single-antenna user to the TMA-BS. Furthermore, matrix B represents the harmonic characteristic matrix, denoted as...

[0025]

[0026] n is defined as the additive white Gaussian noise vector introduced during the process, ranging from -Q to Q harmonics, and is expressed as follows:

[0027] n = [n -Q ,n -Q+1 ,…,n Q ] T (8)

[0028] Where, n~CN(0,R) out ), R out The covariance of the time-modulated aliasing noise is expressed as follows:

[0029]

[0030] As a further preferred embodiment of the present invention, the number of selected harmonics satisfies 2Q+1≥N.

[0031] As a further preferred embodiment of the present invention, the achievable rate R based on finite character input is calculated:

[0032] The input signal elements are selected from a set of equally probable constellations with cardinality M and unit covariance. The expression for the achievable rate R of the model is:

[0033]

[0034] in, It can be seen that the variables satisfy n′~CN(0,R) out ), and c ij =Hs i -Hs j ;

[0035] Then, using Jensen's inequality, we can obtain an approximate value for the achievable rate R.

[0036]

[0037] As a further preferred embodiment of the present invention, an approximate expression for maximizing the achievable rate is obtained by adjusting the modulation sequence of the time modulation array at the base station, the expression being:

[0038]

[0039] Where, τ={τ n |n∈N} and

[0040] As a further preferred embodiment of the present invention, when calculating the approximate expression for maximizing the achievable rate of the modulation sequence, the block coordinate descent (BCD) method is used to decompose the original problem and handle τ and The coupling between them, for each subproblem, due to its objective function Since the problem is non-convex, the Continuous Convex Approximation (SCA) algorithm is used to make the problem convex.

[0041] As a further preferred embodiment of the present invention, the design of the normalized duty cycle τ is as follows: the optimization of the normalized duty cycle τ is regarded as a power allocation problem among the array elements; therefore, the optimization subproblem is expressed as follows:

[0042]

[0043] The optimization algorithm based on SCA is used to solve this problem. For the objective function (16), when updating the variable τ in the k-th iteration (k>1), Approximated using its first-order Taylor expansion:

[0044]

[0045] Where, τ k-1 This represents the duty cycle after the (k-1)th optimization, where α is a positive constant. express The partial derivative with respect to the normalized duty cycle is expressed as: in, express The partial derivative with respect to the normalized duty cycle on the nth element;

[0046] Therefore, according to formula (17), the SCA-based proxy problem for this subproblem can be expressed as follows:

[0047]

[0048] Since problem (22) is a strictly concave function with convex constraints, the solution to τ can be obtained by using the CVX tool or the Lagrange multiplier method.

[0049] As a further preferred embodiment of the present invention, the normalized conduction intermediate time is... Design: Substitute the optimized τ into the optimization objective to normalize the conduction intermediate time of the TMA elements. Optimization is then performed, and the optimization problem at this point is as follows:

[0050]

[0051] For the objective function (23), the variables are updated in the k-th iteration (k>1). hour, Approximated using its first-order Taylor expansion

[0052]

[0053] in, This represents the intermediate moment of conduction after the (k-1)th optimization. express The partial derivative with respect to the normalized conduction midpoint is expressed as: in, express The partial derivative with respect to the normalized conduction intermediate time relative to the nth element,

[0054] Therefore, according to formula (24), for the design of the normalized turn-on intermediate time, the surrogate problem based on SCA is expressed as follows:

[0055]

[0056] Problem (29) is a strictly concave function associated with convex constraints, therefore The solution can be obtained using CVX tools or the Lagrange multiplier method.

[0057] The beneficial effects of this invention are as follows:

[0058] This invention provides an optimization method for time-modulated array (TMA) spatial division multiple access (SDMA) based on finite character input. Using the achievable rate of the model under finite character input constraints as the optimization objective, it jointly optimizes the modulation timing of the TMA, further improving the system's transmission rate. Compared with existing technologies, the achievable rate-based optimization scheme under finite character input constraints significantly outperforms traditional capacity optimization methods. Simulations demonstrate a significant performance gain, proving that optimizing the TMA modulation sequence design can effectively improve the achievable rate of SDMA. This scheme achieves a lower symbol error rate for dual users while minimizing the performance gap between users compared to comparative schemes.

[0059] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0060] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0061] Figure 1 This is a system model diagram of space division multiple access uplink communication based on time modulation array;

[0062] Figure 2 This is a block diagram of a receiver based on a time-modulation array.

[0063] Figure 3 The achievable rates, corresponding approximations, and capacity plots obtained from Monte Carlo simulations are shown.

[0064] Figure 4 A graph showing the relationship between the achievable system rate and user transmit power under different optimization schemes;

[0065] Figure 5 A graph showing the relationship between the system's achievable data rate and the user's transmit power under different transmission schemes;

[0066] Figure 6 This is a graph showing the relationship between user symbol error rate and user transmit power under different transmission schemes. Detailed Implementation

[0067] like Figures 1-6 As shown, this invention proposes a time modulation timing optimization method under finite character input constraints, and its direct application scenario is a multi-user wireless communication system using digital modulation technology (such as QAM, PSK).

[0068] This invention establishes a model of a space division multiple access uplink transmission system based on a time-modulated array. Based on this model, the achievable rate of the system is analyzed from the perspective of finite character input. However, since the rate expression is not closed-form, the optimization calculation is very difficult. This invention utilizes Jensen's inequality to obtain an approximate value of the achievable rate, thereby simplifying the parameter optimization process. Furthermore, to improve the system's achievable rate performance, a time-modulated timing optimization method based on finite character input is proposed. Compared with the traditional optimization method based on the Gaussian input assumption, this method can further improve the system's achievable rate performance. To achieve the above objectives, this invention provides the following solution:

[0069] 1. For example Figure 1 As shown, an uplink scenario based on a time-modulated array (TMA) spatial division multiple access (SDMA) is considered. The base station is configured with a uniform linear TMA consisting of N array elements. The TMA operates in receive mode and simultaneously communicates with K mobile users equipped with single antennas via SDMA. The block diagram of the TMA-based receiver in the proposed SDMA uplink scenario is shown below. Figure 2 As shown, the TMA-BS receives a signal with K user data points and performs time modulation at the RF front end. The time modulation module is a single-pole single-throw (SPST) RF switch, controlled by a single FPGA.

[0070] 2. Spatial Division Multiple Access (SDMA) Receiving Signal Model Based on Time Modulation Array:

[0071] Assuming the TMA-BS has channel state information for all users, the channel from the k-th user to the n-th element of the TMA can be represented by h. n,k Indicated. The k-th user uses the center frequency f c Send complex baseband signal s k (t).

[0072] Therefore, the received signal on the nth array element can be expressed as

[0073]

[0074] The front end of the TMA antenna element is equipped with an SPST switch, and each SPST switch achieves square wave modulation through special timing control. In each modulation period T... p (for integers) ), switch at t n,on +mT p Always open, in t n,off +mT p It is always turned off; otherwise, it remains disconnected. Therefore, the nth element has a period of T. p The time switching function is

[0075]

[0076] Since the time-switching function is a periodic function, therefore U n (t) can be expanded by a Fourier series as follows

[0077]

[0078] in, Indicates the time modulation frequency. β represents the order of the harmonic frequency components. n,q The coefficients of the q-th order Fourier series on the n-th array element are expressed as follows:

[0079]

[0080] in, Indicates the normalized on-time. This represents the normalized turn-on intermediate time.

[0081] After passing through the SPST switch, the received signal will be combined into a single RF chain signal by the power divider. Therefore, the modulated single-channel signal in the TMA-based RF front-end can be represented as:

[0082]

[0083] The modulated single-channel signal is down-converted to complex baseband by the receiver, then further down-converted to zero frequency by the mixer, and sampled by the analog-to-digital converter (ADC). This process is repeated as long as the sampling rate f... s If the signal is sufficiently high, the receiver can acquire the entire signal. Then, by performing a Fourier transform, the receiver can separate the -Q to Q-order digital harmonic signals. Using vector notation to represent digital harmonic signals from -Q to Q, the received signal model can be written as follows:

[0084] y = BHs + n (6)

[0085] Where s represents the signal vector transmitted by K single-antenna users, which can be expressed as s=[s1,s2,…,s K ] T Matrix H represents the channel matrix from the user to the TMA-BS, defined by H = [h1, h2, ..., h...]. K The following is given: h. k =[h 1,k ,h 2,k ,…,h N,k ] T This represents the channel from the k-th single-antenna user to the TMA-BS. Furthermore, matrix B represents the harmonic characteristic matrix, which can be expressed as...

[0086]

[0087] n is defined as the additive white Gaussian noise vector introduced during the process, ranging from -Q to Q harmonics. It is statistically independent of the incident signal and can be expressed as...

[0088] n = [n -Q ,n -Q+1 ,…,n Q ] T (8)

[0089] Where, n~CN(0,R) out ),R out The covariance of the time-modulated aliasing noise is expressed as follows:

[0090]

[0091] As shown in (6), BH can be regarded as the equivalent channel between the user and TMA-BS. In order to avoid the rank deficiency of the equivalent channel and to ensure that the main beam mode of the selected harmonics covers all angles to receive signals from all directions, the number of selected harmonics should satisfy 2Q+1≥N.

[0092] 3. Derivation of achievable rate based on finite character input

[0093] The input signal elements are selected from a set of equally probable constellations with cardinality M and unit covariance, such as PSK or QAM. In this context, the achievable rate R of the proposed system is given by the mutual information between the transmitted signal s and the received signal y, and its expression is:

[0094] R = I(y; s) = h(y) - h(n) (10)

[0095] This expression holds true if the received noise *n* is independent of the received signal *y*. The differential entropy *h(n)* of the received noise *n* is:

[0096]

[0097] The differential entropy h(y) of the received signal y can be expressed as:

[0098]

[0099] in, It can be seen that the variables satisfy n′~CN(0,R) out Substituting equations (11) and (12) into equation (10), the expression for the achievable rate R of the TMA-based SDMA system is obtained as follows:

[0100]

[0101] Where, c ij =Hs i-Hs j However, since the reachable rate R of the system involves the mathematical expectation operator, formula (13) is difficult to obtain through a finite number of elementary calculations, which complicates parameter optimization. Therefore, an approximate value for the reachable rate R is obtained through the Jensen inequality.

[0102]

[0103] 4. Optimization Objective: Maximize the achievable rate by adjusting the modulation sequence of the TMA on the BS. Since the achievable rate has a non-closed form and involves a difficult-to-handle logarithmic expectation, this invention uses an approximation of the achievable rate (14) to optimize the variables in order to reduce computational complexity. Specifically, the mathematical expression for this problem is:

[0104]

[0105] Where, τ={τ n |n∈N} and The constraints specify the switching timing limitations of TMA time modulation. The proposed problem is a non-convex optimization problem, its non-convexity stemming from... Caused by. Furthermore, considering τ and The coupling between them makes the optimization problem more challenging.

[0106] 5. Modulation-Timing Joint Optimization Algorithm

[0107] Problem (15) is a modulation timing joint design problem, namely, finding the normalized duty cycle τ and the normalized intermediate time of conduction. In order to handle τ and To address the coupling between subproblems, this invention uses the BCD method to decompose the primal problem. For each subproblem, due to its objective function... Since the problem is non-convex, the SCA algorithm is used to make it convex.

[0108] 1) Design of Normalized Duty Cycle: Since this subproblem is a non-convex function related to the normalized duty cycle, a solution based on SCA is proposed. Due to the specific setting of the normalized turn-on center time, the optimization of the normalized duty cycle τ can be regarded as a power allocation problem among the array elements. Therefore, the optimization subproblem can be expressed as follows:

[0109]

[0110] st0≤τ≤1

[0111] Since the original problem is nonconvex, it can be solved using an optimization algorithm based on SCA. For the objective function (16), when updating the variable τ in the k-th iteration (k>1), It can be approximated using its first-order Taylor expansion:

[0112]

[0113] Where, τ k-1 This represents the duty cycle after the (k-1)th optimization, where α is a positive constant. express The partial derivative with respect to the normalized duty cycle can be expressed as: in, express The partial derivative of the normalized duty cycle with respect to the nth element is expressed as follows:

[0114]

[0115] in, The partial derivative of the harmonic characteristic matrix with respect to the normalized duty cycle at the nth element is expressed as follows:

[0116]

[0117] matrix The partial derivative of the noise covariance matrix with respect to the normalized duty cycle at the nth element can be expressed as:

[0118]

[0119] in, express Relative to τ n The gradient of the i-th, j-th term is expressed as:

[0120]

[0121] Therefore, according to formula (17), for this subproblem, the SCA-based proxy problem can be expressed as follows:

[0122]

[0123] st0≤τ≤1

[0124] Since problem (22) is a strictly concave function with convex constraints, the solution to τ can be easily obtained by CVX tools or the Lagrange multiplier method.

[0125] 2) Design of Normalized On-Time Intermediate Moments: Substitute the optimized τ into the optimization objective to optimize the normalized on-time intermediate moments of the TMA elements. The optimization problem can then be written as...

[0126]

[0127] Similar to the previous optimization problem, this subproblem is a non-convex function related to the intermediate time of normalized conduction of TMA elements. The SCA method is still used, and the specific details of the cost function and surrogate problem are as follows. For the objective function (23), the variables are updated in the k-th iteration (k>1). hour, Its first-order Taylor expansion can be used to approximate it.

[0128]

[0129] in, This represents the intermediate moment of conduction after the (k-1)th optimization. express The partial derivative with respect to the normalized conduction midpoint can be expressed as: in, express The expression for the partial derivative with respect to the normalized turn-on intermediate time relative to the nth element is as follows:

[0130]

[0131] in, The partial derivative of the harmonic characteristic matrix with respect to the normalized turn-on midpoint with respect to the nth element is expressed as follows:

[0132] matrix The partial derivative of the noise covariance matrix with respect to the normalized turn-on midpoint at the nth element can be expressed as:

[0133] in, express Compared to The gradient of the i,j term. In τ n When ∈(0,1), The expression is

[0134]

[0135] When τ n =0 or 1, Therefore, according to formula (24), for the design of the normalized conduction intermediate time, the surrogate problem based on SCA can be expressed as follows:

[0136]

[0137] Similar to the previous optimization problems, problem (29) is a strictly concave function with convex constraints, therefore The solution can be easily obtained using CVX tools or the Lagrange multiplier method.

[0138] This invention takes the achievable system rate under finite character input constraints as the optimization objective and performs joint optimization of the modulation timing of TMA, thereby further improving the system's transmission rate.

[0139] To verify the accuracy of the achievable rate approximation, Figure 3 Three transmission scenarios (QPSK, BPSK, and Gaussian input) were considered. In these scenarios, the conduction time of each array element was the same. And it adopts a one-by-one conduction sequence. (By...) Figure 3 As shown, for QPSK and BPSK inputs, the approximate achievable rate is very close to the actual achievable rate simulated by the Monte Carlo method. Clearly, the computational task of deriving the approximate achievable rate is not as complex as that of deriving the actual achievable rate simulated by the Monte Carlo method. Furthermore, there is a performance gap between the system capacity under Gaussian input and the system achievable rate under finite character input constraints. This gap widens with increasing user transmit power.

[0140] To evaluate the achievable rate performance under finite character input constraints Figure 4 The achievable rate of user-transmitted BPSK signals as transmit power increases was compared under different input assumptions and TMA timing optimizations. Figure 4 It can be seen that, for both system and rate, the achievable rate-based optimization scheme under finite character input constraints significantly outperforms the traditional capacity optimization method. This is attributed to the explicit introduction of BPSK modulation constraints during the optimization process, ensuring a strict match between the receiving strategy and the finite constellation signal structure. For different user rates, within the power range of -2 to 14 dBm, the achievable rate scheme achieves a more balanced user rate allocation. In contrast, the capacity optimization scheme is completely unable to activate users with poor channel conditions (User 1). This is because, in actual BPSK signal transmission, the achievable rate scheme allocates additional power to weaker channels that are far from saturation. Furthermore, the capacity optimization scheme is essentially geared towards optimal configuration for Gaussian input signals and lacks sensitivity to finite constellation signals.

[0141] Figure 5This paper compares the performance of different transmission schemes under BPSK signal input, showing the achievable rate of users as a function of transmit power. All schemes employ a single-radio link for multi-user communication. Simulation results show that the achievable rate of each scheme monotonically increases with increasing transmit power. Notably, as transmit power increases, the scheme using single-radio NOMA communication and this paper approach the theoretical limit, while the scheme using single-radio TDMA communication only converges to log2M. This difference stems from the time-slot exclusivity of the TDMA framework—each time slot can only serve a single user. In particular, compared to the existing TMA-SDMA scheme, this paper exhibits a significant performance gain, demonstrating that optimizing the TMA modulation sequence design can effectively improve the achievable rate of the SDMA system.

[0142] To evaluate the bit error rate performance under finite character input constraints, Figure 6 This demonstrates the impact of different transmission schemes on the user's symbol error rate (SER). For example... Figure 6 As shown, when BPSK modulation is used as the user input signal, this scheme significantly outperforms the existing TMA-SDMA benchmark scheme and the single-radio NOMA communication scheme within the indicated transmit power range. Notably, this scheme achieves a lower symbol error rate for both users while minimizing the performance gap between users compared to the comparison schemes. This performance advantage highlights the effectiveness of time-domain modulation optimization in suppressing multi-user interference. Although the existing TMA-SDMA benchmark employs multi-antenna spatial multiplexing technology, the SER (Self-Signal Rate) of the user with better channel conditions (User 2) is actually higher than that of the user with poorer channel conditions, reflecting that the potential of spatial multiplexing has not been effectively explored. In contrast, while the single-radio NOMA communication scheme provides a steep SER decrease curve for User 2 with better channel conditions, it offers limited performance improvement for User 1 with weaker channels, exposing the inherent asymmetry of power domain multiplexing.

[0143] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A time modulation array space division multiple access optimization method based on limited character input, characterized in that: Construct a time modulation array-based space division multiple access uplink transmission model, including a base station end and a user end, the base station end is provided with a uniform linear time modulation array TMA composed of N Array elements, the time modulation array TMA works in a receiving state, and simultaneously performs space division multiple access communication with K A mobile user equipped with a single antenna at the user end; The base station end of the time modulation array receives a signal with K user data, and performs time modulation at a radio frequency front end. The time modulation module uses a single-pole single-throw (SPST) radio frequency switch and is controlled by a field programmable gate array (FPGA). Assume the time modulation array base station TMA-BS has channel state information for all users, the first... The first user to the time modulation array TMA The channel on each element is used Indicates; the Individual users at center frequency Send complex baseband signals Therefore, the first The received signal on each element is represented as （1） and the front end of the TMA antenna element is provided with an SPST switch, each SPST switch is square wave modulated by timing control, in each modulation period , for integer , the switch is opened at , closed at , and otherwise remains in an open state, therefore, the first array element has a time switch function with a period of . （2） Since the time switch function is a periodic function, the Fourier series expansion is performed on the time switch function （3） wherein, denotes the time modulation frequency, denotes the order of the harmonic frequency component; denotes the Fourier series coefficient of order on the th array element, which is expressed as （4） wherein, denotes the normalized on-time, denotes the normalized on-time mid-point; After the SPST switch, the received signal will be combined into a radio frequency chain signal by the power divider, therefore, the modulated single channel signal in the radio frequency front end based on TMA is represented as （5） The modulated single channel signal is down-converted to complex baseband by the receiver, and then further down-converted to zero frequency by the mixer, and sampled by the analog-to-digital converter ADC; Increasing the sampling rate The receiving end obtains the entire signal and then performs Fourier transform, and the receiving end separates out to the digital harmonic signal of the order, and the receiving signal model is to the digital harmonic signal of the order, and the receiving signal model is （6） in, express K The signal vector transmitted by a single-antenna user can be represented as: ,matrix This represents the channel matrix from the user to the TMA-BS, composed of... Given, where, Represented as the first k A single-antenna user to TMA-BS channel, in addition, matrix The harmonic characteristic matrix is ​​represented as follows: （7） is defined as the additive white Gaussian noise vector introduced in the process from to the kth order harmonic, denoted as （8） wherein , denotes the covariance of the aliasing noise after time modulation, which is expressed as （9） The number of selected harmonics satisfies ; Computing achievable rates based on limited character input : The input signal elements are chosen from a set of equally probable constellations of cardinality M and with unit covariance, the achievable rate of the model is given by the expression （13） wherein, It can be seen that the variables satisfy and ; The achievable rate is obtained by Jensen's inequality is approximated by （14） 2. The method of claim 1, wherein: By adjusting the modulation sequence of the base station end time modulation array, the approximate expression of the maximum achievable rate is maximized, which is: （15） wherein and | .

3. The method of claim 2, wherein: In computing the modulation sequence maximizing the achievable rate approximation expression, the block coordinate descent (BCD) method is used to decompose the original problem, handling the coupling between and For each sub-problem, since its objective function is non-convex, the successive convex approximation (SCA) algorithm is used to convexify the problem.

4. The time modulation array space division multiple access optimization method based on limited character input according to claim 2, characterized in that: Normalized on-time duty cycle Design: Normalized on-time duty cycle Optimization of the normalized on-time duty cycle is considered as a power allocation problem among the individual elements. Therefore, the optimization sub-problem is expressed as （16） Using the SCA-based optimization algorithm to solve for the objective function (16), at the k first iteration update the variable , , using its first order Taylor expansion to approximate: （17） wherein, denotes the on-duty cycle after the th optimization, is a positive constant, denotes the partial derivative of the normalized on-duty cycle with respect to the wherein, denotes the partial derivative of the normalized on-duty cycle with respect to the th element; Therefore, according to formula (17), for this sub-problem, the proxy problem based on SCA is expressed as （22） Since problem (22) is a strictly concave function with convex constraints, the solution is obtained by CVX tool or Lagrange multiplier method. The solution is obtained by CVX tool or Lagrange multiplier method.

5. The time modulation array space division multiple access optimization method based on limited character input according to claim 4, characterized in that: Normalized on-time mid-point Design: the optimized TMA element is brought into the optimization objective, and the normalized on-time mid-point of the TMA element is optimized. The optimization problem at this time is shown below （23） For the objective function (23), at the k second iteration update variable , , is approximated using its first order Taylor expansion （24） wherein, denotes the on-intermediate time after the first optimization, denotes the partial derivative of the normalized on-intermediate time with respect to the wherein, denotes the partial derivative of the normalized on-intermediate time with respect to the element, Therefore, according to formula (24), for the normalized on-off intermediate time design, the proxy problem based on SCA is expressed as （29） Problem (29) is a strictly convex function with respect to the convex constraint, thus the solution is obtained by the CVX tool or the Lagrange multiplier method.

Images