A beam codebook design method based on a terahertz MIMO system

Abstract

The application belongs to the technical field of terahertz communication, and particularly relates to a beam codebook design method based on a terahertz MIMO system. Due to the serious scattering and reflection loss of terahertz waves, line-of-sight communication is considered as the main communication mode of the terahertz multiple-input multiple-output system. Beam training does not need to utilize channel state information, and beam alignment can be realized by designing beam code words, so as to complete line-of-sight communication. In the codebook design, narrow beams can be realized by array response vectors, and for the design of wide beams, a low-complexity algorithm in real-time state, i.e. a symmetric array vector summation algorithm, is proposed, which can approximate the wide beam in the ideal case. The algorithm has good performance in terms of beam pattern error, and has the advantage of low complexity compared with the auxiliary target tracking algorithm based on successive convex approximation, thereby providing a favorable reference for the beamforming technology of terahertz communication.

Description

Technical Field

[0001] This invention belongs to the field of terahertz communication technology, specifically relating to a beamcodebook design method based on a terahertz MIMO system. Background Technology

[0002] Terahertz waves are electromagnetic waves with frequencies ranging from 0.1T to 10THz. Due to their high frequency, high spatial resolution, and strong security, they have broad application prospects in communications, medicine, and security. Multiple-input multiple-output (MIMO) technology, employing dozens or hundreds of antenna elements to enhance array gain, is considered a promising technology in terahertz systems. Because of the short wavelength of terahertz waves, a large number of antenna elements can be packaged in a small array with a half-wavelength antenna spacing, thus helping to compensate for severe transmission losses. Early beam training often used exhaustive search methods, resulting in excessively long training times, making them unsuitable for terahertz communication. To reduce the overhead of beam training, multi-stage beam training combined with wide beams has been widely applied to terahertz MIMO systems. However, most existing multi-stage beam training methods are heuristic or based on exhaustive search, and their performance is judged by observing the beam pattern. Currently, there is still a lack of accurate mathematical metrics for beam training performance and corresponding beam training algorithms. Summary of the Invention

[0003] To address the multi-stage beam training problem in terahertz MIMO communication systems, this invention proposes a beam codebook design method, namely the sum of symmetrical array response vectors (S-SARV). This algorithm is suitable for real-time design and has the advantage of low complexity. Wide beam codewords are predefined in the codebook for wide beam design. Based on convex optimization techniques, the S-SARV algorithm is developed with high performance as the goal.

[0004] The technical solution of this invention is:

[0005] A beamcodebook design method based on a terahertz MIMO system is proposed, defining the antenna arrays at both the transmitter and receiver ends of the system as uniform linear arrays, with the transmitter having N... t There are N antennas and N receivers. r One antenna, the channel is a narrowband terahertz communication channel, and the beamcodebook design method is as follows:

[0006] A tritree hierarchical codebook is used to design a wide beam at the upper layer through a narrow beam at the lower layer, specifically defined as follows: This represents the s-th codeword of the n-th layer, S = log3. N represents the bottom layer, i.e., the narrow beam layer. The top layer, the wide beam, is designed from the S-th layer upwards based on the ternary tree structure. ω(θ) is defined.- ,θ ) ) represents wide-beam codeword, θ - ,θ ) Representing the left and right angles of the beam, under ideal beam conditions, [θ] - ,θ ) Within the specified range, the radiated energy of the beam is γ. A model for approximating an ideal beam with a wide beam is established as follows:

[0007]

[0008]

[0009]

[0010] Where, ε{ω(θ) - ,θ ) )} is an error metric describing the difference between the ideal beam and the actual beam.

[0011]

[0012] It is the value of radiant energy that varies with angle. It is a predefined narrow-beam codebook;

[0013] Solving the model yields the wide-beam codeword, specifically:

[0014] Define the angle to the left of the beam transmission midpoint and the angle to the right of the beam transmission midpoint

[0015]

[0016] exist In sinusoidal space, a narrow beam is uniformly divided into M points, resulting in the beam angle distribution as follows: in

[0017]

[0018] Narrow beam superposition Obtain the wide-beam codeword ω(θ) - ,θ ) Let ω m The phase shift of the m-th narrow beam is expressed as:

[0019]

[0020] Where β represents the power scaling factor;

[0021] Define f(x) = sinx, and substitute it into... and Afterwards, ω(θ) is re-adjusted. - ,θ ) ) is represented as:

[0022]

[0023] in For symmetric array vectors:

[0024]

[0025] The phase at the midpoint of the array is 0, and the parameters are...

[0026] Set β to:

[0027]

[0028] The final wide-beam codeword is:

[0029] The beneficial effects of this invention are as follows: Based on the leading advantages of terahertz communication massive MIMO systems, this invention designs beamcodebooks. It provides a design error metric for wide-beam codewords and, based on this, presents a symmetric array vector summation algorithm, namely the S-SARV algorithm, which can quickly derive the optimal wide-beam codeword in the real-time design of multi-antenna arrays. This algorithm is suitable for real-time design, providing the optimal wide-beam codeword in real-time conditions for application in terahertz communication, thus providing a valuable reference for beam design methods in terahertz MIMO communication systems. Attached Figure Description

[0030] Figure 1 This is a diagram of the ternary tree hierarchical codebook of the present invention.

[0031] Figure 2 This is a simulation diagram of the beam design of the present invention.

[0032] Figure 3 This is a diagram showing the amplitude calculation in the direction of the present invention.

[0033] Figure 4 This is a graph showing the amplitude calculation of the edge of the transition range of the present invention.

[0034] Figure 5 This is a comparison chart of beam amplitude under different algorithms of this invention.

[0035] Figure 6 This is a graph showing the average running time of different algorithm designs in this invention. Detailed Implementation

[0036] The effectiveness and practicality of the present invention will be demonstrated below with reference to the accompanying drawings and embodiments:

[0037] Narrow beams are formed by array response vectors. This invention proposes a Beampattern Error (BPE) metric for wide beam design, which describes the difference between the actual beam pattern and the ideal beam pattern, i.e., the mean square error. Considering the finite resolution of the actual beam pattern, a transition range is introduced into the ideal beam pattern, the length of which can be characterized as half the beamwidth of the narrow beam. The wide beam design problem is formulated as minimizing the BPE while optimizing the beam pattern within the transition range.

[0038] The application scenario of the method of this invention is as follows: Consider a terahertz communication MIMO system, where the antenna arrays at the transmitting and receiving ends are uniform linear arrays (ULA), and the transmitting end has N... t There are N antennas and N receivers. r One antenna, the channel is a narrowband terahertz communication channel.

[0039] During beam training, the receiver receives the signal as follows:

[0040]

[0041] Where P is the transmission power and s is the training pilot signal. These are the normalized beamforming vector and the combination vector. H LoS and H NLoS This corresponds to the line-of-sight transmission channel matrix and non-line-of-sight transmission. It is a noise vector. The line-of-sight channel matrix is... Where a(f,d) is the path loss, including free space propagation loss and molecular absorption loss. and These are the Angle of Arrival (AoA) and the Angle of Departure (AoD). Path loss. Where c, f, τ(f), and d represent the speed of light, signal frequency, medium absorption factor, and transmission distance, respectively. There is N t The array response vector of each antenna.

[0042] Because pilot signals suffer severe path loss in terahertz channels, transceivers may be unable to effectively estimate the channel matrix. Therefore, during beam training, the system needs to guide narrow beam pairs along the Loss of State (LoS) link to find a high-quality beamformer and corresponding combiner under conditions of unknown Channel State Information (CSI).

[0043]

[0044] F and W are predefined narrow-beam codebooks for the transmitter and receiver, respectively. If beam training is achieved by exhaustively searching all narrow beam pairs in the narrow beam codebook, the time consumption would be too long, making it unsuitable for high-speed communication systems. Therefore, multi-level beam training is an effective way to reduce search complexity and time consumption.

[0045] In this invention, a narrow-beam design at the bottom layer and a wide-beam design at the top layer are employed, using a tritree hierarchical codebook. This codebook has unique advantages compared to the traditional binary hierarchical design. Representing the s-th codeword at level n, the structure of the ternary tree hierarchical codebook is as follows: Figure 1 As shown. Here, S = log3 N represents the bottom layer, i.e., the narrow beam layer. The design of the upper wide beam layer is obtained through mathematical derivation.

[0046] Let ω(θ) - ,θ ) ) represents wide-beam codeword, θ - ,θ ) Represents the left and right corners of the beam. In the case of an ideal beam, it is desirable to achieve [θ] - ,θ + Within the range, the beam's radiated energy is γ; Within the range, the beam's radiated energy gradually decreases from γ to 0; That is, within the beam edge range, the beam radiation energy is 0. The actual beam will differ from the ideal beam described above; therefore, this invention aims to design a wide beam ω(θ). - ,θ + This invention proposes a BPE (Browser Optimization and Precision) error metric to describe the difference between the ideal beam and the actual beam. For a wide beam, ω(θ)... - ,θ + Its BPE metric value is

[0047]

[0048] It is the value of radiant energy that varies with angle. Therefore, the problem of approximating an ideal beam with a wide beam can be written as:

[0049]

[0050] Within the energy decay range, i.e. and The range should be no less than the array beam resolution, which is the distance between the peak and the first null. In this invention, it is set and for like Figure 2 As shown, it demonstrates The ideal beam and the actual beam pattern.

[0051] For a real-time system that uses arbitrary parameters to compute codewords, the SCA-ATP algorithm is unsuitable for real-time implementation due to its high time consumption. To overcome this limitation, the S-SARV algorithm is proposed below.

[0052] First, define and The midpoint of the transmission range, i.e.

[0053]

[0054] Then In sinusoidal space, a narrow beam is uniformly divided into M points, resulting in the beam angle distribution as follows:

[0055]

[0056] Then, the narrow beam is superimposed. Obtain the wide-beam codeword ω(θ) - ,θ + Let ω m To represent the phase shift of the m-th narrow beam, the codeword can be expressed as:

[0057]

[0058] Here, β represents the power scaling factor. The following section will explain how to implement a wide-beam design and how to define the factor β and the phase shift. First, define a phase shift and assume β = 1 for ease of explanation. Codeword ω(θ) - ,θ + The beam pattern in the θ direction can be represented as follows.

[0059]

[0060] Define the following two formulas

[0061]

[0062]

[0063] Therefore, Equation 6 can be simplified to...

[0064]

[0065] Since T(x) is an even function, S m It can be by It is derived from sinθ, that is

[0066]

[0067] Substituting formula 4 into formula 9, we can see that the function T(S) m The M points in the equation have equal spacing, i.e.

[0068]

[0069] To make Formula 9 more concise, we use f(x) to represent the sine function, i.e.

[0070] f(x) = sinx. (Formula 14)

[0071] Formula 9 can be written as

[0072]

[0073] The last item is by get.

[0074] Figure 3 The result of formula 9 can be considered as the scale representing... The range of T(x) is given, and the peak value of T(x) indicates the direction of θ. According to Formula 13, we know... and and all {S m} m They all have the same spacing. Therefore, the circles under the scale can represent T(S1) to T(S) M All values ​​of ) can be calculated by adding the values ​​of M circles. - ,θ + Each circle has a phase shift e, θ). jc(m) .

[0075] Figure 3 In the two cases shown, θ∈[θ] can be understood. - ,θ + When [the value of T(x)] is below the scale, the peak value of T(x) remains below the scale. At that time, the peak value is not below the scale. By appropriately selecting e... jc(m) Hopefully for [θ] - ,θ + For any θ in ], the sum of M circles (with phase shift) is large. Therefore, corresponding to positive {T(S m )} m The phases are expected to be in the same phase, and the only solution is to set

[0076]

[0077] Thus, since the circle value on the primary leaf is greater than the circle value on the lateral leaf, θ∈[θ - ,θ + The amplitude of the beam pattern is much greater than

[0078] Note 1. The solution to Formula 14 makes all e jc(m) They are all the same. And... Figure 3 In the diagram, some circles represent negative values, which decreases the sum. In this respect, it should be mentioned that although... There is a solution to convert these negative values ​​to positive values; however, this solution cannot be used for all θ∈[θ]. - ,θ + By multiplying all the circles by the same phase, i.e., using Equation 14, another advantage is the magnitude of the amplitude. The sum of positive values ​​is close to zero because the circle lies on the lateral leaflet, and the sum of negative values ​​is approximately equal to the sum of positive values. This explains why Equation 15 can produce a broad beam pattern that approximates the ideal solution.

[0079] Substituting Formula 14 into Formula 5, the codeword can be rewritten in a concise form, namely...

[0080]

[0081] definition It is a symmetric array vector, that is

[0082]

[0083] The phase at the midpoint of the array is 0, and the parameters are...

[0084] Next, we will explain why and Set as Figure 4 The endpoints of the scale. Regarding ω(θ) - ,θ + Regarding the beam pattern, it is hoped that The upward range is quite large, and The amplitude on is close to zero, which indicates that from θ- to θ * - (or from θ) + to θ * + The magnitude of ) will decrease significantly. Let Let θ be the left endpoint of the scale. Taking Formula 14 as an example, then from θ... - to θ * - The amplitude difference can be written as:

[0085]

[0086] The choice of the left endpoint is equivalent to solving

[0087]

[0088] Through one-dimensional search, the optimal solution to Equation 18 is obtained as follows: Right now Similarly, the optimal choice for the right endpoint is To better understand the optimization in Equation 18, Figure 4 It shows that at θ - and θ * - Calculation of magnitude in direction. The scale in case 2 can be obtained by referring to the scale in case 1. The scale is moved to the right to obtain the amplitude interval. The main characteristic of the amplitude interval is the sum of the dots, lines, and circles. When... Similar to Case 1, the circle in Case 2 is located near the peak of the main leaf, thus producing the largest amplitude interval.

[0089] Finally, the following propositions determine β.

[0090] Proposition 1. To make the main lobe size close to that of a beam pattern with γ, the power scaling factor β of S-SARV is:

[0091]

[0092] Proof: Define a function f(θ) = πsinθ and let P f (ω(θ - ,θ + As energy in beam mode, i.e.

[0093]

[0094] By restating the codeword energy and beam pattern energy, P can be... f (ω(θ - ,θ + Rewritten as

[0095]

[0096] The last equation is based on Passevar's theorem, that is...

[0097]

[0098] For any vector Both hold true. On the other hand, the energy of the beam model can be approximated as...

[0099]

[0100] Substituting Formula 22 into Formula 21, the energy of a codeword can be written as follows:

[0101]

[0102] This completes the proof.

[0103] The proposed S-SARV algorithm is very simple, with a computational complexity of O(MN). t Even if N t The S-SARV algorithm is very large, with thousands of antennas, and can also be used for offline design, while the SCA-ATP algorithm cannot output the target codeword in the required time.

[0104] In the algorithm, N t Where θ is the number of transmitting antennas, M is the number of elements in the linear array, and θ is the number of transmitting antennas. - θ + γ represents the angles to the left and right of the beam, and γ is the maximum value of the radiated energy amplitude within the beamwidth.

[0105] Example

[0106] This embodiment uses N t =32, M=64, γ=1, For example, the implementation steps are as follows:

[0107] Step 1: Calculate the angle to the left of the beam transmission midpoint using Formula 5. and the angle to the right of the beam transmission midpoint

[0108] Given condition N t θ - θ + It can be found

[0109]

[0110] Step 2: Calculate the beam angle distribution using Formula 6.

[0111] According to the formula and the transmission angle obtained in step 1 and Calculate the beam angle

[0112] Step 3: Let Substituting into the formula, we get

[0113] Step 4: Calculation

[0114] Step 5: Obtain the wide-beam codeword

[0115] The beam pattern is obtained from the wide-beam codeword derived by the SCA-ATP algorithm. Four traditional algorithms proposed by researchers are presented here: Real-Objective Pursuit (ROP), Complex-Objective Pursuit (COP), Sum Narrow Beams (SNB), and Sum Narrow Beams with Gradient Phases (SNB-GP). The performance of the S-SARV algorithm proposed in this invention is compared with these four algorithms. Figure 5 As shown, the codewords of the S-SARV proposed in this invention have high performance because its main leaf is flatter than all benchmarks and its lateral leaves are well suppressed.

[0116] To compare computational complexity, the average runtime of different wide-beam designs is shown, with all algorithms executed on a 3.20GHz AMD Ryzen 7 5800HPC with 32GB of RAM. Figure 6 The average running time of different algorithms with more than 100 antennas is plotted in the figure, let θ - = -π / 6, θ + =π / 6, γ = 1, N t =32, M=2N t It can be seen that the running time of COP, SNB-GP, and SCA-ATP varies with N. t The runtime increases significantly with the increase of N. Therefore, these algorithms are not suitable for large-scale MIMO systems that require online design of dynamic wide beams. In contrast, ROP, SNB, and S-SARV have much lower runtimes, i.e., when N... t When the value is 100, they are all below 0.01 seconds. However, it can be seen from the beam pattern and BPE that the performance of ROP and SNB is unacceptable. Therefore, the proposed S-SARV algorithm is the only effective solution to date for real-time wide-beam design.

Claims

1. A beamcodebook design method based on a terahertz MIMO system, defining the antenna arrays at both the transmitter and receiver ends of the system as uniform linear arrays, with the transmitter having N... t There are N antennas and N receivers. r One antenna, the channel is a narrowband terahertz communication channel, characterized in that... include: A tritree hierarchical codebook is used to design a wide beam at the upper layer through a narrow beam at the lower layer, specifically defined as follows: This represents the s-th codeword of the n-th layer, S = log3. N represents the bottom layer, i.e., the narrow beam layer. The top layer, the wide beam, is designed from the S-th layer upwards based on the ternary tree structure. ω(θ) is defined. - ,θ + ) represents wide-beam codeword, θ - ,θ + Representing the left and right angles of the beam, under ideal beam conditions, [θ] - ,θ + Within the specified range, the radiated energy of the beam is γ. A model for approximating an ideal beam with a wide beam is established as follows: Where, ε{ω(θ) - ,θ + )} is an error metric describing the difference between the ideal beam and the actual beam. It is the value of radiant energy that varies with angle. It is a predefined narrow-beam codebook; Solving the model yields the wide-beam codeword, specifically: Define the angle to the left of the beam transmission midpoint and the angle to the right of the beam transmission midpoint exist In sinusoidal space, a narrow beam is uniformly divided into M points, resulting in the beam angle distribution as follows: in Narrow beam superposition Obtain the wide-beam codeword ω(θ) - ,θ + Let ω m The phase shift of the m-th narrow beam is expressed as: Where β represents the power scaling factor; Define f(x) = sinx, and substitute it into... and Afterwards, ω(θ) is re-adjusted. - ,θ + ) is represented as: in For symmetric array vectors: The phase at the midpoint of the array is 0, and the parameters are... Set β to: The final wide-beam codeword is:

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