A learning method for selecting beams in mmWave MIMO systems

Abstract

The present disclosure uses a transmitter antenna codebook that indexes a plurality of beam patterns and a receiver antenna codebook that indexes a plurality of beam patterns, where at least one beam pattern is selected in the transmitter antenna codebook and at least one beam pattern is selected in the receiver antenna codebook, where the selected beam patterns form one or more pairs of beams, which pairs form a channel for transmitting information between the transmitter antenna and the receiver antenna, and includes the steps of sounding only a subset of the beam pairs, measuring a transmission quality parameter of the subset of beam pairs to be indexed in the matrix, and using a learning model to select the beam pair having a maximum value of the transmission quality parameter to form a channel for transmitting information between the transmitter antenna and the receiver antenna.

Description

[Technical field]

[0001] The present invention relates to a method for finding accurate beam alignment between beams radiated by transmitter and receiver antennas in a mm-wave Multiple-Input Multiple-Output (MIMO) system.

[0002] mmWave MIMO systems are widely used in 5G and will be implemented even more extensively for 6G. In such mmWave MIMO systems, a large number of antennas are used at both the transmitter and the receiver. With such antennas, narrow beams with directional gain must be used to mitigate the severe path loss attenuation inherent in mmWave propagation. Moreover, in such systems with a large number of antennas, narrow transmitter and receiver beams are chosen from a large codebook that indexes multiple beams.

[0003] In order to form a channel with a high Signal to Noise Ratio (SNR), which is required to establish a link between the transmitter and receiver sides, the beams selected at both the transmitter and receiver need to be well aligned. [Background technology]

[0004] In known methods, an exhaustive search is implemented to find a well-aligned pair of beams. To do so, it proceeds by sounding all available beams in both the transmitter and receiver codebooks and by searching for the beam pair that results in the maximum SNR. The main drawback of this method is the fact that the resulting signaling overhead required to sound both the transmitter and receiver codebooks scales as a product of the codebook size, i.e., the number of beam patterns indexed in the codebook. Although this method can be adapted for small codebook sizes, for example for the LTE or Wi-Fi standards, its signaling overhead becomes prohibitive for massive mmWave MIMO systems, where the codebook size may be many more than 32×32.

[0005] The paper "Kolmogorov Model for large Millimeter-wave antenna arrays: Learning-based Beam Alignment" by CHAN WAI MING et al. describes a method for solving the beam alignment problem in MIMO systems, in which only the SNR of 25% of the beam pairs is measured, and the SNR of the remaining pairs is predicted by applying the Kolmogorov model.

[0006] There is a need for a method to find the best beam pair, i.e., one beam from the transmitter codebook and one beam from the receiver codebook that maximizes the SNR, that can be adapted to a large number of antennas and a large size of codebook through a blind approach, i.e., without requiring channel state information at either the transmitter or the receiver.

[0007] The present invention specifically seeks to meet this need. [Prior art documents] [Non-patent literature]

[0008] [Non-Patent Document 1] CHAN WAI MING et al., “Kolmogorov Model for large Millimeter-wave antenna arrays: Learning-based Beam Alignment” Summary of the Invention [Means for solving the problem]

[0009] One subject of the invention is a method for selecting beams in a massive mmWave MIMO system, the method comprising at least a transmitter antenna codebook indexing a plurality of beam patterns and a receiver antenna codebook indexing a plurality of beam patterns, in which at least one beam pattern is selected in the transmitter antenna codebook and at least one beam pattern is selected in the receiver antenna codebook, the selected beam patterns forming one or more pairs of beams, the pairs forming channels for transmitting information between a transmitter antenna and a receiver antenna, The method includes at least a. sounding only a subset of beam pairs selected from a set of all possible combinations of beam patterns of a transmitter antenna codebook and a receiver antenna codebook forming beam pairs; b. measuring transmission quality parameters of said subset of previously sounded beam pairs, to be represented by a matrix (S); c. applying a learning model to the subset of beam pairs to be sounded and / or to a predefined training set of beams to determine at least two latent vectors corresponding to a factorization of the matrix (S); d. using the at least two previously determined latent vectors to predict values ​​of the transmission quality parameters of non-sounded beam pairs and complete the matrix (S); e. Comparing all values ​​of the transmission quality parameter in the matrix (S) and selecting a beam pair having a maximum value of the transmission quality parameter to form a channel for transmitting information between a transmitter antenna and a receiver antenna.

[0010] The transmission quality parameter may be a signal-to-noise ratio (SNR) and / or a received signal energy (RSE).

[0011] The method according to the present invention makes it possible to sound fewer beam pairs than the methods used in the prior art, while still being able to find the best pair of beams, thereby significantly reducing the signaling overhead.

[0012] By sounding only a subset of beam pairs, the search for aligned pairs of beams is computationally less complex, allowing for reduced signaling overhead and low hardware complexity.

[0013] Contrary to exhaustive search methods, the method according to the invention is well adapted for communication between multiple antennas, such as those used in mmWave MIMO systems.

[0014] A subset of the sounded beam pairs may be used as a training set to train the learning model, and the remainder of the beam pairs may be used as a test set, so it is not necessary to have access to a previously collected data set.

[0015] The latent vectors determined by the learning model may be saved in a database, which allows for almost instantaneous recovery of the latent vectors from the database at any time without the need for cross-validation of hyper-parameters.

[0016] To evaluate the performance of the learning model used, the predictive quality of the model may be compared to an exhaustive search.

[0017] Both the transmitter antenna and the receiver antenna may be connected to at least one radio frequency (RF) chain, in particular to one radio frequency (RF) chain, resulting in a fully analog architecture used in both the transmitter and the receiver. No digital precoding or combining is used. Thus, the system architecture has low hardware complexity.

[0018] The applied learning model may be a matrix factorization model and / or a non-negative matrix factorization model.

[0019] In another embodiment, the learning model may be implemented by a deep neural network and / or by a convolutional neural network. The learning model may be an autoencoder or a multi-layer perceptron.

[0020] The use of matrix factorization and / or non-negative matrix factorization models allows for offline training and accurate prediction throughout the mmWave coherence time where the channel remains static. Cross-validation of the hyper-parameters of these models is done entirely offline, resulting in the storage of optimal latent vectors and optimal hyper-parameters for different setup combinations in a dedicated dataset.

[0021] The subset of beam pairs may correspond to at most 90%, better at most 75%, better at most 50%, better at most 30%, better at most 20%, for example, about 10%, of the set of all possible beam pairs of combinations of beam patterns in the transmitter antenna codebook and the receiver antenna codebook.

[0022] The method according to the invention makes it possible to predict with high accuracy the SNR of all pairs of beams by sounding only 10% of the possible pairs of beams.

[0023] The number of beam pairs sounded may depend on the number of indexed beam patterns in each codebook. The more indexed beam patterns there are in each codebook, the smaller the ratio between the number of beam pairs sounded and the number of all possible beam pairs. Conversely, the fewer indexed beam patterns there are in each codebook, the larger the ratio between the number of beam pairs sounded and the number of all possible beam pairs.

[0024] The condition information of the channel over which information is transmitted between the transmitter and receiver antennas may be unknown and / or known.

[0025] Contrary to some known methods, blind approaches, i.e. approaches where the channel state information is unknown and / or known, are compatible with the method according to the invention: neither the transmitter nor the receiver need to have any knowledge of the channel state information.

[0026] This allows the method to be easily implemented in many mmWave MIMO systems, and also allows the computation time and memory required to carry out the process according to the invention to be reduced.

[0027] The channel may be quasi-static while the method is applied, ie, during the coherence time, the channel remains unchanged.

[0028] The SNR for each pair of beams may be approximated by the received signal energy (RSE).

[0029] This approximation may be performed when the channel state information is unknown, which allows to simplify the step of measuring the SNR of said subset of previously sounded beam pairs, and therefore the method according to the invention is easier to implement.

[0030] Each codebook may have more than 16, better than 32, better than 64, better than 128, better than 256, better than 512, and better than 1024 indexed beam patterns.

[0031] The prior art exhaustive search can work for communication protocols that have a small number of indexed beam patterns in the antenna codebook. For example, in the LTE protocol, each codebook has 8 indexed beam patterns. Therefore, the number of beams to be sounded is only 64.

[0032] However, for standards using a large number of antennas, such as 5G or 6G, the number of indexed beam patterns in each antenna may be more than 16 or even more. Therefore, the number of beams to be sounded to perform an exhaustive search will be more than 256. In this case, the number of sounded beams required by the exhaustive search is very large, making this conventional method inefficient.

[0033] The method according to the invention is particularly suitable for codebooks with a large number of indexed beam patterns.

[0034] The matrix (S) may be a low-rank matrix.

[0035] By "low-rank matrix" it is to be understood that a matrix has a rank that is smaller than its number of rows or columns, for example smaller than 3, better still smaller than 2, and even better still smaller than 1.

[0036] The minimum number of pieces of data required in the training set may be proportional to the rank of the matrix (S): having a low-rank matrix makes it possible to have a small training set and therefore to sound only a small number of beams.

[0037] The dimension (D) indicating the model complexity, which represents the number of latent factors of the matrix factorization model, may be smaller than the dimensions corresponding to the number of rows and columns of the matrix (S).

[0038] The coefficients of the at least two latent vectors may be determined by using block gradient descent and / or block coordinate descent.

[0039] The standard for transmitting information about a channel for transmitting information between a transmitter antenna and a receiver antenna may be 5G or 6G.

[0040] Said method according to the invention is advantageously carried out by a computer program running automatically on any electronic device equipped with a processor, such as a mobile phone, a tablet or a mobile or fixed computer.

[0041] According to another aspect, the present invention also relates to a computer program product for selecting beams in a mmWave MIMO system, using at least a transmitter antenna codebook indexing a plurality of beam patterns and a receiver antenna codebook indexing a plurality of beam patterns, wherein at least one beam pattern is selected in the transmitter antenna codebook and at least one beam pattern is selected in the receiver antenna codebook, the selected beam patterns forming one or more pairs of beams, the pairs forming channels for transmitting information between a transmitter antenna and a receiver antenna, The computer program product comprises a support on which instructions readable by a processor are stored, the instructions comprising: a. sounding only a subset of beam pairs selected from a set of all possible combinations of beam patterns of the transmitter antenna codebook and the receiver antenna codebook that form beam pairs; b. measuring transmission quality parameters, in particular signal-to-noise ratio (SNR) values, of said subset of previously sounded beam pairs to be indexed in matrix (S); c. applying a learning model to the subset of beam pairs to be sounded and / or to a predefined training set of beams to determine at least two latent vectors corresponding to a factorization of the matrix (S); d. predicting values ​​of transmission quality parameters of non-sounded beam pairs and completing said matrix (S) using said at least two previously determined latent vectors; e. configured to compare all values ​​of the transmission quality parameters of said matrix (S) and select the beam pair having the maximum value of the transmission quality parameters to form a channel for transmitting information between the transmitter antenna and the receiver antenna.

[0042] The features explained above with respect to the method apply to the computer program product.

[0043] The invention can be better understood on reading the following detailed description of its non-limiting implementations and on examining the accompanying drawings, in which: [Brief description of the drawings]

[0044] [Figure 1] FIG. 1 is a schematic representation of an example of a millimeter wave MIMO system. [Diagram 2] FIG. 1 is a schematic representation of a radio frequency chain connected to a transmitter and a receiver. [Diagram 3] FIG. 1 illustrates a matrix resulting from a conventional exhaustive search. [Figure 4] FIG. 4 illustrates a matrix obtained from the method according to the invention. [Diagram 5] FIG. 2 illustrates a matrix decomposition into two rectangular matrices representing the latent factors of the matrix factorization model. [Figure 6] FIG. 2 is a block diagram of the various steps of the method according to the invention; DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0045] In Fig. 1 a mmWave MIMO system 1 is represented. The latter comprises a transmitter Tx with several transmitter antennas and a receiver Rx with several receiver antennas. In the illustrated example, the transmitter Tx is a base station and the receiver Rx is a user terminal. Each antenna radiates along a beam 10. Both the transmitter Tx and the receiver Rx have a codebook of potentially realizable beams.

[0046] When two beams 10, i.e., beam 10 from the transmitter side and beam 10 from the receiver side, are aligned, a communication channel is established and information can be transmitted from the transmitter to the receiver. In the example of Figure 1, the transmitter beam Tx beam 3 is aligned with the receiver beam Rx beam 1.

[0047] As can be seen in FIG. 2, both the transmitter and receiver antennas may be connected to one radio frequency chain 11, resulting in a fully analog architecture being used in both the transmitter and receiver.

[0048] In the example of FIGS. 3 and 4, each transmitter and receiver codebook indexes four beam patterns 10.

[0049] Figure 3 shows the matrix 12a resulting from the exhaustive search used in the prior art. In this method, all beams 10 are sounded and the SNR of all 16 channels formed by the combination of beams is evaluated. The matrix 12a has no unknown coefficients. Based on this matrix 12a, it is possible to determine the maximum SNR value. The optimal pair of beams, i.e. the pair of beams forming the channel allowing the best quality for exchanging information between the transmitter and the receiver, is the pair of beams that gives the maximum SNR. This method required sounding 16 beams.

[0050] Figure 4 shows the matrix 12b resulting from the method of the invention, where only a subset of the beams 10 are sounded. In the example shown, only three beams 10 are sounded on each side, and the SNR of the nine channels formed by the combination of beams is evaluated. In the matrix 12b, six coefficients are unknown.

[0051] It is necessary to fill in matrix 12b in order to determine the maximum SNR and therefore to select the pair of beams that corresponds to this maximum SNR. To do so, the method of the invention is based on the prediction of said unknown coefficients by applying a learning model to determine at least two latent vectors corresponding to a factorization of said matrix.

[0052] The learning model that may be applied is a matrix factorization model and / or a non-negative matrix factorization model. By applying such a model, a matrix may be decomposed into matrices with smaller dimensions.

[0053] 5 is an example of a decomposition of matrix 12b determined by applying a learning model. Matrix 12b is decomposed into matrix 13 corresponding to latent vectors and matrix 14 representing channels.

[0054] One embodiment of the method according to the invention will now be described with reference to FIG.

[0055] Each, N T pcs and N R Consider a mmWave Massive MIMO system in which a transmitter Tx and a receiver Rx equipped with antennas wish to select the best beam aligned pair. Each transmitter and receiver is connected to one radio frequency chain. Thus, the architecture is a low complexity and low energy architecture.

[0056] The transmitter derives its analog beamformer f from a codebook T of potentially realizable beam patterns. u Select.

[0057]

number

[0058] Similarly, the receiver derives its analog beamformer w from a codebook R of potentially realizable beam patterns. i Select.

[0059]

number

[0060] The cardinality of the codebook at the transmitter and receiver is C T = |T| and CR = |R|. Hence, the transmitter and receiver beams satisfy the constant modulus constraint.

[0061]

number

[0062] where |x| is the absolute value of x and [x] t is the entry t of vector x.

[0063] Henceforth, we define a beam pair (u;i)∈T×R as a beam u∈T from the transmitter codebook and a beam w∈R from the receiver codebook.

[0064] Furthermore, the signal at the receiver corresponding to the beam pair (u;i) is

[0065]

number

[0066] where:

[0067]

number

[0068] (power P u (having)f u is a pilot symbol associated with

[0069]

number

[0070] is unit variance

[0071]

number

[0072] The matrix representing the MIMO channel is

[0073]

number

[0074] As shown by:

[0075] The MIMO channel may be a narrowband or wideband channel model. The matrix representing the MIMO channel has rank L=rank(H), where L<<(N T ,N R ).

[0076] We further assume that H is quasi-static during the beam alignment procedure and that H is completely unknown to both the transmitter and the receiver.

[0077] The first step 21 of the method according to the invention is to randomly generate subsamples for each codebook from the codebooks of transmitter and receiver beam patterns 20. The transmitter subsample codebook is T S and the receiver subsample codebook is denoted as R S The subsampled codebook is denoted as R S ⊂ R and T S ⊂ T. The subsampled codebook is chosen to be small in size, i.e., |R S |<<|R| and |T S |<<|T|. Subsample codebook T S ×R S is two codebooks T S and R S This corresponds to the combination of

[0078] The next step 22 is to extract the subsampled codebook T S and R SThe objective of the present invention is to sound a pair of beams.

[0079] After sounding only a subset of the beam pairs, a step 23 is performed in which the SNR values ​​corresponding to the channels formed by each pair are recorded in a matrix.

[0080] The received SNR for the beam pair (u;i) is

[0081]

number

[0082] Define it as:

[0083] However, since the channel state information is assumed to be unknown, the receiver cannot calculate the SNR. Instead, the SNR at the receiver is approximated by the received signal energy (RSE), which is defined as follows:

[0084]

number

[0085] In detail, to evaluate the RSE,H,f u , P u You do not need to know the value of

[0086] We assume that the RSE is close to the true SNR for each beam pair. Therefore, the beam pair (u*,i*) selected is the beam pair that leads to the largest RSE.

[0087]

number

[0088] Rather than sounding the entire transmitter and receiver codebooks, as is done in exhaustive beam alignment methods, a subsampled codebook of the beam pair is used.

[0089] Denote a beam pair (u;i) as the combination of a beamforming vector u in the transmitter codebook of beampatterns and a combining vector i in the receiver codebook of beampatterns.

[0090] Then, the subsampled codebook T S ×R S We sound only beam pairs from the subsampled codebook T S ×R S The RSE (corresponding to the SNR) of the beam pair (u;i) from

[0091]

number

[0092] where y u,i is the receiver signal obtained from beam pair (u;i).

[0093] Then, the incomplete SNR matrix

[0094]

number

[0095] of,

[0096]

number

[0097] where [S] u,i ,∀(u,i)∈T×R denotes element (u;i) of S.

[0098] Since the receiver has been sounded, it is able to estimate the SNR of the entries in S that correspond to the subsampled codebook TS×RS.

[0099] The known SNRs, i.e., the SNRs of the sounded beam pairs, are used as the training set K for the learning model. The training set K is defined as the beam pairs indexed in the subsampled codebook, i.e., K:={(u;i)|(u;i)∈T S ×R S}.

[0100] The applied learning model may be a Matrix Factorization Model (MF Model) or a Non-Matrix Factorization Model (NMF).

[0101] The following describes the case where the MF model is selected, which corresponds to step 24a in FIG.

[0102] The training set K is used to train an MF model, preferably a low-rank MF model, which is then applied to predict the SNR of entries in S that are labeled as "unknown".

[0103] The low-rank MF model is based on two D-dimensional latent vectors θ u , ψ i This allows us to model the SNR of the beam pair being sounded (i.e., the known entries of S) as the dot product between

[0104] Therefore, the SNR of the beam pair (u;i) is

[0105]

number

[0106] where D is the dimension of the MF model. Due to the low-rank MF model, D is smaller than the dimension of S, i.e., D<<(C T ,C R ) is assumed.

[0107] The goal of the MF method is to find the latent vectors {θ u , ψ i} (u,i)∈K The purpose of this study is to learn:

[0108] A latent vector θ corresponding to sample (u;i) in the training set K u , ψ i Learning is

[0109]

number

[0110] where l u,i (θ u , ψ i ) is the loss function for sample (u;i) in the training set K.

[0111] We then sum over all samples (u;i) in the training set K to obtain the total loss function, and write the resulting optimization problem (P) as

[0112]

number

[0113] where the cost function of (P) is

[0114]

number

[0115] It is defined as:

[0116] In the above problem (P), the SNR of the beam pair to be sounded is known, i.e., {[S] u,i |∀(u,i)∈K}, and the optimization variables that need to be learned are the latent vectors {θ u , ψ i |∀(u,i)∈K}.

[0117] In another embodiment, the selected learning model may be an NMF model, which corresponds to step 24b in Figure 6. The steps for applying an NMF model are the same as for applying an MF model, with the difference being that in the NMF model the latent vectors are constrained to be non-negative.

[0118] In this NMF model, the SNR of a beam pair is given by

[0119]

number

[0120] is given by:

[0121] The optimization problem (P1) corresponding to the NMF problem is expressed as follows:

[0122]

number

[0123] where 0 is an all-zero vector of dimension D, and the cost function for problem (P1) is the same as the cost function for problem (P) for the MF model.

[0124] Both (P) and (P1) are non-convex optimization problems.

[0125] The overhead ratio is

[0126]

number

[0127] where 0<η<1.

[0128] It estimates the signaling overhead of all the methods of the present invention compared to the exhaustive search method. The smaller the value of η, the smaller the signaling overhead. However, a small η implies a small size of the training set and therefore a large prediction error. Therefore, there is a trade-off between η and the prediction error.

[0129] The total cost functions for both problems (P) and (P1) may be rewritten as follows:

[0130]

number

[0131] where {λ i ≧0,μ u ≥ 0|∀(u,i)∈K} is a set of regularization hyperparameters for balancing the MF or NMF model to prevent overfitting or underfitting. These hyperparameters are optimized by offline cross-validation search.

[0132] After selecting the MF model in step 24a, the problem (P) may be solved in FIG. 6 by using the Block Coordinate Descent (BCD) method (step 25a) or by using Block Gradient Descent (BGD) (step 25b).

[0133] When the BCD method is applied, one block of variables is iteratively optimized and all remaining blocks are assumed to be known.

[0134] Each block is assumed to be convex. Therefore, the solution to the MF problem is unique.

[0135]

number

[0136] can be derived in closed form as:

[0137] where (k) is the iteration index and I is the D×D identity matrix.

[0138] Furthermore, the optimal latent vector solution

[0139]

number

[0140] is reached when the distance between successive iterations reaches a predefined number ε or the maximum number of iterations I M It is acquired when it reaches

[0141] The sequence of updates generated by the BCD formula above

[0142]

number

[0143] is non-increasing and converges to a stationary point as k → ∞.

[0144] When the BGD method is applied, rather than having a closed-form solution for each block (which would lead to significant complexity), the BGD proceeds by taking T gradient steps for each block, i.e.

[0145]

number

[0146] where (k) is the iteration index and α (k) is (0<α (k) <1).

[0147] If the NMF model is selected, the problem (P1) may also be solved by using the block coordinate descent (BCD) method (step 25a) or by using block gradient descent (BGD) (step 25b).

[0148] The BCD and BGD methods are applied in the same manner as the MF method is applied, as explained above.

[0149] The solution to the NMF problem (P1) solved by the BCD method is

[0150]

number

[0151] where (k) is the BCD iteration index, and for a, [a] + =max(a,0) is applied element-wise, i.e.

[0152]

number

[0153] is the Euclidean projection of a onto a. The solution of the BCD equation for NMF is the same as the solution of the BCD equation for MF,

[0154]

number

[0155] An upward projection operation follows.

[0156] The solution of the NMF problem (P1) solved by the BGD method is

[0157]

number

[0158] where (k) is the iteration index and α (k) is (0<α (k) <1).

[0159] The application of BCD and / or BGD determines the optimal latent vector

[0160]

number

[0161] and feeding it back into the learning model during step 26.

[0162] After obtaining the optimal latent vectors by solving the MF problem (P) or the NMF problem (P1), step 27 is performed in which these optimal latent vectors are used to predict the SNRs of the beam pairs that were not sounded.

[0163] The predicted SNR for beam pair (u;i) for the unsounded beam pair is

[0164]

number

[0165] where L is a test set such that L∪K={}, L∩K=T×R.

[0166] The predicted SNR is used to fill in the incomplete matrix.

[0167] Finally, to select the optimal beam pair, we search for the maximum SNR in the matrix (step 28). The best SNR is searched over both the training set K and the test set L.

[0168] The best SNR is defined as:

[0169]

number

[0170] Next, f u* and w i* are used as the transmitter beam and receiver beam for data transmission.

[0171] Working Example In the following example, the following algorithm is executed:

[0172] [Table 1]

[0173] In this example, the number of simulated transmitter and receiver antennas is in the range of 16, 32, 64, 128, 256, 512, 1024. The overhead ratio is in the range of (0.7, 0.6, 0.5). The trade-off to be solved is to find the smallest overhead value that gives an accurate prediction, i.e., the smallest prediction error of the beam pair corresponding to the largest SNR value. Thus, the low overhead ratio configuration that still gives accurate results confirms that the best beam pair can be selected in a large dimensional dataset matrix without the traditional need to sound all beams.

[0174] For MF and NMF calculations, two algorithms were used: BCD, also called alternating least squares, and BGD. In total, four models were used: - MF using BCD (MF_ALS), - MF using BGD (MF_GD), - NMF using BCD (NMF_ALS), and - Evaluate the performance of NMF using BGD (NMF_GD).

[0175] For robustness purposes, all entities that derive the dataset matrix (channel, beamformer, Tx symbols) are randomly generated.

[0176] Model complexity refers to the number of latent vectors required to perform the matrix factorization.

[0177] Trained performance is based on tracking the Mean Squared Error (MSE) in an error function applied to the training set samples as a function of the overhead ratio.

[0178] The test performance analysis is primarily based on tracking the MSE for test set samples with unknown entries.

[0179] The prediction error is the distance between the maximum measured SNR and the maximum predicted SNR by the exhaustive search.

[0180] The results are shown in Table 7 below.

[0181] [Table 2]

[0182] The results show that the trained MSE has extremely small values, and the four learned models predict accurately on the trained samples for all the proposed overhead values.

[0183] The four models show accurate predictions and fairly short distances from the true SNR values.

[0184] Thanks to the method according to the invention it is possible to sound only 10% of the beams and to select well-aligned beam pairs with very good accuracy compared to an exhaustive search.

[0185] Naturally, the invention is not limited to the embodiments described above.

[0186] For example, the method can be applied to massive antenna systems other than MIMO, for example, to systems using Orthogonal frequency-division multiplexing (OFDM). Other applications, such as the automotive industry, massive IoT systems, wireless sensor networks, and multi-user MIMO, are also compatible with the method. [Explanation of symbols]

[0187] 1. Millimeter Wave MIMO System 10 Beam, Beam Pattern 11 Radio Frequency Chain 12. Matrices 13. Matrix 14. Matrix

Claims

1. A method for selecting beams in a mmWave MIMO system (1), the method using at least a transmitter (Tx) antenna codebook indexing a plurality of beam patterns and a receiver (Rx) antenna codebook indexing a plurality of beam patterns, at least one beam pattern (10) being selected in the transmitter antenna codebook and at least one beam pattern being selected in the receiver antenna codebook, the selected beam patterns forming one or more pairs of beams, the pairs forming channels for transmitting information between a transmitter antenna and a receiver antenna, The method comprises at least a. sounding only a subset of beam pairs selected from a set of all possible combinations of beam patterns of the transmitter antenna codebook and the receiver antenna codebook that form beam pairs; b. measuring a transmission quality parameter of said subset of previously sounded beam pairs to be indexed in a matrix (S); c. applying a learning model to the subset of beam pairs to be sounded and / or to a predefined training set of beams to determine at least two latent vectors corresponding to a factorization of the matrix (S); d. using the at least two previously determined latent vectors to predict values ​​of the transmission quality parameters of non-sounded beam pairs and complete the matrix (S); e. comparing all values ​​of the transmission quality parameter in the matrix (S) and selecting the beam pair having a maximum value of the transmission quality parameter to form the channel for transmitting information between the transmitter antenna and the receiver antenna; A method comprising:

2. The method of claim 1 , wherein the transmission quality parameter may be a signal-to-noise ratio (SNR) and / or a received signal energy (RSE).

3. The method of claim 1 or 2, wherein the applied learning model is a matrix factorization model and / or a non-negative matrix factorization model.

4. 4. The method according to claim 1, wherein the learning model is implemented by a deep neural network and / or by a convolutional neural network.

5. 5. The method of claim 1, wherein the subset of beam pairs corresponds to at most 90%, better at most 75%, better at most 50%, better at most 30%, better at most 20%, for example about 10%, of the set of all possible beam pairs of the combination of beam patterns of the transmitter (Tx) antenna codebook and the receiver (Rx) antenna codebook.

6. The method according to any one of claims 1 to 5, wherein state information of the channel transmitting information between the transmitter (Tx) antenna and the receiver (Rx) antenna is unknown.

7. 7. The method according to claim 1, wherein each codebook has more than 16, better than 32, better than 64, better than 128, better than 256, better than 512, better than 1024 indexed beam patterns (10).

8. 8. The method of claim 1, wherein the matrix (S) is a low-rank matrix.

9. 9. The method according to claim 1, wherein a dimension D indicating a model complexity representing a number of latent factors of the matrix factorization model is smaller than a dimension of the matrix (S).

10. 10. The method of claim 1, wherein the coefficients of the at least two latent vectors are determined by using a block gradient descent (BGD) method or a block coordinate descent (BCD) method.

11. 11. The method according to claim 1, wherein a standard for transmitting information about the channel for transmitting information between the transmitter (Tx) antenna and the receiver (Rx) antenna is 5G or 6G.

12. 1. A computer program product for selecting beams in a mmWave MIMO system, comprising: a transmitter (Tx) antenna codebook indexing a plurality of beam patterns; and a receiver (Rx) antenna codebook indexing a plurality of beam patterns; at least one beam pattern is selected in the transmitter antenna codebook; and at least one beam pattern is selected in the receiver antenna codebook; the selected beam patterns form one or more pairs of beams, the pairs forming channels for transmitting information between a transmitter antenna and a receiver antenna; The computer program product comprises a support on which instructions readable by a processor are stored, the instructions comprising: a. sounding only a subset of beam pairs selected from a set of all possible combinations of beam patterns of the transmitter antenna codebook and the receiver antenna codebook that form beam pairs; b. measuring values ​​of a transmission quality parameter of said subset of previously sounded beam pairs to be indexed in matrix (S); c. applying a learning model to the subset of beam pairs to be sounded and / or to a predefined training set of beams to determine at least two latent vectors corresponding to a factorization of the matrix (S); d. predicting values ​​of the transmission quality parameters of non-sounded beam pairs and completing the matrix (S) using the at least two previously determined latent vectors; e. comparing all values ​​of the transmission quality parameter in the matrix (S) and selecting the beam pair having a maximum value of the transmission quality parameter to form the channel for transmitting information between the transmitter antenna and the receiver antenna; A computer program product configured to:

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