ESTIMATE OF BEAM SHAPING WITH IMPROVED PERFORMANCE

Abstract

According to one aspect of an embodiment, a base station configured for beamforming estimation in a massive multiple-input multiple-output (mMIMO) radio access network (RAN) (mMIMO-RAN) may include a processing device and a transceiver. The processing device may be configured to compute a precoder at the base station based on the joint maximization of the signal with respect to noise and minimization of interference with respect to noise using a proximity decoder. Alternatively, the processing device may be configured to compute the precoder at the base station based on a power constraint. Finally, the processing device may be configured to generate the precoder at the base station for precoding a downlink signal for transmission from the base station to a user device (UE).The transceiver can be configured to transmit the DL signal to the UE.

Description

RELATED APPLICATION

[0001] This application claims the benefits of US Provisional Application No. 63 / 487,256, filed on February 27, 2023, the disclosure of which is incorporated herein by reference in full.

[0002] The embodiments discussed in the present disclosure relate to the estimation of the beam shaping. BACKGROUND

[0003] Unless otherwise stated herein, the materials described herein are not prior art with regard to the claims of the present application and are not recognized as prior art by inclusion in this section.

[0004] Beamforming is a signal processing technique used for directed signal transmission. There are various types of beamforming, including analog, digital, and hybrid beamforming; two-dimensional beamforming; three-dimensional beamforming (as used in Multiple Input Multiple Output (MIMO)); and others. Beamforming can be used to achieve spatial selectivity in various wireless communication standards such as 5G and IEEE 802.11ac, and beyond.

[0005] The subject matter claimed in the present disclosure is not limited to embodiments that overcome any disadvantages or function only in environments such as those described above. Rather, this background is provided only to illustrate an exemplary technological field in which some embodiments described in the present disclosure may be practiced. SUMMARY

[0006] In some embodiments, a base station (BS) can be configured for beamforming estimation in a Massive Multiple Input Multiple Output (mMIMO) radio access network (RAN) (mMIMO-RAN). The BS can include a processing device and a transceiver. The processing device can be configured to compute a precoder at the base station based on the joint maximization of the signal with respect to noise and minimization of interference with respect to noise using a proximity decoder. Alternatively, the processing device can be configured to compute the precoder at the base station based on a power constraint. Finally, the processing device can be configured to generate the precoder at the base station for precoding a downlink signal for transmission from the base station to a user device (UE).The transceiver can be configured to transmit a DL signal from the base station to the UE.

[0007] In some embodiments, a computer-readable storage medium may contain computer-executable instructions. When executed by one or more processors, the computer-readable instructions may cause a base station (BS) in an mMIMO RAN to compute a precoder at the base station based on the joint maximization of the signal with respect to noise and the minimization of interference with respect to noise using a proximity decoder; to compute the precoder at the base station based on a power constraint; and to generate the precoder at the base station to precode a downlink signal for transmission from the BS to a user device (UE).

[0008] In some embodiments, a beamforming estimation method in an mMIMO-RAN may include: calculating a pre-encoder at a base station based on the joint maximization of the signal with respect to noise and minimization of interference with respect to noise using an approximation decoder; calculating the pre-encoder at the base station based on a power constraint; and generating the pre-encoder at the base station to pre-encode a downlink signal for transmission from the BS to a user device (UE).

[0009] In some embodiments, a base station in an mMIMO RAN may comprise: a processing device that is operable to: compute a precoder based on the common maximization of a signal with respect to noise and the minimization of interference with respect to the noise; compute the precoder based on a power constraint using block coordinate descent; and generate the precoder to precode a downlink (DL) signal for transmission from the base station to a user device (UE); and a transceiver that is operable to transmit the DL signal to the UE.

[0010] In some embodiments, a computer-readable storage medium may contain computer-executable instructions. When executed by one or more processors, the computer-readable instructions may cause a base station (BS) in an mMIMO RAN to compute a precoder based on the joint maximization of a signal with respect to noise and the minimization of interference with respect to noise; to compute the precoder based on a power constraint using block coordinate descent; and to generate the precoder for precoding a downlink (DL) signal for transmission from the base station to a user device (UE).

[0011] In some embodiments, a method for a base station in an mMIMO RAN may include the following steps: calculating a pre-encoder at the base station based on the common maximization of a signal with respect to noise and minimization of interference with respect to noise; calculating the pre-encoder at the base station based on a power constraint using block coordinate descent; and generating the pre-encoder at the base station to pre-encode a downlink (DL) signal for transmission from the base station to a user device (UE).

[0012] The objectives and advantages of the embodiments are realized and achieved at least through the elements, features and combinations particularly highlighted in the claims.

[0013] Both the preceding general description and the following detailed description are to be understood as examples and serve for clarification and are not limiting to the claimed invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Exemplary embodiments are described and explained with additional specificity and detail using the attached drawings, in which: Fig. Figure 1 shows an example of an antenna radiation pattern in conjunction with a beamforming estimate; Fig. Figure 2 shows an example of an antenna radiation pattern associated with a beamforming estimate; Fig. Figure 3 shows an example of an antenna radiation pattern in conjunction with a beamforming estimate; Fig. Figure 4 shows an example of a reference signal transmission in conjunction with a beamforming estimation; Fig. Figure 5 shows an example of a communication system configured to perform a beamforming estimation; Fig. Figure 6 illustrates a block diagram of another example communication system configured to perform a beamforming estimation; Fig. Figure 7 illustrates a block diagram of an example system configured to perform a beamforming estimation; Fig. Figure 8 illustrates an example of a channel model associated with a beam shaping estimate; Fig. Figure 9 shows an example of a resource grid associated with beamforming estimation; Fig. Figure 10 illustrates a block diagram of an example signal flow associated with beamforming estimation; Fig. Figure 11 illustrates an example of a channel model associated with a beam shaping estimate; Fig. Figure 12 illustrates an example of a channel mapping in conjunction with a beam shaping estimation; Fig. Figure 13 illustrates an example of a channel mapping in conjunction with a beam shaping estimation; Fig. Figure 14 shows a diagram of an exemplary channel mapping in conjunction with a beam shaping estimate; Fig. Figure 15 illustrates a process flow of a base station (BS) used for beam shaping estimation; Fig. Figure 16 illustrates a process flow of a user device (UE) used for beam shaping estimation; Fig. Figure 17 illustrates a process flow for a computer-readable medium used for beam shaping estimation; Fig. 18 illustrates a process flow for a method for beam shaping estimation; Fig. 19 illustrates a process flow for a beam shaping estimation method; Fig. Figure 20 shows a schematic representation of a machine in the example form of a computer, in which a set of instructions can be executed to cause the machine to perform one or more of the procedures discussed here; Fig. 21 illustrates an example of power distribution across transmitting antennas for regulated null forcing; Fig. Figure 22 shows an example of the power distribution via transmitting antennas for regulated zero-forcing; Fig. 23 shows an example of the power distribution via transmitting antennas for transmission with maximum ratio; Fig. Figure 24 shows an example of the power distribution across transmitting antennas for minimum mean square error; Fig. Figure 25 shows the throughput for zero-forcing, regularized zero-forcing, transmission with maximum ratio and minimum mean squared error; Fig. Figure 26 shows an example of the capacity of a system with multiple users and multiple user inputs and multiple outputs (MU-MIMO); and Fig. Figure 27 illustrates an example of the capacity of a multi-user multiple input multiple output (MU-MIMO) system. DESCRIPTION OF THE EXECUTION FORMS

[0015] Beamforming is a signal processing technique used for directed signal transmission. Directed signal transmission can be used to steer patterns of constructive and destructive interference so that user devices (UEs) receive better signals due to greater spatial diversity.

[0016] In multi-user multiple-input multiple-output (MU-MIMO) networks (e.g., mMIMO), downlink (DL) and uplink (UL) beamforming and beamforming weight estimation can be used with a zero-forcing algorithm. Zero forcing (ZF) refers to a class of techniques that attempt to eliminate interference between users in MU-MIMO situations. Zero forcing can be used to find the solution for the following optimization: ‖W‖F2→min st HW=I where W can be the precoder matrix, H the channel matrix, and I the identity matrix. Based on the definition of the channel matrix H, several variants of ZF can be used.

[0017] Another variant of ZF is Regularized ZF (RZF), which can be used to solve the following optimization: ‖HW−I‖2F+r‖W‖F2→min where r is a regularization parameter that can be selected based on various parameters such as the signal-to-noise ratio (SNR), the number of user devices (UE), the number of antennas (transmitting and / or receiving antennas), and the like.

[0018] RZF and ZF have a similar level of complexity because both can be solved using analytical expressions that reduce to solving a system of linear equations, although RZF may perform better than ZF depending on the choice of r. The dependence of r on complexity may be non-trivial and could include factors such as the number of users and the signal-to-noise ratio (SNR). Furthermore, RZF may not account for power constraints, which can lead to an unbalanced power distribution across different power amplifiers. The power distribution can depend on the choice of the parameter r and the distribution of users. The higher the value of r and the greater the number of groups (i.e., the smaller the number of shifts), the more balanced the power distribution across the different power amplifiers can be (as measured by variance, etc.).), but increasing r and increasing the number of groups can negatively affect throughput.

[0019] It may be desirable to have an approach that has comparable complexity to IF / RZF but maximizes the power transmitted via the antennas without sacrificing spatial diversity. One way to achieve this is to develop an optimization similar to IF / RZF, with the following constraint: ∑i|W(:,i)|2≤1 / N where N is the number of power amplifiers. However, this generally does not result in any significant performance improvement, as the additional power is not properly directed to the UEs. A scheme known as Maximum Ratio Transmission (MRT), for example, can provide a more even power distribution, but with approximately 25% less throughput. Furthermore, the closed-loop IF / RZF form is lost when MRT is used.

[0020] The systems, devices, and methods presented here enable the use of power constraints in beamforming estimation without significantly increasing complexity. This disclosure differs from ZF (which attempts to eliminate interference, e.g., by maximizing SINR without considering SNR, which can degrade the signal), whereas this disclosure reduces interference to a selected level while also addressing other factors that affect system performance. These factors may include: (i) balancing SNR and signal-to-noise ratio (SINR), (ii) power constraints for the power amplifiers, as each amplifier may have a specific maximum power output, (iii) reducing interference for weak UEs, and (iv) adapting to small changes in channel conditions through iteration.

[0021] Furthermore, systems, devices and methods for using power constraints in beamforming estimation to compute a pre-encoder using one or more stochastic gradient descent methods, block coordinate descent methods, iteration, parallelization or similar techniques are disclosed here.

[0022] Embodiments of the present disclosure are explained with reference to the accompanying drawings.

[0023] As in the Fig. As shown, beamforming can be used to add an additional dimension to the channel, which depends on the spatial position of the UEs. In some embodiments, it is desirable to eliminate or reduce interference between the UEs by diagonalizing the channel so that it is diagonal after decoding at the UE. For a matrix product of channel H and precoder W that has no extra-mathematical entries, each message xi can be restored after equalization at its designated UE.

[0024] An example of a line-of-sight situation shows Fig. 1. An antenna radiation pattern 104, emitted by an antenna 106 coupled to a power source 102 in the communication system 1100, which has not been pre-coded. Since no pre-coding has been used, the antenna radiation pattern 104 is a spherical radiation pattern that does not radiate in the direction of a specific UE (110a, 110b, 110c).

[0025] In contrast, it shows Fig. 2 in a different line-of-sight situation, an antenna radiation pattern 204 in the communication system 200, which has been pre-coded. The antenna radiation pattern 204 from the antenna 206, which is connected to a power source 202, can include a first lobe 204 directed towards a UE 210b, a second lobe 206 directed towards a UE 210a, and a third lobe 208 directed towards a UE 201c. The radiation pattern in Fig. Figure 2 is an example of beam shaping. That is, the channel assigned to each UE 210a, 210b, 210c was diagonalized to eliminate interference between the UEs.

[0026] In some embodiments, wireless standards can exhibit a certain granularity of W: (i) the channel H is frequency-selective, or (ii) the channel H can be estimated at certain frequencies. A channel, H, can be frequency-selective due to the stochastic and multipath properties of the channel. That is, if a signal arrives at the UE via different paths (i.e., multipaths), even with a purely geometric model y = s(t - t1) + s(t - t2), the gain is frequency-dependent. Synchronization cannot reverse the frequency-dependent properties of the channel.

[0027] In some embodiments, a channel H can be frequency-insensitive if H is available at a coarse scale. The minimum granularity in some wireless standards is 2 resource blocks (RB), consisting of 12 subcarriers and 14 orthogonal frequency-division multiplex (OFDM) symbols. Consequently, the matrix W is shared by at least 168 distinct channels (i.e., 12 x 14 = 168 channels).

[0028] In some embodiments, such as in the Fig. 3 and Fig. As shown in Figure 4, a communication system can comprise 300 or 400 antenna elements (e.g., 302, 304, 306, 308, 310, 312, 314, 316 in communication system 300 and 402, 404, 406, 408, 410, 412, 414 and 416 for communication system 400). As shown in Fig. As shown in Figure 3, a grid of rays 320a, 320b, 320c, 320d, 320e, 320f, 320g and 320h can be transmitted as separate data streams. As shown in Fig. As shown in Figure 4, pilot signals can be transmitted from a UE 418 to the antenna elements 402, 404, 406, 408, 410, 412, 414 and 416.

[0029] In some embodiments, the communication system 300, 400 can be designed to be (i) robust against estimation errors and (ii) to design the precoding matrix within a selected time interval (e.g., one slot). The precoder is designed to be robust against estimation errors because, although channel H can be estimated at the UE (e.g., 418) and at the BS, it may not be measured precisely. If designed within one time slot, the precoder can, in the worst case, produce 550 precoders within 500 µs.

[0030] Channel diagonalization can be achieved through two different techniques: (a) open loop and (b) closed loop. In open-loop channel diagonalization, the pre-encoder W can be designed in the UE (User Environment). In this technique, the BS (Base Station) sends refined pilot signals (e.g., the CSI reference signal (CSI-RS) based on the synchronization signal block (SSB)), and the UE calculates the pre-encoder based on its channel estimation. The UE obtains the channel estimation through type 1 feedback in single-user mode or type 2 feedback in multi-user mode. This open-loop approach generates zeros (i.e., narrow beams) during transmission to separate data streams (e.g., transmitted using beams 320a, 320b, 320c, 320d, 320e, 320f, 320g, and 320h). An example of this open-loop approach is a dual-polarized system with 64 transmitting antennas (64T) with 4 UEs and 8 layers.In this open-loop approach, the middle antennas consume more power than the other antennas.

[0031] In some embodiments, the pre-coder W can be designed for closed-loop diagonalization based on channel estimates available in the BS and specific constraints. With the closed-loop approach, the superposition of the transmit (TX) and receive (RX) beams can be close. An example of the closed-loop approach is the zero-forcing (IF) algorithm.

[0032] Fig. Figure 5 shows an embodiment of a communication system 500 that can be configured for beamforming estimation and activation. A base station (BS) 502 can be operated in an mMIMO RAN. In one example, the BS 502 can be operated using a low-level split (i.e., functional split options 6, 7, or 8) where: (i) functional split option 6 splits the baseband functionality at the MAC-PHY layer boundary, (ii) functional split option 7 splits the physical layer, and (iii) functional split option 8 splits the physical layer and the radio frequency functions. In an example, a function split option 7 could be: (a) a function split option 7.1 (a function split between the functionality of the inverse fast Fourier Transform (iFFT) in the radio unit (RU) and the beamforming functionality in the distributed unit (DU), (b) a function split option 7.2 (a function split between beamforming and resource element allocation in the RU and precoding in the DU), and (c) a function split option 7.3 (a pure downlink function split between modulation and scrambling). In an example, function split option 7.2 can be an open RAN (O-RAN) radio unit (RU) (O-RAN) split 7.2. Alternatively or additionally, the BS 502 can be operated in a Third Generation Partnership Project (3GPP) network.

[0033] In some embodiments, the communication system 500 may have a cell coverage 504, which may include a near coverage area 506 and an edge coverage area 508. The near coverage area 506 may be located closer to the BS 502 compared to the edge coverage area 508. When configured for beamforming estimation and triggering as disclosed herein, the BS 502 may improve the network capacity for UEs in the near coverage area 506 compared to the network capacity for the near coverage area 506 when the BS 502 is not configured for beamforming estimation and triggering as disclosed herein.

[0034] Alternatively or additionally, when configured for beamforming estimation and activation as disclosed herein, the BS 502 can improve network coverage for UEs in the perimeter coverage area 508 relative to the network coverage for the perimeter coverage area 508 when the BS 502 is not configured for beamforming estimation and activation as disclosed herein. Alternatively or additionally, the BS 502 can be configured to reduce an amount of radio power loss when configured for beamforming estimation and activation, compared to the amount of power loss when not configured for beamforming estimation and activation as disclosed herein.

[0035] In some embodiments, such as in Fig. As shown in Figure 6, a BS (e.g., 502) can operate in an mMIMO RAN. The BS can comprise an mMIMO O-RU 600 and a distributed O-RAN unit (O-DU). In an O-RAN 7.2B split, precoding and beamforming can be performed in the mMIMO O-RU 600. The mMIMO O-RU can contain one or more modules, including: Ethernet (ETH) / Enhanced Common Public Radio Interface (eCPRI) 602, O-RAN Fronthaul (FH) 604, IQ Compression / Decompression 606, Downlink (DL) / Uplink (UL) Beamforming 608, Beamforming Weighting Estimation 610, LowPHY 612, Digital Front End (DFE) 614, Transmit / Receive (TRx) 616, Radio Frequency Front End (RFFE) 618, or similar.

[0036] Fig. Figure 7 shows a block diagram of an exemplary communication system 700 configured for estimating and activating beamforming, in accordance with at least one embodiment described in the present disclosure. The communication system 700 may comprise a digital transmitter 702, a radio frequency circuit 704, a device 714, a digital receiver 706, and a processing device 708. The digital receiver 706 and the processing device may be configured to receive a baseband signal via a link 710. A transceiver 716 may comprise the digital transmitter 702 and the radio frequency circuit 704.

[0037] In some embodiments, the Communication System 700 may comprise a system of devices that can be configured to communicate with each other via a wired or connected link. For example, a wired link in the Communication System 700 may include one or more Ethernet cables, one or more fiber optic cables, and / or other similar wired communication media. Alternatively or additionally, the Communication System 700 may comprise a system of devices that can be configured to communicate via one or more wireless links. For example, the Communication System 700 may include one or more devices configured to transmit and / or receive radio waves, microwaves, ultrasonic waves, optical waves, electromagnetic induction, and / or similar wireless communications.Alternatively or additionally, the communication system 700 can also include combinations of wireless and / or wired connections. In these and other embodiments, the communication system 700 can include one or more devices that can be configured to receive a baseband signal, perform one or more operations on the baseband signal to generate a modified baseband signal, and transmit the modified baseband signal, for example, to one or more loads.

[0038] In some embodiments, the communication system 700 may include one or more communication channels that can communicatively couple systems and / or devices included in the communication system 700. For example, the transceiver 716 may be communicatively coupled with the device 714.

[0039] In some embodiments, the transceiver 716 can be configured to receive a baseband signal. For example, the transceiver 716, as described herein, can be configured to generate a baseband signal and / or receive a baseband signal from another device. In some embodiments, the transceiver 716 can be configured to transmit the baseband signal. For example, after receiving the baseband signal, the transceiver 716 can be configured to transmit the baseband signal to a separate device, such as the device 714. Alternatively or additionally, the transceiver 716 can be configured to modify, condition, and / or transform the baseband signal before transmitting it. For example, the transceiver 716 can include a quadrature boost converter and / or a digital-to-analog converter (DAC), which can be configured to modify the baseband signal.Alternatively or additionally, the 716 transceiver can include a direct high-frequency sampling converter, which can be configured to modify the baseband signal.

[0040] In some embodiments, the digital transmitter 702 can be configured to receive a baseband signal via the junction 710. In some embodiments, the digital transmitter 702 can be configured to upconvert the baseband signal. For example, the digital transmitter 702 can include a quadrature upconverter applied to the baseband signal. In some embodiments, the digital transmitter 702 can include an integrated digital-to-analog converter (DAC). The DAC can convert the baseband signal into an analog signal or a continuous-time signal. In some embodiments, the DAC architecture can include a direct RF sampling DAC. In some embodiments, the DAC can be a separate element from the digital transmitter 702.

[0041] In some embodiments, the Transceiver 716 may include one or more subcomponents that can be used in preparing and / or transmitting the baseband signal. For example, the Transceiver 716 may include an RF front end (e.g., in a wireless environment) that incorporates a power amplifier (PA), a digital transmitter (e.g., 702), a digital front end, an IEEE 1588v2 (Institute of Electrical and Electronics Engineers) compliant device, an LTE physical layer (L-PHY), an S-plane device, a management plane (M-plane) device, an Ethernet media access control (MAC) / personal communications service (PCS), a resource controller / scheduler, and the like. In some embodiments, a radio device (e.g., a radio frequency circuit 704) of the transceiver 716 can be synchronized with the resource controller via the S-plane device, which can contribute to highly accurate timing with respect to a reference clock.

[0042] In some embodiments, the transceiver 716 can be configured to receive the baseband signal for transmission. For example, the transceiver 716 can receive the baseband signal from a separate device, such as a signal generator. The baseband signal might originate, for example, from a converter that transforms a variable into an electrical signal, such as an audio signal output by a microphone picking up a speaker's voice. Alternatively or additionally, the transceiver 716 can be configured to generate a baseband signal for transmission. In these and other embodiments, the transceiver 716 can be configured to transmit the baseband signal to another device, such as the device 714.

[0043] In some embodiments, the device 716 can be configured to receive a transmission from the transceiver 716. For example, the transceiver 716 can be configured to send a baseband signal to the device 714.

[0044] In some embodiments, the radio frequency circuit 704 can be configured to transmit the digital signal received from the digital transmitter 702. In some embodiments, the radio frequency circuit 704 can be configured to transmit the digital signal to the device 714 and / or the digital receiver 706. In some embodiments, the digital receiver 718 can be configured to receive a digital signal from the RF circuit and / or send a digital signal to the processing device 708.

[0045] In some embodiments, the processing device 708, as shown, can be a standalone device or system. Alternatively or additionally, the processing device 708 can be a component of another device and / or system. In some embodiments, for example, the processing device 708 can be integrated into the transceiver 716. In cases where the processing device 708 is a standalone device or system, it can be configured to communicate with additional devices and / or systems located remotely from the processing device 708, such as the transceiver 716 and / or the device 714. For example, the processing device 708 can be configured to send and / or receive transmissions from the transceiver 716 and / or the device 714.In some embodiments, the processing device 708 can be combined with other elements of the communication system 700.

[0046] In some embodiments, the processing device 708 (e.g., in a base station) can be configured to obtain a channel estimate for a wireless device, such as a UE. The channel estimate can be obtained using a suitable reference signal that provides an appropriate channel estimate, such as a sounding reference signal (SRS), which can be transmitted by a wireless device, such as a UE. If time-duplex duplex (TDD) is used, an SRS may be sufficient to provide a BS with a channel estimate, since channel reciprocity can be established between the BS and the UE in the TDD case.

[0047] In some embodiments, the processing device 708 can be configured to calculate an initial power level adjustment for a downlink signal for transmission to a wireless device such as a UE (e.g., in a base station). The initial power level adjustment can be calculated using the channel estimation obtained from the wireless device, such as the UE (e.g., using the SRS).

[0048] In some embodiments, the initial power level adjustment for the downlink signal can be calculated using a precoding matrix, W, which can be used for beamforming. The precoding matrix W can correspond to a decoding matrix D on the receiving wireless device (e.g., a UE), which can be used to decode messages received at the wireless device that have been precoded using matrix W.

[0049] In some embodiments, the DL signal can be generated based on a number of inputs, including one or more of: (i) a number of downlink layers (e.g., for a component carrier), (ii) a number of transmit antenna elements, (iii) a number of receive antenna elements, (iv) a polarization, (v) a number of antenna connections, or the like. In one example, the number of downlink layers can be any suitable value greater than or equal to 1 and less than or equal to 64. In another example, the number of downlink layers can be at least 8. In another example, the number of transmit antenna elements can be any suitable number greater than or equal to 2 and less than or equal to 128. In another example, the number of transmit antenna elements can be at least 32. In another example, the number of receive antenna elements can be any number greater than or equal to 2 and less than or equal to 16.In one example, the number of receive antenna elements can be at least 32. In another example, the number of antenna ports can be any number greater than or equal to 2 and less than or equal to 64. In other examples, the number of downlink layers, transmit antenna elements, receive antenna elements, and antenna ports can be any suitable number that can be supported by the network (e.g., a Massive MIMO network).

[0050] In some embodiments, the precoding matrix W can be optimized together with D. A signal-to-noise ratio measure can be used for the joint optimization of W and D, including one or more of the following: a signal-to-noise-plus-noise ratio (SINR), a signal-to-noise-plus-noise ratio (INSR), a signal-to-noise ratio (SNR), or a similar measure, or a combination thereof. In another example, a measure of the power distribution across the antennas can be used for joint optimization of W and D.

[0051] In some embodiments, the precoding matrix W and the decoding matrix D can be calculated together using the objective function: MinimizeD,W‖DHW−I||(2)(F)+λ(0) ‖D‖(2)(F)+λ1∑i‖D(i) H(i) W(i)−I‖(2)F), where: (i) H is a matrix for the channel, where each row of matrix H represents a user i and each column of row i of matrix H represents jten (ii) layer of user i corresponds to, (iii) I is the identity matrix, (iii) λ0 and λ1 are regularization parameters, and (iv) D = blkdiag(Di) has a block diagonal structure, subject to the condition that ∑i‖ek'Wij‖2≤1N where k = 1, ..., N and ek' This is the transposition of a unit series basis vector.

[0052] In some embodiments, if there is no performance limitation for the joint optimization of the precoding matrix W and the decoding matrix D__ When used, the Lagrange can be calculated as follows: L(W,D)=Tr(W'H(')D'DHW)−2Tr(DHW)+λ0Tr(D(')D)+λ1∑(Wi'Hi'Di'DiHiWi−2DiHiWi)+const.

[0053] In some embodiments, the gradients can be calculated as follows: ∇(W)L=2H'D'DHW−2H'D'+2λ(1) [H(i)' D(i) H(i) W(i) −H(i) 'Di]i, where [v] ithe concatenation in the form of a row vector, and ∇(D)L=2DHWW(') H'−2W(') H'+2λ0D+2λ1blkdiag[D(i) H(I) Wi Wi' Hi'−Wi' Hi']

[0054] In some embodiments, the (partial) Hessians can be calculated as follows: HWW=DHH'D'+λ1[Di'Hi' H(i) D(i)](i), and HDD=W'HH'W+λ0I+λ1 blkdiag[Wi' H(i),H(i) Wi]

[0055] In some embodiments, iterations of the Newton method with projection can be calculated as follows:

[0056] In this algorithm: (i) the number of layers, ℓ, can be defined for each UE, (ii) H can be mxn (iii) the channel matrix for m transmitting antennas and n UEs, (iv) r can be the power limit for each of the m antennas, (iv) W nxℓcan be the precoder matrix for n UEs, where each UE has ℓ layers, (v) t is an iteration counter, (vi) " ' " is the partial derivative with respect to the specific matrix (zg, H' is the partial derivative of the Lagrange function with respect to W (for ∇(W) L ) or the partial derivative of the Lagrange function with respect to D (for ∇(D) L ), (vii) [v] i gives the concatenation in row vector form, (viii) HWW† is the transposed partial Hessian and HDD† is the transposed partial Hessian, and (ix) η is the step size.

[0057] In some embodiments, the following variant of the objective function can also be considered: MinimizeD,W‖DHW−I‖(2)( F)+λ(0)‖D‖(2)( F)+λ1∑i‖D(i)H(i)W(i)−1‖(2)( F), subject to the constraint ∑i‖ek'Wij‖2≤1N where k=1,…,N and DiHiWi=I where projection is used to subject the objective function to the equality conditions.

[0058] In some embodiments, zero forcing (ZF) can be a class of algorithms that do not adapt to the noise or the decoding method in the UE. In one embodiment, a ZF algorithm can be computed using the objective function: ‖HW −I‖F→min

[0059] For a matrix of dimensions mxn (with m > n), ZF can be computed with a computational complexity of 2m^3 operations. This computation may not be a minimum-energy solution because the computation is not power-constrained. That is, the computation may not utilize all power amplifiers (i.e., there may not be a unique solution if H is a fat matrix or H has fewer rows than columns). If HH' is invertible, a particular minima may be the right inverse of H: W = H'(HH')^{-1}. The right inverse can also be considered as a solution to the following restricted minimum-energy problem: ‖W‖F2→min st HW=I which provides an objective function that balances the total energy consumption of the power amplifiers and delivers a unique solution.

[0060] In some embodiments, an IF algorithm can be a reduced-order IF algorithm. In this case, if the number of receiving antennas is greater than the number of layers, IF can be performed on a restricted subspace within the (line) span of the channel to save computational effort and improve performance. For example, the principal directions can be used to reduce the channel dimension, as calculated in the objective function. ‖DH W −I‖F→min where D is the IF decoder and the channel for each UE is replaced by its topLi dominant modes using singular value decomposition (SVD).

[0061] More precisely, if D = [D1, D2, ..., D k ) and H = [H1, ..., H k The IF decoder can be calculated as follows: Dir=∑i≤Liσiμiν'i

[0062] If you Dr=[[D1r,…,Dkr] setting this up, one can determine the result W(r) =H' D (r)' (D r HH'D' r)- 1 receive.

[0063] In some embodiments, the ZF algorithm may include a complex multiplication (cMAC) calculated as follows: (nm)(m+1) / 2 + 2m 3 + nm 2 for a total cMAC of 1.5nm 2 + 2m 3 , where the first term is the cMAC for calculating HH', the second term is the cMAC for calculating the inverse (HH') -1 , and the third term of the cMAC for calculating the final product.

[0064] For example, with m=16 and n=64, the cMAC can be calculated as follows: [(1.5*(64)*16 2 ) + (2*16 3 )] = 33000 complex multiplications (which are approximately 10 5Real multiplications can be calculated if one defines 3 MACs = 1 c MAC). For a 0.5 ms signal at 200 MHz with 550 RBs, the c MAC can be performed 550 times. In some examples, the power consumed can be approximately 110 c MACs (which can correspond to an actuator with 18 modulators). Since the algorithm can be active once per frame (i.e., once every 20 slots), the power consumption can be 1 / 20. th of the electricity that would be consumed by an 18-module actuator.

[0065] In some embodiments, the reduced-order ZF algorithm may have a cMAC calculated as follows: nm 2 + nm 2 + nm 2 , for a total cMAC of 3nm 2The first term can be computed using Cholesky decomposition via Gram-Schmidt orthogonalization (i.e., QR decomposition) to compute H=RQ; the second term can be computed by setting F=HW and solving FR'=H'; and the third term can be computed using HW=F. The computation for the reduced-order ZF algorithm is less efficient than other alternative computations.

[0066] In some embodiments, the reduced-order ZF algorithm may have a cMAC calculated as follows: nm 2 + nm 2 = 2nm 2 The first term can be the cMAC for solving the factor S such that S'H'HS=I; and the second term can be the cMAC for determining W = H'S'S.

[0067] In some embodiments, the reduced-order ZF algorithm can be further improved and exhibit a cMAC calculated as follows: 1.5 nm 2 + m 3The first term includes the cMAC for calculating the upper triangular matrix and the cMAC for multiplying the triangular inverses, and the second term includes the cMAC for inverting the upper triangular matrix. In one example, the cost might be around 29,000 cMACs, and similar calculations yield a value of 100 units in performance-adjusted form. Thus, this approach has a lower cMAC value compared to the ZF algorithm.

[0068] In some embodiments, the improved reduced-order ZF algorithm can include the computation of the right inverse (HW = I) without explicitly computing the Cholesky decomposition. In one example, the right inverse can be computed using a Gram-Schmidt operation to obtain HW_1 as a lower triangular matrix with 1s on the diagonal.

[0069] The calculation may include the definition: H=[H1'...Hm'] where W = [W (1) ... Wm ] and H' = [H1 ... H (m) ], where each H i a column (that is, H' can be the conjugate transpose of the matrix H).

[0070] In some embodiments, the precoder, W̃, can be computed such that HW̃ = I, where such an equation can be solved for each frequency and time resource (e.g., each resource element). The computation may involve two operations: (i) computing W such that HW is an upper triangular matrix (m x m) with len on the diagonal, and (ii) computing the inverse of HWP = I and determining W̃ = WP.

[0071] In some embodiments, W can be calculated iteratively column-wise. For the initial set of columns, H1 and W1 can be calculated as shown: W1=H1|H1|2 and H1=[h11...h1n] where n can be the number of power amplifiers such that |H (1)| (2) =h ' (11)h(11)+h ' 12)h(12) +... + h' (1n) h1n. Linear combinations of the columns of the H' matrix and the columns of the W matrix (e.g., W) i ) can be defined such that: F k = H (k)-W(1) c(1,k) - ... - W (k-1) ck-1,k , where c ij They can be constants. For example, F2 can be calculated such that F2 = H (2) - W (1) c(12) ist , and if H' (1) W2 If the constant c is set to 0, then the constant c can be used. 12 as H' (1)H2 W2 can be calculated as W2 = F2 / H (2) ' F2 can be set and further iterations of F can be recursively performed with W. i = F i / H (i)' F i to be calculated. A simplified calculation of F k can be calculated using: Fki=Hk−Wzc1−k−⋯−Wi−1ci−1,k

[0072] Based on these definitions, it can be verified that cik=Hi'Fki−1 (based on Hi'Wi=I). By setting W k = F k / H (k) 'F k Can an upper triangular matrix with 1s along the diagonal be calculated?

[0073] In some embodiments, HW can be computed as an upper triangular matrix using the following MatLab code: Function W=utriagGS(H) W=[] for i=1:size(H,1) Hi=H(i,:)'; F=Hi; for j=1:i-1 Hj=H(j,:); F=F-Hj*F*W(:,j); end W=[W,F / (Hi'*F)]; end end

[0074] In some embodiments, the cMAC can be higher. For example, multiplying the quadrature amplitude modulation (QAM) symbols with the beamforming matrix may require at least 64*L multiplications per RE. In the specific example of the reduced IF algorithm, L=m, which uses 64 * 16 * 550 * 12 * 14 * 2000 = 190 cMAC / sec, or 550 units / sec in power-adjusted form. In a downlink scenario, the reduced IF algorithm can operate throughout the entire transmission, so the actuation may consume at least 1000 times the energy compared to the standard IF algorithm.

[0075] In some embodiments, the processing device 708 can be configured to calculate a second power level adjustment for the DL signal for transmission to the wireless device (e.g., a UE) (e.g., in the BS). In one example, the second power level adjustment can be calculated by adjusting the first power level adjustment based on an antenna power limitation. In some examples, the processing device 708 can be configured to precode a DL signal for transmission to a device 714 (e.g., a UE) using the second power level adjustment (e.g., in a BS). In some examples, the transceiver 716 can be configured to send the DL signal to the device 714 (e.g., a UE).

[0076] In some embodiments, the device 714 (e.g., a UE) can be configured for beamforming estimation. The device 714 can be configured to receive a downlink signal with a pre-coded message from a transceiver 716 (e.g., at a base station). In one example, the device 714 can include a processing device. The processing device can be configured to receive a channel estimation. The channel estimation can be obtained using a reference signal that includes one or more of the following: channel state information reference signal (CSI-RS), demodulation reference signal (DM-RS), phase tracking reference signal (PTRS), sounding reference signal (SRS), or the like. The channel estimation can be transmitted from the device 714 to the transceiver 716 (e.g., in a base station) using an SRS.

[0077] In some embodiments, the processing device can be configured to generate a decoder (e.g., D) by: (i) initializing the decoder using channel estimation, and (ii) adjusting the decoder to decode the precoded message, wherein the precoded message received at the device 714 was precoded based on an antenna power constraint (e.g., using MMSE). The processing device can be configured to decodecode the precoded message using the decoder. The decoder can be further initialized by applying zero-forcing to a precoding matrix constrained to minimize noise, measured by a ratio comprising one or more of the following: a signal-to-noise-plus-noise ratio (SINR), a signal-to-noise-plus-noise ratio (INSR), a signal-to-noise ratio (SNR), or the like.

[0078] In some embodiments, a different calculation method can be used, e.g., the minimum mean squared error (MMSE), to adjust the first power level based on the antenna power limit. In some examples, a class of pre-encoders can be defined as W = W̅diag (p ij ) are defined, where p ij real scalars are those that adjust the power level for the j te layer of i ten Users specify the matrix W̅. The matrix can be defined using ZF (e.g., ZF, reduced-order ZF, reduced-order ZF improved as disclosed here, or similar), and the power levels can be calculated using MMSE.

[0079] In some embodiments, a pre-encoder can be W = [W i ] in the loop of a communication model. The signal received by user i can be calculated as follows: Yi=Hi∑jWjxj+zi where: (i)x i = (x il ) ∈ (channel) L i the intended message for user i with L i -layers may be, (ii) Z i the sum of inter-cell interference and thermal noise at user i may be and (iii) H i which may be the true channel.

[0080] In some embodiments, the BS can calculate the received signal at user i as: Yi=H^i∑jWjxj+Δi∑jWjxj+zi where Δ(i) = H (i)- Ĥ i The error of the channel estimation is (based on the premise that the channel can be learned using reference signals that are independent of the message x) j are). For example, SRS can be used to give the BS a channel assessment independent of message x. j to deliver. If one defines W iℓ as the precoder for the ℓ(th)-Layer of user i and D iℓ For its decoder, the estimated symbol for user i for layer l can be calculated as follows: x^il=DilYi=DilH^iWilxil+DilHi∑r,j≠iWjrxjr+DilΔi∑j,rWjrxjr+DilZi.

[0081] In some embodiments, assuming that the UE has perfect knowledge of the channel (due to the higher and more detailed resolution of the downlink pilots), the decoder can be defined such that D (il) H(i) W(iℓ) =1. After a rearrangement, the estimated symbol for user i on layer l can be calculated as follows: x^il=DilYi=xil+DilHi∑r,j≠iWjrxjr+DilΔi∑j,rWjrxjr+DilZi, where Ni can be defined as follows: . D il H i ∑ r,j≠i W jr x jr + DilΔi∑j,rWjrxjr+DilZi

[0082] Assuming that |x ilIf | = 1, the signal-to-noise ratio (INSR) can be calculated as follows: INSRi=var(N)≤∑j≠i,r≤Lj‖DilHiWjr‖F2+∑j,r≤Lj‖DilΔiWjr‖F2+σi2‖Dil‖F2, can be calculated so that the limit for the INSR ratio can be used to determine the power reallocation in beam shaping.

[0083] In some embodiments, W il as pilVil to be calculated, where V il can be calculated using ZF (e.g., ZF, reduced-order ZF, reduced-order ZF improved as disclosed herein, or the like). Alternatively or additionally, the decoder can be configured such that D i = (H (i) W(i) ) For a total of M units, the INSR can be minimized using the objective function: minimize. ∑i≤MLilog(ti) subject to the following condition: 1pil(σi2‖Dil‖F2+∑j≠i,L≤Ljpjl‖DilH^iVjl‖F2 +λ∈i2∑j≠i,r≤Ljpjl‖Dil‖F2‖H^i‖F2‖Vjr‖F2)≤ti and subject to the following conditions: pil≥0 ti≥1 / 256 ∑pil‖ekVil‖2≤(1NR) k=1…N, where N is the number of antennas, e k a unit series basis vector, R the total number of RBs available for beam shaping, ε(i) = | Δ(i)|F / Hi / / (F) , λ is a regularization parameter (e.g. λ = 0,1) and σ is the noise level.

[0084] In some embodiments, this can be done at the i ten User received signal using Y i = H i ∑ j W j x j + Z i be defined and the estimated vector for i ten User fees can be calculated as follows: x^i=DiYi=DiHi∑jWjxj+DiZi,

[0085] The signal-to-noise ratio (SINR) can be calculated as follows: SINRi(W,D)=|DiHiWi|F2σ2|Di|2+∑j≠i|DiHiWj|2

[0086] In some embodiments, a power limit can be used to reduce the power level by maximizing a SINR for a i th Users can customize using the target function: maximize∑i≤klog(SINRi+1) subject to restrictions: DiHi∑Wj=I ∀i≤k |∑ei'Wj|2≤1n∀i≤n where the third term compensates for the power limitation (e.g., for the power amplifiers). In an example, a solution can be calculated using local maxima determined by gradient descent.

[0087] In some embodiments, the decoder can be omitted from the objective function. That is, the derivative can be computed with respect to the decoder in the form of the precoder, and with each subsequent update, the precoder can be updated without updating the decoder. This method of computing the precoder without explicitly including the decoder in the objective function can achieve performance comparable to that of an objective function that includes an explicit decoder. However, the method of computing the precoder without explicitly including the decoder in the objective function can be approximately 10 times faster than the method that includes the decoder in the objective function, due to fewer variables and constraints.

[0088] In some embodiments, MMSE can use a pair of precoders, W i, and decoder, D i , as defined, are implemented: Di=Di+Pi−1 Wi=PiWi+

[0089] The power scales can be provided in a matrix, Pi, as defined: Pi=[√pi1⋯0⋮⋱⋮0⋯√piL] where P i a diagonal matrix. For each unit, the matrices can be... Tue+Wi+ with ZF and the power scale, e.g. p (i) , can be calculated using convex optimization (e.g., a geometric program). The power matching can be calculated based on the MMSE objective function with respect to the power scalars instead of the complete precoder / decoder matrix pair.

[0090] In some embodiments, a coverage-based MMSE can be used to increase a wireless coverage area relative to a wireless base coverage area where IF is used without an MMSE. In some embodiments, a coverage-based MMSE can include a worst-case MMSE that uses IF decoding to calculate a power level adjustment to increase a wireless coverage area compared to a wireless base coverage area where IF is used. Assuming there are K users in each group, where the decoder des i (ten) UE in line form as D i = [D i1 ; D i2 ; ...; D (iL) ] is defined and the precoder is in column form as W i = [W il , ..., W (iL) The performance limitation (dhdh, minimize) is defined. (p1, ..., pK) t) can be used to calculate a power level adjustment (assuming the UE uses an IF decoder, so that D (i)H(i)Wi = I), so that: σ2|Dij|F2pij+∑k≠i,lpk,l|DijHiWil+|2 / pij≤t ∀k,j |∑ei'Wj+|2≤1n ∀i≤n

[0091] Worst-case MMSE with IF decoding allows for an improvement in SINR per UE. Some or all UEs can have the same QAM, thus increasing the worst-case quality of service for the UE compared to the worst-case quality of service for the UE without worst-case MMSE with IF decoding, but potentially not providing an increase in throughput in the same comparison. For example, worst-case MMSE with IF decoding could be an anti-waterfilling approach, where more power is allocated to the lowest-quality channels (e.g., as determined by SRS) and less power to the highest-quality channels (e.g., as determined by SRS).

[0092] In some embodiments, a throughput-based MMSE can be used to increase the average throughput compared to a baseline throughput using IF without MMSE. In one example, the throughput-based MMSE can include an average MMSE with IF decoding, which can be used to calculate a power adjustment to increase the average throughput compared to a baseline throughput using IF. In this example, the same QAM can be maintained on all layers corresponding to the same UE, but different UEs can use different QAMs. This example is a water-filling approach where power is allocated to the channels based on increasing the average throughput. Assuming there are K users in each group, the decoder des i (ten) UE in line form as D i = [Di1 ; D i2 ; ...; D (iL)] is defined and the precoder is in column form as W i = [W i1 , ..., W (iL)] The performance limitation (dhdh, minimize) is defined. p1, ..., pK ∑ i logt i ) can be used to calculate a power level adjustment (assuming the UE uses an IF decoder, so that D (i) H(i) Wi = I), so that: σ2|Dij|F2pij+∑k≠i,lpk,l|DijHiWil|2 / pij≤ti ∀k,j |∑ei'pjlWjl|2≤1n ∀i≤n

[0093] The computational effort for the average MMSE with ZF decoding can be applied in a first operation (i.e., ZF) and a second stage (i.e., average MMSE) with respect to a small number of variables (i.e., the number of variables can correspond to the number of units in each group, which might be, for example, 3-4 units per group). Consequently, least squares or another Newton-based method can calculate the performance matching with less computational effort compared to other methods.

[0094] In some embodiments, a robust MMSE may include a robust average MMSE with IF decoding, which can be used to compute a power level adjustment to: (i) increase the average throughput level relative to a baseline throughput level using IF without MMSE, and (ii) increase the robustness of the average throughput level relative to a baseline throughput level using IF without MMSE. In this example, as with average MMSE decoding using IF, the same QAM can be maintained in all layers corresponding to the same UE, but different UEs can use different QAMs. Assuming there are K users in each group, the decoder is defined des i (ten) UE in line form as D i = [D i1 ; D i2 ; ...; D (iL)] , and defines the precoder in column form as W i = [W i1 , ..., W (iL) ], the performance limitation (dhdh, minimize) p1, ..., pK ∑ i logt i ) can be used to calculate a power matching (assuming that the UE uses an IF decoder, so that D (i) H(i) Wi = I), namely under the condition that: σ2|Dij|F2pij+∑k≠i,lpk,l|DijHiWil|2 / pij+λi≤ti ∀k,j |∑ei'pjlWjl|2≤1n ∀i≤n

[0095] The robust average MMSE with IF decoding can differ from the average MMSE with IF decoding by using a channel estimation error term (e.g., λ). i) differs, which is used to calculate a power matching that, in the presence of channel estimation errors, can enable a higher average throughput level compared to the average throughput level when using the average MMSE with IF decoding. The robust average MMSE with IF decoding can have a computational complexity similar to that of the average MMSE with IF decoding.

[0096] In some embodiments, the computational effort for calculating the pre-coding matrix in the BS can be increased without performance degradation. In this example, the pre-coding matrix W can be computed without explicitly basing the computation on decoding procedures at the UE by approximating the decoding procedures at the UE (e.g., using stochastic gradient descent or another predictive technique). The objective function can be based on a performance constraint without constraints related to the decoding procedures in the UE. The performance can be configured to increase average and worst-case performance by weighting SINR and SNR without explicitly including SINR or SNR in the objective function. The objective function can also be constrained by performance limitations resulting from the number of power amplifiers by using stochastic gradient descent.

[0097] Compared to calculating the precoding matrix explicitly based on decoding methods in the end device, performance can be 3-5% lower, but with higher computational speed. This means that approximating gradient descent using stochastic gradient descent can increase computational speed without a significant reduction in performance. In an example implemented on an 8-core CPU, the computational effort was comparable to that of ZF. In another example, for a power distribution of RZF on a 100 MHz band with 4 groups and 32 UEs and 64 Tx (dual polarized, arranged in a 4x8 panel with 16 layers per transmitted resource element), for which each user had 4 antennas, received 2 layers of data and received about 25 MHz of the spectrum, and for which the worst-case scenario thus provided for 128 instances of the precoding design (e.g.(based on 16 layers and 64 antennas), the precoding design is carried out in less than 0.5 ms or the duration of a slot.

[0098] In another example, adding an iteration can further increase computation speed by using the precoder from the previous iteration as input. The performance may be comparable to that without iteration, but including the iteration ensures faster convergence and can allow the precoding design to be configured to adapt to changes in channel conditions with reduced computational complexity and time.

[0099] In some embodiments, a processor in a base station can be configured to compute an approximate decoder for a user entity (UE). An approximate decoder can be computed using a suitable prediction method, such as supervised machine learning. For example, an approximate decoder can be computed based on one or more of the following steps: training a model on a dataset and using the model to generate an approximate decoder for a UE based on parameters associated with the UE (e.g., number of layers, number of receiving antennas, a reference signal). The model can be based on one or more artificial neural networks, a decision tree, a support vector machine, regression analysis, Bayesian networks, a Gaussian process, a genetic algorithm, or a combination thereof.

[0100] In another example, the processor can be configured to compute the pre-encoder based on jointly maximizing the signal with respect to the noise and minimizing interference with respect to the noise, using the approximate decoder. The signal can be jointly maximized while the interference is jointly minimized by using a weight for the signal and a weight for the interference as an additional constraint on an objective function.

[0101] In another example, the processor can be configured to calculate the precoder based on a performance constraint. The performance constraint can be formulated as shown: |∑jei'Wj|2≤1n ∀i≤n

[0102] In another example, the processor can be configured to create the precoder for precoding a downlink signal for transmission from the BS to a user device (UE).

[0103] In some embodiments, the signal can be maximized using a signal-to-noise ratio (SNR) constraint, and the noise can be minimized using a signal-to-noise-plus-noise (SINR) constraint. In some examples, neither the SNR nor the SINR can be included in the objective function. That is, the objective function can be: ‖W‖2→min st HW=I subject to the following conditions: Di*Hi∑Wj=I ∀i≤k|∑ej'Wj|2≤1n ∀i≤n where Di* The approximate decoder is... In some embodiments, the pre-encoder can be computed based on the power constraint (i.e., the third expression shown above) using stochastic gradient descent.

[0104] In some embodiments, stochastic gradient descent can provide an approximation of the values ​​for the precoder or other parameters (e.g., the decoder). For example, an approximate gradient (e.g., for the precoder) can be calculated using a gradient on a sample w (e.g., W = w - η (VQ(w))), where η is the step size and Q is the gradient. As shown, stochastic gradient descent can be used to calculate the precoder as follows:

[0105] In some embodiments, the pre-encoder can be computed using an iterative process. An example of an algorithm for computing the pre-encoder using an iterative process might be: 1: Inputs: ℓ(number of layers), H (m) (×) (n) , r (per antenna power limitation) 2: Output: Precoder matrix W (n)(×)ℓ 3: W 0 ← W (initialize) 4: D (0) (Initialization using an approximation) 5: for itr= 1 to numItr do 6: W (t)(+1) = f(W t ) (Matching based on joint maximization of the signal and minimization of interference) 7: W (t)(+1) = PW (t)(+1) (projects W onto the set of power-limited precoders) 8: end for 9: Return W

[0106] In some embodiments, the computational complexity for calculating the pre-encoder matrix in the BS can be improved without performance loss by other methods. In this example, the pre-encoding matrix W can be calculated without explicitly basing the computation on decoding procedures at the UE by approximating the decoding procedures at the UE. The objective function can also be constrained by performance limitations resulting from the number of power amplifiers.

[0107] In another example, the processor can be configured to calculate the precoder based on the joint maximization of the signal with respect to the noise and the minimization of interference with respect to the noise, using the approximate decoder. The signal can be maximized while interference is minimized.

[0108] In another example, the processor can be configured to compute the precoder based on a performance constraint using block coordinate descent. In yet another example, the processor can be configured to generate the precoder for pre-coding a downlink signal for transmission from the BS to a user device (UE).

[0109] In some embodiments, the signal can be maximized using a signal-to-noise ratio (SNR) constraint, and interference can be minimized using a signal-to-noise-plus-noise (SINR) constraint. In some examples, neither the SNR nor the SINR can be included in the objective function. That is, the objective function can be: ‖W‖2→min st HW=I subject to the following conditions: Di*Hi∑Wj=I ∀i≤k|∑ei'Wj|2≤1n ∀i≤n where Di* The approximated decoder is used. In some embodiments, the pre-encoder can be adapted based on the power constraint (i.e., the third expression shown above) using block coordinate descent.

[0110] In some embodiments, block coordinate descent can provide an approximation of the values ​​for the precoder or other parameters. As shown, block coordinate descent can be used to compute the precoder as follows:

[0111] In some embodiments, the precoder can be computed by parallelization. In other embodiments, random sampling can be used to compute the precoder asynchronously. An example of an algorithm for computing the precoder using parallelization and / or random sampling might be:

[0112] In some embodiments, the pre-encoder can be projected onto a boundary based on the power constraint. A local optimum can be computed on the boundary. In some embodiments, the pre-encoder can be computed by iteration. An example of an algorithm for computing the pre-encoder using an iterative process and / or projection might be:

[0113] In some embodiments, the base station may be able to perform a joint configuration with the UE.

[0114] The blocks used in block coordinate descent can be any row of antenna ports in the precoder matrix. For example, with 16 layers and 64 antenna ports, the precoder matrix can be a 64 × 16 precoder matrix. Each of the 64 rows can be connected to an antenna port, which can have 16 coefficients.

[0115] In some embodiments, the blocks used in block coordinate descent can comprise any number of antenna connections. For example, with 16 layers and 64 antenna connections, more than one row of the precoding matrix can be used for block coordinate descent. That is, 2 rows can be used for block coordinate descent (which can yield 32 separate blocks), or 4 rows (which can yield 16 separate blocks), or 8 rows (which can yield 8 separate blocks), or similar.

[0116] In some embodiments of parallel block coordinate descent, a block can be a row of a precoder matrix corresponding to an antenna port, with many blocks being processed in parallel. That is, a first block can correspond to the first row of a precoder matrix, which can correspond to a first antenna port, and a second block can correspond to the second row of a precoder matrix, which can correspond to a second antenna port. The first and second blocks can be processed in parallel instead of sequentially. Any suitable number of blocks can be processed in parallel.

[0117] In some embodiments, the performance difference between block coordinate descent and / or parallel block coordinate descent compared to the basic truth can be about 2 to 3 dB. In other embodiments, the performance difference between block coordinate descent and / or parallel block coordinate descent and zero-forcing can be about 6 dB. In some embodiments, parallel block coordinate descent can provide a performance improvement in an FPGA (Field Programmable Gate Array).

[0118] The communication system 700 may be modified, supplemented, or omitted without exceeding the scope of this disclosure. For example, in some embodiments, the processing device 708 may be integrated into the transceiver 716. Alternatively or additionally, the communication system 700 may include any number of other components that may not be explicitly shown or described.

[0119] In some embodiments, as in Fig. Figure 8 shows a linear transmission model for MIMO (Multiple In, Multiple Out) communication with k UEs and p antenna connections (i.e., RF chains) as follows: y = HWs + n. In this model, (i)y ∈ ℂ m the received signal for k UEs (each UE with m i antennas and m = ∑ imi) be (i.e., m is the total number of receiving antennas), (ii) s = [si] : where si ∈ ℂ(ℓ)i the intended message for the i ten The user is (assuming that ℓ i Layers). The transmit vectors can be randomly generated from a quadrature amplitude modulation (QAM) configuration; (iii) n can be the additive noise (e.g., Gaussian noise) introduced through the channel, (iv) W∈ℂ n×ℓ (can be the combined effect of the pre-encoder and the digital beamformer), where ℓ = ∑ℓi, and where n is the total number of transmitting antennas; and (v)H ∈ℂ m×n: can be the communication channel, where m is the number of receiving antennas and n is the number of transmitting antennas. This linear transmission model may not model the data before or after the inverse fast Fourier transform (iFFT), which may not account for the effects of optical distortion, pre-fix addition, upsampling, crest factor reduction (CFR), digital pre-distortion (DPD), power amplification, and digital-to-analog or analog-to-digital conversion.

[0120] In some embodiments, a communication system 800 can be configured to receive bits, as shown in 802, process the bits, and send the processed bits to a device. The bits 802 can be received for encoding and modulation operations, as shown in block 804. The encoding and modulation operations can include one or more error-correcting code (ECC) encodings, quadrature amplitude modulation (QAM), layer mapping, resource element mapping, or the like. Alternatively or additionally, the processed bits can be pre-coded and digitally beamshaped, as shown in block 806.The processed bits can be subjected to numerous operations, including one or more OFDM (Orthogonal Frequency Division Multiplexing) modulations, which are processed at a digital front end, converted into an analog signal by a digital-to-analog converter (DAC), and amplified at one or more power amplifiers (PAs) before being transmitted by one or more antennas (810, 812) on communication channel H. Alternatively or additionally, an analog beamformer (i.e., a phase shifter) can process the analog signal received by the PAs before transmission.

[0121] In some embodiments, the UE can receive a signal y on the communication channel H and make an estimate x=Dy of the transmitted QAM symbols, passing the estimate to an error correction code (ECC) decoder to provide bits, as shown in block 832. The signal received at the one or more antennas 816, 820 can also contain additive noise (e.g., 822, 824) introduced by each channel. The signal can be demodulated and converted into a digital signal by an analog-to-digital converter (ADC). The resulting signal can be decoded by a decoder D, as shown in block 826. The decoded signal can be further processed, as shown in block 828, and detected and decoded, as shown in block 830, to provide estimated bits, as shown in block 832.

[0122] In some embodiments, the low-rate feedback path 838 can contain quantized channel state information (CSI) that can be reported back to the BS by the receiving device, as shown in block 834. The quantized CSI-related information can be channel quality indicators (CQI), precoding matrix indices (PMI), or similar information such as those used in codebook-based CSI. The low-rate feedback path 838 can provide a weight update 840 that the precoder W in block 806 can use in beamforming. That is, the intended messages can be weighted with a weight w provided via the low-rate feedback path 838.

[0123] In some embodiments, the decoded message x can be calculated as follows: DHWs + Dn, where D is the decoding operation, H is the communication channel, W is the precoding operation, s is the message intended for the UE, and n is the additive Gaussian noise introduced through the communication channel H.

[0124] In some embodiments, the linear transmission model described here can represent a model for a fixed time and frequency resource (i.e., a specific resource element (RE)). The linear transmission model can further be indexed by the number of REs available during a transmission. Thus, the communication channel ℂ can be defined by: (i) the transmitting antenna m i and the receiving antenna r i, (ii) n, the Gaussian noise introduced into the communication channel, (iii) the number of subcarriers, q, and (iv) f, the number of OFDM symbols used in a transmission. That is, there can be one communication channel for each RE in the resource grid.

[0125] In some embodiments, such as in Fig. As depicted, a grid with q subcarriers and f OFDM symbols can provide a channel H for a fixed q and a fixed f. That is, any combination of f and q can be assigned to a specific channel H, which can have m rows based on the number of transmitting antennas and n columns based on the number of receiving antennas. In an example for a 200 MHz signal in a fifth-generation (5G) 3GPP network, q can have a value equal to the product of 550 (i.e., 275 RBs in 100 MHz and therefore 550 RBs in 200 MHz) and 12 (i.e., the number of subcarriers), and f can have the value of 14 OFDM symbols per slot.

[0126] In some embodiments, the channels may be correlated but are not necessarily identical. The channels may differ for various reasons, including: (i) propagation physics (e.g., variations in the center frequency leading to different phase shifts at different frequencies), (ii) multipath effects (e.g., frequency-selective channel amplification), (iii) Doppler effects (e.g., time-selective channel amplification), or (iv) stochastic effects (channel models based on clusters, where each geometric ray is replaced by a cluster of random rays whose statistics may be determined by the geometry).

[0127] In at least some embodiments, only the data portion of the channel can be modeled. Additionally or alternatively, the non-data portions of the channel (e.g., synchronization signals and CSI-RS) can also be modeled.

[0128] In some embodiments, such as in Fig. Figure 10 shows an example of a 3GPP 5G signal chain in the downlink. A signal can be generated as a synchronization signal (e.g., a primary synchronization signal (PSS) or a secondary synchronization signal (SSS), as in block 1002, or a cell-specific reference signal (CRS), as in block 1004). Various control channels can be used to transmit control information, e.g.,: (a) a physical hybrid ARQ indicator channel (PHICH) (for indicating the reception of a physical downlink shared channel transmission (PDSCH) in LTE), as shown in block 1006, (b) a physical broadcast channel (PBCH) (for transmitting a master information block (MIB), as shown in block 1008, (c) a physical downlink control channel (PDCCH) (for transmitting downlink control information (DCI), as shown in block 1008, and (d) a physical control format indicator channel (PCFICH) (for transmitting information about OFDM symbols in the time domain and frequency domain), as shown in block 1008.

[0129] In other embodiments, data can be transmitted via the PDSCH, as in Block 1010. The data can be transmitted using a number of transmission modes, including: (i) Transmission Mode 1 (1 TX), as in Block 1014, (ii) Transmit Diversity (TxD), as in Block 1016, (iii) Spatial Multiplexing Large Delay Cyclic Delay Diversity (SM LD CDD), as in Block 1018, (iv) Spatial Multiplexing No Cyclic Delay Diversity (SM No CDD), as in Block 1020, and (v) UE Specific Transmission Mode, as in Block 1022, or similar.

[0130] In some embodiments, the synchronization signals can be generated as in Block 1024. The sequences for the CRS can be generated as in Block 1026. The control channels and the data channels can transmit signals that may be scrambled, as in Block 1028a for a PHICH, or as in Block 1028b for a PBCH, PDCCH, PCFICH, or as in Block 1028c for a 1 TX transmission mode, or as in Block 1028d for a TxD transmission mode, or as in Block 1028e for an SM LD CDD transmission mode, or as in Block 1028f for an SM No CDD transmission mode, or as in Block 1028g for a UE-specific transmission mode. For a PDSCH channel used with a UE-specific transmission mode, a demodulation reference signal (DM-RS) can be generated as in Block 1030. Alternatively or additionally, a channel state information reference signal (CSI-RS) can be generated as in block 1032.

[0131] In some embodiments, the resulting digital signal can be QAM-modulated after signal generation, sequence generation, scrambling, or reference signal generation for each individual case, as described in blocks 1034a to 1034k. For certain transmission modes (e.g., SM LD CDD, SM No CDD, and UE-specific), layer mapping can further process the digital signal, as described in blocks 1036a to 1036c. The digital signal can also be mapped to resource elements, as described in block 1038. Additionally, IQ compression and / or IQ decompression can be used, as described in blocks 1040 and 1042.

[0132] In some embodiments, the digital signal can be further mapped onto layers, as in blocks 1044a to 1044d. The signal can be pre-coded based on the respective channel and transmission mode. This means: (i) transmission diversity precoding can be used for the PHICH, the PBCH, the PDCCH, and the PCFICH, as in blocks 1046a and 1046b; (ii) transmission mode 1 precoding can be used for the PDSCH used in a transmission mode 1, as in block 1048; (iii) transmission diversity precoding can be used for the PDSCH used in a transmission diversity transmission mode, as in block 1046c; (v) SM LD CDD precoding can be used for the PDSCH used in an SM LD CDD transmission mode, as in block 1050; and (vi) SM No CDD precoding can be used for the PDSCH used in an SM No CDD transmission mode, as in block 1052.Precoding and beamforming can also be used when a UE-specific transmit mode is used for a PDSCH, as in block 1054. The beamforming itself can be used with a CSI-RS, as in block 1056. In some examples, an optional transmit beam 1058 can be used for common channels or signals (e.g., PSS, SSS, CRS, PHICH, PBCH, PDCCH, PCFICH, non-UE-specific PDSCH, or similar).

[0133] In some embodiments, the digital signal can be modulated using orthogonal frequency-division multiplexing (OFDM), employing an iFFT to generate an OFDM signal in digital form, as shown in block 1060. A cyclic prefix (CP) can be added to the guard intervals between the OFDM symbols. The OFDM signal can drive a digital-to-analog converter (ADC) to generate an analog signal, as shown in block 1062. The analog signal can be subjected to analog beamforming, as shown in block 1064. After upconversion to a higher frequency and amplification by a power amplifier, the analog signal can be transmitted over the air to be received by a receiver, such as a UE.

[0134] In some embodiments, such as in Fig. As shown in Figure 11, a communication channel can be modeled for each transmit / receive antenna pair (e.g., 1112, 1114, and 1116). In this example, some or all paths / rays along which the signal can be routed to the handheld device 1108 can be modeled with a delay value and a gain value. The model can be constructed for the center of the transmit array (e.g., the origin of the graph) and then extrapolated to the remaining arrays based on geometric considerations (e.g., 1118 is the distance between the center of the array and an offset in the positive z-direction (1106), and 1120 is the distance between a first and second offset in the y-direction (1104), and offsets can also be calculated in the x-direction (1102)). The angular deviations with respect to each axis (e.g.,The values ​​for y (as represented by Φ) and z (as represented by Θ) can also be used for extrapolation to the remaining arrays based on geometric considerations. The channel gain from the transmitting antenna, t, to the receiving antenna, r, at a frequency, f, can be calculated as follows: h. t(,)r (f) = ∑(ℓ) α ℓ,t,r exp (2πτ ℓ,t,r f), where the sum is calculated over all possible paths (e.g., 1110 combines the three paths 1112, 1114, and 1116, which can be used to calculate the channel gain). The channel gain can be estimated for each antenna pair (e.g., each possible path) for each resource element.

[0135] In some embodiments, such as in the Fig. As shown, extrapolation between antennas and frequencies can be performed. For example, a codebook-based estimation can be used to determine the channel in beamspace for a large number of antennas. A subset of the antennas can then be used for extrapolation to a complete matrix by mapping channels in space and frequency.

[0136] In some embodiments, the multipath characteristics of the transmission paths between a base station and a terminal device can be used to map a channel from a first set of antennas at a first frequency to a second set of antennas at a second frequency. As in Fig. As shown in Figure 12, a user device 1200 can be configured to communicate with a first set of antennas 1202 at a first frequency via a first 1210, 1212, and second 1218 transmission path, and with a second set of antennas 1204 at a second frequency via a third 1214, 1216, and fourth 1220 transmission path. The first set of antennas 1202 and the second set of antennas 1204 can be arranged together or distributed. A channel assignment can connect the first set of antennas 1202 with the second set of antennas 1204. The first transmission path can be deflected by an obstacle (e.g., 1206) so that the first transmission path includes one path 1210 and another path 1212. The third transmission path can be diverted by an obstacle (e.g. 1208), so that the third transmission path includes a path 1214 and another path 1216.

[0137] In some embodiments, a neural network 1300 can be used to map the channel, as in Fig. Figure 13 illustrates this. As shown, data associated with the first and second transmission paths between a UE and a first set of antennas can be categorized by subcarrier index and antenna index, as shown in blocks 1302 and 1304. The data can be vectorized, as shown in block 1306, processed by several layers (1308, 1310, 1312, 1314) of a neural network, and further processed by 2D transformation, as shown in block 1316, to produce mapped data associated with the first and second transmission paths between the UE and a second set of antennas, which can be categorized by subcarrier index and antenna index, as shown in blocks 1318 and 1320.

[0138] An example of channel allocation based on the number of selected antennas in the first group of antennas and the achievable spectral efficiency (bits per second (bps) per hertz (Hz)) is shown in Fig. The lower bound method, shown in triplicate, demonstrates that the achievable spectral efficiency increases linearly with the number of antennas in the first antenna set. That is, for the lower bound method, the achievable spectral efficiency is: for one antenna approximately 0.5 bps / Hz; for two antennas approximately 0.7 bps / Hz; for three antennas approximately 1.1 bps / Hz; for four antennas approximately 1.3 bps / Hz; for eight antennas approximately 2.0 bps / Hz; for sixteen antennas approximately 2.7 bps / Hz; and for thirty-two antennas approximately 3.7 bps / Hz.

[0139] In contrast, the channel mapping method, as shown in triplicate, demonstrates that the achievable spectral efficiency increases exponentially up to an asymptote as the number of antennas in the first antenna set increases. That is, for the channel mapping method, the average achievable spectral efficiency is: for one antenna approximately 0.7 bps / Hz; for two antennas approximately 1.3 bps / Hz; for three antennas approximately 3.2 bps / Hz; for four antennas approximately 4.2 bps / Hz; for eight antennas approximately 4.6 bps / Hz; for sixteen antennas approximately 4.6 bps / Hz; and for thirty-two antennas approximately 4.6 bps / Hz. The channel mapping method approaches the upper limit that arises from perfect channel knowledge.

[0140] Fig. Figure 1500 shows the procedure of an exemplary method 1500 for beam shaping estimation according to at least one embodiment described in the present disclosure. Method 1500 can be carried out in accordance with at least one of the embodiments described in the present disclosure.

[0141] The method 1500 can be performed by a processing logic that may include hardware (circuits, dedicated logic, etc.), software (such as that executed on a computer system or dedicated machine), or a combination of both, the processing logic being located in the processing device 708. Fig. 7, the 800 communication system from Fig. 8 or any other device, combination of devices or systems.

[0142] Procedure 1500 can begin in block 1505, where the processing logic in a BS can obtain a channel assessment for a UE. The channel assessment can be received by the UE using a SRS.

[0143] In block 1510, the processing logic in the BS can calculate an initial power level adjustment for a downlink (DL) signal for transmission to the UE. In some embodiments, the initial power level adjustment can be calculated using the channel estimation for the UE. In some embodiments, the initial power level adjustment can also be calculated using null forcing to minimize noise and maximize the signal, as measured by a ratio.

[0144] In block 1515, the processing logic in the BS can calculate a second power level adjustment for the DL signal for transmission to the UE. In some embodiments, the second power level adjustment can be calculated by adjusting the first power level adjustment based on an antenna power limit. In some embodiments, the second power level can be calculated using MMSE.

[0145] In block 1520, the processing logic in the BS can pre-code the DL signal for transmission to the UE using the second power level adjustment.

[0146] Method 1500 may be modified, supplemented, or omitted without departing from the scope of this disclosure. For example, in some embodiments, Method 1500 may include any number of other components that are not explicitly shown or described.

[0147] Fig. Figure 1600 shows the sequence of an exemplary method that can be used for beam shaping estimation according to at least one embodiment described in this disclosure. Method 1600 can be set up in accordance with at least one embodiment described in this disclosure.

[0148] Method 1600 can be performed by processing logic that may include hardware (circuits, dedicated logic, etc.), software (such as that executed on a computer system or dedicated machine), or a combination of both, the processing logic being located in the processing device 708. Fig. 7, the 800 communication system from Fig. 8 or any other device, combination of devices or systems.

[0149] Method 1600 can begin in block 1605, where the processing logic in the UE can obtain a channel estimate for the UE. In some embodiments, the channel estimate can be obtained directly or based on a reference signal. The channel estimate can be transferred to the BS using the SRS.

[0150] In block 1610, the processing logic in the UE can create a decoder by initializing it using channel estimation and setting it to decode the pre-coded message. In some embodiments, the pre-coded message can be pre-coded based on an antenna power constraint (e.g., using MMSE). In some embodiments, the decoder can be initialized using null forcing to minimize noise and maximize the signal, measured against a ratio.

[0151] In block 1615, the processing logic can decode the pre-coded message using the decoder at the UE.

[0152] Modifications, additions, or omissions may be made to Method 1600 without departing from the scope of this disclosure. For example, in some embodiments, Method 1600 may include any number of other components that are not explicitly shown or described.

[0153] Fig. Figure 17 shows the sequence of an exemplary method 1700, which can be used for beam shaping estimation in accordance with at least one embodiment described in the present disclosure. The method 1700 can be carried out in accordance with at least one embodiment described in the present disclosure.

[0154] Method 1700 can be performed by processing logic that may include hardware (circuits, dedicated logic, etc.), software (such as that executed on a computer system or dedicated machine), or a combination of both, the processing logic being located in the processing device 708. Fig. 7, the 800 communication system from Fig. 8 or any other device, combination of devices or systems.

[0155] Method 1700 can begin in block 1705, where the processing logic can initialize a pre-encoder that uses zero-forcing based on a channel estimation. In some embodiments, the processing logic can initialize the pre-encoder based on one or more of a number of downlink layers for a component carrier, a number of UEs, a number of transmit antenna elements, a number of receive antenna elements, a number of resource blocks available for beamforming, an error parameter, or a regularization parameter.

[0156] In block 1710, the processing logic can adjust the precoder based on the combined maximization of the signal relative to the noise and minimization of interference relative to the noise. In some embodiments, the SINR can be optimized together with the SNR. In some embodiments, the processing logic can simultaneously maximize the signal relative to the noise using a signal-to-noise ratio (SNR) and minimize interference relative to the noise using a signal-to-noise-plus-noise ratio (SINR).

[0157] In block 1715, the processing logic can match the precoder based on a power constraint using the minimum mean squared error (MMSE). In some embodiments, the processing logic can project the decoder into a set of decoders connected to the set of power-constrained precoders. In some embodiments, the processing logic can match the precoder based on a power constraint using gradient descent.

[0158] In block 1720, the processing logic can generate the pre-encoder for pre-coding a downlink signal for transmission from the BS to a user device (UE).

[0159] In some embodiments, the processing logic can generate the precoder based on a precoding gradient and a precoding partial hessian. In some embodiments, the processing logic can generate the decoder based on a decoding gradient and a partial decoding hessian. In some embodiments, the processing logic can generate the precoder using the minimum mean squared error (MMSE) and a signal-to-noise ratio (INSR) limit or an SNR limit.In some embodiments, the processing logic can generate the precoder based on one or more downlink layers for a component carrier, a total number of UEs, a total number of transmit antenna elements, a total number of receive antenna elements, a total number of resource blocks (RBs) available for beamforming, an error parameter, or a regularization parameter.

[0160] In some embodiments, the processing logic can initialize a decoder using a channel estimate and the precoder. In some embodiments, the processing logic can generate the decoder based on a decoding gradient and a partial decoding hessian. In some embodiments, the processing logic can project the decoder into a set of decoders connected to the set of power-limited precoders.

[0161] Method 1700 may be modified, supplemented, or omitted without exceeding the scope of this disclosure. For example, in some embodiments, Method 1700 may include any number of other components that are not explicitly shown or described.

[0162] Fig. Figure 18 shows the sequence of an exemplary method 1800, which can be used for beam shaping estimation according to at least one embodiment described in the present disclosure. The method 1800 can be carried out in accordance with at least one embodiment described in the present disclosure.

[0163] Method 1800 can be performed by a processing logic that may include hardware (circuits, dedicated logic, etc.), software (such as that executed on a computer system or dedicated machine), or a combination of both, the processing logic being located in the processing device 708. Fig. 7, the 800 communication system from Fig. 8 or any other device, combination of devices or systems.

[0164] Method 1800 can begin in block 1805, where the processing logic can compute the precoder based on jointly maximizing the signal with respect to the noise and minimizing the interference with respect to the noise. In some embodiments, the SINR can be optimized jointly with the SNR. In some embodiments, the processing logic can jointly maximize the signal with respect to the noise using a signal-to-noise ratio (SNR) and minimize the interference with respect to the noise using a signal-to-noise-plus-noise ratio (SINR).

[0165] In block 1810, the processing logic can compute the precoder based on a power constraint. In some embodiments, the processing logic can compute the precoder based on a power constraint using stochastic gradient descent. In some embodiments, the processing logic can compute the precoder by iteration. In some embodiments, the processing logic can compute the precoder using iteration based on a change in the channel conditions.

[0166] In block 1815, the processing logic can generate the pre-coder for pre-coding a downlink signal for transmission from the BS to a user device (UE). In some embodiments, the DL signal can be based on one or more of a number of downlink layers for a component carrier, a number of transmit antenna elements, a number of receive antenna elements, a polarization, or a number of antenna ports.

[0167] In some embodiments, the processing logic in the base station can calculate the approximate decoder based on the UE.

[0168] Fig. Figure 19 shows the sequence of an exemplary method 1900, which can be used for beam shaping estimation in accordance with at least one embodiment described in the present disclosure. The method 1900 can be carried out in accordance with at least one of the embodiments described in the present disclosure.

[0169] Method 1900 can be performed by a processing logic that may include hardware (circuits, dedicated logic, etc.), software (such as that executed on a computer system or dedicated machine), or a combination of both, the processing logic being located in the processing device 708. Fig. 7, the 800 communication system from Fig. 8 or any other device, combination of devices or systems.

[0170] Method 1900 can begin in block 1905, where the processing logic can compute a pre-encoder based on the joint maximization of a signal with respect to noise and the minimization of interference with respect to noise. In some embodiments, the SINR can be optimized jointly with the SNR. In some embodiments, the processing logic can jointly maximize the signal with respect to noise using a signal-to-noise ratio (SNR) and minimize interference with respect to noise using a signal-to-noise-plus-noise ratio (SINR).

[0171] In block 1910, the processing logic can calculate the pre-encoder based on a power constraint using block coordinate descent. The one or more blocks used in the block coordinate descent can be connected to one or more antenna connections.

[0172] In block 1915, the processing logic can generate the pre-coder for pre-coding a downlink (DL) signal for transmission from the base station to a user device (UE). In some embodiments, the DL signal can be based on one or more downlink layers for a component carrier, a number of transmit antenna elements, a number of receive antenna elements, a polarization, or a number of antenna connections.

[0173] In some embodiments, the processing logic can project onto a boundary based on the performance constraint. In some embodiments, the processing logic can compute a local optimum at the boundary.

[0174] In some embodiments, the processing logic can compute the precoder by iteration. In some embodiments, the processing logic can compute the precoder using parallelization. In some embodiments, the processing logic can compute the precoder asynchronously. In some embodiments, the processing logic can perform a joint configuration with the UE.

[0175] For the sake of simplicity, the procedures and / or processes described herein are presented and described as a series of actions. However, the operations described in this disclosure can be carried out in different sequences and / or simultaneously, as well as in conjunction with other operations not presented or described here. Furthermore, not all of the actions presented can be used to carry out the procedures according to the disclosed subject matter. In addition, those skilled in the art will understand and recognize that the procedures can alternatively be represented as a series of interconnected states via a state diagram or events. Moreover, the procedures disclosed in this description can be stored on a manufactured item, such as a non-transient computer-readable medium, to facilitate the transport and transfer of such procedures to computers.The term "product" as used here refers to a computer program accessible from any computer-readable device or storage medium. Although represented as individual blocks, various blocks can be subdivided into additional blocks, combined into fewer blocks, or eliminated, depending on the desired implementation.

[0176] Fig. Figure 2 shows a schematic representation of a machine in the exemplary form of a Computer 2000, in which a set of instructions can be executed to cause the machine to perform one or more of the procedures discussed herein. The Computer 2000 can be a rackmount server, a router computer, a server computer, a mainframe, a laptop computer, a tablet computer, a desktop computer, or any computer with at least one processor, etc., in which a set of instructions can be executed to cause the computer to perform one or more of the procedures discussed herein. In alternative embodiments, the machine can be connected (e.g., networked) to other machines in a local area network (LAN), an intranet, an extranet, or the Internet. The computer can operate in the function of a server in a client-server network environment.Even if only a single computer is depicted, the term "computer" can also encompass any collection of computers that, individually or collectively, execute a set (or multiple sets) of instructions to perform one or more of the procedures discussed herein.

[0177] The example computer device 2000 comprises a processing device (e.g. a processor) 2002, a main memory 2004 (e.g. read-only memory (ROM), flash memory, dynamic random access memory (DRAM) such as synchronous DRAM (SDRAM)), a static memory 2006 (e.g. flash memory, static random access memory (SRAM)) and a data storage device 2016, which communicate with each other via a bus 2008.

[0178] The processing device 2002 is one or more general-purpose processing devices, such as a microprocessor, a central processing unit, or the like. Specifically, the processing device 2002 may include a CISC (Complex Instruction Set Computing) microprocessor, a RISC (Reduced Instruction Set Computing) microprocessor, a VLIW (Very Long Instruction Word) microprocessor, a processor implementing other instruction sets, or a processor implementing a combination of instruction sets. The processing device 2002 may also include one or more specialized processing devices, such as an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a digital signal processor (DSP), a network processor, or the like.The processing device 2002 is configured to execute instructions 2026 to carry out the operations and steps discussed here.

[0179] The computer 2000 may further include a network interface device 2022 that can communicate with a network 2018. The computer 2000 may also include a display device 2010 (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)), an alphanumeric input device 2012 (e.g., a keyboard), a cursor control device 2014 (e.g., a mouse), and a signal generation device 2020 (e.g., a loudspeaker). In at least one embodiment, the display device 2010, the alphanumeric input device 2012, and the cursor control device 2014 may be combined in a single component or device (e.g., an LCD touchscreen).

[0180] The data storage device 2016 may contain a computer-readable storage medium 2024 on which one or more sets of instructions 2026 are stored, embodying one or more of the procedures or functions described herein. The instructions 2026 may also reside wholly or at least partially in the main memory 2004 and / or the processing device 2002 while being executed by the computer 2000, the main memory 2004 and the processing device 2002 also being computer-readable media. The instructions may furthermore be transmitted or received over a network 2018 via the network interface device 2022.

[0181] While the computer-readable storage medium 2024 is depicted as a single medium in one embodiment, the term "computer-readable storage medium" can encompass a single medium or multiple media (e.g., a central or distributed database and / or associated caches and servers) that store one or more sets of instructions. The term "computer-readable storage medium" can also encompass any medium capable of storing, encoding, or carrying a set of instructions for execution by the machine, and which causes the machine to perform one or more of the methods disclosed herein. Accordingly, the term "computer-readable storage medium" can include, but is not limited to, solid-state storage media, optical media, and magnetic media. EXAMPLES

[0182] The following are examples of the performance characteristics according to the embodiments of the present disclosure. EXAMPLE 1: Power distribution for regulated ZF in a 4-group case and an 8-group case

[0183] As in the Fig. The power distribution across the transmitting antennas for Regularized IF was compared for: (i) a 100 MHz band with 4 groups, 32 UEs, 64 transmitting antennas (dual polarized and arranged in a 4 x 8 panel), in which each user has 4 receiving antennas and receives about 25 MHz of the spectrum, and (ii) a 100 MHz band with 8 groups, 32 UEs, 64 transmitting antennas (dual polarized and arranged in a 4 x 8 panel), in which each user has 4 receiving antennas and receives about 12 MHz of the spectrum.

[0184] As in Fig. As shown in Figure 21, each user unit (UE) in the 4 groups had 4 antennas and received approximately 25 MHz of the spectrum in the 100 MHz band. Since channel variations within a group are generally smaller, the shape does not vary due to randomness caused by the multi-user nature of the channel. Most users received 2 data layers. Consequently, in Fig. Sixteen layers per resource element transmit. The power distribution shows that some of the transmitting antennas are operating near capacity (e.g., the peaks at antenna 1, antenna 33, and antenna 64). However, a few transmitting antennas (e.g., antennas 6 to about 30 and antennas 40 to 60) are operating at less than half capacity. Consequently, the power distribution across the transmitting antennas is not near capacity.

[0185] As in Fig. Figure 22 shows that with an increased number of groups (e.g., 8 groups versus 4 groups in Fig. 21) Each UE had 4 antennas and received approximately 12 MHz of the spectrum within the 100 MHz band. The added cross-group diversity to the channel provided more variability, resulting in a more even power distribution. Most users received 2 data layers. Consequently, in Fig. Eight layers were transmitted per resource element. The power distribution shows that some of the transmitting antennas were operating near capacity (e.g., the peaks at antenna 1, antenna 33, and antenna 64). Furthermore, some of the transmitting antennas (e.g., antennas 6 to approximately 30 and antennas 40 to 60) were operating at more than half capacity, and in many cases, at more than 60% capacity. Consequently, the power distribution across the transmitting antennas was not operating near capacity. In this particular example, while power was used more efficiently, the overall power was lower compared to the 4-group case because the spatial diversity was reduced by the scheduler. EXAMPLE 2: Power distribution for Maximum Ratio Transmission in a case with 4 groups

[0186] As in Fig. Figure 23 shows the power distribution over the transmitting antennas for Maximum Ratio Transmission (MRT) for a 100 MHz band with 4 groups, 32 UEs, 64 transmitting antennas (double polarized and arranged in a 4 x 8 panel), in which each user has 4 receiving antennas and receives about 25 MHz of the spectrum.

[0187] With four groups, each unit had four antennas and received approximately 25 MHz of the spectrum within the 100 MHz band. The power distribution was improved compared to the 4-group RTF case in Example 1 because more power was transmitted from each antenna, and the power amplifiers operated more efficiently. The power distribution shows that each of the transmitting antennas was utilized to more than 80% (e.g., antennas numbered 1 to 64). Furthermore, some of the transmitting antennas operated at a capacity of more than 90% (e.g., antennas numbered 40 to 64). Consequently, the power distribution across the transmitting antennas was improved compared to the 4-group RTF and 8-group RTF cases. Nevertheless, the throughput was about 25% lower than with RTF, although the throughput was similar to that of IF. EXAMPLE 3: Performance distribution for MMSE in a 4-group case

[0188] As shown in FIGURE 24, the power distribution over the transmitting antennas for MMSE for a 100 MHz band with 4 groups, 32 UEs, 64 transmitting antennas (double polarized and arranged in a 4 x 8 panel) was shown, in which each user has 4 receiving antennas and receives about 25 MHz of the spectrum.

[0189] With four groups, each unit had four antennas and received approximately 25 MHz of the spectrum within the 100 MHz band. The power distribution was very similar to the four-group RZF case, the eight-group RZF case, and the four-group MRT case. The power distribution shows that each of the transmitting antennas was utilized at approximately 100% (e.g., antennas numbered 1 to 64). Furthermore, the throughput was about 14% higher than with RZF. EXAMPLE 4: Comparison of throughput

[0190] As in Fig. Figure 25 shows that the throughput (in megabits per second (Mbps)) was compared for the 4-group IF case, the 4-group RIF case, the 4-group MRI case, and the 4-group MMSE case. The regularization factor was r = r sc x r0, where r0 was determined based on various parameters such as SNR, number of users, number of antennas, etc.)

[0191] As shown, ZF had the lowest throughput compared to the other cases, at approximately 2500 Mbps. MRT also had a relatively low throughput of approximately 2600 Mbps, comparable to that of ZF. RZF had a higher throughput compared to ZF and MRT, depending on the regularization factor. The MMSE case had the highest throughput at approximately 4100 Mbps. Therefore, the MMSE case had a higher throughput than the ZF, RZF, and MRT cases.

[0192] EXAMPLE 5: SINR comparison between ZF, average MMSE, worst-case MMSE, worst-case MMSE with ZF, and robust average MMSE with ZF

[0193] The SINR for 8 groups of 3-4 users was measured for an average and an unfavorable case. The SINR was defined as follows: WSINRi(W,D)=minj|DijHiWij|F2 / σ2|Dij|F2+∑j≠i|DijHiWj|F2

[0194] For each unit, the SINR for its worst shift (due to QAM limitations) and its average (inverse) SINR of the worst shift per group were calculated. That is, the average (inverse) SINR of the worst shift per group was calculated as follows: AIWSINR=(−1K)∑ilog WSINR(W,D)

[0195] The (inverse) worst-case SINR of the worst shift per group was calculated as follows: WIWSINR=−mini logWSINRi(W,D) Table I ZF Durchschnittlicher MMSEmit ZF SchlechtesterFall MMSE AIWSINR(dB) WIWSINR(dB) AIWSINR(dB) WIWSINR(dB) AIWSINR / WIWSINR(dB) -30.7475 -23.4957 -32.0941 -23.8877 -27.8781 -34.5373 -26.3529 -35.4629 -26.7708 -31.3785 -29.9110 -28.1860 -30.7024 -27.6318 -29.6657 -37.2222 -32.7087 -38.0751 -34.5161 -36.3502 -30.7703 -28.1792 -31.5582 -27.9850 -29.8514 -47.6850 -37.8295 -48.8404 -37.6936 -42.2262 -39.6487 -30.9760 -40.7654 -33.6225 -36.7086 -31.2017 -29.1092 -33.2020 -27.7493 -31.1332

[0196] As shown in Table I, the worst-case MMSE with IF (calculated using AIWSINR / WIWSINR) performed worse than the IF calculated using the average (inverse) worst layer (i.e., AIWSINR), but better than the IF calculated using the worst (inverse) worst layer (i.e., WIWSINR). For one group, for example, the worst-case AIWSINR / WIWSINR value for MMSE with IF was -27.8781 dB, which was worse than the corresponding value for IF calculated using AIWSINR (i.e., -30.7475 dB). For the same group, the worst-case AIWSINR / WIWSINR (inverse MMSE) with IF was -27.8781 dB, which was better than the corresponding value for IF calculated using WIWSINR (i.e., -23.4957 dB). It should be noted that AIWSNINR and WIWSINR yield the same results for the worst-case scenario (inverse MMSE with ZF).

[0197] In contrast, the AIWSINR for the average MMSE with IF was better than for IF (measured with AIWSINR). For example, an AIWSINR of -32.0941 dB was measured for one group of average MMSE with IF, while the AIWSINR for the corresponding IF group was -30.7475 dB. In general, the cross-group results for MMSE with IF were up to 2 dB better than the cross-group results for IF with respect to AIWSINR.

[0198] Furthermore, the WIWSINR for the average MMSE with IF was better than IF (measured with WIWSINR). For example, the WIWSINR for the average MMSE with IF was measured at -23.8877 dB for one group, while for the corresponding IF group, the WIWSINR was measured at -23.4957 dB. In general, the cross-group results for MMSE with IF were slightly better than the cross-group results for IF with respect to WIWSINR. Table II Worst-Case MMSE mit ZF ZF RobustedurchschnittlicheMMSE mit ZF AIWSINR(kein Fehler)(dB) AIWSINR'(10% Fehler)(dB) AIWSINR(10% Fehler)(dB) WIWSINR(10% Fehler)(dB) AIWSINR(10% Fehler) (dB) -27.8781 -17.9563 -25.5473 -20.4628 -23.1256 -31.3785 -13.6739 -26.3314 -24.7768 -25.0416 -29.6657 -24.7519 -26.7204 -24.9854 -25.9464 -36.3502 -20.8808 -28.5261 -26.4457 -26.2744 -29.8514 -18.4151 -26.1046 -25.0499 -26.0898 -42.2262 -13.6747 -29.2111 -26.9239 -26.8693 -36.7086 -11.7767 -26.3920 -25.3671 -24.3994 -31.1332 -22.3219 -29.1031 -25.4238 -26.5261

[0199] As shown in Table II, the AIWSINR for the worst-case MMSE with ZF without channel estimation errors was better than the AIWSINR for ZF, as noted in the previous Table I. However, when 10% channel estimation errors were introduced, the AIWSINR for the worst-case MMSE with ZF was worse than the AIWSINR for ZF. For example, the worst-case AIWSINR for MMSE with ZF was -17.9563 for one group, while the AIWSINR for the corresponding group in ZF was -25.5473. Thus, the worst-case scenario with ZF was not robust compared to ZF when channel estimation errors were included in the tests.

[0200] As shown in Table II, the AIWSINR for the robust average MMSE with IF was slightly worse than the AIWSINR for IF, but better than the AIWSINR for the worst MMSE with IF when 10% channel estimation errors were included. For example, the AIWSINR for the robust average MMSE with IF was -26.0898 for one group, and for the corresponding group in IF, the AIWSINR was slightly better at -26.1046. However, compared to the worst MMSE with IF, the AIWSINR for the robust average MMSE with IF (-26.0898) was better than the AIWSINR for the worst MMSE with IF (18.4151). EXAMPLE 6:

[0201] These tests compared the performance characteristics of the MU-MIMO network between MMSE with IF and regularized IF, and IF and SU-MIMO. A 100 MHz band was assumed to be distributed approximately evenly across a specific number of groups (4 and 5 in our examples). The number of groups was determined by the scheduler (along with the assignment of users to the groups) to maximize performance. EXAMPLE 6-A: 64 TX and 33 UEs with 20% channel estimation error

[0202] For case 1, the comparison was performed based on the following properties of the MU-MIMO network. • 64 Tx (arranged in 8x4x2), • 33 units, • 4 groups, • Average number of shifts: 14.75, • Average error in channel estimation: 20%.

[0203] As in Fig. As shown in Figure 26, MMSE with IF delivered, with a channel estimation error of 20% (for MMSE with IF, regularized IF, SF, and SU-MIMO): (1) a higher overall throughput (Mbit / s) (i.e., MMSE with IF, 1956.0 Mbit / s; regularized IF, 1378.0; IF, 521.5; SU-MIMO, 479.0), (2) a higher 10 ten Percentile throughput (Mbit / s) (i.e., MMSE with IF, 11.9 Mbit / s; regulated IF, 2.9 Mbit / s; IF, 6.7; SU-MIMO, 10.0 Mbit / s) and (3) higher efficiency per bit (megabits per watt (Mb / W)) (i.e., MMSE with IF, 1.6 Mb / W; regulated IF, 1.0 Mb / W; IF, 0.8 Mb / W; SU-MIMO, 0.4 Mb / W). MMSE with IF was less computationally intensive compared with regulated IF, IF, and SU-MIMO (i.e., MMSE with IF, 0.0; regulated IF, 55.0; IF, 60.0; SU-MIMO, 100.0). EXAMPLE 6-B: 32 TX and 32 UEs with 14% channel estimation error

[0204] For case 2, the comparison was performed based on the following properties of the MU-MIMO network. • 32 Tx (arranged in 8x4x2), • 32 units, • 5 groups, • Average number of shifts: 11.8, • Average error in channel estimation: 14%.

[0205] As in Fig. As shown in Figure 27, MMSE with IF delivered, with a channel estimation error of 14% (for MMSE with IF, regularized IF, SF, and SU-MIMO): (1) a higher overall throughput (Mbit / s) (i.e., MMSE with IF, 1455.0 Mbit / s; regularized IF, 1157.0; IF, 475.5; SU-MIMO, 425.0), (2) a higher 10 - ten Percentile throughput (Mbit / s) (i.e., MMSE with IF, 17.1 Mbit / s; regulated IF, 11.8 Mbit / s; IF, 11.0; SU-MIMO, 10.5 Mbit / s) and (3) higher efficiency per bit (megabits per watt (Mb / W)) (i.e., MMSE with IF, 2.3 Mb / W; regulated IF, 2.0 Mb / W; IF, 1.1 Mb / W; SU-MIMO, 0.6 Mb / W). MMSE with IF was less computationally intensive compared with regulated IF, IF, and SU-MIMO (i.e., MMSE with IF, 0.0; regulated IF, 55.0; IF, 60.0; SU-MIMO, 100.0).

[0206] In some embodiments, the various components, modules, machines, and services described here can be implemented as objects or processes that run on a computer system (e.g., as separate threads). While some of the systems and procedures described here are generally described as being implemented in software (stored on and / or executed by hardware), specific hardware implementations or a combination of software and specific hardware implementations are also possible and should be considered.

[0207] The terms used here and in particular in the attached claims (e.g. the main parts of the attached claims) are generally to be understood as “open” terms (e.g. the term “including” should be interpreted as “including but not limited to”, the term “with” as “with at least”, the term “comprises” as “comprises but not limited to”, etc.).

[0208] If a specific number of inserted claims is intended, this will be expressly stated in the claim; if no such statement is made, no such intention exists. For better understanding, the introductory phrases "at least one" and "one or more" may be used to introduce claim formulations in the following appended claims, for example. However, the use of such phrases should not be interpreted as limiting a particular claim containing such an introduced claim principle to embodiments containing only such a principle, even if the same claim contains the introductory phrases "one or more" or "at least one" and indefinite articles such as "a" or "an" (e.g.,, “a” and / or “an” should be interpreted as meaning “at least one” or “one or more”; the same applies to the use of certain articles to introduce claim formulations.

[0209] Even if a specific number of introduced lists of claims is expressly stated, it is to be understood that such a list means at least the stated number (e.g., the mere listing "two lists" without other modifiers means at least two lists or two or more lists). Furthermore, in cases where a convention is used analogously to "at least one of A, B, and C, etc." or "one or more of A, B, and C, etc.", such a construction is generally to be understood as including A alone, B alone, C alone, A and B together, A and C together, B and C together, or A, B, and C together, etc. For example, the use of the term "and / or" is to be understood in this sense.

[0210] Furthermore, any disjunctive word or clause containing two or more alternative terms, whether in the description, claims, or drawings, should be understood to include the possibility of including one, one, or both of the terms. For example, the phrase "A or B" should be understood to include the possibilities of "A" or "B" or "A and B".

[0211] Furthermore, the terms "first," "second," "third," etc., are not necessarily used here to denote a specific order or number of elements. Generally, the terms "first," "second," "third," etc., are used as generic terms to distinguish between different elements. Unless it is proven that the terms "first," "second," "third," etc., denote a specific order, these terms should not be understood as denoting a specific order. Similarly, unless it is proven that the terms "first," "second," "third," etc., denote a specific number of elements, these terms should not be understood as denoting a specific number of elements. For example, a first widget can be described as a first page, and a second widget as a second page.The use of the term "second page" in relation to the second widget can serve to distinguish this page of the second widget from the "first page" of the first widget, and is not intended to imply that the second widget has two pages.

[0212] All examples and conditional expressions cited herein are intended for educational purposes, to facilitate the reader's understanding of the invention and the concepts that the inventor has contributed to the advancement of the prior art, and are to be interpreted as applying without limitation to these specifically cited examples and conditions. Although the embodiments of the present disclosure have been described in detail, it is to be assumed that the various modifications, substitutions, and alterations can be made without departing from the spirit and scope of the present disclosure. QUOTES INCLUDED IN THE DESCRIPTION

[0000] This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited patent literature

[0000] US 63 / 487,256

[0001]

Claims

[1] A base station in a radio access network (RAN) with Massive MIMO (massive multiple input multiple output system) (mMIMO-RAN) comprising the following: a processing device which is set up to: Calculating a pre-encoder based on a joint maximization of a signal with respect to noise and a minimization of interference with respect to the noise; Computation of the precoder based on a performance constraint using block coordinate descent; and Generating the pre-coder to pre-code a downlink (DL) signal for transmission from the base station to a user device (UE); and a transceiver that is set up to transmit the DL signal to the UE. [2] The base station according to claim 1, wherein one or more blocks used in the block coordinate descent are assigned to one or more antenna ports. [3] The base station according to claim 1, wherein the processing device is further configured to project the pre-encoder onto a boundary set based on the power constraint. [4] The base station according to claim 3, wherein the processing device is further configured to calculate a local optimum on the marginal set. [5] The base station according to claim 1, wherein the processing device is further configured to calculate the precoder using one iteration. [6] The base station according to claim 1, wherein the pre-encoder is calculated using parallelization. [7] The base station according to claim 1, wherein random sampling is used for asynchronous calculation of the precoder. [8] The base station according to claim 1, wherein the processing device is further configured to perform joint training with the UE. [9] A computer-readable storage medium containing computer-executable instructions which, when executed by one or more processors, cause a base station in a Massive MIMO (massive multiple input multiple output system) (mMIMO-RAN) radio access network to: Calculating a pre-encoder based on a joint maximization of a signal with respect to noise and a minimization of interference with respect to the noise; Computation of the precoder based on a performance constraint using block coordinate descent; and Generating the precoder to precode a downlink (DL) signal for transmission from the base station to a user device (UE). [10] The computer-readable storage medium according to claim 9, wherein one or more blocks used in block coordinate descent are assigned to one or more antenna ports. [11] The computer-readable storage medium according to claim 9, wherein the instructions, when executed by the one or more processors, further cause the base station to do the following: Projecting the precoder onto a boundary set based on the performance constraint. [12] The computer-readable storage medium according to claim 9, wherein the instructions, when executed by the one or more processors, further cause the base station to do the following: Calculating the precoder using parallelization. [13] The computer-readable storage medium according to claim 9, wherein the instructions, when executed by the one or more processors, further cause the base station to do the following: Calculating the precoder using one iteration. [14] A method for beamforming estimation in a Massive MIMO (massive multiple input multiple output system) (mMIMO-RAN) radio access network (RAN), comprising the following: Calculating a pre-encoder in a base station, based on a joint maximization of a signal with respect to noise and a minimization of interference with respect to noise using an approximate decoder; Calculating the pre-encoder in the base station based on a power constraint; and Generating the pre-encoder in the base station to pre-encode a downlink signal for transmission from the BS to a user device (UE). [15] The method of claim 14, which further comprises: joint maximization of the signal at the base station using a signal-to-noise ratio (SNR) constraint; and joint minimization at the base station of interference using a constraint of the SINR (signal-to-interference-plus-noise ratio). [16] The method of claim 14, which further comprises: Calculating the pre-encoder at the base station based on the power constraint using a stochastic gradient descent. [17] The method according to claim 14, which further comprises: Calculating the pre-encoder at the base station using one iteration. [18] The method of claim 17, which further comprises: Calculating the pre-encoder at the base station using iteration based on a channel state change. [19] The method of claim 14, which further comprises: Calculate, at the base station, the approximate decoder based on the UE. [20] The method according to claim 14, wherein the DL signal is based on one or more of a number of downlink layers for a component carrier, a number of transmit antenna elements, a number of receive antenna elements, a polarization or a number of antenna ports.

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