Apparatus and method for a network device

Abstract

An apparatus for a network device, the apparatus comprising at least one processor, and at least one memory storing instructions that, when executed by the at least one processor, cause the network device to: jointly determine, for a plurality of terminal devices, first information characterizing at least two of the following elements: a) a rank, or b) a resource scheduling, or c) a transmit power, transmit at least a respective part of the first information to a respective terminal device.

Description

[0001]Title: Apparatus and Method for a Network Device Specification Field of the Disclosure Various example embodiments relate to an apparatus for a network device. Further example embodiments relate to a method for a network device. Background Communication systems such as, e.g., wireless communication systems may be used for wireless exchange of information between two or more entities, e.g., comprising one or more terminal devices, e.g., user equipment (UE), and one or more network devices such as, e.g., base stations. In some approaches, a plurality of terminal devices, e.g., UE, may be served by one network device, e.g., gNB, and may, e.g., be co-scheduled, e.g., to same time-frequency resources as the other terminal devices, which may be denoted as extreme multi- user (MU)-MIMO (multiple-input multiple-output). Summary Various example embodiments of the disclosure are set out by the independent claims. The example embodiments and features, if any, described in this specification, that do not fall under the scope of the independent claims, are to be interpreted as examples useful for understanding various example embodiments of the disclosure. Some examples relate to an apparatus for a network device, the apparatus comprising at least one processor, and at least one memory storing instructions that, when executed by the at least one processor, cause the network device to: jointly determine, for a plurality of terminal devices, first information characterizing at least two of the following elements: a) a rank, or b) a resource scheduling, or c) a transmit power, transmit at least a respective part of the first information to a respective terminal device. In some examples, the network device may adhere to and / or may be based on some accepted (and / or planned) specification, e.g., standard, such as, e.g., 3G, 4G, 5G, 6G, or some other wireless communication standard. In some examples, similarly, the terminal device may adhere to and / or may be based on some accepted (and / or planned) specification, e.g., standard, such as, e.g., 3G, 4G, 5G, 6G, or some other wireless communication standard. In some examples, the network device may, e.g., be a base station, e.g., gNB. In some examples, the terminal device may, e.g., be a user equipment, UE. In some examples, jointly determining, for the plurality of terminal devices, the first information may enable to maximize a capacity, e.g., of a physical uplink shared channel (PUSCH). In some examples, the rank or a selection of the rank for a terminal device may refer to a number of data layers that the terminal device may use for data transmission, e.g., to the network device. In some examples, the resource scheduling, e.g., resource allocation, for the terminal device may refer to frequency resources, e.g., sections of an overall frequency band as, e.g., allocated to a terminal device, e.g., in an OFDM (Orthogonal Frequency Division Multiplexing) system, e.g., either in terms of physical resource blocks (PRB), or resource block groups (RBG) that may, e.g., consist of several PRBs. In some examples, the transmit power, e.g., UE transmit power, may refer to a transmit power used by a terminal device, e.g., for an uplink (UL) transmission. In some examples, jointly determining the first information for the plurality of terminal devices may address, e.g., to overcome, at least some disadvantages of some conventional approaches, wherein aspects of rank selection, transmit power control and resource allocation are performed independently from each other, e.g., sequentially, so that each aspect may suffer from constraints imposed by decisions made for at least one of the other aspects. In some examples, jointly determining the first information comprises jointly determining the rank and the resource scheduling and the transmit power, e.g., all three aspects. In some examples, the instructions, when executed by the at least one processor, cause the network device to: include at least the respective part of the first information into downlink control information, transmit the downlink control information with the included respective part of the first information. In some examples, this way, the terminal device may be notified of the jointly determined aspects of the rank, the resource scheduling, and the transmit power. In some examples, the terminal device may use this information, e.g., for determining a transmit power per frequency resource, e.g., per subcarrier, and for performing uplink transmission(s) to the network device, e.g., using the so determined transmit power. In some examples, the instructions, when executed by the at least one processor, cause the network device to: receive reference signals from the plurality of terminal devices, perform channel estimation of respective uplink channels of the plurality of terminal devices with a predetermined (e.g., configurable) frequency granularity based on received reference signals to obtain estimated uplink channels, determine the first information based on the estimated uplink channels using at least one of a) a multi-stage optimization procedure, or b) a neural network-based approximation, e.g., of the multi-stage optimization procedure. In some examples, the reference signals may, e.g., be pre-coded, e.g., PUSCH-pre-coded, sounding reference signals, SRS. In some examples, the instructions, when executed by the at least one processor, cause the network device to: determine diagonal elements of a Gram matrix inverse of a whitened channel matrix, e.g., a composite noise-whitened channel matrix, based on the estimated uplink channels at the predetermined frequency granularity (e.g., the same frequency granularity as used for the channel estimation), perform a convex optimization procedure based on the diagonal elements using a geometric mean of the terminal devices' throughputs as an objective function and constraints associated with a transmit power of the terminal devices and with a quality of service-defined rate to obtain a first result characterizing transmit powers per frequency resource and layer for at least some, for example each, of the terminal devices. In some examples, based on the estimated uplink channels, the network device may, e.g., perform an interference-plus-noise ("I+N") whitening, e.g., of each terminal device's estimated uplink channel, e.g., with the same granularity as used for the channel estimation. In some examples, e.g., for the convex optimization procedure, it may be assumed that all frequency resources, e.g., PRB or RBG, are allocated to a plurality of, e.g., co-scheduled, terminal devices. In some examples, the first result represents a set of, e.g., temporarily optimized, allocated transmit powers per frequency resource (e.g., PRB and / or RBG), e.g., for each layer, e.g., for each terminal device. In some examples, the instructions, when executed by the at least one processor, cause the network device to: determine, based on the first result, a second result characterizing at least one of a) useful frequency resources, or b) useful ranks, for at least some, for example each, of the terminal devices, perform, based on the second result, a further optimization procedure to obtain a third result characterizing optimized transmit powers per frequency resource and layer for at least some, for example each, of the terminal devices. In some examples, useful frequency resources, e.g., RBGs, and / or useful ranks are considered to support a minimum predetermined data rate. In other words, in some examples, determining the second result may, e.g., comprise removing such frequency resources, e.g., RBGs, and / or ranks that do not support the minimum predetermined data rate. In some examples, the instructions, when executed by the at least one processor, cause the network device to perform at least one of: a) provide a, for example deep, neural network for determining the first information, or b) train the neural network for determining the first information, or c) use the neural network to determine the first information. In some examples, the neural network may be a deep neural network, DNN, comprising one input layer, one output layer, and one or more intermediate, e.g., hidden, layers arranged between the input layer and the output layer. In some examples, the neural network may be of the convolutional network type, e.g., a convolutional neural network, CNN, e.g., having K many layers, wherein, e.g., K > 2. In some examples, the neural network-based approximation, e.g., using the DNN, e.g., CNN, may, e.g., be used to enable a real- time determination of the first information, e.g., for such cases, wherein the multi-stage optimization procedure may not be feasible, e.g., due to restrictions in processing resources or the like. In some examples, the instructions, when executed by the at least one processor, cause the network device to perform at least one of: a) provide training data for training of the neural network based on received reference signals (e.g., from a real operation of the network device), or b) provide training data for training of the neural network based on synthetic data (as may, e.g., be obtained from one or more simulations). In some examples, the instructions, when executed by the at least one processor, cause the network device to: determine the first information based on the estimated uplink channels using the multi-stage optimization procedure, transmit at least a respective part of the first information to at least one respective terminal device, receive data transmitted by the at least one terminal device based on the respective part of the first information, decode at least a part of the received data, and, based on the decoding, add the first information to the training data (e.g., if a sufficiently large portion of the decoded data is correctly decoded). In some examples, the reference signals are pre-coded, for example physical uplink shared channel, PUSCH, - pre-coded, sounding reference signals, SRS. Some examples relate to an apparatus for a network device, the apparatus comprising means for: jointly determining, for a plurality of terminal devices, first information characterizing at least two of the following elements: a) a rank, or b) a resource scheduling, or c) a transmit power, transmitting respective portions of the first information to a respective terminal device. In some examples, the means for jointly determining the first information and for transmitting may, e.g., comprise at least one processor, and at least one memory storing instructions that, when executed by the at least one processor, cause the network device to perform at least one of the aforementioned aspects of determining the first information and transmitting. In some examples, the means for determining the first information and for transmitting may, e.g., comprise circuitry configured to perform at least one of the aforementioned aspects of determining and / or transmitting. Some examples relate to a method for a network device, comprising: jointly determining, for a plurality of terminal devices, first information characterizing at least two of the following elements: a) a rank, or b) a resource scheduling, or c) a transmit power, transmitting respective portions of the first information to a respective terminal device. Some examples relate to an apparatus for a terminal device, the apparatus comprising at least one processor, and at least one memory storing instructions that, when executed by the at least one processor, cause the terminal device to: receive at least a respective part of first information characterizing at least two of the following elements jointly determined by the network device for a plurality of terminal devices: a) a rank, or b) a resource scheduling, or c) a transmit power, determine a transmit power per subcarrier based on the respective part. Some examples relate to an apparatus for a terminal device, the apparatus comprising means for: receiving at least a respective part of first information characterizing at least two of the following elements jointly determined by the network device for a plurality of terminal devices: a) a rank, or b) a resource scheduling, or c) a transmit power, determining a transmit power per subcarrier based on the respective part. In some examples, the means for receiving and determining may, e.g., comprise at least one processor, and at least one memory storing instructions that, when executed by the at least one processor, cause the network device to perform at least one of the aforementioned aspects of receiving and determining. In some examples, the means for receiving and determining may, e.g., comprise circuitry configured to perform at least one of the aforementioned aspects of receiving and / or determining. Some examples relate to a method for a terminal device, comprising: receiving a at least a respective part of first information characterizing at least two of the following elements jointly determined by a network device for a plurality of terminal devices: a) a rank, or b) a resource scheduling, or c) a transmit power, determining a transmit power per subcarrier based on the respective part. Some examples relate to a network device, e.g., base station, e.g., gNB, comprising at least one apparatus according to the disclosure. Some examples relate to a terminal device, e.g., user equipment, comprising at least one apparatus according to the disclosure. Some examples relate to a communication system comprising at least one apparatus according to the disclosure. Some examples relate to a computer program comprising instructions which, when executed by an apparatus, cause the apparatus to perform at least some aspects of the method according to the examples. In some examples, the computer program may be provided on a computer readable storage medium, e.g., a non-transitory computer readable medium. Some examples relate to a data carrier signal carrying and / or characterizing the computer program according to the example embodiments. Brief Description of the Figures Fig. 1A schematically depicts a simplified block diagram according to some examples, Fig. 1B schematically depicts a simplified block diagram according to some examples, Fig. 2 schematically depicts a simplified block diagram according to some examples, Fig. 3 schematically depicts a simplified flow chart according to some examples, Fig. 4 schematically depicts a simplified block diagram according to some examples, Fig. 5 schematically depicts a simplified flow chart according to some examples, Fig. 6 schematically depicts a simplified flow chart according to some examples, Fig. 7 schematically depicts a simplified flow chart according to some examples, Fig. 8 schematically depicts a simplified flow chart according to some examples, Fig. 9 schematically depicts a simplified flow chart according to some examples, Fig. 10 schematically depicts a simplified flow chart according to some examples, Fig. 11A schematically depicts a simplified block diagram according to some examples, Fig. 11B schematically depicts a simplified block diagram according to some examples, Fig. 12 schematically depicts a simplified flow chart according to some examples, Fig. 13 schematically depicts a simplified block diagram according to some examples, Fig. 14 schematically depicts a simplified signaling diagram according to some examples, Fig. 15 schematically depicts a simplified flow chart according to some examples, Fig. 16 schematically depicts a simplified flow chart according to some examples, Fig. 17 schematically depicts a simplified block diagram according to some examples. Description of some Example Embodiments Some examples, Fig. 1A, 2, 3, relate to an apparatus 100 (Fig. 1A) for a network device 10 (Fig. 2), the apparatus 100 comprising at least one processor 102, and at least one memory 104 storing instructions 106 that, when executed by the at least one processor 102, cause the network device 10 to: jointly determine 300, for a plurality 20 of terminal devices 20a, 20b, 20c, first information I-1 characterizing at least two of the following elements: a) a rank RNK (Fig. 4), or b) a resource scheduling SCHED, or c) a transmit power TX-PWR, transmit 302 (Fig. 3) at least a respective part I-1a, I-1b, I-1c of the first information I-1 to a respective terminal device 20a, 20b, 20c. As an example, the part I-1a associated with the first terminal device 20a may be transmitted by the network device 10 to the first terminal device 20a, and so on. In some examples, Fig. 2, the network device 10 may adhere to and / or may be based on some accepted (and / or planned) specification, e.g., standard, such as, e.g., 3G, 4G, 5G, 6G, or some other wireless communication standard. In some examples, similarly, the terminal device 20a, 20b, 20c may adhere to and / or may be based on some accepted (and / or planned) specification, e.g., standard, such as, e.g., 3G, 4G, 5G, 6G, or some other wireless communication standard. In some examples, the network device 10 may, e.g., be a base station, e.g., gNB. In some examples, the terminal device 20a, 20b, 20c may, e.g., be a user equipment, UE. In some examples, Fig. 3, jointly determining 300, for the plurality 20 of terminal devices, the first information I-1 may enable to maximize a capacity, e.g., of a physical uplink shared channel (PUSCH). In some examples, Fig. 4, the rank RNK or a selection of the rank for a terminal device 20a may refer to a number of data layers that the terminal device 20a may use for data transmission, e.g., to the network device 10. In some examples, Fig. 4, the resource scheduling SCHED, e.g., resource allocation, for the terminal device 20a may refer to frequency resources, e.g., sections of an overall frequency band as, e.g., allocated to the terminal device 20a, e.g., in an OFDM (Orthogonal Frequency Division Multiplexing) system, e.g., either in terms of physical resource blocks (PRB), or resource block groups (RBG) that may, e.g., consist of a few PRBs. In some examples, Fig. 4, the transmit power TX-PWR, e.g., UE transmit power, may refer to a transmit power used by a terminal device 20a, e.g., for an uplink (UL) transmission, e.g., to the network device 10. In some examples, Fig. 3, jointly determining 300 the first information I-1 may comprise jointly determining 300a the rank RNK and the resource scheduling SCHED and the transmit power TX- PWR, e.g., all three aspects RNK, SCHED, TX-PWR. In some examples, Fig. 3, jointly determining 300, 300a the first information I-1 for the plurality 20 of terminal devices 20a, 20b, 20c may address, e.g., overcome, at least some disadvantages of some conventional approaches, wherein aspects of rank selection, transmit power control and resource allocation are performed independently from each other, e.g., sequentially, so that in some conventional approaches each aspect may suffer from constraints imposed by decisions made for at least one of the other aspects. In some examples, Fig. 5, the instructions 106, when executed by the at least one processor 102, cause the network device 10 to: include 310 at least the respective part I-1a of the first information I-1 into downlink control information DCI, transmit 312 the downlink control information DCI with the included respective part I-1a of the first information I-1, e.g., to a respective terminal device 20a. In some examples, this way, the terminal device 20a may be notified of the jointly determined aspects of the rank, the resource scheduling, and the transmit power. In some examples, the terminal device 20a may use this information I-1a, e.g., for determining a transmit power per frequency resource, e.g., per subcarrier, and for performing uplink transmission(s) to the network device 10, e.g., using the so determined transmit power. In some examples, Fig. 6, the instructions 106, when executed by the at least one processor 102, cause the network device 10 to: receive 320 reference signals RS-20 from the plurality 20 of terminal devices 20a, 20b, 20c, perform 322 channel estimation of respective uplink channels of the plurality 20 of terminal devices 20a, 20b, 20c with a predetermined frequency granularity based on received reference signals to obtain estimated uplink channels CH-UL-20a, CH-UL-20b, CH-UL-20c, determine 324 the first information I-1 based on the estimated uplink channels CH- UL-20a, CH-UL-20b, CH-UL-20c using at least one of a) a multi- stage optimization procedure OPT-MS, or b) a neural network- based approximation NN-APPROX. In some examples, further aspects and example embodiments of the multi-stage optimization procedure OPT-MS are explained further below, with respect to, e.g., Fig. 15, 16. In some examples, Fig. 6, the reference signals RS-20 may, e.g., be pre-coded, e.g., PUSCH-pre-coded, sounding reference signals, SRS. In some examples, Fig. 7, the instructions 106, when executed by the at least one processor 102, cause the network device 10 to: determine 330 diagonal elements of a Gram matrix inverse of a whitened channel matrix, e.g., a composite noise-whitened channel matrix, based on the estimated uplink channels CH-UL- 20a, CH-UL-20b, CH-UL-20c at the predetermined frequency granularity (e.g., the same frequency granularity as used for the channel estimation), perform 332 a convex optimization procedure based on the diagonal elements using a geometric mean of the terminal devices' throughputs as an objective function and constraints associated with a transmit power of the terminal devices 20a, 20b, 20c and with a quality of service-defined rate to obtain a first result RES-1 characterizing transmit powers per frequency resource and layer for at least some, for example each, of the terminal devices 20a, 20b, 20c. In some examples, based on the estimated uplink channels CH-UL- 20a, CH-UL-20b, CH-UL-20c, the network device 10 may, e.g., perform an interference-plus-noise ("I+N") whitening, e.g., of each terminal device's estimated uplink channel CH-UL-20a, CH- UL-20b, CH-UL-20c, e.g., with the same granularity as used for the channel estimation. In some examples, e.g., for the convex optimization procedure PROC-OPT, it may be assumed that all frequency resources, e.g., PRB or RBG, are allocated to the plurality 20 of, e.g., co- scheduled, terminal devices 20a, 20b, 20c. In some examples, Fig. 7, the first result RES-1 represents a set of, e.g., temporarily optimized, allocated transmit powers per frequency resource (e.g., PRB and / or RBG), e.g., for each layer, e.g., for each terminal device 20a, 20b, 20c. In some examples, Fig. 7, the instructions 106, when executed by the at least one processor 102, cause the network device 10 to: determine 334, based on the first result RES-1, a second result RES-2 characterizing at least one of a) useful frequency resources, or b) useful ranks, for at least some, for example each, of the terminal devices 20a, 20b, 20c, perform 336, based on the second result RES-2, a further optimization procedure PROC-OPT' to obtain a third result RES-3 characterizing optimized transmit powers per frequency resource and layer for at least some, for example each, of the terminal devices 20a, 20b, 20c. In some examples, useful frequency resources, e.g., RBGs, and / or useful ranks are considered to support a minimum predetermined data rate. In other words, in some examples, Fig. 7, determining 334 the second result RES-2 may, e.g., comprise removing such frequency resources, e.g., RBGs, and / or ranks, that do not support the minimum predetermined data rate. In some examples, Fig. 8, the instructions 106, when executed by the at least one processor 102, cause the network device 10 to perform at least one of: a) provide 340 a, for example deep, neural network NN for determining the first information I-1, or b) train 342 the neural network NN for determining the first information I-1, or c) use 344 the neural network NN to determine the first information I-1. The optional block 346 of Fig. 8 symbolizes transmitting at least a respective part I-1a of the first information I-1 (as, e.g., obtained by the neural network NN, see, for example, block 344) to a respective terminal device 20a. In some examples, the neural network NN may be a deep neural network, DNN, comprising one input layer (not shown), one output layer, and one or more intermediate, e.g., hidden, layers arranged between the input layer and the output layer. In some examples, Fig. 8, the neural network NN may be of the convolutional network type, e.g., a convolutional neural network, CNN, e.g., having K many layers, wherein, e.g., K > 2. In some examples, Fig. 6, the neural network-based approximation NN-APPROX, e.g., using 344 (Fig. 8) the DNN, e.g., CNN, may, e.g., be used to enable a real-time determination of the first information I-1, e.g., for such cases, wherein the multi-stage optimization procedure OPT-MS (Fig. 6) is not feasible, e.g., due to restrictions in processing resources or the like. In some examples, Fig. 9, the instructions 106, when executed by the at least one processor 102, cause the network device 10 to perform at least one of: a) provide 350 training data DAT-TRAIN for training 342 (Fig. 8) of the neural network NN based on received reference signals RS-20 (e.g., from a real operation of the network device 10, see, for example, block 320 of Fig. 6), or b) provide 352 training data DAT-TRAIN for training 342 of the neural network NN based on synthetic data (as may, e.g., be obtained from one or more simulations). In some examples, Fig. 10, the instructions 106, when executed by the at least one processor 102, cause the network device 10 to: determine 360 the first information I-1 based on the estimated uplink channels using the multi-stage optimization procedure MS-OPT, transmit 362 at least a respective part I-1a, I-1b, I-1c of the first information I-1 to at least one respective terminal device 20a, 20b, 20c, receive 364 data DAT- 20 transmitted by the at least one terminal device 20a, 20b, 20c based on the respective part I-1a, I-1b, I-1c of the first information I-1, decode 366 at least a part of the received data DAT-20, and, based on the decoding 366, add the first information I-1 to the training data DAT-TRAIN (e.g., if a sufficiently large portion of the decoded data is correctly decoded). In some examples, e.g., if it was not possible to decode a sufficiently large portion of the received data DAT-20, the first information I-1 may not be added to the training data DAT-TRAIN. In some examples, Fig. 10, at least some aspects 360, 362, 364, 366, 368 may be repeated, see the dashed arrow 369, e.g., until a sufficient amount of training data DAT-TRAIN has been collected. Some examples, Fig. 1B, relate to an apparatus 100' for a network device 10, the apparatus 100' comprising means 102' for: jointly determining 300, for a plurality 20 of terminal devices 20a, 20b, 20c, first information I-1 characterizing at least two of the following elements: a) a rank RNK, or b) a resource scheduling SCHED, or c) a transmit power TX-PWR, transmitting 302 respective portions I-1a, I-1b, I-1c of the first information I-1 to a respective terminal device 20a, 20b, 20c. In some examples, Fig. 1B, the means 102' for jointly determining 300 the first information I-1 and for transmitting 302 may, e.g., comprise at least one processor 102 (see, for example, Fig. 1A), and at least one memory 104 storing instructions 106 that, when executed by the at least one processor 102, cause the network device 10 to perform at least one of the aforementioned aspects of determining 300 the first information and transmitting 302. In some examples, Fig. 1B, the means 102' for determining 300 the first information I-1 and for transmitting 302 may, e.g., comprise circuitry 104' configured to perform at least one of the aforementioned aspects of determining 300 and / or transmitting 302. Some examples, Fig. 3, relate to a method for a network device 10, comprising: jointly determining 300, for a plurality 20 of terminal devices, first information I-1 characterizing at least two of the following elements: a) a rank, or b) a resource scheduling, or c) a transmit power, transmitting 302 respective portions I-1a, I-1b, I-1c of the first information I-1 to a respective terminal device 20a, 20b, 20c. Some examples, Fig. 2, 11A, 12, relate to an apparatus 200 for a terminal device 20a, the apparatus 200 comprising at least one processor 202, and at least one memory 204 storing instructions 206 that, when executed by the at least one processor 202, cause the terminal device 20a to: receive 400 at least a respective part I-1a of first information I-1 characterizing at least two of the following elements jointly determined by the network device 10 for a plurality 20 of terminal devices 20a, 20b, 20c: a) a rank RNK, or b) a resource scheduling SCHED, or c) a transmit power TX-PWR, determine 402 a transmit power per subcarrier TX-PWR-SC based on the respective part I-1a. Some examples, Fig. 11B, relate to an apparatus 200' for a terminal device 20a, the apparatus 200' comprising means 202' for: receiving 400 at least a respective part I-1a of first information I-1 characterizing at least two of the following elements jointly determined by the network device 10 for a plurality 20 of terminal devices: a) a rank, or b) a resource scheduling, or c) a transmit power, determining 402 a transmit power per subcarrier TX-PWR-SC based on the respective part I- 1a. In some examples, Fig. 11B, the means 202' for receiving 400 and determining 402 may, e.g., comprise at least one processor 202 (see, for example, Fig. 11A), and at least one memory 204 storing instructions 206 that, when executed by the at least one processor 202, cause the terminal device 20a to perform at least one of the aforementioned aspects of receiving 400 and determining 402. In some examples, Fig. 11B, the means 202' for receiving 400 and determining 402 may, e.g., comprise circuitry 204' configured to perform at least one of the aforementioned aspects of receiving 400 and / or determining 402. Some examples, Fig. 12, relate to a method for a terminal device 20a, comprising: receiving 400 a at least a respective part I-1a of first information I-1 characterizing at least two of the following elements jointly determined by a network device for a plurality of terminal devices: a) a rank, or b) a resource scheduling, or c) a transmit power, determining 402 a transmit power per subcarrier TX-PWR-SC based on the respective part I- 1a. In some examples, Fig. 12, the terminal device 20a may perform 404 at least one uplink transmission DAT-20, e.g., based on the determined transmit power per subcarrier TX-PWR-SC. Some examples, Fig. 2, relate to a network device 10, e.g., base station, e.g., gNB, comprising at least one apparatus 100, 100' according to the disclosure. In some examples, the apparatus 100, 100' or its functionality, respectively, may be integrated into the network device 10. Some examples, Fig. 2, relate to a terminal device 20a, e.g., user equipment, comprising at least one apparatus 200, 200' according to the disclosure. In some examples, the apparatus 200, 200' or its functionality, respectively, may be integrated into the terminal device 20a. In some examples, the further terminal devices 20b, 20c may, for example, also comprise an apparatus 200, 200' according to the disclosure (not shown). Some examples, Fig. 2, relate to a communication system 1000 comprising at least one apparatus 100, 100', 200, 200' according to the disclosure, and / or at least one network device 10 according to the disclosure, and / or at least one terminal device 20a, 20b, 20c according to the disclosure. In the following, further aspects and examples are disclosed, which, in some examples, may be combined with at least one of the aspects and / or examples disclosed above. Fig. 13 schematically depicts a simplified block diagram of an example communication system according to some examples, e.g., similar to Fig. 2, wherein a network device, e.g., gNB 10 serves a plurality of, presently for example three, terminal devices 20a, 20b, 20c (e.g., UE). In some examples, the terminal devices 20a, 20b, 20c may be co-scheduled, e.g., to same time-frequency resources. The arrows a1, a2, a3 of Fig. 13 symbolize respective uplink data transmissions from the terminal devices, e.g., UE 20a, 20b, 20c to the gNB 10. In some examples, at least one of the devices 10, 20a, 20b, 20c may, e.g., at least temporarily, perform aspects according to the disclosure, e.g., to maximize an uplink throughput of the UE 20a, 20b, 20c. Fig. 14 schematically depicts a simplified signaling diagram according to some examples, wherein element E1 symbolizes the gNB 10 of Fig. 13, wherein elements E2a, E2b, E2c symbolize the UE 20a, 20b, 20c. The arrows a1', a2', a3' of Fig. 14 symbolize respective transmissions of PUSCH-pre-coded sounding reference signals, SRS, from the UE 20a, 20b, 20c to the gNB 10. Element E3 symbolizes the gNB 10 performing channel estimation based on the received sounding reference signals. Element E4 symbolizes the gNB 10 jointly determining, e.g., estimating, ranks, resource scheduling and transmit powers for the UE E2a, E2b, E2c, e.g., in the form of the first information I-1 according to the disclosure (also see, for example, block 300 of Fig. 3). The arrows a4, a5, a6 symbolize the gNB E1 transmitting, to each UE E2a, E2b, E2c, a respective part of the first information I-1 to the respective UE, e.g., in the form of downlink control information, DCI. In other words, in some examples, arrow a4 may characterize a rank, frequency resources (e.g., expressed in PRB), and a transmit power for the first UE E2a, e.g., as jointly determined by the gNB, see block E4, e.g., with the rank, frequency resources (e.g., expressed in PRB), and the transmit power for the second UE E2b, see arrow a5, and with the rank, frequency resources (e.g., expressed in PRB), and the transmit power for the third UE E2c, see arrow a6. In some examples, Fig. 14, using PUSCH-pre-coded sounding reference signals (SRS) a1', a2', a3' from the UEs E2a, E2b, E2c, the gNB E1 may perform the channel estimation E3, e.g., of each UE's uplink channel, e.g., with a predetermined, e.g., configurable, frequency granularity. In some examples, Fig. 14, the gNB E1 may perform interference- plus-noise (I+N) whitening, e.g., of each UE’s estimated channel, e.g., with the same granularity as for the channel estimation E3. In some examples, the diagonal elements of a Gram matrix inverse of the composite noise-whitened channel matrix are obtained (also see, for example, block 330 of Fig. 7), e.g., at the same granularity as that of the channel estimates. In some examples, Fig. 7, 14, e.g., based on the diagonal elements, the gNB E1 may perform a first stage ("Stage 1") optimization, comprising at least one of the following aspects: Using the aforementioned diagonal elements and, e.g., assuming that all the frequency resources, e.g., PRBs / RBGs, are allocated, e.g., to all the co-scheduled UEs E2a, E2b, E2c, a convex optimization procedure is executed (see, for example, also block 332 of Fig. 7). In some examples, for the convex optimization procedure, the geometric mean of the UEs’ throughputs may serve as an objective function, e.g., under a UE transmit power constraint and UE quality of service (QoS)-defined rate constraint. In some examples, this may yield a set of, e.g., temporarily optimized, allocated transmit ("Tx") powers per PRB / RBG and for each layer for each UE (e.g., at least similar to the first result RES-1, see, for example, block 332 of Fig. 7). In some examples, e.g., as an aspect of a further, e.g., second, stage, e.g., "Stage 2", a PRB allocation and rank determination may be performed. In some examples, e.g., based on the obtained temporary allocated transmit powers, the useful PRBs / RBGs and ranks (e.g., PRBs / RBGs and ranks considered to support a minimum predetermined data rate) for each UE may be identified (see, for example, also block 334 of Fig. 7). In some examples, e.g., as a further aspect of the second stage, an optimization may be performed. In some examples, using the determined PRB / RBGs, e.g., characterized by respective PRB / RBG indices, and UE ranks, as, e.g., obtained by the previous step, a second, e.g., final, optimization may be performed, e.g., to obtain a final set of allocated transmit powers per PRB / RBG and layer for each UE (see, for example, also block 336 of Fig. 7). In some examples, e.g., for practical implementation reasons, e.g., to be able to execute at least some of the aforementioned aspects in real time, a resource allocation according to the disclosure, e.g., related to determination of the first information I-1, may be approximated, e.g., using a, for example deep, neural network NN (see, for example, blocks 324 of Fig. 6 and 344 of Fig. 8). In some examples, the neural network NN may take as inputs the diagonal elements of the Gram matrix obtained as explained above, and the neural network NN may output the allocated transmit power, e.g., per PRB / RBG, e.g., for each UE, e.g., on its allocated layers. In some examples, using the neural network NN for determining the first information I-1 may enable to employ aspects of the disclosure even in systems with comparatively limited processing resources, which, e.g., may not be capable of performing the multi-stage optimization procedure OPT-MS (see, for example, block 324 of Fig. 6) in real-time. In some examples, as already mentioned above, see, for example the arrows a4, a5, a6 of Fig. 14, the UE ranks, the assigned PRB / RBG indices, and the transmit power information may be transmitted to the respective UE E2a, E2b, E2c, e.g., using downlink control information (DCI) for PUSCH scheduling. In some examples, e.g., at each UE E2a, E2b, E2c, a transmit power per subcarrier may be determined from, e.g., based on, the transmit power information sent by the gNB E1, e.g., in the DCI. In some examples, Fig. 2, 13, a communication system 1000 of the MU-MIMO (Multi-User Multiple-Input Multiple-Output) type may be considered, e.g., with ^^^^Rx antennas (not shown) at the gNB 10 (Fig. 13) and ^^^^co-scheduled users or UE 20a, 20b, 20c. In some examples, the following signal model assuming an uplink transmission in an OFDM system may be considered. In someexamples, on any resource element (RE) indexed by the pair (^^, ^^)where ^^ denotes a subcarrier index and ^^ denotes a time index, In some examples, ∈ ℂ^^^^×1characterizes a received signalvector, characterizes a compositechannel matrix with^^ (^^) ^^×^^ ∈ ℂ ^^denoting a channel matrix (e.g., (^^) to the gNB E1) from UE ^^ equipped with ^^^^transmit antennas, being an ^^^^ℎ user’s UE's, respectively) transmit vector, e.g., after possible PUSCHprecoding, and ^^^^+^^ ∈ ℂ^^^^×1characterizes an interference-plus- noise (I+N) with a covariance matrix ^^^^. some examples, further, let ^^^^ ∈ ℂ^ (^^) (^^)In^^^×^^^^be a PUSCH precoding matrix (e.g., frequency flat), e.g., for UE ^^ that transmits ^^(^^)≤ ^^(^^) streams (or layers) of data ^^(^^)×1 ℚ^^^^ , e.g., with each entry taking values from a unit energy ℚ^^-QAM constellation of size 2^^^^ for some ^^^^ = 2,4,6,8,⋯. In someexamples, further, let denote a transmit power matrix used by UE ^^. In some examples,let ^^ = be a total number of layers from all the users UE, respectively. In some examples, e.g., with where ^^^^,^^is a whitened noise with a covariance equal to the matrix, and is the whitened channel matrix from all the co-scheduled UEs to the gNB. In some examples, it is assumed that a receiver (not shown) of the gNB 10 uses Linear Minimum Mean Squared Error (LMMSE) detection. In some examples, an LMMSE weight matrix is given by In some examples, a post-equalization signal-to-interference-noise ratio (SINR) per layer under the LMMSE detection on RE (^^, ^^)may be determined, e.g., calculated, as follows from (3): ^^ = diag CalculateIn some examples, a SINR on RE (^^, ^^) for Layer ^^ is given by1, where [^^ ] i ( )^^ℎ[^^^^,^^]s the ^^, ^^ entry^^,^^ In some examples, aspects of LMMSE approximation, e.g., using Zero-Forcing Detection, may be used. In some examples, e.g., instead of using the LMMSE weight matrix in (3), a zero-forcing (ZF) detector according to some examples may use While in some examples, the LMMSE detector’s performance may be superior to that of the ZF detector, in some examples, e.g., for at least some, e.g., many, practical scenarios, the LMMSE detector is only marginally better than the ZF detector. Thus, in some examples, the ZF detector may be used. In some examples, a post-equalization SINR per layer, e.g.,under the ZF detection on RE (^^, ^^), may be calculated as follows1from (4): SINR on RE (^^, ^^) for Layer ^^ is given by[^^^^,^^] , where ^^,^^[^^^^,^^] is the(^^, ^^) entry of . In some examples, the ZF- detector allows a comparatively simple closed form expression for the post-equalization SINR, e.g., as compared to the LMMSE detector. Thus, as mentioned above, in some examples, the ZF detector is used. In the following, example aspects of a baseline scheme according to some examples are disclosed, e.g., related to a baseline UE rank selection and baseline uplink power control. In some examples, let the channel covariance (e.g., at a UE) for (^^) (^^) UE ^^ be ^^ℎ,^^^^ ≝ ^^[^^^^^^^^^^] ∈ ℂ^^^^×^^(^^) ^^ . In some examples, let ^^1 ≥ ^^2 ≥ ⋯ ≥ (^^) the ordered eigenvalues of ^^ . In some examples, a rank ℎ,^^^^^^(^^) ^^of UE ^^is taken to be where ^^ ∈ (0,1] is a predefined threshold. In some examples, ^^ maybe taken to be 0.5. Regarding a baseline uplink power control, in some examples, the transmit power for UE ^^ may be obtained by setting Open LoopPower Control (OLPC) parameters (^^0, ^^) in the following equation:^^^^^^^^^^^^,^^(dBm ) = min{^^^^^^^^^^,^^ , ^^0 + 10 log ^^^^^^^^,^^ + ^^^^^^ + ^^^^ }where ^^^^^^^^^^,^^is a UE configured maximum output power for UE ^^ in dBm, ^^^^^^^^,^^is a number of PRBs allocated to UE ^^, ^^ is a fractional power control compensation parameter, ^^^^ is a downlink pathloss estimate in dBm, ^^^^ is a closed-loop power control adjustment in dBm and ^^0in dBm is a power per PRB that may be received under full pathloss compensation. In some examples, e.g., for ^^0and ^^, the following values may bechosen: ^^0 ∈ [−110,−85], ^^ ∈ [0.8,1].Regarding a baseline UE PRB allocation, in some examples, it may be assumed that all frequency resources, e.g., PRBs, are allocated to all the UEs, e.g., unless the UE is power limited. In the latter case, in some examples, a number of PRBs may be assigned over which the UE has sufficient power to transmit, e.g., choosing the available PRBs with the strongest channel gains for that UE. In some examples, suppose that the minimum number of PRBs to be used is ^^^^^^^^,^^^^^^(as an example, 4 may be a typically used number in some conventional approaches of, e.g., a 5G communication system) and the maximum number of PRBs available be ^^^^^^^^.Then, in some examples, the number of PRBs allocated to the UE is: In some examples, an alternate baseline may be as follows: the list of UEs may be sorted, e.g., according to a UE priority metric, and a resource allocation may be done one UE at a time in sequence. In some examples, it is supposed that the gNB has estimates of the channel ^^′^^,^^,^^ ^^^^ ∈ ℂ^^ (^^) ^^×^^^^ for each UE ^^, ^^ at a resourceblock group (RBG) level, or a PRB level. In some examples, this is possible through sounding reference signal (SRS) channel estimation where the UE sends PUSCH-precoded SRS (precoding the (^^) (^^SRS with the full-ranked PUSCH UE precoding matrix ^^^^ ×^ ) ^^ ∈ ℂ ^^^^^), see, for example, the arrows a1', a2', a3' of Fig. 14, or blocks 320, 322 of Fig. 6. In some examples, SRS from all transmit antennas of each UE may be used for the purpose of UE rank (^^) (^^) selection, hence the size of ^^^^may be ^^^^ × ^^^^. In some examples, the estimate of the channel may be denoted by ^^^^,^^, where the subscript ^^denotes an RBG / PRB index. In some examples, it is assumed that ^^ denotes the RBG index (or PRB index, used interchangeably with RBG, in some examples), e.g., rather than a subcarrier index. In some examples, next, the channel estimate is multiplied by an estimate of an interference plus noise ("I+N") whitening matrix which, in some examples, may be used by the gNB, e.g., to estimate either for every RBG or once for a few PRBs. In some −1 / 2 examples, without loss of generality, ^^^^,^^may be denoted to mean a whitening matrix for RBG / PRB ^^. In some examples, let ≝ In some examples, e.g., when UE ^^ uses a transmit power matrix^^^^,^^ = diagon RBG / PRB ^^, an effective composite channel matrix is ^^ ^^^^^^ where ^^^^ = diag(^^1,^^, ⋯ , ^^^^^^,^^).In some examples, e.g., with an LMMSE detector, the expression for a post equalization SINR for each layer as a function of may be comparatively difficult to obtain, but may be comparatively straightforward, e.g., with a ZF-detector: In some examples, e.g., assuming that ^^^^is full-ranked and that the are all non-zero, the post-equalization SINR ^^^^,^^,^^for the ^^^^ℎlayer on RBG ^^ of UE ^^ is the inverse . In some examples, this may, e.g., follow from the above explained aspects of LMMSE approximation using ZF detection. In some examples, it is assumed that there are ^^^^^^^^PRBs (orRBGs, as the case may be), and let ^^^^,^^ ∈ {0,1} indicate whether UE ^^is allocated PRB / RBG ^^ (^^^^,^^ = 1) or not (^^^^,^^ = 0). The Shannon rateestimate for UE ^^ (in bits normalized by number of subcarriers per PRB or RBG and OFDM symbols per slot) in a slot is In some examples, it is noted that when ^^^^,^^ = 0 for any ^^, thecorresponding channel components of ^^^^involving UE ^^ may be removed while calculating In some examples, the problem can now be stated as follows: such that 1. In each RBG / PRB and in each layer, the rate does not exceed the spectral efficiency (SE) of the highest Modulation and Coding Scheme (MCS). In some examples, this may ensure that power is not needlessly used beyond what is needed. In some examples, e.g., since the channel estimates are provided with a granularity at the PRB or RBG level, it may be assumed that this, e.g., the rate, is constant within that PRB / RBG. 2. For each UEis the number of PRBs over which UE ^^ is served in the slot, and ^^^^^^^^is the code rate of the lowest MCS. 3. A total UE transmission power constraint is satisfied. In some examples, a proportional fairness objective function may be used which attempts to maximize a product of ratios where ^^^∗^^^,^^is the maximum rate that UE ^^ would get if all the power were allocated only to it (e.g., at the cost of other UE). In some examples, a formal statement of the problem may be provided as shown below: e.g., subject to the following constraints C1, C2, C3:C1. Power constraint: 0 ≤ ^^^^,^^^^ ≤^^^^^^^^^^,^^,^^,^^ ∀^^ = 1,⋯ , ^^^^^^^^, ∀^^ = 1,⋯ , ^^^^, ∀^^ =1,⋯ , ^^(^^)with is the code rate of lowest MCS. C2. Per UE rate C3. Total UE power constraint: ^^^^,^^^^^^,^^,^^ ≤ ^^^^^^^^^^, ∀^^ = 1,⋯ , ^^^^.Note that, in some examples, in constraint C1, ^^^^^^^^may be replaced, e.g., by a UE defined ^^^^^^^^,^^corresponding to a rate- limit which may, e.g., be determined by the UE quality of service (QoS). In some examples, the problem may not be a convex optimization problem, e.g., due to constraint C2, and since an optimization (^^) is performed over ^^^^ , ^^ = 1,⋯ , ^^^^. Thus, in other words, in someexamples, it may be that there is no global minimum. So, in some examples, e.g., instead, a two-stage procedure as follows may be used: subject to the following constraints C1', C2':C1'. Power constraint: 0 ≤ ^^^^^^^^^^^^,^^,^^ ≤^^,^^,^^,^^ ∀^^ = 1,⋯ , ^^^^^^^^, ∀^^ = 1,⋯ , ^^^^, ∀^^ = ^^^^,^^^^^^,^^,^^ ≤ ^^^^^^^^^^, ∀^^ = 1,⋯ , ^^^^. In some examples, e.g., for a fixed ^^is a convex optimization problem which has a unique solution. In some examples, the solution for the convex optimization problem ^^ may be obtained using, for example, a software for solving convex optimization problems. Note that, in some examples, e.g., due to a usage of the ZF- detection approximation for LMMSE, the problem ^^ may be solved independently for each UE. Fig. 15 schematically depicts a simplified flow chart related to aspects of the first stage ("Stage 1") optimization according to some examples. In some examples, aspects of Fig. 15 may, e.g., form part of the multi-stage optimization procedure, see block 324 of Fig. 6. Returning to Fig. 15, element E10 of Fig. 15 symbolizes determining, e.g., estimating, for each UE i, a channel on each RBG or PRB f, e.g., using the PUSCH-pre-coded sounding reference signals. Element E11 of Fig. 15 symbolizes −1 / 2 determining, e.g., obtaining the I+N whitening matrix ^^^^,^^, e.g., from the I+N covariance matrix ^^^^,^^for each RBG or PRB f. Element E12 symbolizes determining, e.g., obtaining, for each UE i, a whitened channel matrix e.g., on each RBG or PRB f. Element E13 symbolizes forming a composite channel matrix e.g., on each RBG or PRB f. Element E14symbolizes determining, e.g., obtaining , e.g., on each RBG or PRB f. Element E15 symbolizes determining, e.g.,obtaining ^^^^,^^,^^ as the inverse of the diagonal entry . Element E16 symbolizes fixing ^^^^,^^ = 1, ∀^^ = 1,⋯ , ∀^^1,⋯ , ^^^^^^^^ e.g., for each UE ^^, ^^ = 1,⋯ , ^^^^ and for all PRBs f (or RBGs, respectively). Element E17 symbolizes solving the problem ^^, e.g., to get the transmit powers{^^∗^^,^^,j}. Thus, in some examples, the instructions 106 (Fig. 1A), when executed by the at least one processor 102, cause the network device 10 to perform at least one of: determining, for each UE i, a channel ^^^^,^^on each RBG or PRB f, or determining the I+N −1 / 2 whitening matrix ^^^^,^^, e.g., from the I+N covariance matrix ^^^^,^^for each RBG or PRB f, or determining, for each UE i, a whitened channel matrix e.g., on each RBG or PRB f, orforming a composite channel matrix ^^ ^^ ≝ or transmit powers In some examples, a purpose of the first stage ("Stage 1") may be to identify useful RBGs / PRBs and layers for the UEs. In some examples, e.g., those RBGs and layers that cannot support a predetermined minimum rate may be removed in the second stage ("Stage 2"). Fig. 16 schematically depicts a simplified flow chart related to aspects of the second stage ("Stage 2") optimization according to some examples. In some examples, aspects of Fig. 16 may, e.g., form part of the multi-stage optimization procedure, see block 324 of Fig. 6, e.g., following a first stage ("Stage 1"). In some examples, it is assumed that a minimum of ^^^^^^^^,^^^^^^PRBs are to be allocated to each UE. In some examples, the outputs of Stage 2, see block E34 of Fig. 16, are the RBG / PRB indices UE ranks {^^(^^)^^},and the per PRB / RBG UE allocated Tx power for each layer {^^^∗^,∗^^,^^}. Referring to Fig. 16, element E20 symbolizes performing thesecond stage optimization for each UE ^^, ^^ = 1,⋯ ,^^^^. Element E21symbolizes determining ^^^^,^^,^^=log2(1 + ^^^^,^^^^^^,^^,^^^^^^,^^,^^) , ∀f = 1,⋯ , ^^^^^^^^, ∀j =. Element E22 symbolizes determining ^ ^^^^^^^^ ^^^,^^,^^ =. Element E23 symbolizes initializing ^^ (^^)^^^^^^^^^^^^^^ = 0, ^^^^^^^^^^ = 0, ^^^^ = 1. Element E26 symbolizes determining whether ^^^^^^^^,^^ > ^^^^^^^^^^^^^^^^ andwhether ^^^^^^^^^^ > ^^^^^^^^. If so, the procedure continues with element=(^^) which symbolizes determining, whether . If (^^) ^^ <> ^(^^) e.g., if ^^^^^, the procedure continues with element E28, (^^) (^^) which symbolizes incrementing ^^^^, e.g., ^^^^ = ^^(^^) ^^ + 1, and, afterthat, returning to element E24. If so, e.g., if element E27 (^^) (^^) yields that ^^^^ = ^^^^, the procedure continues with element E29. Note that, if the determination of element E26 yields, that, ifat least one of the conditions ^^^^^^^^,^^ > ^^^^^^^^^^^^^^^^, or ^^^^^^^^^^ > ^^^^^^^^ is nottrue, the procedure also transitions, from element E26, to element E29. E29 symbolizes determining whether ^^^^^^^^,^^^^^^,if not, the procedure continues with element E30, assigning ^^^∗^,f= ^^^^,^^. Element E31 symbolizes determining, e.g., recalculating,(^^ ^^^^^^ ^^)−1 for those indices ^^, which have < ^^(^^) ^^for at least one index value ^^. Element E32 symbolizes assigning= 0 if ^^∗^^,f = 0, ^^ = 1,⋯ ,^^(^^^^)and ^^∗^^,f,j = 0, ^^(^^)^^ < ^^ ≤ ^^(^^^^). Element E33 symbolizes solving the problem ^^ with ^^∗^^,f,j e.g., to get the per PRB / RBG UE allocated transmit power {^^^∗^,∗^^,^^} for each layer, also see the element E34, characterizing an output block, as mentioned above. In some examples, e.g., if the determination of element E29yields that ^^^^,^^ ≥ ^^^^^^^^,^^^^^^, the procedure transitions fromelement E29 to element E35, which symbolizes setting = 1 for( ^ ^^ ^^)the indices ^ with the ^^ largest valu ∑ ^^ ∗^^^^^^,^^^^^^ es of^^=1^^^^,^^,^^and ^^^^,f = 0otherwise. Note that, in some examples, the output according to element E34 may not necessarily be an optimal solution, because the original problem is not convex. In some examples, the instructions 106 (Fig. 1A), when executed by the at least one processor 102, cause the network device 10 to perform at least one of the aspects or elements E20, or E21, or E22, or E23, or E24, or E25, or E26, or E27, or E28, or E29, or E30, or E31, or E32, or E33, or E34, or E35 of Fig. 16. In the following, example aspects of an example function approximation using a neural network according to some examples are disclosed. In some examples, a neural network NN, e.g., of the CNN type, e.g., a CNN, may be used for approximating an optimization-based scheme, e.g., as explained above with respect to Fig. 15, 16, e.g., for an i-th UE. In other words, in some examples, a neural network-based function approximator may be provided to approximate results of the 2-stage optimization approach according to some examples explained above with respect to, e.g., Fig. 15 and 16. In some examples, the neural network-based function approximator approach may, e.g., be chosen, if performing aspects of the two- stage optimization steps described above with reference to Fig. 15, 16 is not practically feasible, e.g., because the two-stage optimization steps may not be performed in real-time. In some examples, a convolutional neural network, CNN, (not shown) comprising K many layers may be provided for approximating the 2-stage optimization approach according to some examples. In some examples, the CNN may comprise, e.g., three or more intermediate, e.g., hidden, layers.In some examples, let ^^ ∈ ℝ^^^^^^^^×^^^^ be a matrix with the element denoting and ^^ ∈ ℝ^^^^^^^^×^^^^denote the matrix with the element denoting ^^ ∗∗^^,^^,^^, ∀^^ = 1,⋯ , ^^^^, ∀^^ = 1,⋯ ,^^^^ . Here, ^^^^ is themaximum number of transmit antennas for any UE, and, in some (^^) examples, it is assumed that the columns ^^^^ < ^^ ≤ ^^^^ are filledwith zeros. Further, in some examples, {^^^∗^,∗^^,^^} are the outputs of the optimization-based solver of Fig. 16, see, for example element (^^) E34, with the columns ^^^^ < ^^ ≤ ^^^^ filled with zeros.(^^) In some examples, if ^^^^ < ^^(^^)∗∗^^,then, ^^^^,^^,^^ = 0, ∀^^ = ^^(^^)^^ + 1,⋯ , ^^^^, ∀ ^^ =1,⋯ , ^^^^^^^^. Similarly, in some examples, any PRB / RBG index ^^ notselected for any UE ^^ may have the ^^∗∗^^,^^,^^ = 0, ∀^^ = In some examples, the matrix ^^ may form an input feature for the neural network, e.g., CNN, and matrix ^^ may for associated labels. In some examples, e.g., to represent data better for a comparatively wide range of values, every element of matrix ^^ and / or matrix ^^ may be taken, e.g., provided, in the logarithm domain, with "0", e.g., represented by "-100". In some examples, e.g., to train a DNN, e.g., CNN, e.g., for the function approximation, at least one training dataset may be built, e.g., on the fly, e.g., based on at least one of a) real- world conditions, or b) using synthetic data (as, e.g., obtainable by simulation). In some examples, e.g., using real-world conditions, e.g., based on an operation of the gNB 10 (Fig. 2, 13), to obtain training data, at least some aspects A1 to A6 of the following example approach can be employed: Aspect A1: In some examples, for, e.g., every time slot, the gNB 10 uses an approach, e.g., solver as explained with reference to Fig. 15, 16, e.g., to obtain the UE ranks, resource allocation indices, and the transmit powers, e.g., for each co-scheduled UE 20a, 20b, 20c, represented using the input matrix ^^ and output matrix ^^. Aspect A2: In some examples, the gNB 10 then sends downlink control information (DCI) messages containing the PUSCH scheduling decisions to the UEs, also see the arrows a4, a5, a6 of Fig. 14. Aspect A3: In some examples, uplink transmission(s) is / are executed, e.g., with the parameters obtained in Aspect A1. Aspect A4: In some examples, the gNB 10 jointly processes the received data signals from the uplink transmission(s) of the UE(s), decodes received codewords, e.g., after MU-MIMO detection, e.g., using LMMSE detection. Aspect A5: In some examples, e.g., if a pre-determined percentage of the received codewords are correctly decoded (e.g., using cyclic redundancy checks), the gNB 10 may add thecurrent matrices (^^, ^^) to the training data, e.g., organized inform of a training database. Otherwise, in some examples, e.g., if less than the pre-determined percentage of the received codewords could be correctly decoded, the current matrices (^^,^^) may be discarded, e.g., due to channel estimates or I+N covariance estimates possibly being inaccurate. Aspect A6: In some examples, at least some of the Aspects A1 to A5 are repeated, e.g., until a, for example reasonably, useful training dataset is built. In some examples, e.g., once a training dataset is built, a DNN with convolutional layers (e.g., a convolutional neural network (CNN)), e.g., denoted by ^^Ξ, where Ξ is a set of trainable parameters, may be trained, e.g., with the input features and labels described above, e.g., for a Mean Squared Error (MSE) loss function, e.g., in a minibatch ℬ given as where‖^^‖^^denotes the Frobenius norm of a matrix ^^. In some examples, e.g., for faster convergence and robust performance, the order of UE layers may be permuted, e.g., by permuting the respective columns of the matrices ^^and ^^. In some examples, e.g., when transforming the elements of the matrix ^^ and / or the matrix ^^ to the logarithm domain, as mentioned above, at run time, e.g., when the (e.g., trained) DNN, e.g., CNN, is evaluated, the predictions as obtained by the CNN may be converted back, e.g., transformed, to the exponential domain. In some examples, let ^̂^^^,^^,^^denote these values as obtained by the CNN, being transformed back to the exponential domain. In some examples, values below a certain predetermined (^^) threshold ^^^^ℎ^^^^ℎmay be zeroed out, e.g., yielding the UE rank ^^^^and PRB allocation indices In some examples, e.g., in order to satisfy a UE transmit power constraint, a renormalization may be performed, e.g., if Note that, in some examples, e.g., at each UE, the power per subcarrier may be obtained from, e.g., determined based on, ^̂^^^,^^,^^, which represents the power per PRB / RBG. In some examples, this may be done by dividing the value of ^̂^^^,^^,^^by the number of subcarriers in the PRB / RBG. In the following, further aspects and examples, e.g., related to a DCI message, e.g., for PUSCH scheduling, are disclosed, which, in some examples, may be combined with at least one of the aspects and / or examples disclosed above. In some examples, e.g., after having obtained the UE transmit powers, the UE ranks, and the resource allocation indices (e.g., in the form of the first information I-1 or a respective portion or part I-1a, I-1b, I-1c thereof), e.g., by either a method based on one or more optimization procedures (see, for example, blocks 332, 334, 336 and Fig. 15, 16) or based on a neural network-based approximation NN-APPROX as mentioned above, the gNB 10 (Fig. 2) may transmit the first information I-1 or a respective portion I-1a, I-1b, I-1c thereof to each co-scheduled UE, e.g., using a DCI message for PUSCH scheduling. In some examples, while in some accepted specifications such as, e.g., associated with the 5G standard, DCI formats may, e.g., only, encode comparatively low-resolution closed-loop power control commands, in some examples, transmit power control information, e.g., Transmit Power Control (TPC) commands, may be transmitted with a granularity of PRB, slot, layer, and UE. Thus, conventional, e.g., current, e.g., 5G-based, DCI formats may therefore be insufficient to convey aspects of the first information I-1 according to some examples, which, in some examples, may be considered to be comparatively data-rich. For this reason, in some examples, at least one of the following aspects is proposed, e.g., to transmit the first information I-1 or a respective portion I-1a, I-1b, I-1c thereof, e.g., in the form of one or more Transmit Power Control (TPC) commands, e.g., for MU-MIMO TPC commanding. In some examples, e.g., relating to a comparatively high granularity DCI, the DCI may encode a discretized full set of transmit powers for each PRB / RBG on each layer. In some examples, this may incur a comparatively large overhead and may, e.g., be practical in deployments, e.g., 6G deployments, with comparatively large, e.g., extreme, bandwidths. In some examples, e.g., relating to a medium granularity DCI, a, for example condensed, set of discretized transmit powers, e.g., only one per layer, may be provided. In this case, in some examples, the UE may use a same transmit power, e.g., for all scheduled PRBs per layer. In some examples, this approach may yield a trade-off, e.g., between performance and signaling overhead, and, in some examples, this approach may, e.g., be optimal, e.g., in deployments with a comparatively low frequency selectivity, such as, e.g., rural outdoors. In some examples, e.g., relating to a comparatively low granularity DCI, a, for example single, discretized transmit power per UE may be used. In this case, in some examples, the UE may use a common transmit power, e.g., for all the scheduled PRBs and layers. In some examples, this may incur a comparatively small overhead, and depending on the case, might, for example, not significantly degrade a performance, e.g., compared to the having separate transmit powers per PRB and layer. Thus, in some examples, the gNB 10 may determine a granularity to be used for transmitting the first information I-1 or a respective portion I-1a, I-1b, I-1c thereof, and may transmit the first information I-1 or a respective portion I-1a, I-1b, I- 1c thereof, e.g., to at least one UE, with the determined granularity. In some examples, Fig. 5, determining the granularity for transmitting the first information I-1 or a respective portion I-1a, I-1b, I-1c thereof, e.g., as DCI, may, e.g., be performed at block 310 of Fig. 5. Some examples, Fig. 17, relate to a computer program PRG comprising instructions INSTR which, when executed by an apparatus 100, 100', 200, 200', cause the apparatus 100, 100', 200, 200' to perform at least some aspects of the method according to the examples. In some examples, the computer program PRG may be provided on a computer readable storage medium SM, e.g., a non-transitory computer readable medium SM. Some examples, Fig. 17, relate to a data carrier signal DCS carrying and / or characterizing the computer program PRG according to the example embodiments. In some examples, the principle according to the disclosure may, e.g., be used for uplink data transmissions, e.g., of 5G or 6G communication systems. In some examples, the gNB 10 (Fig. 2, 13) may comprise a comparatively large number of antenna elements (AE), e.g., between about 512 and 1024 antenna elements. In some examples, the principle according to the disclosure may be used for extreme multi-user (MU)-MIMO, wherein a gNB may serve several, e.g., four to ten (or even more) co-scheduled terminal devices. While in SU-MIMO (Single-User MIMO) transmissions, an OFDMA scheme may avoid inter-UE interference, when multiple UEs are co-scheduled for transmission in a same time slot (MU-MIMO), their respective transmitted data signals may interfere with one another. Therefore, in (extreme) MU-MIMO, in some examples, the resulting UEs’ throughputs may depend on how the frequency resources are shared between the UEs, which, in turn, may influence respective UE ranks and transmit powers. In some examples, for such (extreme) MU-MIMO configurations, jointly determining 300 (Fig. 3), for a plurality 20 of terminal devices 20a, 20b, 20c, the first information I-1, may enable to maximize the respective terminal devices' throughput. In some examples, the principle according to the disclosure may be used to optimize a UE bitrate distribution, e.g., by dynamically (e.g., during operation) configuring uplink transmit powers, e.g., along with the UE rank and the resource selection.

Claims

Claims 1. An apparatus (100) for a network device (10), the apparatus (100) comprising at least one processor (102), and at least one memory (104) storing instructions (106) that, when executed by the at least one processor (102), cause the network device (10) to: jointly determine (300), for a plurality (20) of terminal devices (20a, 20b, 20c), first information (I-1) characterizing at least two of the following elements: a) a rank (RNK), or b) a resource scheduling (SCHED), or c) a transmit power (TX-PWR), transmit (302) at least a respective part (I-1a, I-1b, I- 1c) of the first information (I-1) to a respective terminal device (20a, 20b, 20c).

2. The apparatus (100) according to claim 1, wherein jointly determining (300) the first information (I-1) comprises jointly determining (300a) the rank (RNK) and the resource scheduling (SCHED) and the transmit power (TX-PWR).

3. The apparatus (100) according to any of the preceding claims, wherein the instructions (106), when executed by the at least one processor (102), cause the network device (10) to: include (310) at least the respective part (I-1a) of the first information (I-1) into downlink control information (DCI), transmit (312) the downlink control information (DCI) with the included respective part (I-1a) of the first information (I-1).

4. The apparatus (100) according to any of the preceding claims, wherein the instructions (106), when executed by the at least one processor (102), cause the network device (10) to: receive (320) reference signals (RS-20) from the plurality (20) of terminal devices (20a, 20b, 20c), perform(322) channel estimation of respective uplink channels of the plurality (20) of terminal devices (20a, 20b, 20c) with a predetermined frequency granularity based on the received reference signals (RS-20) to obtain estimated uplink channels (CH-UL-20a, CH-UL-20b, CH-UL-20c), determine (324) the first information (I-1) based on the estimated uplink channels (CH-UL-20a, CH-UL-20b, CH-UL-20c) using at least one of a) a multi-stage optimization procedure (OPT-MS), or b) a neural network-based approximation (NN-APPROX).

5. The apparatus (100) according to claim 4, wherein the instructions (106), when executed by the at least one processor (102), cause the network device (10) to: determine (330) diagonal elements (DIAG) of a Gram matrix inverse of a whitened channel matrix based on the estimated uplink channels (CH-UL-20a, CH-UL-20b, CH-UL-20c) at the predetermined frequency granularity, perform (332) a convex optimization procedure (PROC-OPT) based on the diagonal elements (DIAG) using a geometric mean of the terminal devices' (20a, 20b, 20c) throughputs as an objective function and constraints associated with a transmit power of the terminal devices (20a, 20b, 20c) and with a quality of service-defined rate to obtain a first result (RES-1) characterizing transmit powers per frequency resource and layer for at least some, for example each, of the terminal devices (20a, 20b, 20c).

6. The apparatus (100) according to claim 5, wherein the instructions (106), when executed by the at least one processor (102), cause the network device (10) to: determine (334), based on the first result (RES-1), a second result (RES-2) characterizing at least one of a) useful frequency resources, or b) useful ranks, for at least some, for example each, of the terminal devices (20a,20b, 20c), perform (336), based on the second result (RES- 2), a further optimization procedure (PROC-OPT') to obtain a third result (RES-3) characterizing optimized transmit powers per frequency resource and layer for at least some, for example each, of the terminal devices (20a, 20b, 20c).

7. The apparatus (100) according to any of the claims 4 to 6, wherein the instructions (106), when executed by the at least one processor (102), cause the network device (10) to perform at least one of: a) provide (340) a, for example deep, neural network (NN) for determining the first information (I-1), or b) train (342) the neural network (NN) for determining the first information (I-1), or c) use (344) the neural network (NN) to determine (300; 300a; 324) the first information (I-1).

8. The apparatus (100) according to claim 7, wherein the instructions (106), when executed by the at least one processor (102), cause the network device (10) to perform at least one of: a) provide (350) training data (DAT-TRAIN) for training of the neural network (NN) based on received reference signals (RS-20), or b) provide (352) training data (DAT-TRAIN) for training of the neural network (NN) based on synthetic data.

9. The apparatus (100) according to any of the claims 7 to 8, wherein the instructions (106), when executed by the at least one processor (102), cause the network device (10) to: determine (360) the first information (I-1) based on the estimated uplink channels (CH-UL-20a, CH-UL-20b, CH-UL- 20c) using the multi-stage optimization procedure (OPT-MS), transmit (362) at least a respective part (I-1a, I-1b, I- 1c) of the first information (I-1) to at least one respective terminal device (20a, 20b, 20c), receive (364)data (DAT-20) transmitted by the at least one terminal device (20a, 20b, 20c) based on the respective part (I-1a, I-1b, I-1c) of the first information (I-1), decode (366) at least a part of the received data (DAT-20), and, based on the decoding (366), add (368) the first information (I-1) to the training data (DAT-TRAIN).

10. The apparatus (100) according to any of the claims 4 to 9, wherein the reference signals (RS-20) are pre-coded, for example physical uplink shared channel, PUSCH, - pre-coded, sounding reference signals, SRS.

11. An apparatus (100') for a network device (10), the apparatus (100') comprising means (102') for: jointly determining (300), for a plurality (20) of terminal devices (20a, 20b, 20c), first information (I-1) characterizing at least two of the following elements: a) a rank, or b) a resource scheduling, or c) a transmit power, transmitting (302) respective portions (I-1a, I-1b, I-1c) of the first information (I-1) to a respective terminal device (20a, 20b, 20c).

12. A method for a network device (10), comprising: jointly determining (300), for a plurality (20) of terminal devices (20a, 20b, 20c), first information (I-1) characterizing at least two of the following elements: a) a rank, or b) a resource scheduling, or c) a transmit power, transmitting (302) respective portions (I-1a, I-1b, I-1c) of the first information (I-1) to a respective terminal device (20a, 20b, 20c).

13. An apparatus (200) for a terminal device (20a), the apparatus (200) comprising at least one processor (202), and at least one memory (204) storing instructions (206)that, when executed by the at least one processor (202), cause the terminal device (20a) to: receive (400) at least a respective part (I-1a) of first information (I-1) characterizing at least two of the following elements jointly determined by the network device (10) for a plurality (20) of terminal devices (20a, 20b, 20c): a) a rank, or b) a resource scheduling, or c) a transmit power, determine (402) a transmit power (TX-PWR-SC) per subcarrier based on the respective part (I-1a).

14. An apparatus (200') for a terminal device (20a), the apparatus (200') comprising means (202') for: receiving (400) at least a respective part (I-1a) of first information (I-1) characterizing at least two of the following elements jointly determined by the network device (10) for a plurality (20) of terminal devices (20a, 20b, 20c): a) a rank, or b) a resource scheduling, or c) a transmit power, determining (402) a transmit power (TX-PWR- SC) per subcarrier based on the respective part (I-1a).

15. A method for a terminal device (20a), comprising: receiving (400) a at least a respective part (I-1a) of first information (I-1) characterizing at least two of the following elements jointly determined by a network device (10) for a plurality (20) of terminal devices (20a, 20b, 20c): a) a rank, or b) a resource scheduling, or c) a transmit power, determining (402) a transmit power (TX-PWR- SC) per subcarrier based on the respective part (I-1a).

16. A network device (10) comprising at least one apparatus (100; 100') according to at least one of the claims 1 to 11.

17. A terminal device (20a, 20b, 20c) comprising at least one apparatus (200; 200') according to at least one of the claims 13 to 14.

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