Combined physical resource block selection, layer selection and power allocation for multiple co-scheduled user devices, and related devices, methods and computer programs

Abstract

Devices, methods and computer programs for combined physical resource block (PRB) selection, layer selection and power allocation for downlink transmission to multiple co-scheduled user devices are disclosed. At least some example embodiments may allow jointly selecting user device ranks, PRBs allocated, and power per user device for the downlink transmission with zero-forcing (ZF) precoding subject to per-antenna power constraints (PAPCs), thereby increasing user device throughputs.

Description

[0001]COMBINED PHYSICAL RESOURCE BLOCK SELECTION, LAYER SELECTION AND POWER ALLOCATION FOR MULTIPLE CO-SCHEDULED USER DEVICES, AND RELATED DEVICES, METHODS AND COMPUTER PROGRAMS TECHNICAL FIELD The disclosure relates generally to communications and, more particularly but not exclusively, to combined phys- ical resource block selection, layer selection and power al- location for multiple co-scheduled user devices, as well as related devices, methods and computer programs. BACKGROUND Upcoming versions of wireless networks (such as fifth generation (5G) advanced and sixth generation (6G)) are ex- pected to enable a few times higher data-rates than 5G for downlink (DL) transmission. As a result, a network node device, such as a base station (gNB) is expected to be equipped with a higher number of antenna elements (AE) (e.g., in the range of 512-1024). This may also necessitate a larger number of transceivers (TRX), around 256-512 compared to 32-64 in 5G, and the frequency band of interest is expected to be 7-20 GHz. Each gNB is expected to serve several (e.g., 4-12) co-scheduled user equipment (UE). This is called an extreme multi-user (MU)- MIMO system. For a physical downlink shared channel (PDSCH) trans- mission, UE rank selection (which refers to a number of data layers for a UE), UE resource allocation (which refers to sections of an overall frequency band allocated to a UE in an orthogonal frequency division multiplexing (OFDM) system), and power allocation (which refers to a power allocated to a UE for DL transmissions) may directly impact resulting UE through- puts. Since multiple UEs are to be served simultaneously, at least in some situations, there may be a need for appropriate selection of these configurations. BRIEF SUMMARY The scope of protection sought for various example embodiments of the invention is 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 inven- tion. An example embodiment of a network node device comprises at least one processor, and at least one memory storing instructions that, when executed by the at least one processor, cause the network node device at least to, in response to at least one channel estimation quality parameter related to radio channels between the network node device and multiple co-scheduled user devices exceeding a respective quality threshold, perform a first minimization of an objective function of a geometric mean of estimated downlink throughputs of each co-scheduled user device subject to at least per- antenna power constraints, PAPCs. The instructions, when executed by the at least one processor, further cause the network node device at least to determine a first downlink power allocation for each candidate physical resource block, PRB, of each layer of each co-scheduled user device. The instructions, when executed by the at least one processor, further cause the network node device at least to determine, based on the determined first downlink power allocation, PRBs and layers to use for each co-scheduled user device from among the candidate PRBs and candidate layers. The instructions, when executed by the at least one processor, further cause the network node device at least to determine a second downlink power allocation via performing a second minimization of the objective function of the geometric mean of the estimated downlink throughputs of each co-scheduled user device by utilizing information about the determined PRBs and layers to use for each co-scheduled user device. In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, the instruc- tions, when executed by the at least one processor, further cause the network node device to determine channel estimates for each radio channel. In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, the instruc- tions, when executed by the at least one processor, further cause the network node device to determine precoding matrices for each radio channel based on the determined channel estimates. In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, the estimated downlink throughputs of each co-scheduled user device are func- tions of elements of the precoding matrices. In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, a per-antenna power of the PAPC is a function of the precoding matrices. In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, the instruc- tions, when executed by the at least one processor, further cause the network node device to perform the determination of the precoding matrices for each radio channel by determining precoding weights of the precoding matrices based on each corresponding co-scheduled user device having a rank equal to a number of receive antennas of the respective co-scheduled user device In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, the channel estimates determined for each radio channel comprise post- whitened channel estimates. In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, the first minimization of the objective function is further subject to at least one of rate constraints defined by quality of service, QoS, of each co-scheduled user device, or a total power constraint. In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, at least one of the performing of the first minimization of the objective function, the determination of the first downlink power allocation, the determination of the PRBs and layers to use, or the determination of the second downlink power allocation comprises applying a neural network, NN, to a function of the estimated radio channels and the determined precoding weights. In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, the instruc- tions, when executed by the at least one processor, further cause the network node device to train the NN via applying a mean squared error, MSE, loss function. In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, each precoding matrix comprises a zero-forcing, ZF, precoding matrix. In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, the instruc- tions, when executed by the at least one processor, further cause the network node device to normalize columns of each precoding matrix to unity. In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, the instruc- tions, when executed by the at least one processor, further cause the network node device to perform the determination of the channel estimates for each radio channel based on data provided by at least one of downlink channel state information, CSI, or an uplink sounding reference signal, SRS. In an example embodiment, alternatively or in addi- tion to the above-described example embodiments, the at least one channel estimation quality parameter comprises at least one of an uplink signal-to-interference noise ratio, SINR, for each co-scheduled user device, or a downlink interference- plus-noise, I+N, for each co-scheduled user device. An example embodiment of a method comprises, in response to at least one channel estimation quality parameter related to radio channels between a network node device and multiple co-scheduled user devices exceeding a respective quality threshold, performing, by the network node device, a first minimization of an objective function of a geometric mean of estimated downlink throughputs of each co-scheduled user device subject to at least per-antenna power constraints, PAPCs. The method further comprises determining, by the network node device, a first downlink power allocation for each candidate physical resource block, PRB, of each layer of each co-scheduled user device. The method further comprises determining, by the network node device, based on the determined first downlink power allocation, PRBs and layers to use for each co-scheduled user device from among the candidate PRBs and candidate layers. The method further comprises determining, by the network node device, a second downlink power allocation via performing a second minimization of the objective function of the geometric mean of the estimated downlink throughputs of each co-scheduled user device by utilizing information about the determined PRBs and layers to use for each co-scheduled user device. An example embodiment of an apparatus comprises means for carrying out a method according to any of the above-de- scribed example embodiments. An example embodiment of a computer program comprises instructions for causing a network node device to perform at least the following: in response to at least one channel estimation quality parameter related to radio channels between the network node device and multiple co-scheduled user devices exceeding a respective quality threshold: performing a first minimization of an objective function of a geometric mean of estimated downlink throughputs of each co-scheduled user device subject to at least per-antenna power constraints, PAPCs; determining a first downlink power allocation for each candidate physical resource block, PRB, of each layer of each co-scheduled user device; determining, based on the determined first downlink power allocation, PRBs and layers to use for each co-scheduled user device from among the candidate PRBs and layers; and determining a second downlink power allocation via performing a second minimization of the objective function of the geometric mean of the estimated downlink throughputs of each co-scheduled user device by utilizing information about the determined PRBs and layers to use for each co-scheduled user device. DESCRIPTION OF THE DRAWINGS The accompanying drawings, which are included to pro- vide a further understanding of the embodiments and constitute a part of this specification, illustrate embodiments and to- gether with the description help to explain the principles of the embodiments. In the drawings: FIG. 1 shows an example embodiment of the subject matter described herein illustrating an example system, where various embodiments of the present disclosure may be imple- mented; FIG. 2 shows an example embodiment of the subject matter described herein illustrating a network node device; FIG. 3 shows an example embodiment of the subject matter described herein illustrating a method for the network node device of Fig. 2; FIG. 4 shows an example embodiment of the subject matter described herein illustrating spectral efficiency ver- sus signal-to-interference noise ratio plots; FIG. 5 shows an example embodiment of the subject matter described herein illustrating a disclosed stage 1 op- timization; FIG. 6 shows an example embodiment of the subject matter described herein illustrating a disclosed stage 2 op- timization after physical resource block allocation and rank selection; FIG. 7 shows an example embodiment of the subject matter described herein illustrating a disclosed decision-mak- ing process that decides when to use the disclosed optimiza- tions; and FIG. 8 shows an example embodiment of the subject matter described herein illustrating a disclosed neural net- work. Like reference numerals are used to designate like parts in the accompanying drawings. DETAILED DESCRIPTION Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying draw- ings. The detailed description provided below in connection with the appended drawings is intended as a description of the present examples and is not intended to represent the only forms in which the present example may be constructed or uti- lized. The description sets forth the functions of the example and the sequence of steps for constructing and operating the example. However, the same or equivalent functions and se- quences may be accomplished by different examples. Fig. 1 illustrates example system 100, where various embodiments of the present disclosure may be implemented. Sys- tem 100 may comprise fifth generation (5G) advanced network 110 or a network beyond 5G advanced wireless networks. An example representation of system 100 is shown depicting net- work node device 200 and co-scheduled user devices 120A, 120B, 120C. At least in some embodiments, network 110 may be com- prised in a massive machine-to-machine (M2M) network, massive machine type communications (mMTC) network, internet of things (IoT) network, industrial internet-of-things (IIoT) network, enhanced mobile broadband (eMBB) network, ultra-reliable low- latency communication (URLLC) network, and / or the like. In other words, network 110 may be configured to serve diverse service types and / or use cases, and it may logically be seen as comprising one or more networks. Co-scheduled user devices 120A, 120B, 120C may in- clude, e.g., a mobile phone, a smartphone, a tablet computer, a smart watch, or any hand-held, portable and / or wearable de- vice. User devices 120A, 120B, 120C may also be referred to as user equipment (UE). Network node device 200 may comprise, e.g., a base station (gNB). The base station may include, e.g., any device suitable for providing an air interface for user devices 120A, 120B, 120C to connect to a wireless network via wireless transmissions. When multiple UEs are co-scheduled for transmission in a time slot, their throughputs are a direct function of a UE rank, physical resource blocks (PRBs) allocated, and powers allocated. Since the UEs are co-scheduled, the total available power at network node device 200 may need to be shared amongst the UEs fairly. All of the above (UE rank, PRBs allocated, and powers allocated) influence one another in determining the resulting UE throughputs. As will be discussed in more detail below, at least some of these example embodiments described herein may allow the UE rank, PRBs allocated, and powers al- located to be optimized jointly (that is, in a combined man- ner). In the following, various concepts and terms that may be relevant to at least some example embodiments will be dis- cussed. The following lists some example concepts and terms: Symbol Meaning ^^^^Total number of co-sched- uled UEs ^^^^Total number of transmit (Tx) antennas of network node device 200 ^^^(^^^)Number of receive (Rx) an- tennas at UE ^^, ^^^^ (^^) ^^ = ∑ ^^^^=1^^^^^^(^^) ^^Number of layers for UE ^^, ^^(^^) ^^ ≤ ^^(^^) ^^x^^(^^) ^^×1^^,^^ ∈ ℚThe transmitted symbol ^^(^^) vector of length ^^^^on subcarrier ^^ where UE ^^ uses unit-energy con-stellation ℚ^^y^^(^^) ^^,^^ ∈ ℂ ^^×1Received signal vector at UE ^^ on subcarrier ^^ H^^,^^ ∈ ℂ^^(^^) ^^ ×^^^^ Channel matrix of UE ^^ on^^ ^^^^ subcarrier ^^, H^^ ≝ [H^^,1 , H^^,2 , ⋯ , H^^^^,^^^^] x^^^^ = [x^^,1 , ⋯ , x^^^^^^ ,^^^^] Transmitted symbol vector of length ^^^^ = ∑^^^^(^^) ^^=1^^^^W^^ ∈ ℂ^^^^×^^^^Precoding matrix on sub- carrier ^^, with W^^ ≝ [W^^,1, ⋯ , W^^,^^^^],^^ ×^^(^^) with W^^,^^ ∈ ℂ ^^ ^^n^^(^^) ^^,^^ ∈ ℂ ^^×1I+N with covariance R^^∈ (^^) (^^) ℂ^^^^×^^^^on subcarrier ^^. A channel model at a receiver of UE ^^ on subcarrier ^^ may be defined, The channels H^^,^^may be estimated on the uplink using, e.g., sounding reference signals (SRS) for a time division duplex (TDD) system. Network node device 200 may estimate −1 −1 R2H , e.g., when the UE2^^^^,^^precodes the SRS using R^^. This is called a post-whitened channel estimate. For a frequency di- vision duplex (FDD) system, a UE may feed back the channel state information (CSI) to network node device 200. In practice, the channel estimates may be available for resource block groups (RBG) comprising 2-8 physical re- source blocks (PRBs), so herein the subscript ^^ may be under- stood to represent an RBG index or an PRB index (used inter- changeably without loss of generality) instead of a subcarrier index. For example, W^^ = W^^^^^^^^,^^P^^ where W^^^^^^^^,^^ ≝ may be obtained by normalizingcolumn of W^^ to unity, and P^^ ≝ diag(P^^,1, ⋯ , P^^,^^^^) ∈ ℝ^^^^×^^^^with: P≝ diag At least in some embodiments, the precoder used maybe a zero-forcing (ZF) -precoder so that H W^^^^^^^^,^^,^^ = O ∀^^ ^^(^^ U^^ ∈^^ ) (^^) ^^×^^^^ ^^^^, ℂsatisfying^^,^^ U^^,^^ = I,with real-valued positive (^^) This may effectively split the channel into ^^^^par- allel Gaussian channels at UE ^^ after equalizing with U^^^^,^^. With an expected Shannon rate (or equiva- lently, an estimated downlink throughput) for UE ^^ (from the perspective of network node device 200) on subcarrier ^^ may be: At least in some embodiments, there may be ^^^^^^^^PRBs(or RBGs or subcarriers as the case may be), and ^^^^,^^ ∈ {0,1} mayindicate whether UE ^^ is allocated PRB ^^ (^^^^,^^ = 1) or not (^^^^,^^ =0). The rate of UE ^^ (in bits normalized by the number of subcarriers per PRB or RBG and OFDM time symbols per slot) in a slot may be expressed as: At least in some embodiments, , ^^ = For baseline UE rank selection, a channel covariance (^^)^^ ^^(^^)× (^^) (at UE) for UE ^^ may be Rℎ,^^^^ ≝ ^^[H^^H^^ ] ∈ ℂ ^^^^^^ . (^^) (^^) may be ordered eigenvalues of Rℎ,^^^^. Rank ^^^^ of UE ^^ may be:^^(^^) (^^ ^^ ^^ = max {^^ ∈ {1, ⋯ , ^^)^^^^}| ^^1 ≥ ^^}where ^^ ∈ (0,1] represents a predefined threshold. Forexample, ^^ may be 0.5. (^^) For baseline UE power allocation, w^^,^^^^^^may denotethe ^^^^ℎ row of W^^, ^^ = 1, ⋯ , ^^^^, ^^ = 1, ⋯ ,^^^^^^^^ . The columns of W^^may be normalized to unity. ^^^^^^^^may denote a per-antenna power constraint (PAPC) for the entire bandwidth of ^^^^^^^^PRBs / RBGs.Thus, the precoder For baseline UE PRB allocation, all the PRBs may be allocated to all the UEs. In the following, various example embodiments will be discussed. At least some of these example embodiments described herein may allow combined physical resource block selection, layer selection and power allocation for multiple co-scheduled user devices. Furthermore, at least some of the example embodiments described herein may allow jointly selecting the UE ranks, PRB allocated, and the power per UE for downlink transmission with ZF precoding subject to per antenna power constraints (PAPC), thereby increasing the UE throughputs. Furthermore, at least some of the example embodiments described herein may allow deciding, based on the quality of channel estimates, whether to perform, e.g., conventional UE rank selection, PRB allocation and power allocation, or whether to switch to the disclosed UE rank selection, PRB allocation and power allocation. Furthermore, at least some of the example embodiments described herein may allow obtaining precoder weights using post-whitened channel estimates assuming that all UEs have full rank (equal to the number of their respective receive antennas) and normalizing columns of a precoder matrix to unity. Furthermore, at least some of the example embodiments described herein may allow (assuming that all the PRBs are allocated to all co-scheduled UEs) performing a convex opti- mization using an objective function that is a geometric mean of UE throughputs subject to a PAPC and UE quality of service (QoS)-defined rate constraints to obtain a set of temporarily optimized allocated powers per PRB and per layer for each UE. Furthermore, at least some of the example embodiments described herein may allow PRB allocation and rank determina- tion, such that based on the obtained temporary allocated pow- ers, useful PRBs and ranks for each UE may be identified. Furthermore, at least some of the example embodiments described herein may allow using the determined PRB indices and ranks to obtain a second set of allocated powers per PRB and layer for each UE. Furthermore, at least some of the example embodiments described herein may allow (e.g., in order to realize the above optimization steps in real time), approximate the above opti- mization steps using a neural network that may take as inputs a function of the estimated channel and the precoder weights, and output the allocated power per PRB for each UE on its allocated layers. Fig. 2 is a block diagram of network node device 200,in accordance with an example embodiment. Network node device 200 comprises one or more proces- sors 202 and one or more memories 204 that comprise computer program code. Network node device 200 may also include other elements, such as transceiver 206 configured to enable network node device 200 to transmit and / or receive information to / from other devices, as well as other elements not shown in Fig. 2. In one example, network node device 200 may use transceiver 206 to transmit or receive signaling information and data in accordance with at least one cellular communication protocol. Transceiver 206 may be configured to provide at least one wireless radio connection, such as for example a 3GPP mobile broadband connection (e.g., 5G advanced or beyond). Trans- ceiver 206 may comprise, or be configured to be coupled to, at least one antenna to transmit and / or receive radio frequency signals. Although network node device 200 is depicted to in- clude only one processor 202, network node device 200 may include more processors. In an embodiment, memory 204 is ca- pable of storing instructions, such as an operating system and / or various applications. Furthermore, memory 204 may in- clude a storage that may be used to store, e.g., at least some of the information and data used in the disclosed embodiments, such as neural network (NN) 800 described in more detail below. Furthermore, processor 202 is capable of executing the stored instructions. In an embodiment, processor 202 may be embodied as a multi-core processor, a single core processor, or a combination of one or more multi-core processors and one or more single core processors. For example, processor 202 may be embodied as one or more of various processing devices, such as a coprocessor, a microprocessor, a controller, a digital signal processor (DSP), a processing circuitry with or without an accompanying DSP, or various other processing devices in- cluding integrated circuits such as, for example, an applica- tion specific integrated circuit (ASIC), a field programmable gate array (FPGA), a microcontroller unit (MCU), a hardware accelerator, a special-purpose computer chip, a neural network (NN) chip, an artificial intelligence (AI) accelerator, a ten- sor processing unit (TPU), a neural processing unit (NPU), or the like. In an embodiment, processor 202 may be configured to execute hard-coded functionality. In an embodiment, processor 202 is embodied as an executor of software instructions, wherein the instructions may specifically configure processor 202 to perform the algorithms and / or operations described herein when the instructions are executed. Memory 204 may be embodied as one or more volatile memory devices, one or more non-volatile memory devices, and / or a combination of one or more volatile memory devices and non- volatile memory devices. For example, memory 204 may be embod- ied as semiconductor memories (such as mask ROM, PROM (pro- grammable ROM), EPROM (erasable PROM), flash ROM, RAM (random access memory), etc.). Network node device 200 may comprise a base station. The base station may include, e.g., a 5G advanced or 6G base station (gNB) or any such device providing an air interface for user devices 120A, 120B, 120C to connect to a wireless network via wireless transmissions. In response to at least one channel estimation quality parameter related to radio channels between network node device 200 and multiple co-scheduled user devices 120A, 120B, 120C exceeding a respective quality threshold, when executed by at least one processor 202, instructions stored in at least one memory 204 cause network node device 200 at least to perform a first minimization of an objective function of a geometric mean of estimated downlink (DL) throughputs of each co- scheduled user device 120A, 120B, 120C subject to at least per-antenna power constraints (PAPCs). For example, the at least one channel estimation quality parameter may comprise an uplink signal-to- interference noise ratio (SINR) for each co-scheduled user device 120A, 120B, 120C, and / or a downlink interference-plus- noise (I+N) for each co-scheduled user device 120A, 120B, 120C. At least in some embodiments, the first minimization of the objective function may further be subject to at least one of rate constraints defined by quality of service, QoS, of each co-scheduled user device 120A, 120B, 120C, or a total power constraint. The instructions, when executed by at least one processor 202, further cause network node device 200 at least to determine a first DL power allocation for each candidate physical resource block (PRB) of each layer of each co- scheduled user device 120A, 120B, 120C. The instructions, when executed by at least one processor 202, further cause network node device 200 at least to determine, based on the determined first DL power allocation, PRBs and layers to use for each co-scheduled user device 120A, 120B, 120C from among the candidate PRBs and candidate layers. The instructions, when executed by at least one processor 202, further cause network node device 200 at least to determine a second DL power allocation via performing a second minimization of the objective function of the geometric mean of the estimated DL throughputs of each co-scheduled user device 120A, 120B, 120C by utilizing information about the determined PRBs and layers to use for each co-scheduled user device 120A, 120B, 120C. At least in some embodiments, the instructions, when executed by at least one processor 202, may further cause network node device 200 to determine channel estimates for each radio channel, e.g., before performing the first minimization of the objective function, and in response to the at least one channel estimation quality parameter related to the radio channels between network node device 200 and multiple co-scheduled user devices 120A, 120B, 120C exceeding the respective quality threshold. For example, the channel estimates determined for each radio channel may comprise post- whitened channel estimates. At least in some embodiments, the instructions, when executed by at least one processor 202, may further cause network node device 200 to perform the determination of the channel estimates for each radio channel based on data provided by downlink channel state information (CSI) and / or an uplink sounding reference signal (SRS). At least in some embodiments, the instructions, when executed by at least one processor 202, may further cause network node device 200 to determine precoding matrices for each radio channel based on the determined channel estimates. For example, each precoding matrix may comprise a zero-forcing (ZF) precoding matrix. At least in some embodiments, the estimated downlink throughputs of each co-scheduled user device 120A, 120B, 120C may be functions of elements of the precoding matrices, as discussed below in more detail. At least in some embodiments, a per-antenna power of the PAPC may be a function of the precoding matrices. At least in some embodiments, the instructions, when executed by at least one processor 202, may further cause network node device 200 to perform the determination of the precoding matrices for each radio channel by determining precoding weights of the precoding matrices based on each corresponding co-scheduled user device 120A, 120B, 120C having a rank equal to a number of receive antennas of respective co- scheduled user device 120A, 120B, 120C At least in some embodiments, the instructions, when executed by at least one processor 202, may further cause network node device 200 to normalize columns of each precoding matrix to unity. In other words, a problem to be solved by the disclo- sure may be stated as follows: such that: - in each resource element (RE) and in each layer, the rate does not exceed spectral efficiency (SE) of a highest modulation and coding scheme (MCS). This ensures that power is not needlessly used beyond what is needed. Since the channel estimates with granularity are at the PRB or RBG level, it may be assumed that this is constant within that PRB / RBG; ^^ - for each UE ^^,^^^^,^^ ≥ ^^^^^ , where ^^ is the number^^(^^)^^^ ^^^^^^,^^^^ ^^^^^^^^,^^of PRBs over which UE ^^ is served in the slot, and ^^^^^^^^is the code rate of the lowest MCS; - a per antenna power constraint is satisfied; and - a total network node device 200 transmission power constraint is satisfied. A proportional fairness objective function attempts to maximize the product of ratios where ^^^∗^^^,^^is the maximum rate that UE ^^ would get if all the power were allo- cated only to it (at the cost of other UE). Diagram 400 of Fig. 4 illustrates plots for the fol- lowing: - spectral efficiency (SE) which has a 1-to-1 mapping with the modulation and coding scheme (MCS) versus a minimum signal-to-noise-ratio (SINR) required for a length 2880 5G low-density parity-check (LDPC) code to achieve a target code- word error rate (CER) of 10−3(marked as “Actual” in Fig. 4); and - a log approximation for the “Actual” SE vs SINRwith 5G LDPC codes using log2(1 + ^^^^^^^^^^) + ^^ with a minimum meansquared error (MSE) with respect to “Actual” achieved for ^^ =0.62, ^^ = 0.The above problem may be formally stated as follows: subject to: is the code rate of the lowest MCS; It is to be noted that in C1, ^^^^^^^^may be replaced by a UE defined ^^^^^^^^,^^corresponding to a rate-limit which is de- termined by a UE quality of service (QoS). In the above equation, the estimated downlink throughputs (or expected Shannon rates) are based on the lamb- das. Thus, the estimated downlink throughputs of each co- scheduled user device 120A, 120B, 120C are functions of the elements of the precoding matrices in this embodiment. The above problem is not a convex optimization prob- (^^) lem due to C2 and since optimizing is performed over ^^^^ , ^^ =there may not be a global minimum.Thus, a two-stage procedure may be used instead, as follows: ∀^^ = For a fixed {^^^^,^^}, the above P is a convex optimiza- tion problem which has a unique solution that can be obtained using, for example, Interior Point OPTimizer (IPOPT) software. Diagram 500 of Fig. 5 illustrates a flowchart for stage 1 of the above two-stage procedure. Operation 501 may assume that all the PRBs are allo- cated to all co-scheduled user devices 120A, 120B, 120C. Op- eration 502 may then perform the first minimization of the objective function to obtain the first DL power allocation. Operations 501-502 may be performed by network node device 200. The purpose of stage 1 is to identify useful RBGs / PRBs and layers for UEs. Those RBGs and layers that cannot support the minimum rate may be removed in stage 2. Diagram 600 of Fig. 6 illustrates a flowchart for stage 2 of the above two- stage procedure where it is assumed that a minimum of ^^^^^^^^,^^^^^^PRBs need to be allocated to each UE. The outputs of stage 2 are the RBG / PRB indices {^^^∗^,^^}, UE ranks and the per PRB / RBG UE allocated power for each layer After initialization at operation 601, operation 602 may estimate the co-scheduled user device 120A, 120B, 120C rates using the first DL power allocation obtained in stage 1 of the above two-stage procedure. Operations 603-609 may it- eratively check if any rate in any PRB or layer is not sup- portable and removes all those unsupportable PRBs and layers for each co-scheduled user device 120A, 120B, 120C. Operations 610-611 may check if any co-scheduled user device has been allocated a number of PRB lower than the minimum number of PRB possible, and if so, reallocate the minimum number of PRBs for that co-scheduled user device. Operation 613 may recalculate the precoding matrix in all those PRBs where at least one UE has not been allocated for transmission. Operations 614-616 may perform a second minimization of the objective function with the determined PRB and layers from operations 603-611 to obtain the final power allocation for each co-scheduled user device 120A, 120B, 120C. Operations 601-616 may be performed by network node device 200. At least in some embodiments, good quality channel estimates of the DL channel (using, e.g., uplink SRS channel estimates and channel reciprocity in a TDD system, or UE CSI feedback in an FDD system) may need to be obtained. It may therefore be useful to make a decision on when to use the disclosure instead of, e.g., conventional schemes. Diagram 700 of Fig. 7 illustrates a flowchart showing an example decision- making process that may be used to decide which scheme to use. In Fig. 7, ^^^^^^^^^^^^^^,^^ℎ^^^^ℎdenotes a threshold for the up- link UE SINR above which the channel estimation quality is expected to be good enough to decide in favor of the disclo- sure. ^^^^^^^^,^^ℎ^^^^ℎdenotes a threshold for the downlink I+N power (measured at each UE) above which there is an incentive to use the disclosure (the higher the I+N power, the better the in- centive to optimize resource allocation and other parameters). At least in some embodiments, values of ^^^^^^^^^^^^^^,^^ℎ^^^^ℎand / or ^^^^^^^^,^^ℎ^^^^ℎmay be predetermined, e.g., via numerical studies. At operation 701, the uplink (UL) channel may be es- timated using the SRS. At operation 702, it may be determined whether for the most co-scheduled user devices 120A, 120B, 120C, the DL I+N power exceeds ^^^^^^^^,^^ℎ^^^^ℎ. If not, the decision- making process may proceed to operation 703 in which a conven- tional method may be used for the co-scheduled user device 120A, 120B, 120C rank selection, PRB allocation, and / or power allocation. If yes, the decision-making process may proceed to operation 704 in which it may be determined whether the UL SINR exceeds ^^^^^^^^^^^^^^,^^ℎ^^^^ℎat network node device 200 for the most co-scheduled user devices 120A, 120B, 120C. If not, the deci- sion-making process may proceed to operation 703. If yes, the decision-making process may proceed to operation 705 in which network node device 200 may proceed with the disclosed joint co-scheduled user device 120A, 120B, 120C rank selection, PRB allocation, and power allocation. Operations 701-705 may be performed by network node device 200. At least in some embodiments, the performing of the first minimization of the objective function, the determination of the first DL power allocation, the determination of the PRBs and layers to use, and / or the determination of the second DL power allocation may comprise applying neural network (NN) 800 to a function of the estimated radio channels and the determined precoding weights. For ex- ample, NN 800 may be configured to predict the first and / or second DL power allocation for each PRB of each layer of each co-scheduled user device 120A, 120B, 120C. At least in some embodiments, the instructions, when executed by at least one processor 202, may further cause network node device 200 to train NN 800 via applying a mean squared error (MSE) loss function. Fig. 8 illustrates an example convolutional neural network (CNN) 800 with ^^ layers 802 for approximating the above-described optimization-based scheme. Since at least in some embodiments it may not be practically feasible (e.g., due to latency requirements) to perform the above-described two-stage optimization steps in real-time, a deep neural network (DNN) -based function approx- imator may be used instead. In theory, to approximate the above-described two- stage optimization steps using a DNN, it needs to be trainedusing both ^^, ^^. However, if the precoderwell-shaped or “flat” so that the ^^^^,^^,^^,^^are all close to one another in value, may be used alone as input features for ^^ (^^)training. Let Λ ∈ ℝ^^^^^^^^×∑ ^^^^=1 ^^^^ be a matrix with the elementdenoting ^^^^,^^,^^ and P denote the matrix with the element denoting ^^ ∗∗(^^) ^,^^,^^, wher ∑^^−1^ e ^^ = ^^=1 ^^^^ + ^^ ∀^^ = 1, ⋯ , ^^^^, ∀^^ = Here, {^^^∗^∗,^^,^^} are the outputs of the above optimization- (^^) sed solver. If ^^^^ <(^^) ba^^^^, then, 1, ⋯ , ^^^^^^^^. Similarly, any PRB / RBG index ^^ not selected for any^^ will have the ^^ ∗∗ = 0, ∀^^ = 1, ⋯ . Thus, Λ forms the feature and P the label. In order to represent the data better for a wide range of values, every element of Λand P may be taken in the logarithmic domain, with 0 represented by -100. In order to train a DNN for function approximation, a training dataset may be built on the fly in real-world con- ditions, or synthetic data may be used. In the former case, the following approach may be employed, for example: - step 1: for every time slot, network node device 200 may use the above two-stage solver to obtain the UE ranks, resource and power allocation indices for each co-scheduled UE, represented using the input matrix Λ 801 and output matrix P 803. Further, network node device 200 may record the UL SINR for the SRS channel estimation of each UE; - step 2: the DL transmission may be executed with the parameters obtained in step 1; - step 3: network node device 200 may receive acknowl- edgements (ACKs) / negative acknowledgements (NACKs) for transmitted codewords from each UE and also the DL I+N powers from each UE; - step 4: if most of the codewords resulted in ACKs,network node device 200 may add (Λ, P) to a training database.Otherwise, (Λ, P) may be discarded;- step 5: in either case in step 4, the UL SINR and DL I+N powers for each UE may be stored in the database and used to decide when the disclosure is to be used; and - step 6: steps 1-5 may be repeated until a useful training dataset has been built. Once a training dataset is built, e.g., a DNN with convolutional layers (a convolutional neural network (CNN)), denoted by where Ξ is the set of trainable parameters, may be trained with the input features and labels described above for a MSE loss function in a minibatch ℬ given as: where ‖P‖^^denotes the Frobenius norm of a matrix P. For faster convergence and robust performance, the order of users (corresponds to appropriate permutations of the columns of Λ and P) may be permuted. Furthermore, to handle a varying number of UEs in each time slot, a limit may be set on a maximum number of UEs, and then represent unused UE data with zeros. In test time, the predictions of the CNN may be con- verted back to the exponential domain. ^̂^^^,^^,^^may denote these values. Values below a predetermined threshold ^^^^ℎ^^^^ℎmay be zeroed out, yielding the UE ranks and PRB allocation indices. In order to satisfy the PAPC and the total power constraint,renormalization may be performed if required as ^̂^^^,^^,^^ ^ ^^1^̂^^^,^^,^^with The power per subcarrier may be further obtained from ^̂^^^,^^,^^which represents the power per PRB / RBG. Fig. 3 illustrates an example flow chart of method 300 for network node device 200, in accordance with an example embodiment. At optional operation 301, network node device 200 may determine whether the at least one channel estimation quality parameter related to the radio channels between network node device 200 and multiple co-scheduled user devices 120A, 120B, 120C exceeds the respective quality threshold. If the at least one channel estimation quality parameter does not exceed the respective quality threshold, method 300 may exit, operation 302. If the at least one channel estimation quality parameter exceeds the respective quality threshold, method 300 may proceed to operation 303. At optional operation 303, network node device 200 may determine the channel estimates for each radio channel. At optional operation 304, network node device 200 may determine the precoding matrices for each radio channel based on the determined channel estimates. At optional operation 305, network node device 200 may normalize the columns of each precoding matrix to unity. At operation 306, network node device 200 performs the first minimization of the objective function of the geometric mean of the estimated DL throughputs of each co- scheduled user device 120A, 120B, 120C subject to at least the PAPCs. At operation 307, network node device 200 determines the first DL power allocation for each candidate PRB of each layer of each co-scheduled user device 120A, 120B, 120C. At operation 308, network node device 200 determines, based on the determined first DL power allocation, the PRBs and layers to use for each co-scheduled user device 120A, 120B, 120C from among the candidate PRBs and the candidate layers. At operation 309, network node device 200 determines the second DL power allocation via performing the second minimization of the objective function of the geometric mean of the estimated DL throughputs of each co-scheduled user device 120A, 120B, 120C by utilizing the information about the determined PRBs and layers to use for each co-scheduled user device 120A, 120B, 120C. Embodiments and examples with regard to Fig. 3 may be carried out by network node device 200 of Fig. 2. Operations 301-309 may, for example, be carried out by at least one pro- cessor 202 and at least one memory 204. Further features of method 300 directly resulting from the functionalities and parameters of network node device 200 are not repeated here. Method 300 can be carried out by computer programs or portions thereof. Another example of an apparatus suitable for carrying out the embodiments and examples with regard to Fig. 3 com- prises means for: in response to the at least one channel estimation quality parameter related to the radio channels between network node device 200 and multiple co-scheduled user devices 120A, 120B, 120C exceeding, at operation 301, the respective quality threshold: performing the first minimization of the objective function of the geometric mean of the estimated DL throughputs of each co-scheduled user device 120A, 120B, 120C subject to at least the PAPCs; determining, at operation 307, the first DL power allocation for each candidate PRB of each layer of each co- scheduled user device 120A, 120B, 120C; determining, at operation 308, based on the determined first DL power allocation, PRBs and layers to use for each co-scheduled user device 120A, 120B, 120C from among the candidate PRBs and layers;and determining, at operation 309, the second DL power allocation via performing the second minimization of the objective function of the geometric mean of the estimated downlink throughputs of each co-scheduled user device 120A, 120B, 120C by utilizing the information about the determined PRBs and layers to use for each co-scheduled user device 120A, 120B, 120C. The functionality described herein can be performed, at least in part, by one or more computer program product components such as software components. According to an embod- iment, network node device 200 may comprise a processor or processor circuitry, such as for example a microcontroller, configured by the program code when executed to execute the embodiments of the operations and functionality described. Al- ternatively, or in addition, the functionality described herein can be performed, at least in part, by one or more hardware logic components. For example, and without limita- tion, illustrative types of hardware logic components that can be used include Field-programmable Gate Arrays (FPGAs), Appli- cation-specific Integrated Circuits (ASICs), Application-spe- cific Standard Products (ASSPs), System-on-a-chip systems (SOCs), Complex Programmable Logic Devices (CPLDs), Tensor Processing Units (TPUs), and Graphics Processing Units (GPUs). In the disclosed example embodiments, it may be pos- sible to train one ML model / NN with a specific architecture, then derive another ML model / NN from that using processes such as compilation, pruning, quantization or distillation. The ML model / NN may be executed using any suitable apparatus, for example a CPU, GPU, ASIC, FPGA, compute-in-memory, analog, or digital, or optical apparatus. It is also possible to exe- cute the ML model / NN in an apparatus that combines features from any number of these, for instance digital-optical or an- alog-digital hybrids. In some examples, weights and required computations in these systems may be programmed to correspond to the ML model / NN. In some examples, the apparatus may be designed and manufactured so as to perform the task defined by the ML model / NN so that the apparatus is configured to perform the task when it is manufactured without the apparatus being programmable as such. Any range or device value given herein may be ex- tended or altered without losing the effect sought. Also, any embodiment may be combined with another embodiment unless ex- plicitly disallowed. Although the subject matter has been described in language specific to structural features and / or acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as examples of implementing the claims and other equivalent features and acts are intended to be within the scope of the claims. It will be understood that the benefits and ad- vantages described above may relate to one embodiment or may relate to several embodiments. The embodiments are not limited to those that solve any or all of the stated problems or those that have any or all of the stated benefits and advantages. It will further be understood that reference to 'an' item may refer to one or more of those items. The steps of the methods described herein may be carried out in any suitable order, or simultaneously where appropriate. Additionally, individual blocks may be deleted from any of the methods without departing from the spirit and scope of the subject matter described herein. Aspects of any of the embodiments described above may be combined with aspects of any of the other embodiments described to form further embodiments without losing the effect sought. The term 'comprising' is used herein to mean includ- ing the method, blocks or elements identified, but that such blocks or elements do not comprise an exclusive list and a method or apparatus may contain additional blocks or elements. It will be understood that the above description is given by way of example only and that various modifications may be made by those skilled in the art. The above specifica- tion, examples and data provide a complete description of the structure and use of exemplary embodiments. Although various embodiments have been described above with a certain degree of particularity, or with reference to one or more individual embodiments, those skilled in the art could make numerous al- terations to the disclosed embodiments without departing from the spirit or scope of this specification.

Claims

CLAIMS 1. A network node device (200), comprising: at least one processor (202); and at least one memory (204) storing instructions that, when executed by the at least one processor (202), cause the network node device (200) at least to: in response to at least one channel estimation quality parameter related to radio channels between the network node device (200) and multiple co-scheduled user devices (120A, 120B, 120C) exceeding a respective quality threshold: perform a first minimization of an objective function of a geometric mean of estimated downlink throughputs of each co-scheduled user device (120A, 120B, 120C) subject to at least per-antenna power constraints, PAPCs; determine a first downlink power allocation for each candidate physical resource block, PRB, of each layer of each co-scheduled user device (120A, 120B, 120C); determine, based on the determined first downlink power allocation, PRBs and layers to use for each co-scheduled user device (120A, 120B, 120C) from among the candidate PRBs and candidate layers; and determine a second downlink power allocation via performing a second minimization of the objective function of the geometric mean of the estimated downlink throughputs of each co-scheduled user device (120A, 120B, 120C) by utilizing information about the determined PRBs and layers to use for each co-scheduled user device (120A, 120B, 120C).

2. The network node device (200) according to claim 1, wherein the instructions, when executed by the at least one processor (202), further cause the network node device (200) to determine channel estimates for each radio channel.

3. The network node device (200) according to claim 2, wherein the instructions, when executed by the at least one processor (202), further cause the network node device (200)to determine precoding matrices for each radio channel based on the determined channel estimates.

4. The network node device (200) according to claim 3, wherein the estimated downlink throughputs of each co- scheduled user device (120A, 120B, 120C) are functions of elements of the precoding matrices.

5. The network node device (200) according to claim 3 or 4, wherein a per-antenna power of the PAPC is a function of the precoding matrices.

6. The network node device (200) according to any of claims 3 to 5, wherein the instructions, when executed by the at least one processor (202), further cause the network node device (200) to perform the determination of the precoding matrices for each radio channel by determining precoding weights of the precoding matrices based on each corresponding co-scheduled user device (120A, 120B, 120C) having a rank equal to a number of receive antennas of the respective co-scheduled user device (120A, 120B, 120C) 7. The network node device (200) according to any of claims 2 to 6, wherein the channel estimates determined for each radio channel comprise post-whitened channel estimates.

8. The network node device (200) according to any of claims 1 to 7, wherein the first minimization of the objective function is further subject to at least one of rate constraints defined by quality of service, QoS, of each co-scheduled user device (120A, 120B, 120C), or a total power constraint.

9. The network node device (200) according to any of claims 6 to 8, wherein at least one of the performing of the first minimization of the objective function, the determination of the first downlink power allocation, the determination of the PRBs and layers to use, or the determination of the second downlink power allocationcomprises applying a neural network, NN, (800) to a function of the estimated radio channels and the determined precoding weights.

10. The network node device (200) according to claim 9, wherein the instructions, when executed by the at least one processor (202), further cause the network node device (200) to train the NN (800) via applying a mean squared error, MSE, loss function.

11. The network node device (200) according to any of claims 3 to 10, wherein each precoding matrix comprises a zero- forcing, ZF, precoding matrix.

12. The network node device (200) according to any of claims 3 to 11, wherein the instructions, when executed by the at least one processor (202), further cause the network node device (200) to normalize columns of each precoding matrix to unity.

13. The network node device (200) according to any of claims 2 to 12, wherein the instructions, when executed by the at least one processor (202), further cause the network node device (200) to perform the determination of the channel estimates for each radio channel based on data provided by at least one of downlink channel state information, CSI, or an uplink sounding reference signal, SRS.

14. The network node device (200) according to any of claims 1 to 13, wherein the at least one channel estimation quality parameter comprises at least one of an uplink signal- to-interference noise ratio, SINR, for each co-scheduled user device (120A, 120B, 120C), or a downlink interference-plus- noise, I+N, for each co-scheduled user device (120A, 120B, 120C).

15. A method (300), comprising: in response to at least one channel estimation quality parameter related to radio channels between a network node device (200) and multiple co-scheduled user devices (120A, 120B, 120C) exceeding (301) a respective quality threshold: performing (306), by the network node device (200), a first minimization of an objective function of a geometric mean of estimated downlink throughputs of each co-scheduled user device (120A, 120B, 120C) subject to at least per-antenna power constraints, PAPCs; determining (307), by the network node device (200), a first downlink power allocation for each candidate physical resource block, PRB, of each layer of each co-scheduled user device (120A, 120B, 120C); determining (308), by the network node device (200), based on the determined first downlink power allocation, PRBs and layers to use for each co-scheduled user device (120A, 120B, 120C) from among the candidate PRBs and candidate layers; and determining (309), by the network node device (200), a second downlink power allocation via performing a second minimization of the objective function of the geometric mean of the estimated downlink throughputs of each co-scheduled user device (120A, 120B, 120C) by utilizing information about the determined PRBs and layers to use for each co-scheduled user device (120A, 120B, 120C).

16. An apparatus, comprising means for carrying out the method (300) according to claim 15.

17. A computer program comprising instructions for causing a network node device to perform at least the follow- ing: in response to at least one channel estimation quality parameter related to radio channels between the network node device and multiple co-scheduled user devices exceeding a respective quality threshold:performing a first minimization of an objective function of a geometric mean of estimated downlink throughputs of each co-scheduled user device subject to at least per- antenna power constraints, PAPCs; determining a first downlink power allocation for each candidate physical resource block, PRB, of each layer of each co-scheduled user device; determining, based on the determined first downlink power allocation, PRBs and layers to use for each co-scheduled user device from among the candidate PRBs and candidate layers; and determining a second downlink power allocation via performing a second minimization of the objective function of the geometric mean of the estimated downlink throughputs of each co-scheduled user device by utilizing information about the determined PRBs and layers to use for each co-scheduled user device.

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