Joint precoding architectures and methods for distributed MIMO systems with delayed global CSI and timely local csi

Abstract

An apparatus (100) of a wireless communication system according to an embodiment is provided. The apparatus (100) is configured to receive a reference signal for channel estimation, and to determine therefrom, local channel state information. Moreover, the apparatus (100) is configured to transmit information on the local channel state information to at least one other entity of the wireless communication system. Furthermore, the apparatus (100) is configured to determine first precoding information depending on the local channel state information. Moreover, the apparatus (100) is configured to receive second information, wherein the second information depends on channel state information of one or more other apparatuses (111, 112) of the wireless communication system, and wherein the second information depends also on the local channel state information of the apparatus (100). Furthermore, the apparatus (100) is configured to generate a transmit signal, which depends on two or more data-bearing signals, using the first precoding information and the second information. The channel state information of the one or more other apparatuses (111, 112) is delayed compared to the local channel state information of the apparatus (100).

Description

[0001]Joint Precoding Architectures and Methods for Distributed MIMO Systems with Delayed Global CSI and Timely Local CSI Description The present invention relates to joint precoding architectures and methods for distributedmultiple input multiple output (MIMO) systems with delayed global CSI and timely localCSI. Distributed MIMO (also referred to as cell-free massive MIMO) is one of the most promising candidate technologies for enhancing the performance of future generation wireless networks. Much of the related research and development effort focuses on the development of system architectures and methods for turning the large theoretical gains of coordinated multi-point concepts (CoMP) into commercially attractive solutions. Of particular relevance is the development of robust joint precoding solutions for downlink coherent joint transmission, in particular by considering practical limitations that deviate from the ideal assumptions typically found in the scientific literature.Precoding can be considered as a generalization of beamforming, and aims to supportmulti-stream or multi-layer transmissions in multi-antenna wireless communications. When multiple data streams are emitted from the transmit antennas, a link throughput to a receiver or a total throughput to multiple receivers shall be maximized. Joint precoding is a generalization of precoding, where the transmit antennas are distributed across multiple access points (APs) (also called transmission points). Theoretically, the best performing solutions for joint precoding are based on so-called centralized architectures. These solutions assume that joint precoders are computed by a CPU as a function of instantaneous global channel state information (CSI) obtained by collecting local channel measurements from the APs via the fronthaul. However, centralized architectures experience significant performance degradation when the delay incurred by the CPU in collecting global CSI, computing the precoders, and forwarding the result to the APs is non-negligible with respect to channel aging (user mobility). In this case, the precoding decisions made by the CPU are generally highly suboptimal because they are based on outdated channel state information (CSI). Some early approaches for centralized architectures focused on fronthaul compression techniques. These techniques can relax the information sharing overhead and hence the required fronthaul capabilities. FH250401PCT-2025112871.DOCX Other approaches for centralized architectures focused on prediction techniques that mitigate the impact of global CSI imperfections due to channel aging. More recently, some approaches focused on so-called fully distributed architectures with no instantaneous CSI sharing. Specifically, these approaches assume that the joint precoders are computed locally by each AP based on local yet timely channel measurements only (local CSI only). A more effective approach is to use partially distributed architectures that combine the benefits of centralized architectures and fully distributed architectures, i.e., the benefits of delayed global CSI and timely local CSI. This invention follows this approach. A similar approach is described in [1].[1] considers a joint precoding architecture similar to the second embodiment. Inparticular, [1] considers different signals to be shared between APs and the CPU: TheAPs forward to the CPU not only the local CSI but also their single-stage localprecoding matrix (complex-valued matrix with dimension NxK, using the notation of this document). The CPU forwards to each AP an updated version of its single-stage NxK local precoding matrices, and another KxK complex-valued matrix carrying parsed information about the global delayed CSI and the local precoding matrices for the otherAPs. [1] provides single-stage precoding method based on the framework of onlineconvex optimization. However, it would be appreciated, if improved concepts for multiple input multiple output systems would be provided.The object of the present invention is to provide improved concepts for multiple inputmultiple output systems. The object of the present invention is solved by the subject-matter of the independent claims. Particular embodiments are provided in the dependent claims. An apparatus of a wireless communication system according to an embodiment is provided. The apparatus is configured to receive a reference signal for channel estimation, and to determine therefrom, local channel state information. Moreover, the apparatus is configured to transmit information on the local channel state information to at least one other entity of the wireless communication system. Furthermore, the apparatus is configured to determine first precoding information depending on the local channel state FH250401PCT-2025112871.DOCX information. Moreover, the apparatus is configured to receive second information, wherein the second information depends on channel state information of one or more other apparatuses of the wireless communication system, and wherein the second information depends also on the local channel state information of the apparatus. Furthermore, the apparatus is configured to generate a transmit signal, which depends on two or more data-bearing signals, using the first precoding information and the second information. The channel state information of the one or more other apparatuses is delayed compared to the local channel state information of the apparatus.Moreover, a method for a wireless communication system according to an embodiment isprovided. The method comprises:- Receiving, by an apparatus of the wireless communication system, a referencesignal for channel estimation, and to determine therefrom, local channel state information.- Transmitting, by the apparatus, information on the local channel state informationto at least one other entity of the wireless communication system.- Determining first precoding information depending on the local channel stateinformation.- Receiving, by the apparatus, second information, wherein the second informationdepends on channel state information of one or more other apparatuses of the wireless communication system. And:- Generating a transmit signal, which depends on two or more data-bearing signalsusing the first precoding information and the second information. The channel state information of the one or more other apparatuses is delayed compared to the local channel state information of the apparatus.Furthermore, a computer program according to an embodiment for implementing theabove-described method when being executed on a computer or signal processor isprovided.Embodiments provide new joint precoding architectures and methods to mitigate theimpact of channel aging and delayed information sharing across APs and CPUs. FH250401PCT-2025112871.DOCX Embodiments are based on the concept to use a two-stage precoding architecture, where the first stage depends on timely local CSI, and the second stage depends on delayed global CSI. The first stage is computed locally by the APs as soon as the local CSI is obtained. The second stage is computed by one or more CPUs or by the APs after a CSI sharing phase, with some delay.According to embodiments, downlink precoding architectures and methods for distributedMIMO (D-MIMO) or cell-free massive MIMO systems are provided to counteract issues related to channel aging and fronthaul delays, or to reduce fronthaul requirements.In embodiments, multiple cooperating access points (AP) serve multiple UEs in the sametime-frequency resource by means of coherent joint transmission. The APs have localprocessing capabilities. According to embodiments, the APs acquire local estimates of the local channel (local CSI) and share them over a fronthaul to form precoders based on global channel estimates (global CSI). In embodiments, a two-stage precoding structure, where the first stage is a function of timely local CSI, and the second stage is a function of delayed global CSI. According to embodiments, the first precoding stages are computed locally at the APs. In embodiments, the second stages can be computed by any entity, e.g., a central processing unit (CPU) endowed with global CSI.According to particular embodiments, different system architectures may, e.g., beprovided, depending on the choice of the entity that performs the computation of the second precoding stages. In particular embodiments, different methods for computing the second precoding stages, mostly depending on complexity and on the capability of the network to acquire and trackchannel statistical properties are provided.Inter alia, in contrast to [1], a two-stage precoding structure is provided, which producessignificantly different transmit signals compared to [1]. In addition, [1] requires additionalsignals to be transmitted between the APs and the CPU. In particular, in [1], each APs FH250401PCT-2025112871.DOCX sends one NxK and one KxK matrix to the CPU. Furthermore, in [1], the CPU sends one NxK and one KxK matrix to each AP. Compared to [1], not only the transmit signals of embodiments are significantly different, but also the fronthaul signaling overhead / architecture of embodiments significantly differs from [1].Embodiments allows to effectively merge the benefits of centralized and fully distributedjoint precoding methods and architectures. Specifically, embodiments provide a jointexploitation of global CSI for centralized interference management, and local CSI for mitigating the impact of fronthaul and processing delays. Overall, embodiments realize significant performance gains compared to the state of the art. In the following, embodiments of the present invention are described in more detail with reference to the figures, in which:Fig. 1 illustrates a wireless communication system according to an embodimentcomprising an apparatus according to an embodiment and one or more other apparatuses of the wireless communication system.Fig. 2 illustrates a system architecture of a first embodiment, which employs adistributed precoding with CSI sharing.Fig. 3 illustrates a system architecture of a second embodiment, which employs acentralized precoding with local refinements, which implements a compress-before-precoding.Fig. 4 illustrates a system architecture of a third embodiment, which employs acentralized precoding with local refinements, which implements a compress-after-precoding.Fig.1 illustrates an apparatus 100 according to an embodiment.The apparatus 100 is configured to receive a reference signal for channel estimation, andto determine therefrom, local channel state information.Moreover, the apparatus 100 is configured to transmit information on the local channelstate information to at least one other entity of the wireless communication system. FH250401PCT-2025112871.DOCXFurthermore, the apparatus 100 is configured to determine first precoding informationdepending on the local channel state information.Moreover, the apparatus 100 is configured to receive second information, wherein thesecond information depends on channel state information of one or more otherapparatuses 111, 112 of the wireless communication system, and wherein the secondinformation depends also on the local channel state information of the apparatus 100.Furthermore, the apparatus 100 is configured to generate a transmit signal, whichdepends on two or more data-bearing signals, using the first precoding information and the second information. The channel state information of the one or more other apparatuses 111, 112 is delayed compared to the local channel state information of the apparatus 100.According to an embodiment, the channel state information of the one or more otherapparatuses 111, 112 may, e.g., be delayed compared to the local channel stateinformation such that the channel state information of the one or more other apparatuses111, 112 may, e.g., relate to one or more earlier points-in-time compared to a point-in-timeto which the local channel state information may, e.g., relate.In an embodiment, the apparatus 100 may, e.g., be configured to determine secondprecoding information from the second information which is received, or may, e.g., beconfigured to receive the second precoding information as the second information fromanother entity of the wireless communication system. The apparatus 100 may, e.g., beconfigured to map the two or more data-bearing signals using the first precoding information and the second information to obtain the transmit signal.According to an embodiment, the apparatus 100 may, e.g., be configured to receive thechannel state information of the one or more other apparatuses 111, 112 of the wirelesscommunication system from the one or more other apparatuses 111, 112. The apparatus100 may, e.g., be configured to determine the second precoding information using thechannel state information of the one or more other apparatuses 111, 112 of the wirelesscommunication system.In an embodiment, the apparatus 100 may, e.g., be configured to receive the secondprecoding information from a centralized unit (e.g., a CPU, central processing unit) 121 of FH250401PCT-2025112871.DOCX the wireless communication system, wherein the second precoding information depends on the channel state information of the one or more other apparatuses 111, 112.According to an embodiment, the apparatus 100 may, e.g., be configured to receive aprecoded signal as the second information from a centralized unit (e.g., a CPU, centralprocessing unit) 122 of the wireless communication system, wherein the precoded signalrepresents a mapping of second precoding information on the two or more data-bearingsignals. The apparatus 100 may, e.g., be configured to apply the first precodinginformation on the precoded signal to obtain the transmit signal.In an embodiment, the transmit signal for the apparatus 100 for a time slot t correspondsto: ^^[^] = ^^[^]^^[^]^[^],wherein: wherein ^^[^] ∈ ℂ^×^ represents the first precoding information, wherein ^^[^] ∈ℂ^×^ represents the second precoding information, wherein ^[^] ∈ ℂ^ represents the twoor more data-bearing signals.According to an embodiment, ^^[^] ∈ ℂ^×^depends on the local channel state informationbeing timely local channel state information. ^^[^] ∈ ℂ^×^ may, e.g., depend on a delayedglobal channel state information which depends on the channel state information of the one or more other apparatuses 111, 112. In an embodiment, the second precoding information is determined for a time slot t depending on a linear system of equations:FH250401PCT-2025112871.DOCX wherein K indicates a number of the two or more data-bearing signals. wherein ^^indicates an identity matrix, wherein ^^[^] indicates a Hermitian positive semidefinitematrix that depends on the channel state information of the one or more otherapparatuses 111, 112 being timely delayed compared to the local channel stateinformation. According to an embodiment, ^[^] = ℇ ^diag( In an embodiment, the apparatus 100 may, e.g., be configured to compute the secondprecoding information from the channel state information of the one or more other apparatuses 111, 112.According to an embodiment, the apparatus 100 may, e.g., be configured to obtain thesecond precoding information from the channel state information of the one or more otherapparatuses 111, 112 by employing a machine-learning concept.In an embodiment, the access point may, e.g., be configured to determine the firstprecoding information by determining a local precoding matrix according to: wherein are vectors of positive parameters which can tuned to balance receivers’ priorities andaccess point power consumption.FH250401PCT-2025112871.DOCXAccording to an embodiment, the apparatus 100 may, e.g., be an access point of thewireless communication system.In an embodiment, the one or more other apparatuses 111, 112 may, e.g., be one or moreother access points of the wireless communication system.According to an embodiment, the one or more data-bearing signals are one or more modulated data-bearing signals.In an embodiment, the transmit signal may, e.g., be a downlink transmit signal.According to an embodiment, the wireless communication system may, e.g., be adistributed multiple input multiple output system.Moreover, Fig. 1 illustrates a wireless communication system according to anembodiment. The wireless communication system comprises a first apparatus 100 beingthe apparatus 100 according to one of the above-described embodiments, and the one ormore other apparatuses 111, 112.According to an embodiment, each of the one or more other apparatuses 111, 112 may,e.g., also be an apparatus 100 according to one of the above-described embodiments.In an embodiment, the first apparatus 100 may, e.g., be a first access point. The one ormore other apparatuses 111, 112 may, e.g., be one or more other access points.According to an embodiment, the wireless communication system may, e.g., furthercomprise the centralized unit 121; 122 described above.In an embodiment, the wireless communication system may, e.g., be a distributed multipleinput multiple output system. In the following, particular embodiments of the present invention are described. At first, joint precoding architectures according to embodiments are described. FH250401PCT-2025112871.DOCXA D-MIMO (distributed MIMO) network composed by L APs (access points) equipped withN antennas each, jointly serving K single-antenna UEs (user equipments) in the sametime-frequency resource, e.g., of an OFDM-based system, using multi-user MIMO coherent joint transmission is considered.The following notation is defined:^^ ^[^] ∈ ℂ^×^is the local estimate of the local MIMO channel ^^[^] ∈ ℂ^×^between theNantennas of the l-th AP and all UEs (local CSI). ∈ ℂ^×^^is the global estimate of the global MIMO channel between the LN antennas of all APs and all UEs (global CSI).The transmit signal of the l-th AP on a given time slot t then takes the following form:^^[^] = ^^[^]^^[^]^[^],where:^^[^] ∈ ℂ^×^is a first precoding stage, and is computed as function of the timely local CSI .^^[^] ∈ ℂ^×^ is a second precoding stage, and is computed as a function of the delayedglobal CSI ^^ [^ − ^] for some delay ^ ≥ 1.^[^] ∈ ℂ^ collects the K modulated data-bearing signals (e.g., QAM signals) for each ofthe K UEs.It is assumed that the local CSI can be obtained via canonical channel estimationschemes based on uplink training and reciprocity calibration techniques for time-division duplex (TDD) systems, via downlink training and CSI feedback techniques in frequency- division duplex (FDD) systems. Then, the local CSI can be forwarded with some delay via the fronthaul to the other APs or to one or more CPUs for the computation of the secondprecoding stage. In the above model, a single parameter ^ ≥ 0 is employed to model thedelay incurred by this CSI sharing step, but also to implicitly model additional delays for computing the second precoding stage and to forward back the result. FH250401PCT-2025112871.DOCXFurthermore, since the true delay seen by different APs may be different, ^ ≥ 0 can bechosen following a worst-case approach, that is, by setting it to max (^^, … , ^^), where^^ ≥ 0 denotes the delays seen by the lth AP.As further common assumptions, it is assumed that the network is appropriatelysynchronized, such that coherent joint transmission is supported.The term “antenna” may, e.g., refer to a distinct antenna port whose signal can beindependently controlled by a digital signal processor; wherein the impact of an eventualanalog beamforming stage may, e.g., be absorbed into the channel matrix.In the following, particular embodiments are provided, which implement the above jointprecoding structure using one of a plurality of system architectures, wherein each of theplurality system architectures of embodiments exhibits different procedures for signallingand for computing the transmit signals.Three particular embodiments, focusing on TDD systems, are provided in the following:Fig. 2 illustrates a system architecture of a first embodiment, which employs a distributedprecoding with CSI sharing. In the first embodiment:The UEs send uplink reference signals for channel estimation.Each AP 100 (111) uses the received reference signals ^^[^] to compute the local CSI, and forwards (e.g., broadcasts) it over the fronthaul to the other APs 111 (100).Each AP 100 (111) uses the local CSI to compute the first precoding stage ^^[^], and theglobal CSI ^^ [^ − ^] collected from other APs to compute the second precoding stage^^[^].Each AP 100 (111) uses the obtained precoding stages ^^[^], ^^[^] to map the modulateddata-bearing signals ^[^] to the downlink transmit signal ^^[^] = ^^[^]^^[^]^[^].FH250401PCT-2025112871.DOCXFig. 3 illustrates a system architecture of a second embodiment, which employs acentralized precoding with local refinements, which implements a compress-before-precoding. In the second embodiment:The UEs send uplink reference signals for channel estimation.Each AP 100, 111 uses the received reference signals ^^[^] to compute the local CSI, and forward it over the fronthaul to the CPU 121.Each AP 100 (111) uses the local CSI to compute the first precoding stage ^^[^].The centralized unit CPU 121 uses the global CSI ^^ [^ − ^] collected from other APs 111(100) to compute the second precoding stage ^^[^] and forward them over the fronthaul tothe corresponding APs 100 (111).Each AP 100 (111) uses the obtained precoding stages ^^[^], ^^[^] to map the modulateddata-bearing signals ^[^] to the downlink transmit signal ^^[^] = ^^[^]^^[^]^[^].Fig. 4 illustrates a system architecture of a third embodiment, which employs a centralizedprecoding with local refinements, which implements a compress-after-precoding. In thethird embodiment: The UEs send uplink reference signals for channel estimation.Each AP 100 (111) uses the received reference signals ^^[^] to compute the local CSI^^ ^[^], and forward it over the fronthaul to the CPU 122.Each AP 100 (111) uses the local CSI to compute the first precoding stage ^^[^].The CPU 122 uses the global CSI ^^ [^ − ^] collected from other APs 111 (100) to computethe second precoding stage ^^[^], apply them to the data-bearing signals ^[^], and forwardthe resulting signals ^^[^]^[^] over the fronthaul to the corresponding APs 100 (111).Each AP 100 (111) uses the first precoding stage ^^[^] to map the received signal^^[^]^[^] from the CPU 122 to the downlink transmit signal ^^[^] = ^^[^]^^[^]^[^].FH250401PCT-2025112871.DOCXThe first embodiment is closer to early implementations of CoMP techniques based onenhancing traditional cellular radio access networks by allowing base station cooperation.The second and third embodiments are closer to more recent implementations of CoMPtechniques based on cloud-RAN concepts. However, in contrast to state of the artconcepts, embodiments provide a two-stage precoding structure, which explicitly takesinto account delayed information sharing.The proposed embodiments can also be extended to comprise multiple cooperating CPUscontrolling different APs. Furthermore, the above embodiments can be modified such that, instead of forwarding thelocal CSI the APs forward the received reference signals ^^[^] as in canonicalcentralized precoding architectures. In addition, in the above embodiments, the signaling overhead and joint processing effortcan be reduced by limiting the information sharing and processing effort to only portions ofthe CSI and precoding matrices that contribute significantly to the quality-of-service of the UEs. More specifically, due to the large path loss between AP-UE pairs with large geographical separations, and due to the application of standard network-centric or user- centric cooperation clustering techniques for D-MIMO systems, many entries of the considered matrices are either close or forced to zero and hence they need not be shared and processed. In the following, joint precoding methods according to embodiments are described. Based on the joint precoding structure described above, several functions can be used for mapping the CSI to the corresponding precoding stages. The choice of the functions essentially depends on the chosen architecture, and on the availability of statistical CSI in some form. In general, the two precoding stages may, e.g., be implemented with practically implementable variations of the following ideal functions, which are obtained by assuming that the time-varying channel can be reasonably modelled as a stationaryrandom process with known distribution. In the following, ℇ[⋅] may, e.g., denote theexpectation operator. For the first precoding stage, in embodiments, variations of the so-called local MMSE precoding matrix may, e.g., be employed: FH250401PCT-2025112871.DOCX where: are vectors of positive parameters that can tuned to balance receivers’ priorities and APpower consumption. They can be chosen heuristically or according to some given utility optimization technique. is a Hermitian positive semidefinite matrix that can be used to mitigate the impact of noise and pilot contamination in estimating the channel between the l-th AP and the k-th UE.For the second precoding stage, in embodiments, the solution to variations of thefollowing linear system of equations may e.g., be chosen: where ^^[^] = ℇ ^diag is a Hermitian positive semidefinite matrix that takes into account the impact of delayedCSI. ^^[^] may, e.g., be obtained as a given function of ^^ ^[^ − ^].In practice, the time-varying channels may well be approximated by a stationary distribution only for some limited time window. Furthermore, the underlying distribution is typically not known. However, the expectations in the above ideal functions can be approximated and tracked by means of adaptive model-driven and / or data-driven approaches. FH250401PCT-2025112871.DOCX The choice of the technique for approximating the expectations gives different methods forcomputing the two precoding stages. Methods for computing the first precoding stage,e.g., for approximating the weighted CSI error covariance matrix and for setting theparameters ^ and ^ are extensively studied in the context of standard MIMO precodingmethods. For example, can be omitted by assuming that its impact is negligible with respect to other terms in the matrix inversion step. Alternatively, by assuming Gaussian fading and linear MMSE channel estimation, can be computed as a function of the channel covariance matrices and estimation noise variances, which in turn can be estimated and tracked from periodic reference signals.Furthermore, the parameters ^ and ^ can be tuned to obtain standard regularized zero-forcing (RZF) or maximum ratio transmission (MRT) precoding methods.In light of the above discussion, in the following, two particular embodiments aredescribed focusing on the second precoding stage and on centralized precoding architectures with local refinements. A first particular embodiment is model-driven with a small-delay assumption.The CPU collects the global CSI ^^ [^ − ^].Based on the global CSI, the CPU computes all L matrices^ ^^[^] = diag(^) ^^^ ^[^ − ^]^^[^ − ^]Based on ^^[^], … , ^^[^], the CPU computes the second precoding stagesThe CPU forwards the results to the APs.A second particular embodiment is data-driven employing regression from a training set.The CPU collects the global CSI ^^ [^ − ^].FH250401PCT-2025112871.DOCXUsing the global CSI, the CPU may, e.g., update a training set of n>1 CSI pairs according to some given rule. For example, the CPU can store n consecutive pairs intime, or a set of sufficiently separated pairs in time such that they can be assumed mutually independent.Using the global CSI, the function computes all L matrices^^[^] = ^^^^^ ^[^ − ^]^,where ^^is a function that it is optimized using the training set. In particular, ^^can be chosen to optimize the regression error (Frobenious norm) in some given space of functions that depends on the chosen regression technique. Examples are Bayesian regression methods based on Gaussian processes, or regression methods in reproducing kernel Hilbert spaces (RKHS). The functions ^^may be regularly updated along the training set updates.Based on ^^[^], … , ^^[^], the CPU may, e.g., compute the second precoding stages bysolving the abovementioned linear system of equations The CPU forward the results to the APs. A variant of the second embodiment is obtained by noticing that the regression step could be alternatively implemented in a distributed manner at each AP, since the regression error for the function ^^depends only on a training set composed by local CSI pairs. Embodiments of the present invention may, e.g., be employed in wireless communications, in particular, in Wireless radio access networks based on D-MIMO / cell- free massive MIMO technologies. FH250401PCT-2025112871.DOCXFor example, embodiments may, e.g., be employed in indoor wireless access in campus / private networks. For example, in order to keep deployment and management costs low,indoor campus or private networks may, e.g., comprise a relatively low-qualityinfrastructure with moderate processing and fronthaul capabilities. Therefore, the delayincurred by centralized precoding architectures may be significant and comparable to thechannel coherence time even for low mobility applications. In another example, embodiments may, e.g., be employed for outdoor wireless access inurban public networks. Public network infrastructures may, e.g., be of very high quality,since high deployment and managements costs can often be sustained by a large number of subscribers. However, even if small in absolute terms, the delay incurred by centralized precoding architectures may be comparable to the channel coherence time due to the typically higher mobility patterns that need to be supported in outdoor scenarios. Although some aspects have been described in the context of an apparatus, it is clear that these aspects also represent a description of the corresponding method, where a block or device corresponds to a method step or a feature of a method step. Analogously, aspects described in the context of a method step also represent a description of a corresponding block or item or feature of a corresponding apparatus. Some or all of the method steps may be executed by (or using) a hardware apparatus, like for example, a microprocessor, a programmable computer or an electronic circuit. In some embodiments, one or more of the most important method steps may be executed by such an apparatus. Depending on certain implementation requirements, embodiments of the invention can beimplemented in hardware or in software or at least partially in hardware or at least partiallyin software. The implementation can be performed using a digital storage medium, for example a floppy disk, a DVD, a Blu-Ray, a CD, a ROM, a PROM, an EPROM, an EEPROM or a FLASH memory, having electronically readable control signals stored thereon, which cooperate (or are capable of cooperating) with a programmable computer system such that the respective method is performed. Therefore, the digital storage medium may be computer readable. Some embodiments according to the invention comprise a data carrier having electronically readable control signals, which are capable of cooperating with a programmable computer system, such that one of the methods described herein is performed. FH250401PCT-2025112871.DOCX Generally, embodiments of the present invention can be implemented as a computer program product with a program code, the program code being operative for performing one of the methods when the computer program product runs on a computer. The program code may for example be stored on a machine readable carrier. Other embodiments comprise the computer program for performing one of the methods described herein, stored on a machine readable carrier. In other words, an embodiment of the inventive method is, therefore, a computer program having a program code for performing one of the methods described herein, when the computer program runs on a computer. A further embodiment of the inventive methods is, therefore, a data carrier (or a digital storage medium, or a computer-readable medium) comprising, recorded thereon, the computer program for performing one of the methods described herein. The data carrier, the digital storage medium or the recorded medium are typically tangible and / or non-transitory. A further embodiment of the inventive method is, therefore, a data stream or a sequenceof signals representing the computer program for performing one of the methodsdescribed herein. The data stream or the sequence of signals may for example be configured to be transferred via a data communication connection, for example via the Internet. A further embodiment comprises a processing means, for example a computer, or a programmable logic device, configured to or adapted to perform one of the methods described herein. A further embodiment comprises a computer having installed thereon the computer program for performing one of the methods described herein. A further embodiment according to the invention comprises an apparatus or a system configured to transfer (for example, electronically or optically) a computer program forperforming one of the methods described herein to a receiver. The receiver may, forexample, be a computer, a mobile device, a memory device or the like. The apparatus or system may, for example, comprise a file server for transferring the computer program to the receiver. FH250401PCT-2025112871.DOCX In some embodiments, a programmable logic device (for example a field programmable gate array) may be used to perform some or all of the functionalities of the methods described herein. In some embodiments, a field programmable gate array may cooperate with a microprocessor in order to perform one of the methods described herein. Generally, the methods are preferably performed by any hardware apparatus. The apparatus described herein may be implemented using a hardware apparatus, or using a computer, or using a combination of a hardware apparatus and a computer. The methods described herein may be performed using a hardware apparatus, or using a computer, or using a combination of a hardware apparatus and a computer. The above described embodiments are merely illustrative for the principles of the present invention. It is understood that modifications and variations of the arrangements and the details described herein will be apparent to others skilled in the art. It is the intent, therefore, to be limited only by the scope of the impending patent claims and not by the specific details presented by way of description and explanation of the embodiments herein. FH250401PCT-2025112871.DOCX Reference: [1] Wang, Dong, Liang, Boudreau, Abou-Zeid, “Hierarchical Semi-Online Optimization for Cooperative MIMO Networks with Information Parsing”, IEEE Transactions on Wireless Communications, July 2023. FH250401PCT-2025112871.DOCX

Claims

Claims1. An apparatus (100) of a wireless communication system,wherein the apparatus (100) is configured to receive a reference signal for channelestimation, and to determine therefrom, local channel state information, wherein the apparatus (100) is configured to transmit information on the localchannel state information to at least one other entity of the wireless communication system, wherein the apparatus (100) is configured to determine first precoding informationdepending on the local channel state information,wherein the apparatus (100) is configured to receive second information, whereinthe second information depends on channel state information of one or more other apparatuses (111, 112) of the wireless communication system, and wherein thesecond information depends also on the local channel state information of the apparatus (100), wherein the apparatus (100) is configured to generate a transmit signal, whichdepends on two or more data-bearing signals, using the first precoding informationand the second information, wherein the channel state information of the one or more other apparatuses (111, 112) is delayed compared to the local channel state information of the apparatus (100).

2. An apparatus (100) according to claim 1,wherein the channel state information of the one or more other apparatuses (111, 112) is delayed compared to the local channel state information such that thechannel state information of the one or more other apparatuses (111, 112) relatesto one or more earlier points-in-time compared to a point-in-time to which the local channel state information relates.

3. An apparatus (100) according to claim 1 or 2,FH250401PCT-2025112871.DOCXwherein the apparatus (100) is configured to determine second precodinginformation from the second information which is received, or is configured to receive the second precoding information as the second information from another entity of the wireless communication system, wherein the apparatus (100) is configured to map the two or more data-bearingsignals using the first precoding information and the second information to obtain the transmit signal.

4. An apparatus (100) according to claim 3,wherein the apparatus (100) is configured to receive the channel state informationof the one or more other apparatuses (111, 112) of the wireless communicationsystem from the one or more other apparatuses (111, 112), wherein the apparatus (100) is configured to determine the second precodinginformation using the channel state information of the one or more other apparatuses (111, 112) of the wireless communication system.

5. An apparatus (100) according to claim 3,wherein the apparatus (100) is configured to receive the second precodinginformation from a centralized unit (121) of the wireless communication system, wherein the second precoding information depends on the channel state information of the one or more other apparatuses (111, 112).

6. An apparatus (100) according to claim 1 or 2,wherein the apparatus (100) is configured to receive a precoded signal as thesecond information from a centralized unit (122) of the wireless communication system, wherein the precoded signal represents a mapping of second precodinginformation on the two or more data-bearing signals, andwherein the apparatus (100) is configured to apply the first precoding informationon the precoded signal to obtain the transmit signal.

7. An apparatus (100) according to one of claims 3 to 6,FH250401PCT-2025112871.DOCXwherein the transmit signal for the apparatus (100) for a time slot t corresponds to:^^[^] = ^^[^]^^[^]^[^],wherein: wherein ^^[^] ∈ ℂ^×^ represents the first precoding information,wherein ^^[^] ∈ ℂ^×^represents the second precoding information, wherein ^[^] ∈ ℂ^ represents the two or more data-bearing signals.

8. An apparatus (100) according to claim 7,wherein ^^[^] ∈ ℂ^×^depends on the local channel state information being timely local channel state information, wherein ^^[^] ∈ ℂ^×^depends on a delayed global channel state information which depends on the channel state information of the one or more other apparatuses (111, 112).

9. An apparatus (100) according to one of claims 3 to 8,wherein the second precoding informationis determined for a time slot t depending on a linear system of equations:FH250401PCT-2025112871.DOCXwherein K indicates a number of the two or more data-bearing signals,wherein^^indicates an identity matrix, wherein ^^[^] indicates a Hermitian positive semidefinite matrix that depends onthe channel state information of the one or more other apparatuses (111, 112) being timely delayed compared to the local channel state information.

10. An apparatus (100) according to claim 9,wherein ^^[^] = ℇ ^diag11. An apparatus (100) according to one of claims 3 to 10,wherein the apparatus (100) is configured to compute the second precodinginformation from the channel state information of the one or more other apparatuses (111, 112).

12. An apparatus (100) according to one of claims 3 to 10,wherein the apparatus (100) is configured to obtain the second precodinginformation from the channel state information of the one or more other apparatuses (111, 112) by employing a machine-learning concept.

13. An apparatus (100) according to one of the preceding claims,wherein the access point is configured to determine the first precoding information by determining a local precoding matrix according to: ^^ ^ = ^^ ^[^] diag(^)^ ^[^] + ^^ ^ [] ^ ^ ^^ ^+ ^^^^^ ^^ ^[^]^diag(^) ^, whereinFH250401PCT-2025112871.DOCXare vectors of positive parameters which can tuned to balance receivers’equipment priorities and access point power consumption.

14. An apparatus (100) according to one of the preceding claims,wherein the apparatus (100) is an access point of the wireless communicationsystem.

15. An apparatus (100) according to one of the preceding claims,wherein the one or more other apparatuses (111, 112) are one or more otheraccess points of the wireless communication system.

16. An apparatus (100) according to one of the preceding claims,wherein the one or more data-bearing signals are one or more modulated data- bearing signals.

17. An apparatus (100) according to one of the preceding claims,wherein the transmit signal is a downlink transmit signal.

18. An apparatus (100) according to one of the preceding claims,wherein the wireless communication system is a distributed multiple input multiple output system.

19. A wireless communication system comprising:a first apparatus (100) being an apparatus (100) according to one of the precedingclaims, and the one or more other apparatuses (111, 112).

20. A wireless communication system according to claim 19,FH250401PCT-2025112871.DOCXwherein each of the one or more other apparatuses (111, 112) is also anapparatus (100) according to one of claims 1 to 18.

21. A wireless communication system according to claim 19 or 20,wherein the first apparatus (100) is a first access point,wherein the one or more other apparatuses (111, 112) are one or more otheraccess points.

22. A wireless communication system according to one of claims 19 to 21,wherein the first apparatus (100) is an apparatus (100) according to claim 5 oraccording to claim 6, wherein the wireless communication system further comprises the centralized unit (121; 122).

23. A wireless communication system according to one of claims 19 to 22,wherein the wireless communication system is a distributed multiple input multiple output system.

24. A method for a wireless communication system, wherein the method comprises:receiving, by an apparatus (100) of the wireless communication system, areference signal for channel estimation, and to determine therefrom, local channel state information, transmitting, by the apparatus (100), information on the local channel stateinformation to at least one other entity of the wireless communication system, determining first precoding information depending on the local channel state information, receiving, by the apparatus (100), second information, wherein the second information depends on channel state information of one or more other apparatuses (111, 112) of the wireless communication system, and wherein theFH250401PCT-2025112871.DOCXsecond information depends also on the local channel state information of the apparatus (100), generating a transmit signal, which depends on two or more data-bearing signalsusing the first precoding information and the second information, wherein the channel state information of the one or more other apparatuses (111, 112) is delayed compared to the local channel state information of the apparatus (100).

25. A computer program for implementing the method of claim 24 when beingexecuted on a computer or signal processor. FH250401PCT-2025112871.DOCX

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