Channel estimation for massive MIMO hybrid antenna systems

Abstract

Examples of the invention relate to channel estimation for massive MIMO hybrid antenna systems. Thus, it is disclosed a first communication device (100) comprising a set of antenna elements (120) divided into two or more subsets of antenna elements (122). The first communication device (100) is configured to: receive reference signals (510) from a second communication device (300) via one or more subsets of antenna elements (122); determine a subchannel estimation (Formula (I)) for a subset of antenna elements (122) based on a received reference signal (510); determine a decoupled subchannel estimation (Formula (II)) for the subset of antenna elements (122) based on the subchannel estimation (Formula (I)) and a coupling transfer (Formula (III)) or a mutual coupling (Formula (IV)) for the subset of antenna elements (122); determine a decoupled channel estimation (Formula (V)) for all antenna elements of the set of antenna elements (120) based on the decoupled subchannel estimation (Formula (II)); and determine a channel estimation (Formula (VI)) for all antenna elements of the set of antenna elements (120) based on the decoupled channel estimation (Formula (V)) and a coupling transfer (A) or a mutual coupling (C) for all antenna elements of the set of antenna elements (120). Furthermore, examples of the invention also relate to corresponding method and a computer program.

Description

[0001]CHANNEL ESTIMATION FOR MASSIVE MIMO HYBRID ANTENNA SYSTEMS TECHNICAL FIELDExamples of the invention relate to channel estimation for massive MIMO hybrid antenna systems. Furthermore, examples ofthe invention also relate to corresponding method and a computer program.BACKGROUND Massive MIMO has been widely adopted in the base stations (BSs) of the existing 3GPP 5G wireless communication systems to significantly enhance the system performance in various aspects such as throughput, degrees-of-freedom (DoF), power gain and diversity, etc. Conventionally, the BS of a massive MIMO system adopts a large antenna array with a full digital structure,i.e., each antenna element is driven by a distinct radio frequency (RF) chain, which involves very high hardware complexityand power consumption.Benefit from the fact that, in practice, the number of antenna elements in a BS is always much larger than the number ofconcurrent signal streams that can be supported by the BS, antenna arrays with hybrid structures, realized by driving all antennaelements with a less number of RF chains, are regarded as a more economical alternative to those with full digital structures,and have been a popular selection for the BSs of many existing massive MIMO systems. SUMMARY An objective of examples of the invention is to provide a solution which mitigates or solves the drawbacks and problems of conventional solutions.Another objective of examples of the invention is to provide a solution for improved channel estimation in massive MIMOhybrid antenna systems. The above and further objectives are solved by the subject matter of the independent claims. Further examples of the invention can be found in the dependent claims.According to a first aspect of the invention, the above mentioned and other objectives are achieved with a first communicationdevice comprising a set of antenna elements divided into two or more subsets of antenna elements, the first communicationdevice being configured to: receive one or more reference signals from a second communication device via one or more subsets of antenna elements, wherein different reference signals are received via different subsets of antenna elements; determine a subchannel estimation ^^^^for a subset of antenna elements based on a received reference signal, where ^^is an index of the subset of antenna elements used to receive a ^-th reference signal;determine a decoupled subchannel estimation for the subset of antenna elements based on the subchannel estimation ^^^^and a coupling transfer ^^^or a mutual coupling ^^^,^^for the subset of antenna elements, wherein the couplingtransfer ^^^ for the subset of antenna elements is a transfer of a mutual coupling effect between the antenna elements in thesubset of antenna elements, and the mutual coupling ^^,^ for the subset of antenna elements is a mutual antenna couplingbetween the antenna elements in the subset of antenna elements; determine a decoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements based on thedecoupled subchannel estimation ^^(^) ^^; and determine a channel estimation ^^ for all antenna elements of the set of antenna elements based on the decoupledchannel estimation ^^(^) and a coupling transfer ^ or a mutual coupling ^ for all antenna elements of the set of antennaelements, wherein the coupling transfer ^ for all antenna elements of the set of antenna elements is a transfer of a mutualcoupling effect between all antenna elements in the set of antenna elements, and the mutual coupling ^ for all antenna elementsof the set of antenna elements is a mutual antenna coupling between all antenna elements in the set of antenna elements. An advantage of the first communication device according to the first aspect is that it enables an efficient and accurateestimation of the channel in a massive MIMO system having a dense array of antenna elements with a hybrid structure. On onehand, it significantly reduces the overhead and time delay involved in the channel estimation by only receiving reference signalsfrom one or more subsets of antenna elements that is less than the total number of subsets of antenna elements in the wholearray of antenna elements. On the other hand, it significantly increases the accuracy of the estimated channel by taking intoaccount both the mutual coupling effect among the antenna elements in each subset of antenna elements and the mutual couplingeffect among all antenna elements in the set of antenna elements. In an implementation form of a first communication device according to the first aspect, the first communication device is configured to: determine a beamforming configuration for all antenna elements of the set of antenna elements based on the channel estimation ^^; and receive a first communication signal from the second communication device, the first communication signal being received via all antenna elements of the set of antenna elements based on the beamforming configuration; and / or transmit a second communication signal to the second communication device, the second communication signal being transmitted via all antenna elements of the set of antenna elements based on the beamforming configuration.An advantage with this implementation form is that it enables an enhanced beamforming performance in the subsequent datareception and data transmission based on the determined channel estimation. In an implementation form of a first communication device according to the first aspect, the coupling transfer ^^^for the subset of antenna elements is an inverse half of the mutual coupling ^^^,^^for the subset of antenna elements.An advantage with this implementation form is that it provides a simple and accurate characterization of the coupling transfer^^^for the subset of antenna elements based on the mutual coupling ^^^,^^for the subset of antenna elements. In an implementation form of a first communication device according to the first aspect, the decoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements is determined based on positions of all antenna elements of the set of antenna elements and an estimated signal propagation direction, wherein the estimated signal propagation direction is based on the decoupled subchannel estimation and positions of the antenna elements in the subset of antenna elements.An advantage with this implementation form is that it enables a concrete approach to accurately construct the decoupled channelestimation ^^(^) for all antenna elements of the set of antenna elements from the decoupled subchannel estimation Thisapproach is applicable to the scenario when the propagation channel between the first and second communication devices is aline-of-sight channel. In an implementation form of a first communication device according to the first aspect, the decoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements is determined based on an interpolation of the decoupled subchannel estimation ^^(^) ^^.An advantage with this implementation form is that it provides a general approach to construct the decoupled channel estimation^^(^)for all antenna elements of the set of antenna elements from the decoupled subchannel estimation This approach is applicable to more general scenarios when the propagation channel between the first and second communication devices is either a line-of-sight channel or a multi-path channel. In an implementation form of a first communication device according to the first aspect, the decoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements is determined based on an interpolation of the decoupled subchannel estimationand a projection of the interpolated channel estimation into a ^ dimensional vector space, where ^ is a positiveinteger, and the ^ dimensional vector space is spanned by first ^ eigenvectors of a correlation matrix ^^(^) of the decoupledchannel ^(^)for all antenna elements of the set of antenna elements, the projection being based on a weighting factor per each eigenvector.An advantage with this implementation form is that it provides a refined approach to construct the decoupled channel estimation^^(^)for all antenna elements of the set of antenna elements from the decoupled subchannel estimation in the general multi- path channel scenario between the first and second communication devices. The corresponding channel estimation performance can be further improved by taking into account the correlation property of the decoupled channel ^(^)for all antenna elements of the set of antenna elements that is reflected by its correlation matrix ^^(^). In an implementation form of a first communication device according to the first aspect, a weighting factor per each eigenvectoris equal to 1, or dependent on a corresponding eigenvalue of the eigenvector.An advantage with this implementation form is that it provides concrete approaches to utilize the correlation property of thedecoupled channel ^(^) for all antenna elements of the set of antenna elements to improve the channel estimation further.In an implementation form of a first communication device according to the first aspect, a sum of the eigenvalues of first ^eigenvectors comprises more than 1- ^ of a sum of all eigenvalues of the correlation matrix ^^(^), where ^ is a predetermined positive scalar.An advantage with this implementation form is that it provides additional concrete details of utilizing the correlation propertyof the decoupled channel ^(^) for all antenna elements of the set of antenna elements to improve the channel estimation further.In an implementation form of a first communication device according to the first aspect, the interpolation of the decoupled subchannel estimation comprises any of: a piecewise constant interpolation, a linear interpolation, a polynomial interpolation, a spline interpolation, and a mimetic interpolation.An advantage with this implementation form is that it provides concrete interpolation methods to construct the decoupledchannel estimation ^^(^)for all antenna elements of the set of antenna elements from the decoupled subchannel estimation ^^ .In an implementation form of a first communication device according to the first aspect, the channel estimation ^^ for all antennaelements of the set of antenna elements is based on: amultiplication of the coupling transfer ^ for all antenna elements of the set of antenna elements with the decoupledchannel estimation ^^(^)for all antenna elements of the set of antenna elements; or amultiplication of an inverse half of the mutual coupling ^ for all antenna elements of the set of antenna elements withthe decoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements.An advantage with this implementation form is that it provides alternative approaches to determine the channel estimation ^^for all antenna elements of the set of antenna elements from the decoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements, both of which are based on accurate characterization of the mutual coupling effect among all antenna elements in the set of antenna elements.In an implementation form of a first communication device according to the first aspect, the channel estimation ^^ for all antennaelements of the set of antenna elements is expressed as: ^^ = ^ ⋅ ^^(^); or^^ = ^^^ / ^ ⋅ ^^(^).An advantage with this implementation form is that it provides concrete details of both approaches for determining the channelestimation ^^ for all antenna elements of the set of antenna elements from the decoupled channel estimation ^^(^) for all antennaelements of the set of antenna elements.In an implementation form of a first communication device according to the first aspect, the coupling transfer ^ for all antennaelements of the set of antenna elements is an inverse half of the mutual coupling ^ for all antenna elements of the set of antennaelements.An advantage with this implementation form is that it provides a simple and accurate characterization of the coupling transfer^ for all antenna elements of the set of antenna elements based on the mutual coupling ^ for all antenna elements of the set ofantenna elements. In an implementation form of a first communication device according to the first aspect, the mutual coupling ^^^,^^for thesubset of antenna elements is a subset of the mutual coupling ^ for all antenna elements in the set of antenna elements.An advantage with this implementation form is that it provides a concrete relationship between the mutual coupling ^^^,^^ forthe subset of antenna elements and the mutual coupling ^ for all antenna elements in the set of antenna elements.In an implementation form of a first communication device according to the first aspect, the set of antenna elements are arrangedinto two or more subarrays of antenna elements with all antenna elements in each subarray of antenna elements connected to acommon radio frequency chain, and wherein each subset of antenna elements comprises an antenna element in each subarray of antenna elements.An advantage with this implementation form is that it provides a concrete solution to decide different subsets of antennaelements based on the structure of the hybrid antenna array. By this, it guarantees that the first communication device is ableto receive a common reference signal from all the antenna elements in each subset of antenna elements at the same time.According to a second aspect of the invention, the above mentioned and other objectives are achieved with a method for a communication device comprising a set of antenna elements divided into two or more subsets of antenna elements; the method The method according to the second aspect can be extended into implementation forms corresponding to the implementationforms of the first communication device according to the first aspect. Hence, an implementation form of the method comprisesthe feature(s) of the corresponding implementation form of the first communication device.The advantages of the methods according to the second aspect are the same as those for the corresponding implementationforms of the first communication device according to the first aspect.Examples of the invention also relate to a computer program, characterized in program code, which when run by at least oneprocessor causes the at least one processor to execute any method according to examples of the invention. Further, examplesof the invention also relate to a computer program product comprising a computer readable medium and the mentionedcomputer program, wherein the computer program is included in the computer readable medium, and may comprises one ormore from the group of: read-only memory (ROM), programmable ROM (PROM), erasable PROM (EPROM), flash memory,electrically erasable PROM (EEPROM), hard disk drive, etc.Further applications and advantages of examples of the invention will be apparent from the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGSThe appended drawings are intended to clarify and explain different examples of the invention, in which:^Fig. 1 shows a first communication device according to an example of the invention;^Fig. 2 shows a flow chart of a method for a first communication device according to an example of the invention;^ Fig. 3 shows a communication system according to an example of the invention;^ Fig. 4 illustrates an antenna array of the first communication device according to an example of the invention;^ Fig. 5 illustrates transmission and reception schemes including processing steps according to an example of theinvention;^Fig. 6 shows a block diagram of a first communication device according to an example of the invention;^ Fig. 7 illustrate a communication system with a hybrid antenna array at a BS and a single antenna element at a userequipment (UE); ^Fig. 8 shows the relationship between the number of antenna elements per subarray and the resultant spacing in ahybrid antenna array; and ^Figs. 9 and 10 show performance results.DETAILED DESCRIPTIONIn an antenna array with a hybrid structure, all the ^ antenna elements are connected to a smaller number of ^ RF chains soas to reduce the hardware cost and operating complexity. For example, the whole antenna array can be equally divided into ^subarrays of ^ = ^ / ^ antenna elements per subarray, where the ^ antenna elements in each subarray are driven by a commonRF chain each via a switch and an analog phase shifter, as illustrated in Fig. 4. As a consequence, in the uplink (UL) the BSdoes not have direct access to signals received from all the ^ antenna elements simultaneously, but only receives the signalswith a reduced dimension, from ^ to ^, via the ^ RF chains. The corresponding channel estimation is thus a challengingissue.In addition, the massive MIMO technique is continuing evolving towards the future 3GPP 6G wireless communications andbeyond, and holographic MIMO has been considered as one of the most promising approaches in this line of techniqueevolution, which is practically implemented as an array of densely deployed antenna elements with less than half-wavelengthspacing between antenna elements. In this case, the mutual coupling effect between antenna elements becomes stronger and soneeds to be considered in the UL channel estimation as well as the subsequence UL data reception and / or downlink (DL) datatransmission.Therefore, an objective of examples of the invention is to design an efficient and accurate channel estimation solution formassive MIMO systems having a dense antenna array with a hybrid structure. Thus, it is herein disclosed among other thingsa communication device for massive MIMO systems having a dense antenna array with a hybrid structure, such that the channelestimation in such systems can be carried out in an efficient and accurate way. The disclosed solution enables increasing thenumber of antenna elements in the BSs of time division duplex (TDD) massive MIMO systems without the need for increasingthe number of RF chains and UL channel estimation overhead at the BS.The communication device herein disclosed is also denoted a first communication device to differentiate from other communication devices which may be denoted second communication devices. Thus, the terms “first” and “second” are in this context used as labels and do not imply any technical features when used for labelling purpose only.Fig. 1 shows a first communication device 100 according to an example of the invention. In the example shown in Fig. 1, thefirst communication device 100 comprises a processor 102, a transceiver 104 and a memory 106. The processor 102 is coupledto the transceiver 104 and the memory 106 by communication means 108 known in the art. The first communication device100 may be configured for wireless and / or wired communications in a communication system. The wireless communicationcapability may be provided with an antenna or antenna array 110 coupled to the transceiver 104. The antenna 110 comprises aset of antenna elements 120 divided into two or more subsets of antenna elements 122 as shown in Fig. 4. The wiredcommunication capability may be provided with a wired communication interface 112 e.g., coupled to the transceiver 104. The processor 102 may be referred to as one or more general-purpose central processing units (CPUs), one or more digitalsignal processors (DSPs), one or more application-specific integrated circuits (ASICs), one or more field programmable gatearrays (FPGAs), one or more programmable logic devices, one or more discrete gates, one or more transistor logic devices, oneor more discrete hardware components, or one or more chipsets. The memory 106 may be a read-only memory, a randomaccess memory (RAM), or a non-volatile RAM (NVRAM). The transceiver 104 may be a transceiver circuit, a power controller,or an interface providing capability to communicate with other communication modules or communication devices, such asnetwork nodes and network servers. The transceiver 104, memory 106 and / or processor 102 may be implemented in separatechipsets or may be implemented in a common chipset.That the first communication device 100 is configured to perform certain actions can in this disclosure be understood to meanthat the first communication device 100 comprises suitable means, such as e.g., the processor 102 and the transceiver 104,configured to perform the actions.According to examples of the invention the first communication device 100 is configured to: receive one or more referencesignals 510 from a second communication device 300 via one or more subsets of antenna elements 122, wherein different reference signals 510 are received via different subsets of antenna elements 122; determine a subchannel estimation ^^^^for a subset of antenna elements 122 based on a received reference signal 510, where ^^is an index of the subset of antenna elements used to receive a ^-th reference signal; determine a decoupled subchannel estimation ^^ for the subset of antenna elements 122 based on the subchannel estimation ^^^^and a coupling transfer ^^^or a mutual coupling ^^^,^^for the subset of antenna elements 122, wherein the coupling transfer ^^^for the subset of antenna elements 122 is a transfer of a mutual coupling effect between the antenna elements in the subset of antenna elements 122, and the mutual coupling ^^,^for the subset of antennaelements 122 is a mutual antenna coupling between the antenna elements in the subset of antenna elements 122; determine adecoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements 120 based on the decoupled subchannel estimation ^^(^) ^^ ; and determine a channel estimation ^^ for all antenna elements of the set of antenna elements 120based on the decoupled channel estimation ^^(^) and a coupling transfer ^ or a mutual coupling ^ for all antenna elements ofthe set of antenna elements 120, wherein the coupling transfer ^ for all antenna elements of the set of antenna elements 120 isa transfer of a mutual coupling effect between all antenna elements in the set of antenna elements 120, and the mutual coupling^ for all antenna elements of the set of antenna elements 120 is a mutual antenna coupling between all antenna elements in theset of antenna elements 120. Fig. 2 shows a flow chart of a corresponding method 200 which may be executed in a first communication device 100, such asthe one shown in Fig. 1. The method 200 comprises: receiving 202 one or more reference signals 510 from a second.Fig.3 shows a communication system 500 according to an example of the invention. The communication system 500 in the disclosed example comprises a first communication device 100 and a second communication device 300 configured to communicate and operate in the communication system 500. For simplicity, the shown communication system 500 only comprises one first communication device 100 and one second communication device 300. However, the communication system 500 may comprise any number of first communication devices 100 and any number of second communication devices 300 without deviating from the scope of the invention.The first communication device 100 is in this example illustrated as a network access node such as a BS, while the secondcommunication device 300 is illustrated as a client device such as a UE. However, the reverse example is also possible, i.e.,the first communication device 100 is a client device while the second communication device 300 is a network work access node. In yet further examples, both the first communication device 100 and the second communication device 300 may be client devices such as in sidelink communications. It is shown in Fig. 3 how the first communication device 100 receives one or more reference signals or pilots 510 from the second communication device 300 in the UL. A reference signal is a signal that is known at an intended receiver in advance tohelp the receiver to estimate the channel, or certain parameters of the channel, experienced by it. The reference signal may alsobe called a pilot signal. One example of a reference signal is the sounding reference signal (SRS) defined in 3GPP. Based on the received reference signals, the first communication device 100 estimates the UL channel according to examples of the invention. The disclosed interpolated transmission activates or deactivates a subset of antenna elements in the antenna array depending on the transmission / reception mode. Specifically, only a subset of antenna elements is activated each time in the channel estimation phase for the first communication device 100 to first estimate a channel sub-vector experienced by theseactivated antenna elements. Then, the channel vector experienced by the whole antenna array is reconstructed from theestimated channel sub-vector(s). The disclosed reconstruction solution considers both the statistical information of the wirelesschannel, and the mutual coupling effect among the activated antenna elements in each subset of antenna elements as well asthe mutual coupling effect among the activated and deactivated antenna elements in the antenna array characterized by a mutualcoupling model. After obtaining the channel vector estimation for the whole antenna array, all antenna elements may beactivated for the subsequent UL data reception and / or DL pre-coded data transmission. Further details related to examples of the invention will now be described in a 3GPP 5G context. Thus, 3GPP 5G terminology, definitions, expressions and system architecture will be used. Especially, the first communication device 100 according to theinvention may in these examples be configured to perform any of the described functions of a 3GPP BS 100. The secondcommunication device 300 according to the invention may in these examples be configured to perform any of the describedfunctions of a 3GPP UE 300. It may however be noted that examples of the invention are not limited thereto.Consider a TDD massive MIMO system, where the BS 100 is equipped with a dense antenna array 110 of ^ antenna elementswith a hybrid structure as illustrated in Fig. 4, which illustrates a hybrid antenna array with ^ = 16 antenna elements, that aredivided into ^ = 4 sub-arrays each containing ^ = 4 antenna elements connected to a common RF chain 130 via switches132 and analog phase shifters 134. Thus, in examples of the invention, the set of antenna elements 120 are arranged into two or more subarrays of antenna elements with all antenna elements in each subarray of antenna elements connected to a commonRF chain 130 as shown in Fig. 4. Each subset of antenna elements 122 comprises an antenna element in each subarray ofantenna elements. The example in Fig. 4 shows 4 sub-arrays of antenna elements and 4 subsets of antenna elements. Due to the constraint imposed by the hybrid hardware structure, the BS 100 cannot directly receive reference signals from allthe ^ antenna elements simultaneously in each time slot of the UL channel estimation phase, but receives a reduced dimensionlength-^ reference signal vector from the ^ RF chains, which is a projected version of the length-^ reference signal vectorthat can be observed on all the ^ antenna elements into a certain ^-dimensional subspace. In this case, a TDM based methodis a straightforward way to access reference signals from the ^ antennas. Specifically, the UL channel estimation phase isdivided into ^ time slots, equal to the number of antenna elements per subarray, and all the ^ antenna elements are alsocorrespondingly divided into ^ subsets of antenna elements in such a way that the ^ antenna elements in each subarray belongto different subsets of antenna elements 122. That is, each subset of antenna elements contains ^ antenna elements formed byone and only one antenna element selected from each subarray, and the ^ antenna elements per subarray all belong to differentsubsets of antenna elements 122, i.e., it does not exist that two antenna elements belong to both the same subarray and the samesubset of antenna elements 122. In the ^-th (^ = 1, 2, ⋯ , ^) time slot, the UE 300 transmits a reference signal ^^ from one ofits antennas (or antenna ports), and the BS 100 only receives the reference signal from the ^ antenna elements in the ^-thsubset of antenna elements due to the sub-array hybrid structure of the BS antenna array 110. The correspondingly receivedUL reference signal sub-vector, denoted by ^^ (^^ ∈ ^^×^) can be expressed as^^ = ^^^^ + ^^ , (1)where ^^ (^^ ∈ ^^×^) is the channel sub-vector seen by the ^ antenna elements in the ^-th subset of antenna elements thatis activated in the ^-th time slot and ^^ (^^ ∈ ^^×^) is the corresponding noise sub-vector. Note that in each time slot the ^ activated BS antenna elements maybe closely deployed with the mutual coupling effect among them not ignorable, and this mutual coupling effect is included in the channel sub-vector ^^. In general, we have ^^ ≠ ^(^)^ . (2)where ^(^)^ is the decoupled channel sub-vector seen by the ^ activated BS antenna elements in the ^-th time slot, and doesnot include the mutual coupling effect among the ^ activated BS antenna elements. Each entry of the decoupled channel sub-vector represents the coefficient of the wireless channel between the UE 300 antenna (or antenna port) and thecorresponding antenna element in the BS antenna array 110, which remains unchanged regardless whether the other antenna elements in the BS antenna array 110 are activated or deactivated. Therefore, an entry of the decoupled channel sub-vector for one antenna element in a subset of antenna elements is identical to its corresponding entry of the decoupled channelvector for the same antenna element. For simplicity, here we assume that all the BS antenna elements are indexed in asimple way such that Denote by ^^^the estimated channel sub-vector from ^^. The conventional TDM based channel estimation approachreconstructs the whole channel vector by concatenating all ^^^^^ into a long vector, yielding which is expected to well approximate the whole channel vector ^, and is then used for the precoding design of the subsequentDL transmission and / or UL reception. However, ^ differs from its corresponding decoupled channel vector ^(^) as the mutualcoupling effect among all BS antenna elements is included in ^ but not in ^(^). Hence, we have As detailed in the Appendix below, the above TDM based method, besides being time-consuming, is unable to obtain anaccurate estimate of the whole channel vector ^ when the BS antenna elements are densely deployed within the array aperture,i.e., ^^ distinctly differs from ^ even if the noise effect at the BS 100 is ignored.In the present disclosure, a channel estimation scheme is disclosed to solve the above issues. Specifically, in the disclosedsolution, the channel vector ^ is modeled as follows according to the linearity of the system. ^= ^^(^), (6)where the matrix ^ ∈ ^^×^ is referred to as the coupling transfer matrix for the whole BS antenna array 110 that models theimpact of the mutual coupling effect among all the BS antenna elements on the signal transmission / reception via the BS whenall the antenna elements in the BS antenna array are activated. When the BS antenna array 110 is lossless or nearly lossless,e.g., almost all the transmit power fed to the BS antenna array 110 can be radiated out without being consumed inside thetransmit circuit and array as either heat loss or reflection loss, we can analytically express the matrix ^ based on the mutualcoupling model developed as ^= ^^^ / ^, (7)where ^ ∈ ^^×^ is referred to as the mutual coupling matrix for the whole dense antenna array 110. Each entry of the matrix^ in its ^-th row and ^-th column, denoted by ^^,^, can be calculated using the following formula. ∀^, ^ = 1,2, ⋯ ^ (8) where ^^ (^^ ∈ ℛ^×^ with ℛ^×^ being the real space of dimension ^ × ^) and ^^(^) (^^(^) ∈ ℛ) are, respectively, theposition of the ^-th BS antenna element under a certain 3D coordinate system and its radiation power pattern in the spatialdirection ^ (^ ∈ ℛ^×^ , ‖^‖^ = 1).Similarly, the channel sub-vector ^^when only the ^-th subset of BS antenna elements are activated is mathematically modelled as ^(^)^ = ^^^^ , (9)where ^^ (^^ ∈ ^^×^) is the coupling transfer matrix for the ^ activated BS antenna elements in the ^-th time slot, whichcharacterizes the mutual coupling effect among these ^ activated BS antenna elements when the remaining ^ − ^ antennaelements in the set of BS antenna elements are deactivated. By assuming that in each UL channel estimation time slot, all the^ − ^ de-activated antenna elements have ignorable impact on the mutual coupling effect of the ^ activated BS antennaelements in this time slot, the coupling transfer matrix ^^ in Eq. (9) can be similarly expressed as^^^ / ^ ^= ^^,^ , (10)where ^^,^ ∈ ^^×^ is referred to as the mutual coupling matrix for the ^ activated BS antenna elements in this time slot,whose entries can be calculated using the same formula in Eq. (8). As a consequence, the mutual coupling matrix ^^,^for the^ activated BS antenna elements in this time slot is the ^-th ^ × ^ submatrix in the diagonal of the mutual coupling matrix^ for the whole dense antenna array 110, i.e.,Hence, in examples of the invention, the mutual coupling mutual coupling ^ for all antenna elements in the set of antenna elements 120.With the channel vector / sub-vectors and decoupled channel vector / sub-vectors modelled in the above way, a disclosedtransmission / reception scheme is illustrated in Fig. 5 including processing steps according to examples of the invention. Thetransmission / reception scheme involves transmission and / or reception based on the channel estimation previously determinedby the BS 100. Thus, in examples of the invention, the BS 100 is configured to determine a beamforming configuration for all antenna elements of the set of antenna elements 120 based on the channel estimation ^^. With reference to step 5a, the BS 100is further configured to receive a first communication signal 520 from the UE 300. The first communication signal 520 beingreceived via all antenna elements of the set of antenna elements 120 based on the beamforming configuration. With referenceto step 5b, the BS 100 is further configured to transmit a second communication signal 530 to the UE 300. The secondcommunication signal 530 is transmitted via all antenna elements of the set of antenna elements 120 based on the beamformingconfiguration.Fig. 6 shows a block diagram of the BS 100 according to examples of the invention for processing blocks corresponding to thesteps in Fig. 5. The BS 100 comprises five processing blocks coupled in series with each other. Block 1 may be denoted sparseUL sub-channel estimation, Block 2 may be denoted decoupled sub-channel estimation, Block 3 may be denoted decoupledchannel reconstruction, Block 4 may be denoted coupled channel reconstruction, and block 5 may be denoted transmission / reception. Details of the steps and corresponding blocks are discussed below. Step 1 and Block 1: Sparse UL sub-channel estimation The UL channel estimation phase is divided into ^ (^ < ^) time slots. In each ^-th (^ = 1, 2, ⋯ , ^) time slot, the UE 300transmits a reference signal ^^ from one of its antennas (or antenna ports), and the BS 100 consequently activates only the ^antenna elements in the ^^ -th (^^ ∈ {1, 2, ⋯ , ^}) antenna subset to receive the reference signal ^^ . The correspondinglyreceived signal sub-vector, denoted by ^^, is given by ^^ = ^^^^^ + ^^, ^ = 1,2, ⋯ , ^, (12)from which the BS 100 obtains the estimated channel sub-vector ^^^^, e.g., by adopting the minimum mean square error (MMSE) principle either to estimate each entry of the channel sub-vector ^^^separately or to jointly estimate all entries of the channel sub-vector ^^^based on the correlation property of ^^^that is obtainable from the historical estimations. The ^reference signals {^^|^ = 1,2, ⋯ ^} can be either the same or different. The ^ subsets of antenna elements used for referencesignal reception in the ^ time slots are selected from the total ^ subsets of antenna elements. With ^ < ^, the number of timeslots for reference signal transmission is reduced, which in turn reduces the sounding overhead by (1 − ^ / ^) × 100%. In themeanwhile, a consequence of ^ < ^ is that some BS antenna elements are deactivated throughout the UL channel estimationphase, and so the BS 100 cannot have access to the channel coefficients for all antenna elements in the set of BS antennaelements.In one example of the invention, the selected ^ subsets of antenna elements are different from each other, and by this meansthe BS 100 can exploit the antenna correlation among all BS antenna elements in a better way to estimate the whole channelvector ^. In another implementation, at least one subset of antenna elements among the ^ subsets of antenna elements areselected more than one time, and by this means, the BS 100 can achieve a power gain by combining the received signalscorresponding to the same subset of antenna elements, and in turn more accurate estimation of the corresponding channel sub-vector(s) is obtained.In yet another example of the invention, the number of time slots ^ is set to 1, i.e., ^ = 1, and by this means the BS 100 cansignificantly increase the time efficiency of the whole UL channel estimation phase. In practice, the BS 100 may adaptivelyconfigure the number of reference signal transmissions, e.g., ^, depending on channel estimation quality, and so need to signalto the UE 300 (not shown in the Figs.) about the value of ^ and the corresponding time / frequency / sequence resources used forthe reference signal transmission in these ^ time slots.Step 2 and Block 2: Decoupled sub-channel estimationFrom each estimated channel sub-vector ^^^^ for the ^^ -th (^ = 1,2, ⋯ , ^) subset of antenna elements 122, the BS 100estimates its corresponding decoupled channel sub-vector by removing the mutual coupling effect among the ^ antennasin the ^^-th antenna subset from the estimated channel sub-vector ^^^^. In this respect, the decoupled subchannel estimation ^^ may be determined in a number of ways. The decoupled subchannel estimationmay therefore be determined based on: a multiplication of an inverse of the coupling transfer ^^^ for the subsetof antenna elements 122 with the subchannel estimation ^^^^for the subset of antenna elements 122; or a multiplication of a square root of the mutual coupling ^^^,^^for the subset of antenna elements 122 with the subchannel estimation ^^^^for thesubset of antenna elements 122. In an example of the invention, the estimated decoupled channel sub-vector, denoted by ^^(^^)^ , is obtained according to Eq. (9) as where the coupling transfer matrix ^^^for the subset of antenna elements 122 can be calculated using Eq. (10). In another example of the invention, the estimated decoupled channel sub-vector ^^(^^)^ is obtained as ^^(^)^ / ^ ^^ = ^^^,^^ ⋅ ^^^^ , (14)which is equivalent to Eq. (13) according to Eq. (10), and this avoids the calculation of the inverse of matrix ^^^,^^. It is noted that the coupling transfer ^^^for the subset of antenna elements 122 is, in examples of the invention, an inverse halfof the mutual coupling ^^^,^^ for the subset of antenna elements 122 according to Eq. (10).Step 3 and Block 3: Decoupled channel reconstructionGiven the estimated decoupled channel sub-vector(s) ^^^ = 1,2, ⋯ ^^, the BS 100 then estimates the whole decoupledchannel vector seen by all the BS antenna elements to obtain ^^(^) ∈ ^^×^.In an example of the invention, when the wireless channel between the UE 300 and BS 100 is dominated by the line-of-sight(LoS) transmission, the BS 100 can first use ^^^(^) ^^ |^ = 1,2, ⋯ ^^ to obtain an estimated signal propagation direction of the LoSchannel path, denoted by ^^ (^^ ∈ ℛ^×^ , ‖^^‖^ = 1), and then reconstruct the whole decoupled channel vector ^^(^)using ^^. In such cases, the decoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements 120 may bedetermined based on positions of all antenna elements of the set of antenna elements 120 and an estimated signal propagationdirection. The estimated signal propagation direction may be based on the decoupled subchannel estimation and positions of the antenna elements in the subset of antenna elements 122.For example, by normalizing the path loss of the decoupled channel vector ^(^) to 1 for simplicity, we can model the decoupledchannel vector in a LoS channel as ℎ(^) ^= ^^^^^^^^^^ , ∀^ = 0,1, ⋯ , ^ − 1, (15)where ^^ = (sin^cos^ sin^sin^ cos^)^ (16)is a unit vector with ^ ∈ [0, ^] and ^ ∈ [−^, ^] being, respectively, the horizontal and vertical angle of the signal propagationdirection, see Fig. 7 for an illustration. Afterwards, if there is no phase ambiguity between the reference signal receptions inthe ^ time slots, the signal propagation direction of the LoS path can be estimated as^^ = where ℎ^(^) ^^,^ is the ^-th (^ = 1,2, ⋯ , ^) entry of the sub-vector ^^(^) ^^ , and ^^^,^ (^^^,^ ∈ ℛ^×^) is the position of the antennaelement corresponding to ℎ^(^) ^^,^ . Otherwise, if there exists phase ambiguity between the reference signal receptions in the ^time slots, the signal propagation direction of the LoS path can be estimated as ^^ = argmax^∈ℛ^×^, In practice, problems of Eq. (17) and Eq. (18) can be solved by first searching among a pre-determined discrete set of quantizedspatial directions ^ = {^(^)|^ = 1,2, ⋯ , ^ } . After finding the quan(^) ^^ ^ tized spatial direction ^^∗ ∈ ^^ that leads to themaximum value of the function on the right hand-side of Eq. (17) or (18), one can refine the search among another set ofquantized spatial directions (^)(^) = {^^ |^ = 1,2, with smaller granularity in the neighborhood of ^^∗.For example, the set ^ can be constructed from a pre-determined discrete set of quantized spat (^)^ ial directions ^^̅ = {^^ |^ =, ^^} that are distributed in the neighborhood of a given spatial direction (e.g., (100)^) with smaller granularity thanthe quantized spatial directions in the set ^ (^) ^, and is obtained by rotating ^^̅to the neighborhood of ^^∗ . Such refinement can continue until a certain angular resolution requirement is achieved. After obtaining ^^, the estimated whole decoupled channelvector ^^(^) = for all antenna elements in the set of BS antenna elements can be obtained using the following formula: In another example of the invention, when the channel between the UE 300 and BS 100 is generally a multi-path channel, theBS 100 can estimate the whole decoupled channel vector ^^(^)from using a certain interpolation method. In such examples, the decoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements 120 may be determined based on an interpolation of the decoupled subchannel estimation . The interpolation of the decoupled subchannelestimation may in examples of the invention comprise any of: a piecewise constant interpolation, a linear interpolation, a polynomial interpolation, a spline interpolation, and a mimetic interpolation. To guarantee a satisfactory interpolation performance, the BS 100 can further process the interpolated decoupled channel vector, denoted by based on the statistic correlation information of the whole decoupled channel vector ^(^)that areobtainable from historic channel estimations. Thus, the decoupled channel estimation ^^(^) for all antenna elements of the setof antenna elements 120 may be determined based on an interpolation of the decoupled subchannel estimation and a projection of the interpolated channel estimation into a ^ dimensional vector space, where ^ is a positive integer, and the^ dimensional vector space is spanned by first ^ eigenvectors of a correlation matrix ^^(^) of the decoupled channel ^(^)forall antenna elements of the set of antenna elements 120, the projection being based on a weighting factor per each eigenvector.Specifically, denote by ^^(^) (^)^ (^) = E ^^^^ ^^ (20)the correlation matrix of ^(^) with E(⋅) being the expectation operation with respect to the randomness of ^(^), and let itseigenvalue decomposition be where ^^ (^ = is the ^-th largest eigenvalue of ^^(^) and ^^ is the corresponding eigen-vector.In an example of the invention, the decoupled channel vector estimation obtained after interpolation, denoted by ^^(^,^^^), isprojected into the ^ (^ ≤ ^) dimensional vector space spanned by the first ^ eigenvectors of ^^(^), and then this projectedversion of the channel vector is taken as the final estimated decoupled channel vector ^^(^), i.e., )= (^^ ^^ ⋯ ^^)(^^ ^^ ⋯ ^^)^^^(^,^^^). (22) In another example of the invention, the projection of ^^(^,^^^) into the ^ (^ ≤ ^) dimensional vector space spanned by the first^ eigenvectors of ^^(^) is further weighted based on their corresponding eigenvalues , ^^^. Specifically, we extendEq. (22) as IThus, a weighting factor per each eigenvector may be equal to 1, or dependent on a corresponding eigenvalue of the eigenvectorin examples of the invention. Therefore, in examples of the invention, a sum of the eigenvalues of first ^ eigenvectors comprise more than 1- ^ of a sum ofall eigenvalues of the correlation matrix ^^(^), where ^ is a predetermined positive scalar.Step 4 and Block 4: Coupled channel reconstructionDifferent from the channel estimation phase where the reference signals are only received from a subset of antenna elementsin each time slot due to lack of channel knowledge and hybrid hardware constraint, the subsequent UL / DL data can bereceived / transmitted via all antenna elements based on the estimated channel. In this case, the BS 100 reconstructs the whole This implies that the channel estimation ^^ for all antenna elements of the set of antenna elements 120 may be expressed as:^^ = ^ ⋅ ^^(^); or^^ = ^^^ / ^ ⋅ ^^(^).It is therefore noted that the coupling transfer ^ for all antenna elements of the set of antenna elements 120 may be an inversehalf of the mutual coupling ^ for all antenna elements of the set of antenna elements 120. The coupling transfer matrix ^ and mutual coupling matrix ^ for the whole antenna array, are computed based on Eq. (7) and(8) using the positions and radiation power patterns of all antenna elements in the array. Regarding the coupling transfer sub-matrices ^^^and mutual coupling submatrices ^^^,^^for the activated subset of antenna elements in the ^-th time slot, we assume that the other ^ − ^ deactivated antenna elements in the array have ignorable impact to the mutual coupling effectamong the activated subset of antenna elements in the ^-th time slot, and are regarded as transparent to the system. Therefore,both ^^^and ^^^,^^can be computed only based on the positions and radiation power patterns of the selected subset of antennaelements in the same way as that for calculating ^, i.e., using Eq. (10) and (8). As a consequence, the obtained mutual couplingsubmatrices ^^^,^^ are submatrices of the mutual coupling matrix ^ as shown in Eq. (11). ^^^ − ^^^ ^ ‖^‖^^^ Achievable beamforming gain in the subsequent UL data reception and DL data transmission, defined as In what follows, it is considered a BS hybrid antenna array of side length ^ = 2^ with a fixed number of ^ = 25 subarraysand different numbers of antenna elements ^ = 1, 2^ , ⋯ , 8^ in each subarray, and assume that the receiver is in the normaldirection of the transmit antenna array with ^ = 0 and ^ = ^ / 2 (i.e., ^^ = (^ 0 0)^).Fig. 8 shows the relationship between the number of antenna elements ^ per subarray and the resultant spacing ^ in the wholeBS antenna array. For time efficiency, let ^ = 1, i.e., only one subset (e.g., the first subset without loss of generality) of ^ BSantenna elements are activated for reference signal reception in the UL channel estimation phase.A LoS channel is first assumed between the BS and UE, whose decoupled channel vector ^(^)is modelled in Eq. (15), and thecorresponding decoupled channel reconstruction step is performed by Eq. (17) and Eq. (19).In Fig. 9, both the uncoupled and coupled NMSE performance of the UL channel estimation, as well as the correspondingbeamforming gain achieved by Eq. (31) in the subsequent UL data reception and DL data transmission are plotted versus thenumber of antenna elements per subarray ^ . Fig. 9a shows uncoupled and coupled NMSE performances in the UL channelestimation and Fig.9b shows achievable beamforming gain, both of which are measured in a LoS communication system with a hybrid BS antenna array of side length ^ = 2^, ^ = 25 subarrays and different numbers of antenna elements ^ per subarray.From Fig. 9 the following observations can be made:1. For a given antenna array density reflected by the value of antenna spacing ^ in Eq. (28), the achieved coupled NMSEperformance is worse than the corresponding uncoupled NMSE performance, and the gap between them is more significant when the antenna array is denser (i.e., when the antenna spacing ^ is smaller). This implies that the channelvector ^ is more sensitive to the channel estimation error than the decoupled channel vector 2. Both the coupled and uncoupled NMSE performance are getting worse with the densification of the antenna array ina fixed aperture size. This is expected as the portion of the antenna elements involved in the UL channel estimationamong all antenna elements in the array, i.e., 1 / ^, reduces as ^ increases, which leads to an increased NMSE; and3. The increased NMSE performance with antenna array densification does not imply any beamforming performance degradation in the subsequent UL data reception and DL data transmission. Instead, the densification of the antenna array can significantly enhance the achievable beamforming gain. When the UL SNR is set at 0 dB, densifying the array to ^ = 9 antenna elements per subarray can already achieve about 4.3 dB higher beamforming gain than itsconventional counterpart with ^ = 1, and the additional gain achieved by further array densification is marginal. Inaddition, about 1 dB extra beamforming gain is attainable by increasing the UL SNR, e.g., from 0 dB to 10 dB, andthe gain offered by further SNR increasement is ignorable.Next, the channel between the UE 300 and BS 100 is extended to a multi-path channel, generated using a clustered delay line-C (CDL-C) channel model with 30 kHz subcarrier spacing, where the corresponding desired delay spread is set at 0 ns so asto generate a frequency flat fading channel between the UE 300 and the BS 100. The interpolation operation is implementedby using the inherent function Interp2 in MATLAB followed by weighted projection as in Eq. (23) with ^ = 10^^ and ^^ =1.In Fig. 10, the achievable NMSE performance and beamforming gain of the system under the same setting as that in Fig. 9 areplotted, except that the channel between the UE 300 and the BS 100 is changed to a multi-path channel. Fig. 10a showsachievable uncoupled and coupled NMSE performances in the UL channel estimation, and Fig. 10b shows achievablebeamforming gain in the subsequent UL data reception and DL data transmission, in a multi-path communication system witha hybrid antenna array of side length ^ = 2^, ^ = 25 subarrays and different numbers of antenna elements ^ per subarray.Basically, from Fig. 10 similar observations as those for the LoS case in Fig. 9 can be made for the multi-path case, and themain difference is that now a higher UL SNR is needed to achieve distinct beamforming gain in a densified array compared toits conventional counterpart. When the UL SNR is set at 0 dB and 10 dB, such gains from array densification are about 2.1 dBand 3.8 dB, respectively, less than those achieved in the LoS case. The rationale behind this is that in the multi-path channel,the correlation between different entries of the decoupled channel vector becomes weaker compared to that in the LoS case,and so the performance of the channel interpolation is not as good as that in the LoS case.A network access node herein may also be denoted as a radio network access node, an access network access node, an accesspoint (AP), or a base station (BS), e.g., a radio base station (RBS), which in some networks may be referred to as transmitter,“gNB”, “gNodeB”, “eNB”, “eNodeB”, “NodeB” or “B node”, depending on the standard, technology and terminology used.The radio network access node may be of different classes or types such as e.g., macro eNodeB, home eNodeB or pico basestation, based on transmission power and thereby the cell size. The radio network access node may further be a station, whichis any device that contains an IEEE 802.11-conformant media access control (MAC) and physical layer (PHY) interface to thewireless medium (WM). The radio network access node may be configured for communication in 3GPP related long termevolution (LTE), LTE-advanced, fifth generation (5G) wireless systems, such as new radio (NR) and their evolutions, as well as in IEEE related Wi-Fi, worldwide interoperability for microwave access (WiMAX) and their evolutions.A client device herein may be denoted as a user device, a user equipment (UE), a mobile station, an internet of things (IoT)device, a sensor device, a wireless terminal and / or a mobile terminal, and is enabled to communicate wirelessly in a wireless communication system, sometimes also referred to as a cellular radio system. The UEs may further be referred to as mobiletelephones, cellular telephones, computer tablets or laptops with wireless capability. The UEs in this context may be, forexample, portable, pocket-storable, hand-held, computer-comprised, or vehicle-mounted mobile devices, enabled to communicate voice and / or data, via a radio access network (RAN), with another communication entity, such as another receiveror a server. The UE may further be a station, which is any device that contains an IEEE 802.11-conformant MAC and PHYinterface to the WM. The UE may be configured for communication in 3GPP related LTE, LTE-advanced, 5G wireless systems,such as NR, and their evolutions, as well as in IEEE related Wi-Fi, WiMAX and their evolutions.Furthermore, any method according to examples of the invention may be implemented in a computer program, having code means, which when run by processing means causes the processing means to execute the steps of the method. The computer program is included in a computer readable medium of a computer program product. The computer readable medium may comprise essentially any memory, such as previously mentioned a ROM, a PROM, an EPROM, a flash memory, an EEPROM, or a hard disk drive.Moreover, it should be realized that the first communication device comprises the necessary communication capabilities in theform of e.g., functions, means, units, elements, etc., for performing or implementing examples of the invention. Examples of other such means, units, elements and functions are: processors, memory, buffers, control logic, encoders, decoders, rate matchers, de-rate matchers, mapping units, multipliers, decision units, selecting units, switches, interleavers, de-interleavers, modulators, demodulators, inputs, outputs, antennas, amplifiers, receiver units, transmitter units, DSPs, TCM encoder, TCMdecoder, power supply units, power feeders, communication interfaces, communication protocols, etc., which are suitablyarranged together for performing the solution.Therefore, the processor(s) of the first communication device may comprise, e.g., one or more instances of a CPU, a processingunit, a processing circuit, a processor, an ASIC, a microprocessor, or other processing logic that may interpret and execute instructions. The expression “processor” may thus represent a processing circuitry comprising a plurality of processing circuits, such as e.g., any, some or all of the ones mentioned above. The processing circuitry may further perform data processing functions for inputting, outputting, and processing of data comprising data buffering and device control functions, such as call processing control, user interface control, or the like.Finally, it should be understood that the invention is not limited to the examples described above, but also relates to andincorporates all examples within the scope of the appended independent claims. AppendixAccording to Eq. (3) and Eq. (4), even if we assume that the UL subchannel estimation in each time slot is perfect, e.g., ^^^ =^^ = ^^^ / ^ ^,^following Eq. (9), the reconstructed whole channel vector in the conventional TDM based channel estimationapproach will be When all the BS 100 antenna elements are densely deployed within the array, they are strongly coupled with each other, andin general the mutual coupling matrix ^ contains non-zero values in all its entries. Hence, we have Consequently, we have or equivalently (A − 4)Hence, we can conclude that the TDM based channel estimation approach, besides being time-consuming, is unable to obtain an accurate estimate of the whole channel vector ^.

Claims

CLAIMS2. The first communication device (100) according to claim 1, configured to: determine a beamforming configuration for all antenna elements of the set of antenna elements (120) based on thechannel estimation ^^; andreceive a first communication signal (520) from the second communication device (300), the first communication signal (520) being received via all antenna elements of the set of antenna elements (120) based on the beamforming configuration; and / or transmit a second communication signal (530) to the second communication device (300), the second communicationsignal (530) being transmitted via all antenna elements of the set of antenna elements (120) based on the beamformingconfiguration.^^(^) ^^ = ^^ / ^ ^^,^^ ⋅ ^^^^ .

5. The first communication device (100) according to claim 3 or 4, wherein the coupling transfer ^^^for the subset of antenna elements (122) is an inverse half of the mutual coupling ^^^,^^for the subset of antenna elements (122).

6. The first communication device (100) according to any one of the preceding claims, wherein the decoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements (120) is determined based on positions of all antenna elements of the set of antenna elements (120) and an estimated signal propagation direction, wherein the estimated signal propagation direction is based on the decoupled subchannel estimationand positions of the antenna elements in the subsetof antenna elements (122).

7. The first communication device (100) according to any one of the preceding claims, wherein the decoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements (120) is determined based on an interpolation of the decoupled subchannel estimation8. The first communication device (100) according to any one of the preceding claims, wherein the decoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements (120) is determined based on an interpolation of the decoupled subchannel estimationand a projection of the interpolated channel estimation into a ^ dimensional vectorspace, where ^ is a positive integer, and the ^ dimensional vector space is spanned by first ^ eigenvectors of a correlationmatrix ^^(^) of the decoupled channel ^(^) for all antenna elements of the set of antenna elements (120), the projection beingbased on a weighting factor per each eigenvector.

9. The first communication device (100) according to claim 8, wherein a weighting factor per each eigenvector is equal to 1, or dependent on a corresponding eigenvalue of the eigenvector.

10. The first communication device (100) according to claim 8 or 9, wherein a sum of the eigenvalues of first ^ eigenvectorscomprises more than 1- ^ of a sum of all eigenvalues of the correlation matrix ^^(^), where ^ is a predetermined positive scalar.

11. The first communication device (100) according to any one of claims 7 to 10, wherein the interpolation of the decoupled subchannel estimationcomprises any of: a piecewise constant interpolation, a linear interpolation, a polynomial interpolation, a spline interpolation, and a mimetic interpolation.

12. The first communication device (100) according to any one of the preceding claims, wherein the channel estimation ^^ forall antenna elements of the set of antenna elements (120) is based on: amultiplication of the coupling transfer ^ for all antenna elements of the set of antenna elements (120) with thedecoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements (120); or amultiplication of an inverse half of the mutual coupling ^ for all antenna elements of the set of antenna elements(120) with the decoupled channel estimation ^^(^)for all antenna elements of the set of antenna elements (120).

13. The first communication device (100) according to claim 12, wherein the channel estimation ^^ for all antenna elements ofthe set of antenna elements (120) is expressed as: ^^ = ^ ⋅ ^^(^); or^^ = ^^^ / ^ ⋅ ^^(^).

14. The first communication device (100) according to claim 12 or 13, wherein the coupling transfer ^ for all antenna elementsof the set of antenna elements (120) is an inverse half of the mutual coupling ^ for all antenna elements of the set of antennaelements (120).

15. The first communication device (100) according to any one of the preceding claims, wherein the mutual coupling ^^^,^^forthe subset of antenna elements (122) is a subset of the mutual coupling ^ for all antenna elements in the set of antenna elements(120).

16. The first communication device (100) according to any one of the preceding claims, wherein the set of antenna elements(120) are arranged into two or more subarrays of antenna elements with all antenna elements in each subarray of antennaelements connected to a common radio frequency chain (130), and wherein each subset of antenna elements (122) comprises an antenna element in each subarray of antenna elements.

18. A computer program with a program code for performing a method according to claim 17 when the computer program runson a computer.

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