Transmitter distortion mitigation method for multiple-antenna systems

Abstract

Systems and methods for transmitter distortion mitigation for multiple-antenna systems are disclosed. In one embodiment, a method performed by a network node for a Radio Access Network (RAN) of a cellular communications system comprises obtaining baseline beams for downlink transmission to a User Equipment (UE), wherein the baseline beams comprise a first set of baseline beams for a vertical dimension for at least two antenna polarizations, a plurality of subcarriers, and one or more Multiple Input Multiple Output (MIMO) layers and a second set of baseline beams for a horizontal dimension for the at least two antenna polarizations, the plurality of subcarriers, and the one or more MIMO layers. The method further comprises generating a precoding matrix comprising beamforming weights for downlink transmission to the UE, based on the first and second sets of baseline beams such that a directional perturbation is introduced into the beamforming weights over frequency.

Description

TRANSMITTER DISTORTION MITIGATION METHOD FOR MULTIPLE-ANTENNA SYSTEMS Technical Field

[0001] The present disclosure relates to a Multiple-Input Multiple-Output (MIMO) system and, more specifically, to transmitter distortion mitigation in a MIMO system such as, for example, a Radio Access Network (RAN) of a cellular communications system. Background

[0002] Orthogonal Frequency-Division Multiplexing (OFDM) is a core technology of Fourth Generation (4G) and Fifth Generation (5G) cellular networks. OFDM offers multiple benefits such as an ability to cope with frequency-selective channel fading without complex equalization schemes, reduced Inter-Symbol Interference (ISI), and spectrum flexibility.

[0003] Despite having many advantages, OFDM suffers from high Peak-to-Average Power Ratio (PAPR) which is detrimental to efficient power amplifier operation, as discussed in Y. Rahmatallah and S. Mohan, "Peak-To-Average Power Ratio Reduction in OFDM Systems: A Survey And Taxonomy," in IEEE Communications Surveys & Tutorials, vol. 15, no. 4, pp. 1567-1592, Fourth Quarter 2013, doi: 10.1109 / SURV.2013.021313.00164, wherein is hereinafter referred to as the “Rahmatallah Paper”.

[0004] Crest Factor Reduction (CFR) is a primary Radio Unit (RU) function whose purpose consists in limiting the signal dynamic range to improve the downlink transmitter energy efficiency (see, e.g., Seung Hee Han and Jae Hong Lee, "An overview of peak-to-average power ratio reduction techniques for multicarrier transmission," in IEEE Wireless Communications, vol. 12, no. 2, pp. 56-65, April 2005, doi: 10.1109 / MWC.2005.1421929, which is hereinafter referred to as the “Han Paper”). Whilst an abundance of CFR approaches are documented in the literature (see, e.g., the Rahmatallah Paper and the Han Paper), it remains that distortion-based methods such as “Clip-and-Filter” and “Peak Cancellation” are the most widely used techniques in practical implementations due to their simplicity. These methods trade-off PAPR reduction with increased in-band and out-of-band distortion levels. In-band distortionsinclude Error-Vector Magnitude (EVM) while out-of-band distortions consist of Adjacent Channel Leakage Ratio (ACLR) and Operating Band Unwanted Emissions (OBUE).

[0005] The Massive MIMO paradigm introduced by 5G has set the research community on a quest to “hide” the clipping energy from distortion-based CFR methods into the channel null space, i.e., in directions where there are no intended users (see, e.g., H. Bao, J. Fang, Z. Chen, H. Li and S. Li, "An Efficient Bayesian PAPR Reduction Method for OFDM-Based Massive MIMO Systems," in IEEE Transactions on Wireless Communications, vol. 15, no. 6, pp. 4183-4195, June 2016, doi: 10.1109 / TWC.2016.2536662 (hereinafter referred to as the “First Bao Paper”); H. Bao, J. Fang, Q. Wan, Z. Chen and T. Jiang, "An ADMM Approach for PAPR Reduction for Large-Scale MIMO-OFDM Systems," in IEEE Transactions on Vehicular Technology, vol. 67, no. 8, pp. 7407-7418, Aug. 2018, doi: 10.1109 / TVT.2018.2837112 (hereinafter referred to as the “Second Bao Paper”; and Christoph Studer et al., “Democratic Representations,” CORR abs / 1401.3420, April 22, 2015, 43 pages (hereinafter referred to as the “Studer Paper”). These approaches, which are referred to as “Massive-MIMO CFR”, theoretically result in zero EVM at the user receivers in the downlink while achieving significantly lower PAPR than the conventional per-antenna distortion-based CFR techniques of the Rahmatallah Paper and the Han Paper. Summary

[0006] Systems and methods for transmitter distortion mitigation for multiple- antenna systems are disclosed. In one embodiment, a method performed by a network node for a Radio Access Network (RAN) of a cellular communications system comprises obtaining baseline beams for downlink transmission to a particular User Equipment (UE), wherein the baseline beams comprises a first set of baseline beams for a vertical dimension for at least two antenna polarizations, a plurality of subcarriers, and one or more Multiple Input Multiple Output (MIMO) layers and a second set of baseline beams for a horizontal dimension for the at least two antenna polarizations, the plurality of subcarriers, and the one or more MIMO layers. The method further comprises generating a precoding matrix comprising beamforming weights for downlink transmission to the particular UE, based on the first set of baseline beams for the vertical dimension and the second set of baseline beams for the horizontal dimension such that a directional perturbation is introduced into the beamforming weights for theplurality of subcarriers. In this manner, directional perturbations are introduced to beamforming weights over frequency to help decorrelate transmitter in-band and out- of-band distortions when using a 3GPP codebook beamforming or some other predetermined Grid-of-Beam (GoB) transmission scheme.

[0007] In one embodiment, the directional perturbation is applied on both the vertical dimension and the horizontal dimension. In another embodiment, the directional perturbation is applied on the vertical dimension but not the horizontal dimension. In another embodiment, the directional perturbation is applied on the horizontal dimension but not the vertical dimension.

[0008] In one embodiment, the first and second sets of baseline beams are first and second sets of Discrete Fourier Transform (DFT) beams.

[0009] In one embodiment, generating the precoding matrix comprises, for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMOlayers, generating a beam weight vector (^ ^×^^ ^^,^,^ ∈ ℂ ) for the vertical dimensiondefined as:^^^,^,^ = ^ ^^^^^^,^,^^^^^^^^^ !,^,^,^" ^^^^^^,^,^^^^^^^^^ !,^,^,^"%^^&^'1 ^ #^^^ … ^ #^^^ (whereoversampling ratio for the vertical dimension +,,-,. ∈ / 0, … , *^)^ − 12 is an index of thebaseline beam, from among the first set of baseline beams, for polarization ^, subcarrier^, and MIMO layer ^, and Δ45.6789:,,,-,. ∈ ℝ is a randomly generated vertical beamperturbation for polarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values. Generating the precoding matrix further comprises, for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMOlayers, generating a beam weight vector (<:,,,-,. ∈ ℂ^^^=×^) for the horizontal dimensiondefined as:^^^^:^,^,^^^?@^^A@B^ !,^,^,^" ^^^^:^,^,^^^?@^^A@B^ !,^,^,^"%^=&^'Doversampling ratio for the horizontal dimension, E,,-,. ∈, *^)^ − 12 is an index ofthe baseline beam, from among the second set baseline beams, identified forpolarization ^, subcarrier ^, and MIMO layer ^, ΔFG.7HGI69:,,,-,. ∈ ℝ is a randomlygenerated horizontal beam perturbation for polarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values, and%∙'Dis the vector transpose operator. Generating the precoding matrix further comprises generating the precoding matrix per subcarrier ^ as: <<K = > :L,^,L … :L,^,PQ=- M-,N<:=,^,L O … O M-,R&^<:=,^,PQ=Cwhere S is a subcarrier ^ and M ^^^T-,. = ^ ^,^ isa polarization co- a,.offset for ^MIMO layer ^. In one embodiment, < 1, and VΔFG.7HGI9:,,,-,.V < 1.

[0010] In another embodiment, for eachantenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMOlayers, generating a beam weight vector (^ ^×^^ ^^,^,^ ∈ ℂ ) for the vertical dimensiondefined as: corresponds to awithout any perturbation for polarization ^, subcarrier ^ and MIMO layer ^;[∆[[^[,,-,.=^ \^]ab^^^^^^ !,^,^,^c \^]ab^^^^^^ !,^,^,^c%`^Q=' ^×^^1 ^ _^`^ … ^ _^`^ ( ∈ ℂ denotes a complex-valued^, subcarrier ^ and MIMO layer ^; ⊙ denotes elementwise multiplication (i.e., Hadamard product); )^is a number of ports for the vertical dimension; *^is a DFT beam oversampling ratio forthe vertical dimension; +,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, fromamong the first set of baseline beams, for polarization ^, subcarrier ^, and MIMO layer^; and Δ45.6789:,,,-,. ∈ ℝ is a randomly generated vertical beam perturbation forpolarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values. Generating the precoding matrix further comprises, for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers,generating a beam weight vector (<:,,,-,. ∈ ℂ^^^=×^) for the horizontal dimensiondefined as: <:^,^,^ = <X:^,^,^ ,.\^]^! " \^]^! %`=Q=' D[∆[[<[,,-,.=^ \^]ab?@^^A@B^ !,^,^,^c \^]ab?@^^A@B^ !,^,^,^c%`=Q=' D^d ^ _=`= d … ^ _=`= d( ∈ ℂ ^^=×^ denotes a complex-denotes elementwise multiplication (i.e., Hadamard product); )^is a number of ports for the horizontal dimension; *^is a DFT beam oversampling ratio for the horizontaldimension; E,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thesecond set of baseline beams, identified for polarization ^, subcarrier ^, and MIMO layer^; ΔFG.7HGI69:,,,-,. ∈ ℝ is a randomly generated horizontal beam perturbation forpolarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values; and %∙'Dis the vector transpose operator. Generating the precoding matrix further comprises generating the precoding matrix per subcarrier ^ as: <<K = :L,^,L … :L,^,PQ=- >M- <: O … O M- < Cwhere S is asubcarrier ^; and M ^^^T-,. = ^ ^,^ isa polarization co-phasing term representing a U,.phase offset forMIMO layer ^.

[0011] In another embodiment, generating the precoding matrix comprises for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMOlayers, generating a beam weight vector (^ ^×^^ ^^,^,^ ∈ ℂ ) for the vertical dimensiondefined as:^= ^ ^^^^^^,^,^^^^^^^^^ !,^,^,^" ^^^^^^,^,^^^^^^^^^ !,^,^,^"%^^&^'^ ^^^ ^ ^^whereoversampling ratio for the vertical dimension, +,,-,. ∈ / 0, … , *^)^ − 12 is an index of thebaseline beam, from among the first set of baseline beams, for polarization ^, subcarrier^, and MIMO layer ^, and Δ45.6789:,,,-,. ∈ ℝ is a randomly generated vertical beamperturbation for polarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values. Generating the precoding matrix further comprises, for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMOlayers, generating a beam weight vector (< ^:,,,-,. ∈ ℂ ^^=×^) for the horizontal dimensiondefined as:^^^:^,^,^ &^'D <:^,^,^ = > ^,^,^ =^^ # ^^,^,^ ^ = = ^^^,^,^ … ^ #=^= ^^^,^,^Cwhere )^a DFT beam,. , ^ − 12 is an index ofthe baseline beam, from among the second set of baseline beams, identified for polarization ^, subcarrier ^, and MIMO layer ^, and%∙'Dis the vector transpose operator. Generating the precoding matrix further comprises generating the precoding matrix per subcarrier ^ as: <… <K = > :L,^,L :L,^,PQ=- M-,N<:=,^,L O … O M-,R&^<:=,^,PQ=Cwhere S is a subcar ^^^T^,^rier ^ and M-,. = ^ isa polarization co-phasing term representing a U-,.phase offset forMIMO layer ^. In one embodiment,< 1.

[0012] In another embodiment, generating the precoding matrix comprises, for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMOlayers, generating a beam weight vector (^^^,^,^ ∈ ℂ^×^^) for the vertical dimensiondefined as:^^^,^,^ = ^X^^,^,^ ⊙ [ ∆[[^[,,-,.aperturbation for polarization ^, subcarrier ^ and MIMO layer ^;[∆[[^[,,-,.=^ \^]ab^^^^^^ !,^,^,^c \^]ab^^^^^^ !,^,^,^c%`^Q='1 ^ ^ ( ∈ ℂ^×^^ denotes a complex-valued^, subcarrier ^ and MIMO layer ^; ⊙ denotes elementwise multiplication (i.e., Hadamard product);)^is a number of ports for the vertical dimension; *^is a DFT beam oversampling ratio forthe vertical dimension; +,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, fromamong the first set of baseline beams, for polarization ^, subcarrier ^, and MIMO layer^; Δ45.6789:,,,-,. ∈ ℝ is a randomly generated vertical beam perturbation for polarization^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values. Generating the precoding matrix further comprises, for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers, generating (202) a beamweight vector (<:,,,-,. ∈ ℂ^^^=×^) for the horizontal dimension defined as:= <X:^,^,^'Dwhere: ^any d ∈ ℝ^×^^corresponds to the all-ones vector; and )^is a number of ports for the horizontal dimension; *^is a DFT beam oversampling ratio for the horizontal dimension; E,,-,.∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among the second set ofbaseline beams, identified for polarization ^, subcarrier ^, and MIMO layer ^; and %∙'Dis the vector transpose operator. Generating the precoding matrix further comprises generating the precoding matrix per subcarrier ^ as: <K = :L,^,L … <:L,^,PQ=- >M- < O … O M-where S is a subcarrier ^^^T^,^^; and M-,. = ^ isa polarization co-phasing term representing a U-,.phase offset forMIMO layer ^.

[0013] In another embodiment, generating the precoding matrix comprises, for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMOlayers, generating a beam weight vector (^ ^×^^ ^^,^,^ ∈ ℂ ) for the vertical dimensiondefined as:^= ^ ^^^^^,^,^ ^^^^^,^,^%^^&^'^ ^ (where )^is a number of ports for the vertical dimension, *^is a DFT beamoversampling ratio for the vertical dimension, and +,,-,. ∈ / 0, … , *^)^ − 12 is an index ofthe baseline beam, from among the first set of baseline beams, for polarization ^, subcarrier ^, and MIMO layer ^. Generatingmatrix further comprises, for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMOlayers, generating a beam weight vector (<:,,,-,. ∈ ℂ^^^=×^) for the horizontal dimensiondefined as:^^^^:^,^,^^^?@^^A@B^ !,^,^,^" ^^^^:^,^,^^^?@^^A@B^ ! "%^=&^'D<:^,^,^ = > ,^,^,^^^ #^,^,^ ^ =^= ^^ #^,^,^ … ^ =^= ^^^,^,^C,. , ^ ^ − anthe baseline beam, from among the second set of baseline beams, identified forpolarization ^, subcarrier ^, and MIMO layer ^, ΔFG.7HGI69:,,,-,. ∈ ℝ is a randomlygenerated horizontal beam perturbation for polarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values, and %∙'Dis the vector transpose operator. Generating the precoding matrix further comprises generating the precoding matrix per subcarrier ^ as: <K = > :L,^,L … <:L,^,PQ=- M-,N<: O … O M-,R&^< Cwhere S is a subcarrier ^^^T^,^^ and M-,. = ^ isa polarization co-phasing term representing a U,.phase offset forMIMO layer ^. In one embodiment, VΔFG.7HGI9:,,,-,.V < 1.

[0014] In another embodiment, generating the precoding matrix comprises, for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMOlayers, generating a beam weight vector (^ ^×^^ ^^,^,^ ∈ ℂ ) for the vertical dimensiondefined as:^^^,^,^ = ^X^^,^,^where ^ = ^ corresponds to abeamforming (i.e.,without any perturbation for polarization ^, subcarrier ^ and MIMO layer ^; )^is a number of ports for thevertical dimension; *^ is a DFT beam oversampling ratio for the vertical dimension; and+,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among the first set ofbaseline beams, for polarization ^, subcarrier ^, and MIMO layer ^. Generating the precoding matrix further comprises, for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers, generating a beam weight vector(<:,,,-,. ∈ ℂ^^^=×^) for the horizontal dimension defined as:<:^,^,^ = <X:^,^,^ ⊙ [ ∆[[<[,,-,." ^ ' D^any[∆[[<[,,-,.=^ \^]ab c \^]ab @B^ !,^,^,^c% ' D?@^^A@B^ !,^,^,^ ?@^^A `=Q=d ^ _=`= d … ^ _=`= d( ∈ ℂ^^^=×^ denotes a complex-subcarrier ^ and MIMO layer ^; d ∈ corresponds to the all-ones vector; ⊙ denoteselementwise multiplication (i.e., Hadamard product); )^is a number of ports for thehorizontal dimension; *^ is a DFT beamratio for the horizontal dimension;E,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among the second set ofbaseline beams, identified for polarization ^, subcarrier ^, and MIMO layer ^;ΔFG.7HGI69:,,,-,. ∈ ℝ is a randomly generated horizontal beam perturbation forpolarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values; and %∙'Dis the vector transpose operator. Generating the precoding matrix further comprises generating the precoding matrix per subcarrier ^ as: <K = :L,^,L … <O O :L,^,PQ=- < …where S is asubcarrier ^; and M ^^^T-,. = ^ ^,^ isa polarization co-phasing term representing a U-,.phase offset forMIMO layer ^.

[0015] In one embodiment, the method further comprises introducing attenuated complex random noise into the beamforming weights comprised in the precoding matrix.

[0016] In one embodiment, the method further comprises performing a re- orthogonalization procedure on the precoding matrix, thereby providing a modified precoding matrix. In one embodiment, the method further comprises scaling the modified precoding matrix, thereby providing a scaled precoding matrix.

[0017] In one embodiment, the method further comprises applying the scaled precoding matrix for downlink transmission of a signal to the UE.

[0018] Corresponding embodiments of a network node for a RAN of a cellular communications system are also disclosed. In one embodiment, a network node for a RAN of a cellular communications system is adapted to obtain baseline beams for downlink transmission to a particular UE, wherein the baseline beams comprises a first set of baseline beams for a vertical dimension for at least two antenna polarizations, a plurality of subcarriers, and one or more MIMO layers and a second set of baseline beams for a horizontal dimension for the at least two antenna polarizations, the plurality of subcarriers, and the one or more MIMO layers. The network node is further adapted to generate a precoding matrix comprising beamforming weights for downlink transmission to the particular UE, based on the first set of baseline beams for the vertical dimension and the second set of baseline beams for the horizontal dimension such that a directional perturbation is introduced into the beamforming weights for the plurality of subcarriers.

[0019] In one embodiment, a network node for a RAN of a cellular communications system comprises one or more radio units comprising one or more transmitters, and processing circuitry associated with the one or more radio units. The processing circuitry is configured to cause the network node to obtain baseline beams for downlink transmission to a particular UE, wherein the baseline beams comprises a first set of baseline beams for a vertical dimension for at least two antenna polarizations, a plurality of subcarriers, and one or more MIMO layers and a second set of baseline beams for a horizontal dimension for the at least two antenna polarizations, the plurality of subcarriers, and the one or more MIMO layers. The processing circuitry is further configured to cause the network node to generate a precoding matrix comprising beamforming weights for downlink transmission to the particular UE, based on the first set of baseline beams for the vertical dimension and the second set of baseline beams for the horizontal dimension such that a directional perturbation is introduced into the beamforming weights for the plurality of subcarriers.Brief Description of the Drawings

[0020] The accompanying drawing figures incorporated in and forming a part of this specification illustrate several aspects of the disclosure, and together with the description serve to explain the principles of the disclosure.

[0021] Figure 1 is a flow chart that illustrates the operation of a Radio Access Network (RAN) node to introduce small directional perturbations and optionally attenuated complex random noise into beamforming weights over frequency to help decorrelate the transmitter in-ban and out-of-ban distortions when using a 3rdGeneration Partnership Project (3GPP) codebook or some other predetermined Grid-of- Beam (GoB) transmission scheme, in accordance with embodiments of the present disclosure;

[0022] Figure 2 illustrates step 104 of Figure 1 in more detail, in accordance with an embodiment of the present disclosure;

[0023] Figure 3 is a physical layer link simulator block diagram;

[0024] Figure 4 illustrates the simulator Crest Factor Reduction (CFR) model with four pipelined clipping stages for an antenna polarization ^ containing )^)^antenna ports;

[0025] Figure 5 illustrates one example of a cellular communications system according to some embodiments of the present disclosure;

[0026] Figure 6 is a schematic block diagram of a RAN node according to some embodiments of the present disclosure;

[0027] Figure 7 is a schematic block diagram that illustrates a virtualized embodiment of the RAN node of Figure 6 according to some embodiments of the present disclosure; and

[0028] Figure 8 is a schematic block diagram of the RAN node of Figure 6 according to some other embodiments of the present disclosure. Detailed Description

[0029] The embodiments set forth below represent information to enable those skilled in the art to practice the embodiments and illustrate the best mode of practicing the embodiments. Upon reading the following description in light of the accompanying drawing figures, those skilled in the art will understand the concepts of the disclosureand will recognize applications of these concepts not particularly addressed herein. It should be understood that these concepts and applications fall within the scope of the disclosure.

[0030] Radio Node: As used herein, a “radio node” is either a Radio Access Network (RAN) node or a wireless communication device.

[0031] RAN Node: As used herein, a “RAN node” is any node in a RAN of a cellular communications network that operates to wirelessly transmit and / or receive signals. Some examples of a RAN node include, but are not limited to, a base station (e.g., a New Radio (NR) base station (gNB) in a Third Generation Partnership Project (3GPP) Fifth Generation (5G) NR network or an enhanced or evolved Node B (eNB) in a 3GPP Long Term Evolution (LTE) network), a high-power or macro base station, a low-power base station (e.g., a micro base station, a pico base station, a home eNB, or the like), a relay node, a network node that implements part of the functionality of a base station or a network node that implements a gNB Distributed Unit (gNB-DU)) or a network node that implements part of the functionality of some other type of RAN node.

[0032] Core Network Node: As used herein, a “core network node” is any type of node in a core network or any node that implements a core network function. Some examples of a core network node include, e.g., a Mobility Management Entity (MME), a Packet Data Network Gateway (P-GW), a Service Capability Exposure Function (SCEF), a Home Subscriber Server (HSS), or the like. Some other examples of a core network node include a node implementing an Access and Mobility Function (AMF), a User Plane Function (UPF), a Session Management Function (SMF), an Authentication Server Function (AUSF), a Network Slice Selection Function (NSSF), a Network Exposure Function (NEF), a Network Function (NF) Repository Function (NRF), a Policy Control Function (PCF), a Unified Data Management (UDM), or the like.

[0033] Communication Device: As used herein, a “communication device” is any type of device that has access to an access network. Some examples of a communication device include, but are not limited to: mobile phone, smart phone, sensor device, meter, vehicle, household appliance, medical appliance, media player, camera, or any type of consumer electronic, for instance, but not limited to, a television, radio, lighting arrangement, tablet computer, laptop, or Personal Computer (PC). The communication device may be a portable, hand-held, computer-comprised, or vehicle-mounted mobile device, enabled to communicate voice and / or data via a wireless or wireline connection.

[0034] Wireless Communication Device: One type of communication device is a wireless communication device, which may be any type of wireless device that has access to (i.e., is served by) a wireless network (e.g., a cellular network). Some examples of a wireless communication device include, but are not limited to: a User Equipment device (UE) in a 3GPP network, a Machine Type Communication (MTC) device, and an Internet of Things (IoT) device. Such wireless communication devices may be, or may be integrated into, a mobile phone, smart phone, sensor device, meter, vehicle, household appliance, medical appliance, media player, camera, or any type of consumer electronic, for instance, but not limited to, a television, radio, lighting arrangement, tablet computer, laptop, or PC. The wireless communication device may be a portable, hand-held, computer-comprised, or vehicle-mounted mobile device, enabled to communicate voice and / or data via a wireless connection.

[0035] Network Node: As used herein, a “network node” is any node that is either part of the RAN or the core network of a cellular communications network / system.

[0036] Note that the description given herein focuses on a 3GPP cellular communications system and, as such, 3GPP terminology or terminology similar to 3GPP terminology is oftentimes used. However, the concepts disclosed herein are not limited to a 3GPP system.

[0037] Note that, in the description herein, reference may be made to the term “cell”; however, particularly with respect to 5G NR concepts, beams may be used instead of cells and, as such, it is important to note that the concepts described herein are equally applicable to both cells and beams.

[0038] The existing solutions for Massive Multiple Input Multiple Output (MIMO) Crest Factor Reduction (CFR), which are described in the First Bao Paper, the Second Bao Paper, and the Studer Paper, rely on accurate channel estimates to determine the channel null space and are thus better suited for reciprocity-based beamforming, such as Sounding Reference Signal (SRS) or Demodulation Reference Signal (DMRS) reciprocity-based schemes. To limit the signaling overhead, the uplink channel sounding sequences such as SRS and DMRS tend to have transmit periodicities of the order of a few milliseconds, which is typically not sufficient to provide an accurate channel null space estimate in fast fading conditions or with moving users. Therefore, the existingMassive-MIMO CFR methods end-up injecting clipping energy not only in the channel null space but also in the user signal subspace, thus degrading the link performance due to an increased Error Vector Magnitude (EVM) at the downlink receivers. Aperiodic SRS transmissions can alleviate the channel estimation refresh rate problem to some extent, but comes at the cost of increased signaling overhead.

[0039] The uplink link budget is typically limited by the UE transmit power, such that reciprocity-based beamforming rapidly becomes unavailable for many UEs as they move away from the base station. In these situations, the system resorts to simpler beamforming methods such as 3GPP codebooks (see, e.g., 3GGP Technical Specification (TS) 38.214 v17.1.0, “Physical layer procedures for data”, Technical Specification, May 2022) or some other pre-determined Grid-of-Beam (GoB) transmissions.

[0040] One problem with 3GPP codebook-based transmission and other GoB methods when combined with traditional per-branch distortion-based CFR methods is that the EVM stemming from the Peak-to-Average Power Ratio (PAPR) reduction operation is highly correlated with the intended signal. Thus, the distortion is transmitted in the same directions as that of the UE signals which results in increased EVM at the downlink receivers and some consequently reduced link throughputs.

[0041] Systems and methods are disclosed herein that address the aforementioned downlink CFR EVM correlation issue when using 3GPP codebooks or some other predetermined GoB method in radio systems operating with distortion-based CFR methods. In particular, systems and methods are disclosed in which some small direction perturbation and optionally attenuated random noise are added to the beamforming weights over frequency to decorrelate the transmitter distortions such as the CFR EVM when using 3GPP codebooks or some other predetermined GoB transmission scheme.

[0042] While not being limited to or by any particular advantage, embodiments of the systems and methods disclosed herein may provide any one or more of the following advantages over the existing solutions: • Embodiments of the systems and methods disclosed herein may eliminate or greatly reduce the CFR EVM impact on the link throughput. • Embodiments of the systems and methods disclosed herein may improve the radio energy efficiency by improving the link spectral efficiency.• Embodiments of the systems and methods disclosed herein are Channel State Information (CSI) unaware, i.e., they do not rely on knowledge of the wireless channel response. • Embodiments of the systems and methods disclosed herein have low processing complexity. • Embodiments of the systems and methods disclosed herein may also help decorrelate the out-of-band distortions such as the Operating Band Unwanted Emissions (OBUE) and the Adjacent Channel Leakage Ratio (ACLR). • Embodiments of the systems and methods disclosed herein can enable lower CFR clipping thresholds, which in turn enable the use of smaller power amplifiers with more energy efficient operation. • Embodiments of the systems and methods disclosed herein could also be an enabling technology for very high order modulation (super-Quadrature Amplitude Modulation (QAM)) under realistic conditions.

[0043] Figure 1 is a flow chart that illustrates the operation of a RAN node (e.g., a base station such as, e.g., a gNB) in accordance with embodiments of the present disclosure. Optional steps are represented by dashed lines / boxes. This process is performed for downlink beamforming to a particular UE. Note, however, that this process may be performed separately for multiple UEs. In general, the procedure of Figure 1 introduces some small directional perturbations and optionally some attenuated complex random noise to beamforming weights (used for downlink transmission to the UE) over frequency to help decorrelate the transmitter in-band (EVM) and out-of-band (ACLR, OBUE) distortions when using a 3GPP codebook(s) or some other predetermined Grid-of-Beam (GoB) transmission scheme.

[0044] As illustrated, the RAN node optionally determines whether the UE is a suitable candidate for adding directional perturbations to the beamforming weights used for downlink transmission to the UE. In other words, the RAN node determines whether the UE would benefit from EVM decorrelation. More specifically, in this example, the RAN node determines whether a Modulation and Coding Scheme (MCS) used for downlink transmission to the UE is greater than a predefined MCS threshold (step 100). The MCS threshold is such that the remaining steps of the procedure of Figure 1 are performed only if the MCS used for downlink transmission is a medium to high MCS. For example, the MCS threshold may be 64-QAM such that the remaining steps of theprocedure are performed only if the MCS of the UE is 64-QAM or higher (e.g., 256- QAM). If the RAN node determines that the MCS of the UE is not greater than the MCS threshold, the process ends. Otherwise, the process proceeds to step 102.

[0045] The RAN node obtains baseline beams (e.g., baseline Discrete Fourier Transform (DFT) beams) for the UE for multiple subcarriers (e.g., all subcarriers in the full bandwidth of the RAN node), either based on UE feedback or using some other metric (step 102). In the example embodiments descried herein, the RAN node uses a rectangular antenna array with two (or more) antenna polarizations, and the baseline beams includes a first set of baseline beams (e.g., a first set of DFT beams) for the vertical, or elevation, dimension and a second set of baseline beams (e.g., a second set of DFT beams) for the horizonal, or azimuth, dimension.

[0046] The RAN node generates a precoding matrix including beamforming weights for downlink transmission to the UE, based on the baseline beams such that a directional perturbation for the vertical dimension and / or a direction perturbation for the horizontal dimension is(are) introduced into the beamforming weights over frequency (step 104). More specifically, in one example embodiment illustrated in Figure 2, step 104 includes the following. For each antenna polarization ^, for each subcarrier ^, and for each MIMO layer ^ (i.e., for each different combination of antenna polarization ^, subcarrier ^, and MIMO layer ^), the RAN node generates a beamforming weight vector for the vertical dimension in which a small directional perturbation is introduced into each beamforming weight (step 200). For example, when using a 3GPP codebook(s), a^^^,^,^ ∈ ℂ^×^^ beam weight vector for the vertical dimension may be generated as^ \^]a^^,^,^eb^^^^^^ !,^,^,^c \^]a^^,^,^eb^^^ c%`^Q='^^,^,^ = ^^^ !,^,^,^^ ^ ( (1)o )^is a number of ports (e.g., CSI-RS ports in a 3GPP context; otherwise, baseband or digital ports in a broader context) in the vertical dimension; o *^is a DFT beam oversampling ratio for the vertical dimension; o+,,-,. ∈ / 0, … , *^)^ − 12 is a beam index of the baseline beam identified forthe vertical dimension (in step 102) for polarization ^, subcarrier ^ and MIMO layer ^. In some beamforming schemes such as 3GPP Codebook, +,,-,.may be common for both polarizations, i.e., +N,-,. = +^,-,.; ando Δ45.6789:,,,-,. ∈ ℝ is a small and randomly generated directional perturbationfor the vertical dimension for polarization ^, subcarrier ^, and MIMO layer ^. Δ45.6789:,,,-,.can assume both positive and negative values. In one example, VΔ45.6789:,,,-,.V < 1.Alternatively, equation (1) can be more compactly written as follows: ^^^,^,^ = ^X^^,^,^ ⊙ [ ∆[[^[,,-,. %2'where: \^]o^X^^,^,^ = ^1 ^ _^`^ … ^ _^`^ ( ∈ corresponds to adimension without anylayer ^; \^]ab^^ c \^]ab c%`^Q='o [ ∆[[^[,,-,. = ^ ^^^^ !,^,^,^ ^^^^^^ !,^,^,^1 ^ _^`^ … ^ _^`^ ( ∈ ℂ^×^^ denotes aforpolarization ^, subcarrier ^ and MIMO layer ^; and o ⊙ denotes elementwise multiplication (i.e., Hadamard product).

[0047] In addition, for each antenna polarization ^, for each subcarrier ^, and for each MIMO layer ^ (i.e., for each different combination of antenna polarization ^, subcarrier ^, and MIMO layer ^), the RAN node generates a beamforming weight vector for the horizontal dimension in which a small directional perturbation is introduced into each beamforming weight (step 202). For example, when using a 3GPP codebook(s), a <:,,,-,. ∈ ℂ^^^=×^ beamforming weight vector in the horizontal dimension for polarizationand MIMO layer ^ may be generated as follows: \^]a!^,^,^eb?@^^A@B^ !, c \^]a!^,^,^eb c%`=Q='D <= > ^,^,^ ?@^^A@B^ !,^,^,^^ ^ ` ^ ^ C(3)o )^is a number of ports in the horizontal dimension; o *^is a DFT beam oversampling ratio for the horizontal dimension; oE,,-,. ∈ / 0, … , *^)^ − 12 is the beam index of the baseline beam (from step104) for the horizontal dimension for polarization ^, subcarrier ^, and MIMO layer ^. In some beamforming schemes such as 3GPP Codebook, E,,-,.may be common for both polarizations, i.e., EN,-,. = E^,-,..o ΔFG.7HGI69:,,,-,. ∈ ℝ is a small and randomly generated directional perturbationfor the horizontal dimension for some polarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values. In one example, VΔFG.7HGI9:,,,-,.V < 1; ando operator.more compactly written as follows: <:^,^,^ = <X:^,^,^ ⊙ [ ∆[[<[,,-,. %4'where:\^]^!^,^,^" \^]^!^,^,^ =o <X = > _ ` _ ∈ ℂ^^^=×^:^,^,^ ^^^,^,^ ^ = = ^^^,^,^ … ^ =`= ^^^,^,^Cdimension without any perturbation for polarization ^, subcarrier ^ and MIMO layer ^; \^]ab c \^ % ' D?@^^A@B^ !,^,^,^ ]ab?@ c `=Q=o [ ∆[[<[ ^^A@B^ !,^,^,^ ^,,-,. = ^ ^^=×^d ^ _=`= d … ^ _=`= d( ∈ ℂdimension for polarization ^, subcarrier ^ and MIMO layer ^; od ∈ ℝ^×^^ corresponds to the all-ones vector; and⊙ denotes elementwise multiplication (i.e., Hadamard product). In some embodiments, the <:^,^,^beamforming weight vectors are constant over frequency for one or moreResource Blocks (PRBs).

[0049] In the example above, the directional perturbations are added for both the vertical and horizontal dimensions. However, in an alternative embodiment, the directional perturbations are added for only one dimension (i.e., only the vertical dimension or only the horizontal dimension. The single perturbed dimension may be the same across all subcarriers or vary between subcarriers. Note that directional perturbations in only the vertical dimension can be achieved by, for example, modifying Equation (3) above to remove the ΔFG.7HGI69:,,,-,.term. Likewise, directional perturbations in only the horizontal dimension can be achieved by, for example, modifying Equation (1) above to remove the Δ45.6789:,,,-,.term.

[0050] For each subcarrier ^, the RAN node generates the precoding matrix for thesubcarrier ^ by combining the <:^,^,^ beam weights for two polarizations ^ ∈ / 0,12 and amaximum rank S for the given subcarrier ^ to thereby generate a K ^^- ∈ ℂ ^^=×Rprecoding matrix as follows: <K :L,^,L … <:L,^,PQ=- = >M-,N<:=,^,L O … O M-,R&^<:=,^,PQ=C %5'where:• S is a for a subcarrier ^. •M-,. = ^^^^T^,^ is a polarization co-phasing term representing a U-,. phaseoffset for a subcarrier ^ and some MIMO layer ^.

[0051] Returning to Figure 1, additionally, some attenuated complex random noise may be added to the precoding matrix over frequency to further help decorrelate the transmitter distortion (step 106). In one example, the attenuated complex random noise may be added to the precoding matrix K- for each subcarrier ^ as follows: ‖KIG7-j,- = K- + l K-‖n.G o- %6'where:•o- ∈ ℂ^^^^=×R is a matrix containing complex Gaussian noise of zero meanand unit variance; •‖. ‖n.G is the Frobenius norm; and• l is a real-valued scaling factor corresponding to a desired noise attenuation with respect to the beamforming weight matrix K-. For example, l <10&^q / ^N. In some embodiments, l is varied based on an estimated UE Signal-to-Interference-plus-Noise Ratio (SINR).

[0052] For the subcarriers having a transmission rank larger than one (S > 1), theRAN node performs a beam re-orthogonalization procedure to preserve orthogonality between the multiple MIMO layers (steps 108 and 110). In some embodiments, the beam re-orthogonalization procedure uses a Modified Gram-Schmidt (MGS) procedure and can be defined as follows: tu S > 1 vwKx,- = +y^^KIG7-j,-"z{|zz}vwhere +y^%∙' is a Modified Gram-Schmidt procedure that re-orthogonalizes the matrixK ^^^^=×R ^^^^=×^IG7-j,- ∈ ℂ , with columns ^IG7-j,7,- ∈ ℂ , as shown below. The vectorHermitian transpose operation (complex-conjugate) is denoted%∙'^: uw^ ^ = 1 ∶ S^^ = IG7-j,7,-7 ^^IG7-j,7,-^%8

[0053] Additionally, the Kconstraint and / or a maximum . scaling can be performed as defined in either of the following two examples: KK x,-89:5^,- = - ∙^K ^^^^^^^^^y^^ %9 − ^''where:• ^^^^^^^^y^^ is the available transmit power budget; • |∙| is the absolute value operator; and • +^^%∙' is the operator that identifies the maximum matrix element.

[0054] Finally, for at least one of the subcarriers ^, the RAN node uses the beamforming weights included in the scaled precoding matrix K-89:5^,-for that subcarrier ^ for downlink transmission of a downlink signal to the UE in the subcarrier ^ (step 114).

[0055] Some physical layer link simulations were conducted for rank-1 and rank-2 Single-User (SU) MIMO transmissions using 3GPP New Radio Type-I Codebook beamforming. The channel model used in the simulation is a Clustered Delay Line (CDL) type E model which corresponds to some flat-fading channel propagation conditions. Flat fading channels generally lead to higher EVM correlation.

[0056] In the Downlink (DL) path, a four iteration Clip-and-Filter CFR algorithm was inserted between the Cyclic-Prefix appending module and the DL channel model. The Inverse Fast Fourier Transform (IFFT) were performed with four times oversampling compared to the nominal baseband sampling rate to ensure proper CFR operation.

[0057] Figure 3 illustrates the physical layer link simulator block diagram.

[0058] Some specific simulator configuration parameters are displayed in Table 1 below. Parameters Configuration Carrier Frequency 3.5 Gigahertz (GHz) 20 Megahertz (MHz) / 30 kilohertz Bandwidth / Subcarrier Spacing (kHz) CDL-E narrow angular spread (Line- Channel Model of-sight) Delay spread 3e-7 second UE Speed 3 kilometers per hour (kmph) User location Boresight, 100 meters away 8 horizontal ports with 44 millimeter (mm) inter-element spacing. Antenna array configurations 4 vertical ports with 58 mm inter- element spacing and 2x1 vertical subarrays. Information Carrying Capacity (ICC)- based with 10% outer-loop Block Link-Adaptation Error Rate (BLER) target based on Acknowledgement (ACK) / Negative ACK (NACK) reports Modulation and Coding Scheme MCS Table 2 (MCS) MCS Threshold = 19 Precoding 3GPP Codebook Type-I Periodicity : 40 slots CSI-RS configurations Cell-specific: 32 Ports, index 18 UE-specific: 4 Ports, index 5 SCG and bundle size (PRBs) 2 Number of frames 200 Table 1: Physical Layer Link Simulator Configuration

[0059] Figure 4 illustrates the simulator CFR model with four pipelined clipping stages for an antenna polarization ^ containing )^)^antenna ports. The CFR clippingerror z, ∈ ℂ^^^=×^ is computed by subtracting the CFR input vector ^, ∈ ℂ^^^=×^ to theCFR output vector ^, ∈ ℂ^^^=×^ as follows:z, = ^, − ^, %10'

[0060] Finally, an EVM correlation monitor computes a frequency-domain correlation coefficient between the CFR clipping error z,and the CFR input signal ^,for a polarization ^, some OFDM symbols ^ and a subcarrier ^ as follows: ^^5,, = V^^⃗ , ∙ z^⃗ ,Vwhere:•^ ∎^^⃗ denotes a vector of unit norm,• ∙ is the vector inner product operator, • )-j^^is the number of OFDM symbols, • ^ is the number of subcarriers, • %∙'^is the Hermitian transpose operator, i.e., complex-conjugate transpose, and • ‖∙‖^is the vector l2-norm operator.

[0061] Finally, the ^^5,, correlation coefficients for two polarizations ^ ∈ / 0,12 arecombined as shown below: ^+ ^^ ^

[0062] Table 2 shows the CFR EVM correlation coefficient ^^5for different beamforming methods. The results are displayed for various CFR clipping thresholds that are specified relative to the nominal per antenna average power. Beamforming Transmission CFR Clipping Threshold [dB] Method Rank 5.7 6.3 6.9 7.4 1 99% 99% 99% 99% Baseline 3GPP 2 99% 99% 99% 99%Proposed 1 39% 32% 27% 28% method 2 36% 33% 30% 26% Table 2: CFR EVM Correlation Coefficient (¦^z)

[0063] Table 3 displays the relative downlink throughput for different beamforming methods and various CFR clipping thresholds compared to a 3GPP codebook baseline with no CFR. The results are provided for a 30 dB user thermal SNR. Beamforming Transmission CFR Clipping Threshold [dB] Method Rank 5.7 6.3 6.9 7.4 1 68% 77% 85% 94% Baseline 3GPP 2 66% 74% 83% 90% Proposed 1 100% 100% 100% 100% method 2 82% 89% 97% 100% Table 3: Relative Downlink Throughput vs. 3GPP No CFR Baseline

[0064] As seen from the above results, the proposed method significantly helps decorrelating the distortion introduced by the downlink CFR, thus resulting in improved link throughput and radio energy efficiency.

[0065] The Table 3 results also imply that lower CFR clipping thresholds could potentially be afforded while providing link throughputs that are superior to those offered by the 3GPP codebooks at higher clipping thresholds. This could lead to the use of smaller power amplifiers and further boost the radio energy efficiency.

[0066] The proposed method could also be an enabling technology for very high order modulation (super-QAM) under realistic conditions.

[0067] Figure 5 illustrates one example of a cellular communications system 500 in which embodiments of the present disclosure may be implemented. In the embodiments described herein, the cellular communications system 500 is a 5G system (5GS) including a Next Generation RAN (NG-RAN) and a 5G Core (5GC) or an Evolved Packet System (EPS) including an Evolved Universal Terrestrial RAN (E-UTRAN) and an Evolved Packet Core (EPC). However, the cellular communications system 500 is not limited thereto. For example, the cellular communications system 510 may be a 6Gsystem or some other future generation of a 3GPP system. In this example, the RAN includes base stations 502-1 and 502-2, which in the 5GS include NR base stations (gNBs) and optionally next generation eNBs (ng-eNBs) (e.g., LTE RAN nodes connected to the 5GC) and in the EPS include eNBs, controlling corresponding (macro) cells 504-1 and 504-2. The base stations 502-1 and 502-2 are generally referred to herein collectively as base stations 502 and individually as base station 502. Likewise, the (macro) cells 504-1 and 504-2 are generally referred to herein collectively as (macro) cells 504 and individually as (macro) cell 504. The RAN may also include a number of low power nodes 506-1 through 506-4 controlling corresponding small cells 508-1 through 508-4. The low power nodes 506-1 through 506-4 can be small base stations (such as pico or femto base stations) or RRHs, or the like. Notably, while not illustrated, one or more of the small cells 508-1 through 508-4 may alternatively be provided by the base stations 502. The low power nodes 506-1 through 506-4 are generally referred to herein collectively as low power nodes 506 and individually as low power node 506. Likewise, the small cells 508-1 through 508-4 are generally referred to herein collectively as small cells 508 and individually as small cell 508. The cellular communications system 500 also includes a core network 510, which in the 5G System (5GS) is referred to as the 5GC. The base stations 502 (and optionally the low power nodes 506) are connected to the core network 510.

[0068] The base stations 502 and the low power nodes 506 provide service to wireless communication devices 512-1 through 512-5 in the corresponding cells 504 and 508. The wireless communication devices 512-1 through 512-5 are generally referred to herein collectively as wireless communication devices 512 and individually as wireless communication device 512. In the following description, the wireless communication devices 512 are oftentimes UEs, but the present disclosure is not limited thereto.

[0069] In one example embodiment, the procedure of Figure 1 and 2 may be performed by a base station 502 for downlink transmission to a wireless communication device 512.

[0070] Figure 6 is a schematic block diagram of a RAN node 600 according to some embodiments of the present disclosure. Optional features are represented by dashed boxes. The RAN node 600 may be, for example, a base station 502 or 506 or a network node that implements all or part of the functionality of the base station 502 or gNB described herein. As illustrated, the RAN node 600 includes a control system 602 thatincludes one or more processors 604 (e.g., Central Processing Units (CPUs), Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs), and / or the like), memory 606, and a network interface 608. The one or more processors 604 are also referred to herein as processing circuitry. In addition, the RAN node 600 may include one or more radio units 610 that each includes one or more transmitters 612 and one or more receivers 614 coupled to one or more antennas 616. The radio units 610 may be referred to or be part of radio interface circuitry. In some embodiments, the radio unit(s) 610 is external to the control system 602 and connected to the control system 602 via, e.g., a wired connection (e.g., an optical cable). However, in some other embodiments, the radio unit(s) 610 and potentially the antenna(s) 616 are integrated together with the control system 602. The one or more processors 604 operate to provide one or more functions of a RAN node 600 as described herein (e.g., one or more functions of a RAN node as described above with respect to Figures 1 and 2). In some embodiments, the function(s) are implemented in software that is stored, e.g., in the memory 606 and executed by the one or more processors 604.

[0071] Figure 7 is a schematic block diagram that illustrates a virtualized embodiment of the RAN node 600 according to some embodiments of the present disclosure. This discussion is equally applicable to other types of network nodes. Further, other types of network nodes may have similar virtualized architectures. Again, optional features are represented by dashed boxes.

[0072] As used herein, a “virtualized” RAN node is an implementation of the RAN node 600 in which at least a portion of the functionality of the RAN node 600 is implemented as a virtual component(s) (e.g., via a virtual machine(s) executing on a physical processing node(s) in a network(s)). As illustrated, in this example, the RAN node 600 may include the control system 602 and / or the one or more radio units 610, as described above. The control system 602 may be connected to the radio unit(s) 610 via, for example, an optical cable or the like. The RAN node 600 includes one or more processing nodes 700 coupled to or included as part of a network(s) 702. If present, the control system 602 or the radio unit(s) are connected to the processing node(s) 700 via the network 702. Each processing node 700 includes one or more processors 704 (e.g., CPUs, ASICs, FPGAs, and / or the like), memory 706, and a network interface 708.

[0073] In this example, functions 710 of the RAN node 600 described herein (e.g., one or more functions of a RAN node as described above with respect to Figures 1 and2) are implemented at the one or more processing nodes 700 or distributed across the one or more processing nodes 700 and the control system 602 and / or the radio unit(s) 610 in any desired manner. In some particular embodiments, some or all of the functions 710 of the RAN node 600 described herein are implemented as virtual components executed by one or more virtual machines implemented in a virtual environment(s) hosted by the processing node(s) 700. As will be appreciated by one of ordinary skill in the art, additional signaling or communication between the processing node(s) 700 and the control system 602 is used in order to carry out at least some of the desired functions 710. Notably, in some embodiments, the control system 602 may not be included, in which case the radio unit(s) 610 communicate directly with the processing node(s) 700 via an appropriate network interface(s).

[0074] In some embodiments, a computer program including instructions which, when executed by at least one processor, causes the at least one processor to carry out the functionality of RAN node 600 or a node (e.g., a processing node 700) implementing one or more of the functions 710 of the RAN node 600 in a virtual environment according to any of the embodiments described herein is provided. In some embodiments, a carrier comprising the aforementioned computer program product is provided. The carrier is one of an electronic signal, an optical signal, a radio signal, or a computer readable storage medium (e.g., a non-transitory computer readable medium such as memory).

[0075] Figure 8 is a schematic block diagram of the RAN node 600 according to some other embodiments of the present disclosure. The RAN node 600 includes one or more modules 800, each of which is implemented in software. The module(s) 800 provide the functionality of the RAN node 600 described herein. This discussion is equally applicable to the processing node 700 of Figure 7 where the modules 800 may be implemented at one of the processing nodes 700 or distributed across multiple processing nodes 700 and / or distributed across the processing node(s) 700 and the control system 602.

[0076] Any appropriate steps, methods, features, functions, or benefits disclosed herein may be performed through one or more functional units or modules of one or more virtual apparatuses. Each virtual apparatus may comprise a number of these functional units. These functional units may be implemented via processing circuitry, which may include one or more microprocessor or microcontrollers, as well as otherdigital hardware, which may include Digital Signal Processors (DSPs), special-purpose digital logic, and the like. The processing circuitry may be configured to execute program code stored in memory, which may include one or several types of memory such as Read Only Memory (ROM), Random Access Memory (RAM), cache memory, flash memory devices, optical storage devices, etc. Program code stored in memory includes program instructions for executing one or more telecommunications and / or data communications protocols as well as instructions for carrying out one or more of the techniques described herein. In some implementations, the processing circuitry may be used to cause the respective functional unit to perform corresponding functions according to one or more embodiments of the present disclosure.

[0077] While processes in the figures may show a particular order of operations performed by certain embodiments of the present disclosure, it should be understood that such order is exemplary (e.g., alternative embodiments may perform the operations in a different order, combine certain operations, overlap certain operations, etc.).

[0078] Those skilled in the art will recognize improvements and modifications to the embodiments of the present disclosure. All such improvements and modifications are considered within the scope of the concepts disclosed herein.

Claims

Claims 1. A method performed by a network node for a radio access network, RAN, of a cellular communications system, the method comprising: • obtaining (102) a plurality of baseline beams for downlink transmission to a particular User Equipment, UE, wherein the plurality of baseline beams comprises: o a first set of baseline beams for a vertical dimension for at least two antenna polarizations, a plurality of subcarriers, and one or more Multiple Input Multiple Output, MIMO, layers; o a second set of baseline beams for a horizontal dimension for the at least two antenna polarizations, the plurality of subcarriers, and the one or more MIMO layers; • generating (104) a precoding matrix comprising beamforming weights for downlink transmission to the particular UE, based on the first set of baseline beams for the vertical dimension and the second set of baseline beams for the horizontal dimension such that a directional perturbation is introduced into the beamforming weights for the plurality of subcarriers.

2. The method of claim 1, wherein the directional perturbation is applied on both the vertical dimension and the horizontal dimension.

3. The method of claim 1, wherein the directional perturbation is applied on the vertical dimension but not the horizontal dimension.

4. The method of claim 1, wherein the directional perturbation is applied on the horizontal dimension but not the vertical dimension.

5. The method of claim 1, wherein the first and second sets of baseline beams are first and second sets of Discrete Fourier Transform, DFT, beams.

6. The method of claim 5, wherein generating (104) the precoding matrix comprises:• for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers, generating (200) a beam weight vector (^^^,^,^ ∈ ℂ^×^^) for the vertical dimension defined as:^ = ^ ^^^^^^,^,^^^^^^^^^ !,^,^,^" ^^^^^^,^,^^^^^^^^^ !,^,^,^"%^^&^'1 ^ #^^^ … ^ #^^^ (o^o *^is a Discrete Fourier Transform, DFT, beam oversampling ratio for the vertical dimension; o+,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thefirst set of baseline beams, for polarization ^, subcarrier ^, and MIMO layer ^; and oΔ45.6789:,,,-,. ∈ ℝ is a randomly generated vertical beam perturbation for^, subcarrier ^, and MIMO layer ^ which can assume both positiveand negative values; and • for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers, generating (202) a beam weight vector (<:,,,-,. ∈ ℂ^^^=×^) for the horizontal dimension defined as:\^]a!^,^ eb c \^]a! eb c%` Q='D< ,^ ?@^^A@B^ !,^,^,^ ^,^,^ ?@^^A@B^ !,^,^,^ =: ^ _=`= ^^ ^ _=`=o )^is a number of ports for the horizontal dimension; o is a DFT beam oversampling ratio for the horizontal dimension; o,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thebeams, identified for polarization ^, subcarrier ^, and MIMO layer ^; oΔFG.7HGI69:,,,-,. ∈ ℝ is a randomly generated horizontal beam perturbation for^, and MIMO layer ^ which can assume both positive and negative values; and o%∙'Dis the vector transpose operator; • generating (204) the precoding matrix per subcarrier ^ as:<K = > :L,^,L … <L O :L,^,PQ=- M-,N<:=,^, … O M-,R&^<:=,^,PQ=Cwhere:o for the subcarrier ^; and oM ^^^T-,. = ^ ^,^ is a polarization co-phasing term representing a U-,. phaseoffset for subcarrier ^ and MIMO layer ^.

7. The method of claim 5, wherein generating (104) the precoding matrix comprises: • for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers, generating (200) a beam weight vector (^^^,^,^ ∈ ℂ^×^^) for the vertical dimension defined as:^^^,^,^ = ^X^^,^,^ ⊙ [ ∆[[^[,,-,.where:\^]^^^,^ " \^]^^ "%` Q='o ^X^^,^,^ = ^ ,^ ^,^,^ ^1 ^ _^`^ … ^ _^`^ ( ∈ ℂ^×^^ corresponds to adimension without any perturbation for polarization ^, subcarrier ^ and MIMO layer ^; and \^]ab^^^^^ c \^]ab c%`^Q='o [ ∆[[^[,,-,. = ^ ^ !,^,^,^ ^^^^^^ !,^,^,^1 ^ _^`^ … ^ _^`^ ( ∈ ℂ^×^^ denotes afor polarization ^, subcarrier ^ and MIMO layer ^; o ⊙ denotes elementwise multiplication (i.e., Hadamard product); o )^is a number of ports for the vertical dimension; o *^is a Discrete Fourier Transform, DFT, beam oversampling ratio for the vertical dimension; o+,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thefirst set of baseline beams, for polarization ^, subcarrier ^, and MIMO layer ^; oΔ45.6789:,,,-,. ∈ ℝ is a randomly generated vertical beam perturbation forpolarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values; and • for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^of the one or more MIMO layers, generating (202) a beam weight vector (<:,,,-,. ∈ ℂ^^^=×^) for the horizontal dimension defined as:<:^,^,^ = <X:^,^,^ ⊙ [ ∆[[<[,,-,.where: \^]^!^,^,^" \^]^!^,^,^"%`=Q=' Do <X = > _ ` ∈ ℂ^^^=×^:^,^,^ ^^^,^,^ ^ = = ^^^,^,^ … ^ _=`= ^^^,^,^Cand MIMO layer ^; \^]ab?@^^A c \^]ab c%`=Q=' Do [ ∆[[<[ @B^ !,^,^,^ ?@^^A@B^ !,^,^,^ ^^^=×^,,-,. = ^d ^ _=`= d … ^ _=`= d( ∈ ℂdimension for polarization ^, subcarrier ^ and MIMO layer ^; od ∈ ℝ^×^^ corresponds to the all-ones vector; ando ⊙ denotes elementwise multiplication (i.e., Hadamard product); o )^is a number of ports for the horizontal dimension; o *^is a DFT beam oversampling ratio for the horizontal dimension; oE,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thesecond set of baseline beams, identified for polarization ^, subcarrier ^, and MIMO layer ^; oΔFG.7HGI69:,,,-,. ∈ ℝ is a randomly generated horizontal beam perturbation forpolarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values; and o %∙'Dis the vector transpose operator; • generating (204) the precoding matrix per subcarrier ^ as: <K :L,^,L … <:L,^,PQ=- = > O O Cwhere:o S is a maximum number of MIMO layers for the subcarrier ^; and oM-,. = ^^^^T^,^ is a polarization co-phasing term representing a U-,. phaseoffset for subcarrier ^ and MIMO layer ^.

8. The method of claim 6 or 7, wherein VΔ45.6789:,,,-,.V < 1, and VΔFG.7HGI9:,,,-,.V < 1.

9. The method of claim 5, wherein generating (104) the precoding matrix comprises: • for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers, generating (200) a beam weight vector (^^^,^,^ ∈ ℂ^×^^) for the vertical dimension defined as:^ ^^^^^^,^,^^^^^^^^^ !,^,^,^" ^^^^^^,^,^^^^^^^^^ !,^,^ "%^^&^',^ = ^ ,^^^,^ 1 ^ #^^^ … ^ #^^^ (o a o *^is a Discrete Fourier Transform, DFT, beam oversampling ratio for the vertical dimension; o+,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thefirst set of baseline beams, for polarization ^, subcarrier ^, and MIMO layer ^; oΔ45.6789:,,,-,. ∈ ℝ is a randomly generated vertical beam perturbation forpolarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values; and • for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers, generating (202) a beam weight vector (< ^:,,,-,. ∈ ℂ ^^=×^) for the horizontal dimension defined as:^^^:^,^,^ ^^^:^,^ %^ &^'D <= > ,^ =^ ^ #=^= ^ ^ #=^ Cwhere:o )^is a number of ports for the horizontal dimension; o^is a DFT beam oversampling ratio for the horizontal dimension; oE,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thesecond set of baseline beams, identified for polarization ^, subcarrier ^, and MIMO layer ^; and o %∙'Dis the vector transpose operator. • generating (204) the precoding matrix per subcarrier ^ as:<K = > :L,^,L … <L O :L,^,PQ=- M-,N<:=,^, … O M-,R&^<:=,^,PQ=Cwhere:o for the subcarrier ^; and oM ^^^T-,. = ^ ^,^ is a polarization co-phasing term representing a U-,. phaseoffset for subcarrier ^ and MIMO layer ^.

10. The method of claim 5, wherein generating (104) the precoding matrix comprises: • for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers, generating (200) a beam weight vector (^^^,^,^ ∈ ℂ^×^^) for the vertical dimension defined as:^^^,^,^ = ^X^^,^,^ ⊙ [ ∆[[^[,,-,.where:\^]^^^,^ " \^]^^ "%` Q='o ^X^^,^,^ = ^ ,^ ^,^,^ ^1 ^ _^`^ … ^ _^`^ ( ∈ ℂ^×^^ corresponds to adimension without any perturbation for polarization ^, subcarrier ^ and MIMO layer ^; and \^]ab^^^^^ c \^]ab c%`^Q='o [ ∆[[^[,,-,. = ^ ^ !,^,^,^ ^^^^^^ !,^,^,^1 ^ _^`^ … ^ _^`^ ( ∈ ℂ^×^^ denotes afor polarization ^, subcarrier ^ and MIMO layer ^; o ⊙ denotes elementwise multiplication (i.e., Hadamard product); o )^is a number of ports for the vertical dimension; o *^is a Discrete Fourier Transform, DFT, beam oversampling ratio for the vertical dimension; o+,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thefirst set of baseline beams, for polarization ^, subcarrier ^, and MIMO layer ^; oΔ45.6789:,,,-,. ∈ ℝ is a randomly generated vertical beam perturbation forpolarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values; and • for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^of the one or more MIMO layers, generating (202) a beam weight vector (<:,,,-,. ∈ ℂ^^^=×^) for the horizontal dimension defined as:<:^,^,^ = <X:^,^,^where:\^]^!^,^,^"%`=Q=' Do <X = > ^^^=×^:^,^,^ ^^ _^,^,^ ^ =`= ^^ _^,^,^ … ^ =`= ^^^,^,^C ∈ ℂand MIMO layer ^; od ∈ ℝ^×^^ corresponds to the all-ones vector; ando )^is a number of ports for the horizontal dimension; o *^is a DFT beam oversampling ratio for the horizontal dimension; oE,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thesecond set of baseline beams, identified for polarization ^, subcarrier ^, and MIMO layer ^; and o %∙'Dis the vector transpose operator; • generating (204) the precoding matrix per subcarrier ^ as: <K = > :L,^,L … <:L,^,PQ=- M- O … O M-where:o S is a maximum number of MIMO layers for the subcarrier ^; and oM-,. = ^^^^T^,^ is a polarization co-phasing term representing a U-,. phaseoffset for subcarrier ^ and MIMO layer ^.

11. The method of claim 9 or 10, wherein VΔ45.6789:,,,-,.V < 1.

12. The method of claim 5, wherein generating (104) the precoding matrix comprises: • for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers, generating (200) a beam weight vector (^ ^×^^ ^^,^,^ ∈ ℂ ) for the vertical dimension defined as:^ = ^ ^^^^^,^,^ ^^^^^,^,^%^^&^'^ ^ (where: o )^is a number of ports for the vertical dimension; o *^is a Discrete Fourier Transform, DFT, beam oversampling ratio for the vertical dimension; and o+,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thefirst set of baseline beams, for polarization ^, subcarrier ^, and MIMO layer ^; • for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers, generating (202) a beam weight vector (<:,,,-,. ∈ ℂ^^^=×^) for the horizontal dimension defined as:^^^^:^,^,^^^? " ^^^^:^,^,^^^ "%^=&^'D< @^^A@B^ !,^,^,^ ?@^^A@B^ !,^,^,^:^,^,^ = ^ #=^= … ^ #=^=o )^is a number of ports for the horizontal dimension; o is a DFT beam oversampling ratio for the horizontal dimension; oE,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thesecond set of baseline beams, identified for polarization ^, subcarrier ^, and MIMO layer ^; oΔFG.7HGI69:,,,-,. ∈ ℝ is a randomly generated horizontal beam perturbation forpolarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values; and o %∙'Dis the vector transpose operator. • generating (204) the precoding matrix per subcarrier ^ as: <K = > :L,^,L … <O :L,^,PQ=- … Owhere:o S is a maximum number of MIMO layers for the subcarrier ^; and oM ^^^T-,. = ^ ^,^ is a polarization co-phasing term representing a U-,. phaseoffset for subcarrier ^ and MIMO layer ^.

13. The method of claim 5, wherein generating (104) the precoding matrix comprises:• for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers, generating (200) a beam weight vector (^^^,^,^ ∈ ℂ^×^^) for the vertical dimension defined as:^^^,^,^ = ^X^^,^,^where: \^]^^^,^,^" \^]^^^,^ "%` Q='o ^X^^,^,^ = ^ ,^ ^ ^×^^1 ^ _^`^ … ^ _^`^ ( ∈ ℂ corresponds to adimension without anylayer ^; and o )^is a number of ports for the vertical dimension; o *^is a Discrete Fourier Transform, DFT, beam oversampling ratio for the vertical dimension; and o+,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thefirst set of baseline beams, for polarization ^, subcarrier ^, and MIMO layer ^; • for each antenna polarization ^ from among the at least two antenna polarizations for each subcarrier ^ of the plurality of subcarriers for each layer ^ of the one or more MIMO layers, generating (202) a beam weight vector (<:,,,-,. ∈ ℂ^^^=×^) for the horizontal dimension defined as:<:^,^,^ = <X:^,^,^ ⊙ [ ∆[[<[,,-,.where:\^]^!^,^,^" \^]^!^,^,^"%`=Q=' Do <X = >^ ^ _=`= ^ ^ _=` C ∈ ℂ^^^=×^^ ^ ^dimension without any perturbation for polarization ^, subcarrier ^ and MIMO layer ^; \^]ab?@^^A@B^ c \^]ab c%`=Q=' Do [ ∆[[<[ = ^ !,^,^,^ ?@^^A@B^ !,^,^,^ ^^^=×^` ∈ ℂdimension for polarization ^, subcarrier ^ and MIMO layer ^; od ∈ ℝ^×^^ corresponds to the all-ones vector; ando ⊙ denotes elementwise multiplication (i.e., Hadamard product); o )^is a number of ports for the horizontal dimension; o *^is a DFT beam oversampling ratio for the horizontal dimension;o E,,-,. ∈ / 0, … , *^)^ − 12 is an index of the baseline beam, from among thesecond set of baseline beams, identified for polarization ^, subcarrier ^, and^; oΔFG.7HGI69:,,,-,. ∈ ℝ is a randomly generated horizontal beam perturbation forpolarization ^, subcarrier ^, and MIMO layer ^ which can assume both positive and negative values; and o %∙'Dis the vector transpose operator; • generating (204) the precoding matrix per subcarrier ^ as: <K = > :L,^,L … <-,N :=,^,L O :L,^,PQ=- M < … O M-,R&^<:=,^,PQ=Cwhere:o S is a maximum number of MIMO layers for the subcarrier ^; and oM-,. = ^^^^T^,^ is a polarization co-phasing term representing a U-,. phaseoffset for subcarrier ^ and MIMO layer ^.

14. The method of claim 12 or 13, wherein VΔFG.7HGI9:,,,-,.V < 1.

15. The method of any of claims 1 to 14, further comprising introducing (106) attenuated complex random noise into the beamforming weights comprised in the precoding matrix.

16. The method of any of claims 1 to 15, further comprising performing (110) a re- orthogonalization procedure on the precoding matrix, thereby providing a modified precoding matrix.

17. The method of claim 16, further comprising scaling (112) the modified precoding matrix, thereby providing a scaled precoding matrix.

18. The method of claim 17, further comprising applying (114) the scaled precoding matrix for downlink transmission of a signal to the UE.

19. A network node for a radio access network, RAN, of a cellular communications system, the network node adapted to:• obtain (102) a plurality of baseline beams for downlink transmission to a particular User Equipment, UE, wherein the plurality of baseline beams comprises: o a first set of baseline beams for a vertical dimension for at least two antenna polarizations, a plurality of subcarriers, and one or more Multiple Input Multiple Output, MIMO, layers; o a second set of baseline beams for a horizontal dimension for the at least two antenna polarizations, the plurality of subcarriers, and the one or more MIMO layers; • generate (104) a precoding matrix comprising beamforming weights for downlink transmission to the particular UE, based on the first set of baseline beams for the vertical dimension and the second set of baseline beams for the horizontal dimension such that a directional perturbation is introduced into the beamforming weights for the plurality of subcarriers.

20. The network node of claim 19, further adapted to perform the method of any of claims 2 to 18.

21. A network node for a radio access network, RAN, of a cellular communications system, the network node comprising: • one or more radio units comprising one or more transmitters; and • processing circuitry associated with the one or more radio units, the processing circuitry configured to cause the network node to: o obtain (102) a plurality of baseline beams for downlink transmission to a particular User Equipment, UE, wherein the plurality of baseline beams comprises: ^ a first set of baseline beams for a vertical dimension for at least two antenna polarizations, a plurality of subcarriers, and one or more Multiple Input Multiple Output, MIMO, layers; ^ a second set of baseline beams for a horizontal dimension for the at least two antenna polarizations, the plurality of subcarriers, and the one or more MIMO layers;o generate (104) a precoding matrix comprising beamforming weights for downlink transmission to the particular UE, based on the first set of baseline beams for the vertical dimension and the second set of baseline beams for the horizontal dimension such that a directional perturbation is introduced into the beamforming weights for the plurality of subcarriers.

22. The network node of claim 21, wherein the processing circuitry is further configured to cause the network node to perform the method of any of claims 2 to 18.

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