Method and apparatus for uplink MIMO

Abstract

A terminal device (UE) performs a first uplink transmission of a transmission layer through M transmit antenna ports based on a first transmit precoding vector. The terminal device receives, from a ne

Description

Technical Field of the Invention The present invention relates to uplink transmit precoding for Multiple Inputs Multiple Outputs (MIMO) radio communications. Technical Background of the Invention MIMO plays an important role in recent mobile and wireless communication technologies, yielding an increase of the spectral efficiency and multiplexing capability of wireless and mobile communication networks . It is an object of the present disclosure to propose an enhanced scheme for uplink MIMO. Summary of the Invention In accordance with a first example aspect, a first apparatus, for instance a terminal device (e.g., a UE), is disclosed as comprising at least one processor, and at least one memory storing processor instructions that, when executed by the at least one processor, cause the apparatus at least to receive, from a network device, first transmit precoding information indicative of a reference phase shift increment 0ref; receive, from the network device, second transmit precoding information indicative of a transmit precoding vector index for a transmission layer; derive a transmit precoding vector for the transmission layer from the reference phase shift increment 0ref and the transmit precoding vector index; and perform an uplink transmission of the transmission layer through M transmit antenna ports of the apparatus at least based on the transmit precoding vector. In accordance with a second example aspect, a first apparatus, for instance a terminal device (e.g., a UE), is disclosed as comprising means for receiving, from a network device, first transmit precoding information indicative of a reference phase shift increment 0ref; means for receiving, from the network device, second transmit precoding information indicative of a transmit precoding vector index for a transmission layer; means for deriving a transmit precoding vector for the transmission layer from the reference phase shift increment 0ref and the transmit precoding vector index; and means for performing an uplink transmission of the transmission layer through M transmit antenna ports of the apparatus at least based on the transmit precoding vector. In accordance with a third example aspect, a first method is disclosed as comprising, by a terminal device, receiving, from a network device, first transmit precoding information indicative of a reference phase shift increment 0ref; receiving, from the network device, second transmit precoding information indicative of a transmit precoding vector index for a transmission layer; deriving a transmit precoding vector for the transmission layer from the reference phase shift increment 0rer and the transmit precoding vector index; and performing an uplink transmission of the transmission layer through M transmit antenna ports of the terminal device at least based on the transmit precoding vector. In accordance with a fourth example aspect, a first computer program or a first computer readable medium is disclosed as comprising instructions which, when executed by an apparatus, for instance a terminal device (e.g., a UE), cause the apparatus to perform and / or control the actions of the first method according to the third example aspect. In accordance with a fifth example aspect, a second apparatus, for instance a network device (e.g., a base station), is disclosed as comprising at least one processor, and at least one memory storing processor instructions that, when executed by the at least one processor, cause the apparatus at least to transmit, to a terminal device, first transmit precoding information indicative of a reference phase shift increment 0ref; transmit, to the terminal device, second transmit precoding information indicative of a transmit precoding vector index for a transmission layer; and receive an uplink transmission of the transmission layer performed by the terminal device through M transmit antenna ports of the terminal device at least based on a transmit precoding vector derived from the reference phase shift increment 0ref and the transmit precoding vector index. In accordance with a sixth example aspect, a second apparatus, for instance a network device (e.g., a base station), is disclosed as comprising means for transmitting, to a terminal device, first transmit precoding information indicative of a reference phase shift increment 0ref; means for transmitting, to the terminal device, second transmit precoding information indicative of a transmit precoding vector index for a transmission layer; and means for receiving an uplink transmission of the transmission layer performed by the terminal device through M transmit antenna ports of the terminal device at least based on a transmit precoding vector derived from the reference phase shift increment 0rej and the transmit precoding vector index. In accordance with a seventh example aspect, a second method is disclosed as comprising, by a network device, transmitting, to a terminal device, first transmit precoding information indicative of a reference phase shift increment 0rer; transmitting, to the terminal device, second transmit precoding information indicative of a transmit precoding vector index for a transmission layer; and receiving an uplink transmission of the transmission layer performed by the terminal device through M transmit antenna ports of the terminal device at least based on a transmit precoding vector derived from the reference phase shift increment 0ref and the transmit precoding vector index. In accordance with an eight example aspect, a second computer program or a second computer readable medium is disclosed as comprising instructions which, when executed by an apparatus, for instance a network device (e.g., a base station), cause the apparatus to perform and / or control the actions of the second method according to the seventh example aspect. In one embodiment, the first apparatus is further caused to (or further comprises means for) transmit, to the network device, first capability information indicative of a capability of the apparatus to support transmit precoding with enhanced phase-resolution. Likewise, the second apparatus is further caused to (or further comprises means for) receive, from the terminal device, first capability information indicative of a capability of the apparatus to support transmit precoding with enhanced phase-resolution. Likewise, the first method further comprises transmitting, to the network device, first capability information indicative of a capability of the apparatus to support transmit precoding with enhanced phase-resolution. Likewise, the second method further comprises receiving, from the terminal device, first capability information indicative of a capability of the apparatus to support transmit precoding with enhanced phase-resolution. In one embodiment, the first apparatus is further caused to (or further comprises means for) transmit, to the network device, second capability information indicative of a minimum phase shift increment 0min supported by the apparatus for transmit signal precoding. The reference phase shift increment 0ref is at least based on the minimum phase shift increment 0mm. Likewise, the second apparatus is further caused to (or further comprises means for) receive, from the terminal device, second capability information indicative of a minimum phase shift increment 0min supported by the terminal device for transmit signal precoding, and determine the reference phase shift increment 0ret at least based on the minimum phase shift increment 0min- Likewise, the first method further comprises transmitting, to the network device, second capability information indicative of a minimum phase shift increment 0min supported by the apparatus for transmit signal precoding. The reference phase shift increment 0ref is at least based on the minimum phase shift increment 0min. Likewise, the second method further comprises receiving, from the terminal device, second capability information indicative of a minimum phase shift increment 0min supported by the terminal device for transmit signal precoding, and determining the reference phase shift increment 0ref at least based on the minimum phase shift increment 0min- In one embodiment, the reference phase shift increment 0ref is equal (or is determined as being equal) to an integer multiple of the minimum phase shift increment 0min. In one embodiment, wherein the reference phase shift increment 0ref is given by Qref = 2n / N, with N denoting an integer greater than 1. The transmit precoding vector comprises M transmit precoding coefficients associated with the M respective transmit antenna ports, and given by bme^am9ref, with am denoting an integer and bm e {0, 1}, and with me {0, ..., M-l} denoting a transmit antenna port index. In one embodiment, the second transmit precoding information comprises \LogMN + 1)M)1 bits . In one embodiment, the transmit precoding vector is derived by means of a codebook analytical formula having the reference phase shift increment 0ref and the transmit precoding vector index as input variables . In one embodiment, aIfl and bm are given by am = mod + 1) and bm = 1 — 5(am) , with i denoting the transmit precoding vector index, and with 8() and mod () denoting the discrete Kronecker delta and modulo functions respectively. In one embodiment, the second transmit precoding information is received and transmitted as part of Downlink Control Information, DCI, or a Medium Access Control Control Element, MAC CE, scheduling the uplink transmission. In one embodiment, the first transmit precoding information is received and transmitted as part of Downlink Control Information, DCI, or a Medium Access Control Control Element, MAC CE, scheduling the uplink transmission, or as part of Radio Resource Control, RRC, signaling. In one embodiment, the second apparatus is further caused to (or further comprises means for) determine or adjust the reference phase shift increment 0ref based on channel measurement information. Likewise, the second method further comprises determining or adjusting the reference phase shift increment 0ref based on channel measurement information In one embodiment, the second transmit precoding information is indicative of two or more transmit precoding vector indexes for two or more respective transmission layers. The second apparatus is further caused to (or further comprises means for) determine the two or more transmit precoding vector indexes so as two or more corresponding transmit precoding vectors for the two or more transmission layers are linearly independent or are mutually orthogonal. Likewise, the second method further comprises determining the two or more transmit precoding vector indexes so as two or more corresponding transmit precoding vectors for the two or more transmission layers are linearly independent or are mutually orthogonal. In accordance with a ninth example aspect, a third apparatus, for instance a terminal device (e.g., a UE), is disclosed as comprising at least one processor, and at least one memory storing processor instructions that, when executed by the at least one processor, cause the apparatus at least to perform a first uplink transmission of a transmission layer through M transmit antenna ports of the apparatus at least based on a first transmit precoding vector; receive, from a network device, first transmit preceding information indicative of a reference phase shift increment 0ref; and receive, from the network device, second transmit precoding information indicative of one or more phase shifts for the transmission layer associated with one or more respective transmit antenna ports of the apparatus out of the M transmit antenna ports. The one or more phase shifts are integer multiples of the reference phase shift increment 0rer • The apparatus is further caused to determine a second transmit precoding vector by applying the one or more phase shifts to one or more respective transmit precoding coefficients of the first transmit precoding vector associated with the one or more respective transmit antenna ports; and perform a second uplink transmission of the transmission layer through the M transmit antenna ports at least based on the second transmit precoding vector. In accordance with a tenth example aspect, a third apparatus, for instance a terminal device (e.g., a UE), is disclosed as comprising means for performing a first uplink transmission of a transmission layer through M transmit antenna ports of the apparatus at least based on a first transmit precoding vector; means for receiving, from a network device, first transmit precoding information indicative of a reference phase shift increment 0ref; and means for receiving, from the network device, second transmit precoding information indicative of one or more phase shifts for the transmission layer associated with one or more respective transmit antenna ports of the apparatus out of the M transmit antenna ports. The one or more phase shifts are integer multiples of the reference phase shift increment 0ref • The apparatus further comprises means for determining a second transmit precoding vector by applying the one or more phase shifts to one or more respective transmit precoding coefficients of the first transmit precoding vector associated with the one or more respective transmit antenna ports; and means for performing a second uplink transmission of the transmission layer through the M transmit antenna ports at least based on the second transmit precoding vector . In accordance with an eleventh example aspect, a third method is disclosed as comprising, by a terminal device, performing a first uplink transmission of a transmission layer through M transmit antenna ports of the terminal device at least based on a first transmit precoding vector; receiving, from a network device, first transmit precoding information indicative of a reference phase shift increment 0ref; and receiving, from the network device, second transmit precoding information indicative of one or more phase shifts for the transmission layer associated with one or more respective transmit antenna ports of the terminal device out of the M transmit antenna ports. The one or more phase shifts are integer multiples of the reference phase shift increment 0ref. The method further comprises determining a second transmit precoding vector by applying the one or more phase shifts to one or more respective transmit precoding coefficients of the first transmit precoding vector associated with the one or more respective transmit antenna ports; and performing a second uplink transmission of the transmission layer through the M transmit antenna ports at least based on the second transmit precoding vector. In accordance with a twelves example aspect, a third computer program or a third computer readable medium is disclosed as comprising instructions which, when executed by an apparatus, for instance a terminal device (e.g., a UE), cause the apparatus to perform and / or control the actions of the third method according to the eleventh example aspect. In accordance with a thirteenth example aspect, a fourth apparatus, for instance a network device (e.g., a base station), is disclosed as comprising at least one processor, and at least one memory storing processor instructions that, when executed by the at least one processor, cause the apparatus at least to receive a first uplink transmission of a transmission layer performed by a terminal device through M transmit antenna ports of the terminal device at least based on a first transmit precoding vector; transmit, to the terminal device, first transmit precoding information indicative of a reference phase shift increment 0ref; and transmit, to the terminal device, second transmit precoding information indicative of one or more phase shifts for the transmission layer associated with one or more respective transmit antenna ports of the terminal device out of the M transmit antenna ports. The one or more phase shifts are integer multiples of the reference phase shift increment 0ret. The apparatus is further caused to receive a second uplink transmission of the transmission layer performed by the terminal device through the M transmit antenna ports at least based on a second transmit precoding vector determined by applying the one or more phase shifts to one or more respective transmit precoding coefficients of the first transmit precoding vector associated with the one or more respective transmit antenna ports. In accordance with a fourteenth example aspect, a fourth apparatus, for instance a network device (e.g., a base station), is disclosed as comprising means for receiving a first uplink transmission of a transmission layer performed by a terminal device through M transmit antenna ports of the terminal device at least based on a first transmit precoding vector; means for transmitting, to the terminal device, first transmit precoding information indicative of a reference phase shift increment 0ref; and means for transmitting, to the terminal device, second transmit precoding information indicative of one or more phase shifts for the transmission layer associated with one or more respective transmit antenna ports of the terminal device out of the M transmit antenna ports. The one or more phase shifts are integer multiples of the reference phase shift increment 0ref • The apparatus further comprises means for receiving a second uplink transmission of the transmission layer performed by the terminal device through the M transmit antenna ports at least based on a second transmit precoding vector determined by applying the one or more phase shifts to one or more respective transmit precoding coefficients of the first transmit precoding vector associated with the one or more respective transmit antenna ports. In accordance with a fifteenth example aspect, a fourth method is disclosed as comprising, by a network device, receiving a first uplink transmission of a transmission layer performed by a terminal device through M transmit antenna ports of the terminal device at least based on a first transmit precoding vector; transmitting, to the terminal device, first transmit precoding information indicative of a reference phase shift increment 0rer; and transmitting, to the terminal device, second transmit precoding information indicative of one or more phase shifts for the transmission layer associated with one or more respective transmit antenna ports of the terminal device out of the M transmit antenna ports. The one or more phase shifts are integer multiples of the reference phase shift increment 0ref- The method further comprises receiving a second uplink transmission of the transmission layer performed by the terminal device through the M transmit antenna ports at least based on a second transmit precoding vector determined by applying the one or more phase shifts to one or more respective transmit precoding coefficients of the first transmit precoding vector associated with the one or more respective transmit antenna ports. In accordance with a sixteenth example aspect, a fourth computer program or a fourth computer readable medium is disclosed as comprising instructions which, when executed by an apparatus, for instance a network device (e.g., a base station), cause the apparatus to perform and / or control the actions of the fourth method according to the fifteenth example aspect. In one embodiment, the third apparatus is further caused to (or further comprises means for) transmit, to the network device, first capability information indicative of a capability of the apparatus to support differential transmit precoding with enhanced phase-resolution. Likewise, the fourth apparatus is further caused to (or further comprises means for) receive, from the terminal device, first capability information indicative of a capability of the apparatus to support differential transmit precoding with enhanced phase-resolution. Likewise, the third method further comprises transmitting, to the network device, first capability information indicative of a capability of the apparatus to support differential transmit precoding with enhanced phase-resolution. Likewise, the fourth method further comprises receiving, from the terminal device, first capability information indicative of a capability of the apparatus to support differential transmit precoding with enhanced phase-resolution. In one embodiment, the third apparatus is further caused to (or further comprises means for) transmit, to the network device, second capability information indicative of a minimum phase shift increment 0min supported by the apparatus for transmit signal precoding. The reference phase shift increment 0ref is at least based on the minimum phase shift increment 0min. Likewise, the fourth apparatus is further caused to (or further comprises means for) receive, from the terminal device, second capability information indicative of a minimum phase shift increment 0min supported by the terminal device for transmit signal precoding; and determine the reference phase shift increment 0ref at least based on the minimum phase shift increment 0min. Likewise, the third method further comprises transmitting, to the network device, second capability information indicative of a minimum phase shift increment 0min supported by the apparatus for transmit signal precoding. The reference phase shift increment 0ref is at least based on the minimum phase shift increment 0min. Likewise, the fourth method further comprises receiving, from the terminal device, second capability information indicative of a minimum phase shift increment 0min supported by the terminal device for transmit signal precoding; and determining the reference phase shift increment 0rer at least based on the minimum phase shift increment 0rnin • In one embodiment, the reference phase shift increment 0ref is given by 6ref = 2nlN, with N denoting an integer greater than 1. Applying the one or more phase shifts to the one or more respective transmit precoding coefficients comprises multiplying the one or more transmit precoding coefficients by e^amSref, with am denoting an integer, and with me {0, ..., M-l} denoting one or more transmit antenna port indexes of the one or more respective transmit antenna ports. In one embodiment, the second transmit precoding information comprises M phase shift values for the M respective transmit antenna ports . In one embodiment, the second transmit precoding information comprises a bitmap for indicating, among the M transmit antenna ports, M* transmit antenna ports associated with a non-null phase shift; and M* non-null phase shift values for the M* respective transmit antenna ports . In one embodiment, the second transmit precoding information is received as part of Downlink Control Information, DCI, or a Medium Access Control Control Element, MAC CE, scheduling the second uplink transmission. In one embodiment, the first transmit precoding information is received as part of Downlink Control Information, DCI, or a Medium Access Control Control Element, MAC CE, scheduling the second uplink transmission, or as part of Radio Resource Control, RRC, signaling. In one embodiment, the fourth apparatus is further caused to (or further comprises means for) determine or adjust the reference phase shift increment 0ref based on channel measurement information. Likewise, the fourth method further comprises determining or adjusting the reference phase shift increment 0ref based on channel measurement information. Examples of a terminal device are a mobile phone, a smartphone, a tablet, a smartwatch, a laptop, a Personal Digital Assistant (PDA) device, a wearable device, an Internet-of-Things (loT) device, an Industrial loT (IIoT) device, a terrestrial / aerial / maritime vehicle, a satellite, etc, which are generically referred to as a User Equipment (UE) or Mobile Station (MS). Examples of a network device are a Base Transceiver Station (BTS), a nodeB, an evolved node B (eNB), a Next Generation NodeB (gNB), a 6G NodeB, etc, which are generically referred to as a base station or a Radio Access Network (RAN) node. Another example of a network device is a Wireless Local Area Network (WLAN) access point. Detailed Description of the Invention Various example embodiments will now be described more fully with reference to the accompanying drawings wherein: - Fig. 1 represents an overview of a mobile network; - Fig. 2 represents an exemplary implementation for digital transmit precoding; - Fig. 3 represents an exemplary implementation for analog transmit precoding; - Fig. 4 represents a possible layout of antennas within a terminal device; - Fig. 5 and 6 represent message flow charts for enhanced uplink MIMO; - Fig. 7A, 7B and 7C represents performance plots for legacy vs enhanced uplink MIMO; - Fig. 8 to 11 represent flow charts for a method according to the third, seventh, eleventh and fifteenth example aspects respectively; and - Fig. 12 represents a functional representation of an apparatus according to the first, fifth, ninth or thirteenth example aspects. Accordingly, while example embodiments are capable of various modifications and alternative forms, embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that there is no intent to limit example embodiments to the particular forms disclosed, but on the contrary, example embodiments are to cover all modifications, equivalents, and alternatives falling within the scope of the claims. Like numbers refer to like elements throughout the description of the figures . It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of example embodiments. As used herein, the term "and / or" includes any and all combinations of one or more of the associated listed items. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may be present. In contrast, when an element is referred to as being "directly connected" or "directly coupled" to another element, there are no intervening elements present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., "between" versus "directly between," "adjacent" versus "directly adjacent," etc.). The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments. As used herein, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises," "comprising," "includes" and / or "including," when used herein, specify the presence stated features, integers, steps, operations, elements and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which example embodiments belong. It will be further understood that terms, e.g., those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. Portions of example embodiments and corresponding detailed description are presented in terms of software, or algorithms and symbolic representations of operation on data bits within a computer memory. These descriptions and representations are the ones by which those of ordinary skill in the art effectively convey the substance of their work to others of ordinary skill in the art. An algorithm, as the term is used here, and as it is used generally, is conceived to be a self-consistent sequence of steps leading to a desired result. The steps are those requiring physical manipulations of physical quantities. Usually, though not necessarily, these quantities take the form of optical, electrical, or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It has proven convenient at times, principally for reasons of common usage, to refer to these signals as bits, values, elements, symbols, characters, terms, numbers, or the like. In the following description, illustrative embodiments will be described with reference to acts and symbolic representations of operations (e.g., in the form of flowcharts) that may be implemented as program modules or functional processes including routines, programs, obj ects, components, data structures, etc., that perform particular tasks or implement particular abstract data types and may be implemented using existing hardware at existing network elements or control nodes. Such existing hardware may include one or more Central Processing Units (CPU), Digital Signal Processors (DSP), Application Specific Integrated Circuits (ASIC), Field Programmable Gate Arrays (FPGA), System-on-Chip (SoC), micro-controller, or the like. Unless specifically stated otherwise, or as is apparent from the discussion, terms such as "processing" or "computing" or "calculating" or "determining" or "displaying" or the like, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical, electronic quantities within the computer system's registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices. Note also that the software implemented aspects of example embodiments are typically encoded on some form of tangible (or recording) storage medium. The tangible storage medium may be magnetic (e.g., a floppy disk or a hard drive), optical (e.g., a compact disk read only memory, or "CD ROM"), and may be read-only memory (ROM), random access memory (RAM), flash memory (e.g., USB flash drives, memory cards, memory sticks, etc.), for example. The terms "tangible storage medium" and "memory" may be used interchangeably. Example embodiments are not limited by these aspects of any given implementation. There is seen in Fig. 1 part of a mobile network 100 comprising the following network entities: - a base station 110; - a terminal device 120. Although the mobile network 100 is depicted in Fig. 1 as comprising one base station 110 and one terminal device 120, the mobile network 100 is not limited to any particular number of base stations or terminal devices . The mobile network 100 may operate according to any existing Radio Access Technology (RAT) as defined by 3rd Generation Partnership Project (3GPP) or any other Standardization Development Organization (SDO), such as Long Term Evolution (LTE or 4G) or New Radio (NR or 5G), or according to any future RAT that is still to be developed, such as 6G. An example of the base station 110 is an eNB, a gNB, or a 6G NodeB. The base station 110 provides wireless connectivity to terminal devices (including the terminal device 120) within a geographical area or cell. More specifically, a cell refers to the radio resources that are configured and operated by a base station for forward / downlink and reverse / uplink communications with terminal devices located within a given geographical area. The geographical extent of a cell is mostly determined by the transmission power used by the base station and the terminal devices, as well as by environmental conditions (scattering, diffraction, physical obstructions, etc) . Presently, the base station 110 operates 3 sectored-cells that subtend a selected opening angle (e.g., three 120° sectors) and that are served by different antennas or antenna panels 130 of the base station 110. Wireless communications between the base station 110 and the terminal device 120 typically include one or more downlink physical channels for transmitting signals from the base station 110 to the terminal device 120, and one or more uplink channels for transmitting signals from the terminal device 120 to the base station 110. The uplink and / or downlink channels include traffic channels for conveying user traffic, such as Physical Downlink Shared Channel (PDSCH) and Physical Uplink Shared Channel (PUSCH), control channels for conveying control signaling, such as Physical Downlink Control Channel (PDCCH) and Physical Uplink Control Channel (PUCCH), broadcast channels for conveying cell synchronization signals and for broadcasting information within the cell, such as Physical Broadcast Channel (PBCH), access channels for accessing the cell, such as Physical Random Access Channel (PRACH), etc. The channels are multiplexed over the air according to various techniques including time division multiple access (TDMA), frequency division multiple access (FDMA) or orthogonal frequency division multiple access (OFDMA), code division multiple access (CDMA), as well as any combinations of these multiplexing techniques. Although the base station 110 is depicted in Fig. 1 as a single network entity, it may be functionally split between various physical or virtual network entities, such as a Central Unit (CU), one or more Distributed Units (DU), one or more Remote Radio Heads (RRH), etc. The base station 110 is further coupled to a core network (not shown), such as an Evolved Packet Core (EPC) or a 5G core network, and possibly to further base stations (not shown). The base station 110 and the terminal device 120 may be provisioned with multiple antennas for enhancing the radio communication between the base station 110 and the terminal device 120. Originally, multiple antennas were provisioned at the receive side to cope with channel fading and provide independent signal paths. The antennas were placed sufficiently far apart so as the channel gains of the respective antennas fade more or less independently. This scheme (aka receiver diversity) was further enhanced by coherent combining of the radio signals received through the various antennas. Transmitter diversity with multiple antennas provisioned at the transmit side was proposed later on with space-time codes, such as the Alamouti scheme. Those legacy schemes were progressively substituted by more-advanced MIMO techniques that enable spatial multiplexing of multiple data streams (aka transmission layers) onto the same time / frequency radio resources, yielding an increase in the capacity of the radio spectrum (e.g., as quantified by its spectral efficiency or bits . s"1. H"1) . Indeed, by provisioning multiple antennas at the transmit and / or receive side, an additional degree-of-freedom is created for radio communications by spatial discrimination of radio signals through the multiple antennas. For instance, at the transmit side, one may apply appropriate phaseshifts to a signal before transmission through the respective transmit antenna ports so as to steer the EM radiation power in a particular direction of propagation (e.g., as defined by a particular azimuth and / or elevation angle). This technique might also be used to compensate for the higher path loss incurred by radio signals using a higher frequency band, a technique known as transmit beamforming. Likewise, at the receive side, one may apply appropriate phase-shifts to the signals received through the respective antenna ports before signal combining to strengthen the reception of radio signals stemming from a particular direction of propagation while rejecting radio signals coming from another direction (e.g., a radio interferer). This technique is also known as receive beamforming. As an illustration, the base station 110 is depicted in Fig. 1 as applying transmit and / or receive beamforming through respective beams 140, and the terminal device 120 is depicted as applying transmit and / or receive beamforming through respective beams 150. The MIMO radio channel may be modelled in the frequency domain as a NrxNt matrix H with complex coefficients, with NT and Nr denoting the number of antenna ports at the transmit and receive sides respectively. The (i,j)-th component Hi,j of the channel matrix H describes how the radio channel produces a signal on the output of the i-th receive antenna port in response to a signal being fed to the input of the j-th transmit antenna port. Reference signals are transmitted from each and every transmit antenna ports so as to probe and estimate the channel coefficients at each and every receive antenna ports. For instance, in the downlink direction, Channel State Information Reference Signals (CSI-RS) are transmitted from the base station 110 to the terminal device 120 so as to probe and estimate the downlink radio channel; in the uplink direction, Sounding Reference Signals (SRS) are transmitted from the terminal device 120 to the base station 110 so as to probe and estimate the uplink radio channel. A better grasp on the spatial-multiplexing capacity of a MIMO channel may be obtained by Singular Value Decomposition (SVD) of the channel matrix H: H = USE* (1) , wherein U and V are two unitary matrices of dimensions Nr*Nr and NTXNT respectively satisfying UU* = U*U = VV* = V*V = I (all their row and column vectors are orthonormal to each other), wherein * denotes the conjugate transpose matrix and I denotes the identity matrix, and wherein S is a Nr*Nt diagonal matrix comprising non-negative real numbers Xi as diagonal coefficients (aka the singular values of the channel matrix H) . The number of non-null singular values is equal to the rank of the channel matrix H, which rank being upper-bounded by Min(N , Nr) . It is noteworthy that the rank of the channel matrix very much depends on the radio propagation environment in the vicinity of the transmitter and the receiver: the more scattering and reflections from various directions, such as in urban areas or indoor, the higher the rank of the radio channel. In contrast, a Line of Sight (LoS) propagation, such as in rural areas, is often associated with a low-rank radio channel. Let x denote the column vector of the NT signals to be transmitted through the NT respective antenna ports, and let y denote the column vector of the Nr signals received through the Nr respective antenna ports: y = Hx + n (2) , wherein n denotes a column vector of Nr white additive Gaussian noise (AWGN) signals present over the Nr respective receive antenna ports (including thermal noise as well as interference from other nearby users ) . Ideally, if the transmit signal is precoded through the precoding matrix V, and the received signal is postcoded through the postcoding matrix U*, then the overall received signal is given by: y = UVWx + U*n = U*UZV*Vx + U*n = Sx + U*n (3) . Consequently, with proper precoding at the transmit side and proper postcoding at the receive side, the overall channel matrix is reduced to the diagonal matrix S with as many parallel data steams (or transmission layers) as there are singular values that are substantially different from zero. Indeed, the diagonal coefficients of the matrix E actually determines the overall channel gains for the respective transmission layers, and should be high enough to overcome the noise and interference level for reliable communication. Practically, for a given non-null singular value Xi and a corresponding transmission layer, the transmit signal shall be precoded along the corresponding NTX1 column vector v± of the unitary matrix V (or equivalently along the corresponding eigen vector of the 'left-handed' auto-correlation channel matrix H*H = = ) , and the receive signal associated with this transmission layer shall be postcoded along the corresponding Nr><1 column vector u± of the unitary matrix U (or equivalently along the corresponding eigen vector of the 'right-handed' auto-correlation channel matrix HH* = UEFTSU* = UX2U*) . The eigen vectors Vi and uA shall be selected such that their eigen values Xi2 is substantially different from zero. In this way, the various transmissions are diagonalized / orthogonalized and can be superimposed onto the same time / frequency resources. This scheme is known as Zero-Forcing (ZF) MIMO as the off-diagonal coefficients of the overall channel matrix U*HV are forced down to zero. This scheme is particularly advantageous for Single User MIMO (SU-MIMO), yet oyher precoding / postcoding s^ra^egj_es may be contemplated. For instance, for Multi User MIMO (MU-MIMO), the precoding / postcoding vectors and corresponding beams can be chosen so as to reduce / null the interference from another nearby user while still offering good channel gains towards the intended user. Also, it is noteworthy that the unitary matrices U and V preserves the vector norm and thus the power of the signal input to the precoder or postcoder, as well as the noise power. So as to save on the signaling overhead, a DFT quantization is next performed by projecting the respective eigen vectors onto an orthonormal ID or 2D Discrete Fourier Transform (DFT) basis (aka the canonical basis). This canonical DFT basis corresponds to orthogonal ID or 2D beam pattens for linearly-spaced antenna or antenna array with half a wavelength as antenna spacing. For instance, one may select the DFT beam that is the most aligned with an eigen vector of the autocorrelation channel matrix to precode the transmit signal (codebook type I), or one may select the best L DFT beams to express the relevant eigen vectors of the auto-correlation channel matrix and determines the complex combining coefficients of these L DFT beams by projecting each of those eigen vectors onto the L selected orthogonal DFT beams (codebook type IT). Also, one may apply different combining coefficients over different frequency sub-bands to account for the frequency coherence of the MIMO channel (enhanced codebook type II). The precoding coefficients may be applied in the digital domain, or in the analog domain, or in both analog and digital domains (aka hybrid precoding). There is seen in Fig. 2 a first exemplary implementation 200 for transmit signal precoding in the digital domain with e.g. 4 antenna ports . A modulation symbols associated with a respective transmission layer at a respective sub-carrier index k is first passed through a precoding stage 210. More specifically, the modulation symbol is multiplied by a corresponding transmit precoding vector vkf to yield NT=4 precoded modulation symbols for the respective transmit antenna ports AP#0 to AP#3. The precoded modulation symbols of the respective transmission layers are added together by digital adders 220, typically after power normalization, and next input to an Inverse Fast Fourier Transform (IFFT) block 230 to produce a complex discrete time sequence. The complex discrete time sequence is then fed to a Digital-to-Analog Converter (DAC) 240 to produce two analog signals (real / in-phase / cosine and imaginary / quadrature / sine components of the complex time sequence), which are then modulated at carrier frequency by mixers 250. The modulated signal is then amplified by Power Amplifiers (PA) 260, and output through the respective transmit antenna ports 270 to the antennas 280. Although digital precoding offers a great deal of flexibility as the precoding coefficients are implemented in the digital domain and may take any arbitrary value (including complex combining coefficients for codebook type II), it is a rather expensive and power consuming solution as there are as many analog transmit chains as there are transmit antenna ports. Digital precoding may be combined with analog beamforming when operating in higher frequency range, such as Frequency Range 2 (FR2). There is seen in Fig. 3 an exemplary implementation for transmit signal precoding in the analog domain with e.g. 4 antenna ports. Modulation symbols ak>f associated with respective transmission layers f at respective sub-carrier indexes k are input to an IFFT block 310 to produce a complex discrete time sequence. The complex discrete time sequence is then fed to a Digital-to-Analog Converter (DAC) 320 to produce two analog signals, which are then modulated at carrier frequency toc by mixers 330. The analog signals are then amplified by PA 340, and the amplified signals are then split across the various transmit antenna ports 380 through respective ON / OFF circuitries 350 and phase shifters 360. The ON / OFF circuitries 350 control whether the amplified signals for respective transmission layers £ and respective transmit antenna ports m pass though or not depending on their respective ON / OFF status (e.g., bfm = O corresponds to the signal being blocked; = 1 corresponds to the signal being passed through). The ON / OFF circuitries 350 allows to control which transmit antenna ports are enabled / used for a given transmission layer. The phase shifters 360 apply respective phase shifts to the amplified signals for respective transmission layers { and respective antenna ports m. The amplified and appropriately phase-shifted signals of the respective transmission layers are then combined together by combiners 310 before feeding the antenna 390 through the transmit antenna ports 380. Alternatively, the combiners 370 may be omitted and the transmission layers may be beamformed through different antenna ports. For instance, in case of cross-polarization antennas, one transmission layer may be beamformed through one polarization mode (e.g., horizontal polarization), and another transmission layer may be beamformed through another polarization mode (e.g., vertical polarization). Also, full antenna coherence was assumed in Fig. 3 across all the four transmit antenna ports AP #0 to AP #3. Yet, partial antenna coherence might also be applicable, with for instance one transmission layer coherently beamformed through two transmit antenna ports, and another transmission layer coherently beamformed though the other two transmit antenna ports. The analog implementation 300 is cheaper as there are as many analog transmit chains as there are transmission layers (vs as many as there are transmit antenna ports for the digital implementation 200), yet the phase shifters introduce some coupling loss along the transmit path that needs to be compensated by higher amplification gain. Analog precoding is more suited to large antenna arrays comprising a large number of antenna elements, which would make the cost and power consumption of digital precoding prohibitive. Also, the phase shifters typically support a given phase increment, for instance 2n / 4 or 2n / 8, and the signals may only have their phase shifted by an integer multiple of this phase increment. Neither do the phase shifters provide any amplitude scaling nor complex coefficient combining (e.g., for codebook type II) . And last, while reference signals for sounding the various transmit antenna ports AP #1 to AP #4 may be sent simultaneously with the digital implementation 200 and multiplexed over the same time / frequency resources, e.g. by means of Orthogonal Cover Code (OCC), each and every transmit antenna ports AP #1 to AP #4 of the analog implementation 300 shall be sounded sequentially over time, which substantially lengthens the channel sounding procedure. The architectures for receive signal postcoding are similar to the ones depicted in Fig. 2 and 3 with corresponding analog receive chains comprising a Low Noise Amplifier (LNA), a mixer for downconversion to the baseband, an Analog-to-Digital Converter (ADC), a Fast Fourier Transform (FFT) block, and with demultiplexers / splitters substituting for the adders / combiners. For the digital implementation, signal postcoding is applied in the frequency domain after the DFT block. For the analog implementation, signal postcoding is implemented by respective phase shifters after low-noise amplification. Until very recently, terminal devices have rarely supported more than one transmission layer in uplink MIMO as the manufacturers have not deemed the cost (bill of materials, PCB area and power consumption) of adding relevant PAs to support more than one antenna transmitting over the same time / frequency resources worth the performance benefit. However, this trend has started to change recently to satisfy a growing uplink traffic demand. So far, the terminal device relies on a very low-granularity codebook for uplink transmit precoding as specified in 3GPP Technical Specification (TS) 38.211. This codebook assumes Uniform Linear Array (ULA) for the terminal device leading to a DFT-based Grid of Beams (GoB) . However, antenna arrays of the terminal device are not uniform and linear since the antenna patterns have directive variation of gain and phase, as well as inter-antenna distances that are rarely half a wavelength (distances can be up to 5 wavelengths for 9 GHz for example). This will result in a non-optimal codebook. A new enhanced uplink precoding method is thus proposed that can enable a terminal device to perform optimized single or multi-layer codebook-based uplink precoding considering non-uniform spacing properties and non-uniform radiation patterns of antenna elements and / or antenna arrays of the terminal device. These antenna non-uniformity properties increase as the frequency increases and must be carefully accounted for for optimum MIMO performance, especially when considering the new frequency ranges proposed for 6G. Moreover, while 3GPP codebook assume cross-polarized antennas, the proposed scheme and codebook can be used in realistic terminals, in which cross-polarized antennas have not been adopted so far. There is seen in Fig. 4 a realistic placement of various antennas within a smartphone 400. The smartphone 400 is provisioned with 4 antennas designed for one or more low frequency bands (LB), and with 4 antennas designed for one or more medium and / or high and / or ultra-high frequency bands (MHB / UHB). 2 LB antennas (Ant#l and Ant#2) are placed at the top of the smartphone 400, and 2 LB antennas (Ant#3 and Ant#4) are placed at the bottom of the smartphone 400. The 4 MHB / UHB antennas (Ant#5 to Ant#8) are placed at each corner of the smartphone 400. EM simulations with the terminal of Fig. 4 show the limited performance of current 3GPP codebooks with respect to more advanced high-granularity codebooks. Yet, an infinite granularity codebook would be practically infeasible. The size of a practical systematic finite granularity codebook for 4 transmit antenna ports would result in the following signaling overhead (on top of the storage requirements for storing the whole codebook in the terminal memory): - with 45° as phase shift granularity, there are 8 possible phase shift values applied to 3 of the 4 transmit antenna ports (as the first transmit antenna port would be the reference phase), and one additional value for switching ON or OFF the corresponding transmit antenna port, thus a total of 9x9x9=729 entries, so a 10 bit bitfield is needed to select the appropriate transmit precoding vector; - with 22,5° as phase shift granularity, there are 16+1=17 possible values per transmit antenna port, thus a total of 17x17x17=4913 entries, so a 13 bit bitfield is needed to select the appropriate transmit precoding vector; — with 11.25° as phase shift granularity, there are 32+1=33 possible values per transmit antenna port, thus a total of 33x33x33=35937 entries, so a 16 bit bitfield is needed to select the appropriate transmit precoding vector; — with 5,625° as phase shift granularity, there are 64+1=65 possible values per transmit antenna port, and thus a total of 65x65x65=274625 entries, so a 19 bit bitfield is needed to select the appropriate transmit precoding vector. Overall, the problem is to achieve the potential gains of a high granularity codebook without the burden of an exponentially complex codebook table so as to avoid large storage memory and codebook specification. The proposed method will be termed Full Codebook Phase Resolution Enhancement (FCPRE) in the following. Two alternative methods are proposed to efficiently signal a high granularity precoder, namely the direct FCPRE method and the indirect FCPRE method. The direct FCPRE method relies on an effective parameterized uplink codebook formula covering all possible precoding linear combinations for a given phase granularity. The terminal device obtains a phase granularity to use for uplink transmit precoding, and one or more transmit precoding vector indexes which, together with the indicated phase granularity, directly translate via an uplink codebook formula into one or more transmit precoding vectors to use for one or more respective transmission layers. The indirect FCPRE method consists of signaling relative phase shifts with a given phase granularity to apply to respective precoding coefficients of a precoder that was being used by the terminal device for prior uplink transmissions to obtain a new precoder which the terminal device shall use for new uplink transmissions. There is seen in Fig. 5 a signaling flow chart between a terminal device (UE), such as the terminal device 120, and a network device (NW), such as the base station 110, for the direct FCPRE method, with time flowing from top to bottom. At step 510, capability information of the terminal device are sent to the base station by means of Radio Resource Control (RRC) signaling, for example by means one or more UE_CAPABILITY_INFORMATION messages . First capability information indicative of a capability of the terminal device to support transmit precoding with enhanced phaseresolution may be transmitted from the terminal device to the network device. The first capability information may indicate support for the new proposed direct FCPRE method and related signaling for uplink codebook-based coherent or partially-coherent MIMO (FCPREDirect=enable). Second capability information indicative of a minimum phase shift increment 0min (or maximum phase granularity) supported by the terminal device for transmit signal precoding may be transmitted from the terminal device to the network device. For instance, the minimum phase shift increment 0min may correspond to the minimum phase shift increment as supported by analog phase shifter circuitries of the terminal device, such as the analog phase shifters 360 of exemplary analog implementation 300. The minimum phase shift increment 0min may be determined by the terminal device based on further criteria, such as its power consumption, its SNR regime, etc. As part of step 510 or a further step, the terminal device may further report its MIMO capabilities, such as the number of antenna panels, the number of transmit antenna ports (possibly per antenna panel), the maximum number of transmission layers or maximum rank, the phase coherence across antenna panels or antenna ports, etc. So as to save on the signaling overhead, the capability information are typically provided once, for instance when the terminal device first registers with the mobile network. The capability information are then transferred by the first-serving base station to the core network, for instance to the Access and Mobility Function (AMF). The core network then provides the capability information to further base stations with which the terminal device connects. At step 520, SRSs are transmitted from the respective transmit antenna ports of the terminal device to the base station for estimation of the uplink channel matrix H by the base station. The SRSs may be sent sequentially or simultaneously depending on the UE architecture and capabilities. SRS can be setup and configured in many different ways according to e.g. NR specifications. At step 530, the base station determines an estimate H of the uplink channel matrix H based on the received SRSs. The base station next determines the rank R of the estimated channel matrix H, and the number of transmission layers L <R that can be spatially multiplexed over the uplink radio channel, taking into consideration the MIMO capabilities of the terminal device as previously reported by the terminal device, and the number M of transmit antenna ports of the terminal device though which the uplink transmission is to be performed . The base station next selects a reference phase shift increment 6ref to use by the terminal device, taking into consideration the minimum phase shift increment 0min supported by the terminal device for uplink transmit precoding and reported at step 510. The reference phase shift increment 0ref may at least be based on the minimum phase shift increment 0min reported by the terminal device to the network device, for instance shall be greater than or equal to the minimum phase shift increment 0min • For instance, the reference phase shift increment 0ret may be equal to an integer multiple of the minimum phase shift increment 0min: 9ref = n0min, with neN*. The base station may further adapt / adjust the reference phase shift increment 0ref based on channel measurement information. Based on the measurement and estimation of the uplink channel matrix H, the base station decides the best value to use for the reference phase shift increment 0ref, and selects the corresponding new uplink MIMO codebook. For example, a terminal device situated in a point of space where the channel is quasi-isotropic (i.e., the angular spread of the channel is very wide) will require a smaller granularity than a terminal device in LoS condition. The base station may further adapt / adjust the reference phase shift increment 0ref to individual characteristics of the terminal device. For example, a terminal device equipped with close-to-isotropic antennas will require lower granularity than a terminal device with directional antennas . The base station then calculates the optimal uplink precoder the terminal device shall utilize based on the estimated uplink radio channel matrix H. The base station adapts the optimal precoder to the selected reference phase shift increment 0ref and to the corresponding new uplink MIMO codebook. This can be performed, for example, with an exhaustive search among all the elements of the new uplink MIMO codebook, or by performing an SVD of the channel matrix H and by finding the closest finite-granularity precoder in the new uplink MIMO codebook. The base station eventually derives one or more respective transmit precoder vector V / to use for one or more respective transmission layers ^ = 0---1-1, as well as their respective indexes Q. At step 540, transmit precoding information are sent from the base station to the terminal device. First transmit precoding information indicative of the reference phase shift increment 0rer as selected by the base station are transmitted from the base station to the terminal device. Second transmit precoding information indicative of the one or more transmit precoding vector indexes if for the one or more respective transmission layers / = 0---L —1 are transmitted from the base station to the terminal device. The first and second precoding information are depicted in Fig. 5 as being transmitted as part of Downlink Control Information (DCI) scheduling an uplink transmission to be performed by the terminal device using the indicated transmit precoding vectors. The DCI are transmitted via a Physical Downlink Control Channel (PDCCH). Alternatively, the first and second transmit precoding information may be transmitted as part of a Medium Access Control Control Element, MAC CE, which is multiplexed with a Physical Downlink Shared Channel (PDSCH) transmission to the terminal device, and which schedules a new uplink transmission to be performed by the terminal device using the indicated transmit precoding vector(s). Still alternatively, the first transmit precoding information may be transmitted as part of Radio Resource Control, RRC, signaling, while the second transmit precoding information may be transmitted as part of DCI or a MAC CE. At step 550, one or more transmit precoding vectors Vf for the one or more respective transmission layers ^ = 0 L — 1 are then derived by the terminal device from the received reference phase shift increment ©ret and the one or more received transmit precoding vector indexes if. At step 560, a PUSCH transmission is performed by the terminal device through the M transmit antenna ports of the terminal device at least based on the one or more derived transmit precoding vectors Vf for the one or more respective transmission layers / =0 •••£ — !. The reference phase shift increment 0ref may be given by 6ref = 2n / N, with N denoting an integer greater than 1, typically a power of 2 such as N= 4, 8, 16, 32, etc. The transmit precoding vector Vf = [vf 0 Vf^ ... for a given transmission layer £ (omitting the frequency dependence) may comprise M transmit precoding coefficients Vfm associated with the respective transmit antenna ports m = —1. The transmit precoding coefficients Vf,m are given by: Vo = ho = h„ piat,m^ref / 41 with af m G Z and bfm e {0,1}. Typically, with Qref = 2n / N, afm may take any value in the range {0, ..., N-l} or {-N / 2, ..., N / 2-1} or {-N / 2+1, ..., N / 2}. With digital precoding, the precoding coefficients are directly applied to the modulation symbols by complex multiplication. With analog precoding, the amplitude component bfm may be implemented by ON / OFF switching circuitries that activate / enable or deactivate / disable respective transmit antenna ports, such as ON / OFF circuities 350 of exemplary analog implementation 300, whereas the phase shift components may be implemented by appropriately-configured phase shifters that apply the phase shifts 0fm = Uf>mOref to the sine and cosine carrier signals, 300. such as phase shifters 360 of exemplary analog implementation The second transmit precoding information may comprise at most fLogMN + 1)M)1 bits so as to cover all phase shift combinations across the transmit antenna ports of the terminal device, as well as activation / de-activation of any transmit antenna port of the terminal device . Yet, as only the relative phase shifts between respective antenna ports matters, certain phase shift combinations correspond to the same beamforming configuration, and thus certain transmit precoder indexes may be omitted so as to reduce the size of the codebook and save on the signaling overhead. For instance, the following transmit precoding vectors for 4 transmit antenna ports yield the same beamforming configuration: [e^ / 4, e^ / 4, O,of , [e^ / 2, e^ / 2, O,of , [e^3 / 4, ^37r / 4, O,of , etc, and likewise for the following transmit precoding vectors: [eW4,O,O,of , / j1 0<, pw3 / 4,0,0,0] , etc. The uplink codebook included in the current 3GPP specifications may be extended to include higher phase granularity and transmit antenna port combinations. Yet, in order to avoid storing multiple large codebooks for various phase granularities (implying large memory requirements for the terminal device), the one or more transmit precoding vectors Vf may be derived by means of a codebook analytical formula, i.e. a closed-form mathematical expression, having the reference phase shift increment 0ref and a respective transmit precoding vector index Q for a given transmission layer / as input variables, and the respective transmit precoder vector Vf to use for the given transmission layer £ as output. For instance, the phase shift component of the transmit precoding coefficients Vfm may be given by: and the amplitude component bfm of the transmit precoding coefficients may be given by: bem = 1 - 8(af m) (6), with [.J, 5(.) and mod (., n) denoting the floor function, the discrete Kronecker delta function (i.e., 5(x) = 1 if x=0, else 5(+) = 0) and the modulo n function (i.e., mod(x, n) = x — n ) respectively. The transmit precoding vector index if typically ranges from 0 to Nmax-1, with NMAX = (N + 1)" . Equivalently, the phase shift component may be given by: = Xf,m - with = (7) , and the amplitude component by: bym = 1 — 6{mod(a(m,N + 1)) (8 ) . Alternatively, the phase shift component may be given by: = |.m(N+l)+5(m)] ' and the amplitude component by: bf,m = 1 - 5(mod(a<m, N + 1)) (10) , although the resulting uplink MIMO codebook shows less regularities with varying index if. Codebook for multi-layer transmission is created by simply cascading multiple single-layer precoding vectors. In case of linearly dependent vectors, the resulting precoding matrix is eliminated from the codebook. If the system requires orthogonal columns in the precoding matrix, the matrix is eliminated if the columns aren't orthogonal. The presence of at least one combination of orthogonal and linearly independent column is guaranteed. The base station then provides different transmit precoding vector indexes if for each layer f separately. There is seen in Fig. 6 a signaling flow chart between a terminal device (UE), such as the terminal device 120, and a network device (NW), such as the base station 110, for the indirect FCPRE method, with time flowing from top to bottom. At step 610, capability information of the terminal device are sent to the base station by means of Radio Resource Control (RRC) signaling, for example by means of one or more UE CAPABILITY INFORMATION message . First capability information indicative of a capability of the terminal device to support differential transmit precoding with enhanced phase-resolution may be transmitted from the terminal device to the network device. The first capability information may indicate support for the new proposed indirect FCPRE method and related signaling (FCPEIndirect=enable). Second capability information indicative of a minimum phase shift increment 0min (or maximum phase granularity) supported by the terminal device for transmit signal precoding may be transmitted from the terminal device to the network device. For instance, the minimum phase shift increment 0min may correspond to the minimum phase shift increment as supported by analog phase shifter circuitries of the terminal device, such as the analog phase shifters 360 of exemplary analog implementation 300. The minimum phase shift increment 0min may be determined by the terminal device based on further criteria as aforementioned. As part of step 610 or a further step, the terminal device may further report its MIMO capabilities as aforementioned. Step 620 is similar to step 520 in Fig. 5. At step 630, the base station determines an estimate H of the uplink channel matrix H based on the received SRSs. The base station next determines the rank R of the estimated channel matrix H, and the number L <R of transmission layers that can be spatially multiplexed over the uplink radio channel, taking into consideration the MIMO capabilities of the terminal device as previously reported by the terminal device, and the number M of transmit antenna ports of the terminal device though which the uplink transmission is to be performed. The base station then determines one or more first transmit precoding vectors for one or more respective transmission layers f = 0 •••£ — !, which first transmit precoding vectors being signaled to the terminal device. The one or more first transmit precoding vectors may be signaled by means of the direct FCPRE method as described in Fig. 5 through their respective indexes , or may be signaled by means of a legacy signaling method, for instance a signaling method relying on the Transmit Precoding Matrix Index (TPMI) as defined in NR specifications. Alternatively, the terminal device may start with some default transmit precoding vectors for the one or more first transmit precoding vectors for instance 0° phase shifts for the M transmit antenna ports . Still alternatively, the terminal device may determine an appropriate transmit precoder to use based on downlink reference signals (e.g., CSI-RS), assuming reciprocity between the downlink and uplink radio channels (e.g., for Time Division Duplexing (TDD) deployments). The terminal device may then send appropriately precoded SRSs to the base station. At step 640, a first PUSCH transmission is performed by the terminal device through the M transmit antenna ports of the terminal device at least based on the one or more first transmit precoding vectors for the one or more respective transmission layers / =0 •••£—!. At step 650, the base station updates the channel matrix H, e.g. on account of the mobility and / or rotation of the terminal device. The base station then selects a phase increment 0ref, (possibly different from the one used for determination of the first transmit precoding vectors in case the direct FCPRE method was used to determine the first transmit precoding vectors), and taking into consideration the minimum phase shift increment 0min supported by the terminal device for uplink transmit precoding and reported at step 610. The reference phase shift increment 0ref may at least be based on the minimum phase shift increment 0min reported by the terminal device to the network device, for instance shall be greater than or equal to the minimum phase shift increment 0min. For instance, the reference phase shift increment 0rer may be equal to an integer multiple of the minimum phase shift increment 0min: 0ref = with neN*. The base station may further adapt / adjust the reference phase shift increment 0ref to the environment of the terminal device and to the individual characteristics of the terminal device as aforementioned. The reference phase shift increment 0ref may be given by 0rey = 2n / N, with N denoting an integer greater than 1, typically a power of 2 such as N= 4, 8, 16, 32, etc. The base station next determines one or more second transmit H) ... precodrng vectors for the one or more respective transmission layers / =0 •••£ — ! based on the selected phase increment 0rer, and determines one or more relative (or differential) phase shifts to apply to one or more respective precoding coefficients of the one or more first transmit precoding vectors to yield the one or more respective second transmit precoding vectors Let us denote the one or more relative phase shifts as A^m, with £ and m denoting the indexes of the respective transmission layer and of the respective transmit antenna port of the terminal device to which the relative phase shift applies. The one or more relative phase shifts A^m are integer multiples of the reference phase shift increment 6ref: A%n = n0ref, with nel. At step 660, transmit precoding information are sent from the base station to the terminal device. First transmit precoding information indicative of the reference phase shift increment 0ref as selected by the base station are transmitted from the base station to the terminal device. Second transmit precoding information indicative of the one or more relative phase shifts A6^>m are transmitted from the base station to the terminal device. The second transmit precoding information may comprises the relative phase shift values A^m for the M respective transmit antenna ports of the terminal device, including null relative phase-shift values for the precoding coefficients whose phase is unchanged. For instance, the second transmit precoding information may comprises a matrix of relative phase shifts values of size MxL, with each column corresponding to a transmission layer. The matrix may comprise e.g. two bits per element with e.g. '00' and '11' corresponding to a negative and positive relative phase shift of one reference phase shift increment respectively (i.e., +0ref) , and with e.g. '01' and / or '10' corresponding to a 'no change' value. Alternatively, one may use one of '01' or '10' value to encode a negative or positive relative phase shift of two reference phase shift increments (i.e., +20ref) • Still alternatively, one may use more than two or more bits per element so as to encode further relative phase shifts (e.g., 12 0r ef , ±30ref , e t C ) « Alternatively, the second transmit precoding information may comprises a bitmap or bit array for indicating, among the M transmit antenna ports, M* transmit antenna ports associated with a non-null phase shift, and M* non-null phase shift values for the M* respective transmit antenna ports. As there is no need to encode the 'no change' value, one single bit per element is enough for encoding a negative and positive relative phase shift of one reference phase shift increment (i.e. , ±6ref) . The first and second precoding information are depicted as being transmitted as part of Downlink Control Information (DCI) scheduling an uplink transmission to be performed by the terminal device using the indicated phase increment 0ref and the one or more relative phase shifts A^m. The DCI are transmitted via a Physical Downlink Control Channel (PDCCH). As aforementioned, the first and second transmit precoding information may alternatively be transmitted as part of a Medium Access Control Control Element, MAC CE, which is multiplexed with a Physical Downlink Shared Channel (PDSCH) transmission to the terminal device, and which schedules a new uplink transmission to be performed by the terminal device using the indicated phase increment 0ler and the one or more relative phase shifts Still alternatively, the first transmit precoding information may be transmitted as part of Radio Resource Control, RRC, signaling, while the second transmit precoding information may be transmitted as part of DCI or a MAC CE. At step 670, the terminal device determines one or more second transmit precoding vectors for the one or more respective transmission layers ^ = 0 •••£ — ! by applying the one or more relative phase shift values A0ym to one or more respective first transmit precoding coefficients of the one or more first transmit precoding vector V® associated with respective transmission layer { and respective transmit antenna port m: = d1)' wherein and respectively denote the phases of first transmit precoding coefficients of the one or more first transmit precoding vectors and of second transmit precoding coefficients of the one or more second transmit precoding vectors } associated with respective transmission layer / and respective transmit antenna port m. For instance, in the digital domain, applying the one or more relative phase shifts to the one or more respective first transmit precoding coefficients comprises multiplying the one or more first transmit precoding coefficients by . In the analog domain, the relative phase shifts may be implemented by appropriately updating the phase shifters based on their previous value. At step 680, a second PUSCH transmission is performed by the terminal device through the M transmit antenna ports of the terminal device at least based on the one or more newly determined second transmit .. ri) precoding vectors . There are seen in Fig. 7A, 7B and 7C performance plots for EM simulations at 1900 MHz, 3700 MHz and 9000 MHz carrier frequency respectively. The EM simulations have been carried out with the UE model and antenna placement of Fig. 4. The effect of an enhanced high granularity uplink codebook is evaluated at three different frequencies; 1900 MHz, 3700 MHz and 9000 MHz, where the first two frequencies are currently part of FR1 (410 MHz to 7125 MHz), and the third frequency is a possible frequency for a possible new 6G 3GPP frequency range (currently referred to as FR3). The enhancement of the uplink codebook is evaluated for 2 transmit antenna ports to limit the EM simulation effort. However, the improvement shown for 2 transmit antenna ports will also be obtainable for 4 transmit antenna ports or even better for angular directions where all four antennas have similar antenna gain values. In addition, the improvements are only shown for single layer configuration, but similar improvements will also be seen for multiple layer configuration. The combined gain values shown in Fig. 7A, 7B and 7C are for the total gain of both the co-polarization and the cross-Polarization components, while the results shown in Table 1 are for a single polarization. As such, the total gain evaluation is applicable when the channel between the base station and the terminal device has circular polarization characteristics, while the per polarization evaluation is applicable when the channel between the base station and the terminal device has linear polarization characteristics. The total combined antenna gain improvement (both polarizations) at 1900 MHz, 3700 MHz and 9000 MHz for legacy 3GPP reference 90° granularity (dashed line) vs finer 5° granularity (solid line) are shown in Fig. 7A, 7B and 7C respectively as a function of the azimuth angle. It can be seen that gain improvements of up to 0.7 dB are observed when increasing the granularity from 90° to 5° phase shift increment. The combined gain variation as a function of the applied phase offset will often be higher for single polarization evaluation than for dual polarization evaluation since the single applied phase offset value (analog or digitally applied to one of the transmit branches in the device) can theoretically always be fully optimized for the signal polarization evaluation. However, that is not always possible for dual polarization evaluation as the optimum phase offset values can be different for the two polarizations. Our simulation results are summarized in Table 1 below where a phase shift granularity of 90°, as currently specified by 3GGP, can result in sub-optimal combined antenna gain, resulting in a practical combined antenna gain between 0.7 to 3.1 dB. A phase shift granularity of 30° will only result in a reduced combined antenna gain difference between 0.1 to 0.8 dBi. Noticeably, the largest amount of the gain can be reached with a 5° granularity, which establishes a lower bound for the effective granularity. The results shown in Table 1 are at a single angular point for a single linear polarization where the effect of the combined antenna gain is shown with different phase offsets from 0° to 45° in steps of 15°. This illustrates the potential combined antenna gain when increasing the phase shift granularity of the uplink codebook. Phase Offset 0° +15° ±30° ±45° Gain @1900 MHz 3.4 dBi 2.6 dBi 1.6 dBi 0.3 dBi Gain @ 3700 MHz 4.1 dBi 4.0 dBi 3.8 dBi 3.4 dBi Gain @ 9000 MHz 6.2 dBi 5.9 dBi 5.4 dBi 4.7 dBi Table 1 There is seen in Fig. 8 a flow chart for a method 800 according to the third example aspect. The method 800 is performed by a terminal device, such as the terminal 120, and comprises, at step 810, receiving, from a network device, such as the base station 120, first transmit precoding information indicative of a reference phase shift increment Gref. The method 800 further comprises, at step 820, receiving, from the network device, second transmit precoding information indicative of a transmit precoding vector index for a transmission layer. The method 800 further comprises, at step 830, deriving a transmit precoding vector for the transmission layer from the reference phase shift increment 0rer and the transmit precoding vector index. The method 800 further comprises, at step 840, performing an uplink transmission of the transmission layer through M transmit antenna ports of the terminal device at least based on the transmit precoding vector. There is seen in Fig. 9 a flow chart for a method 900 according to the seventh example aspect. The method 900 is performed by a base station, such as the base station 110, and comprises, at step 910, transmitting, to a terminal device, such as the terminal device 120, first transmit precoding information indicative of a reference phase shift increment 0ref. The method 900 further comprises, at step 920, transmitting, to the terminal device, second transmit precoding information indicative of a transmit precoding vector index for a transmission layer. The method 900 further comprises, at step 930, receiving an uplink transmission of the transmission layer performed by the terminal device through M transmit antenna ports of the terminal device at least based on a transmit precoding vector derived from the reference phase shift increment 0ref and the transmit precoding vector index . There is seen in Fig. 10 a flow chart for a method 1000 according to the eleventh example aspect. The method 1000 is performed by a terminal device, such as the terminal 120, and comprises, at step 1010, performing a first uplink transmission of a transmission layer through M transmit antenna ports of the terminal device at least based on a first transmit precoding vector. The method 1000 further comprises, at step 1020, receiving, from a network device, such as the base station 110, first transmit precoding information indicative of a reference phase shift increment 0ref. The method 1000 further comprises, at step 1030, receiving, from the network device, second transmit precoding information indicative of one or more phase shifts for the transmission layer associated with one or more respective transmit antenna ports of the terminal device out of the M transmit antenna ports. The one or more phase shifts are integer multiples of the reference phase shift increment 0ref • The method 1000 further comprises, at step 1040, determining a second transmit precoding vector by applying the one or more phase shifts to one or more respective transmit precoding coefficients of the first transmit precoding vector associated with the one or more respective transmit antenna ports. The method 1000 further comprises, at step 1050, performing a second uplink transmission of the transmission layer through the M transmit antenna ports at least based on the second transmit precoding vector. There is seen in Fig. 11 a flow chart for a method 1100 according to the fifteenth example aspect. The method 1100 is performed by a network device, such as the base station 110, and comprises, at step 1110, receiving a first uplink transmission of a transmission layer performed by a terminal device, such as the terminal device 120, through M transmit antenna ports of the terminal device at least based on a first transmit precoding vector. The method 1100 further comprises, at step 1120, transmitting, to the terminal device, first transmit precoding information indicative of a reference phase shift increment 0ref. The method 1100 further comprises, at step 1130, transmitting, to the terminal device, second transmit precoding information indicative of one or more phase shifts for the transmission layer associated with one or more respective transmit antenna ports of the terminal device out of the M transmit antenna ports. The one or more phase shifts are integer multiples of the reference phase shift increment 0ref- The method 1100 further comprises, at step 1140, receiving a second uplink transmission of the transmission layer performed by the terminal device through the M transmit antenna ports at least based on a second transmit precoding vector determined by applying the one or more phase shifts to one or more respective transmit precoding coefficients of the first transmit precoding vector associated with the one or more respective transmit antenna ports . There is seen in Fig. 12 a schematic block diagram of an apparatus 1200, e.g. a terminal device or a network device, according to any of the first, second, fifth, sixth, ninth, tenth, thirteenth and fourteenth example aspects . Apparatus 1200 comprises a processor 1210, program memory 1220, working or main memory 1230, communication interface (s) 1240, and optionally a user interface 1250. Apparatus 1200 may for instance be configured to perform and / or control or comprise respective means (at least one of 1210 to 1250) for performing and / or controlling a method according to the third, seventh, eleventh and fifteenth example aspects. Apparatus 1200 may comprise at least one processor 1210 and at least one memory 1220 storing instructions that, when executed by the at least one processor, cause a UE at least to perform and / or control the method according to any or all example aspects. Processor 1210 may for instance control at least one of the memories 1220 to 1230, the communication interface(s) 1240, and / or the optional user interface 1250. Processor 1210 (and also any other processor mentioned in this specification) may be a processor of any suitable type. Processor 1210 may comprise but is not limited to one or more microprocessor (s) , one or more processor(s) with accompanying one or more digital signal processor (s), one or more processor(s) without accompanying digital signal processor(s), one or more special-purpose computer chips, one or more field-programmable gate array(s) (FPGA(s)), one or more controller (s), one or more application-specific integrated circuit(s) (ASIC(s)), etc. The relevant structure / hardware has been programmed in such a way to carry out the described function. Program memory 1220 stores instructions, such as a program code, which, when executed by processor 1210, causes the processor 1210 to perform a method according to the third, seventh, eleventh and fifteenth example aspects. Program memory 1220 may also be included into processor 1210. This memory may for instance be fixedly connected to processor 1210, or be at least partially removable from processor 1210, for instance in the form of a memory card or stick. Program memory 1220 may for instance be non-volatile memory. It may for instance be a FLASH memory (or a part thereof), any of a ROM, PROM, EPROM and EEPROM memory (or a part thereof) or a hard disc (or a part thereof), to name but a few examples. Program memory 1220 may comprise an operating system for processor 1210. Program memory 1220 may comprise a firmware for apparatus 1200. One or more communication interface) 1240 enable the apparatus 1200 to communicate with other network entities, e.g., one or more terminal devices and / or one or more network devices. The communication interfaces 1240 typically include one or more wireless transceivers and 5 RF circuitry for communicating through a wireless interface, e.g. a cellular radio communication interface and / or a Wireless Local Area Network WLAN) interface, and one or more wireline transceivers for communicating through a wireline interface, e.g. an Unshielded Twisted Pair (UTP) interface and / or a coaxial interface and / or an optical fiber 10 interface. User interface 1250 is optional and may comprise a display for displaying information to a user and / or an input device (e.g. a keyboard, touchscreen, touchpad, mouse, etc.) for receiving inputs from a user. Some or all of the components of the apparatus 12 00 may for 15 instance be connected via a bus. Some or all of the components of the apparatus 1200 may for instance be combined into one or more modules.

Claims

1. An apparatus comprising at least one processor, and at least one memory storing processor instructions that, when executed by the at least one processor, cause the apparatus at least to:perform a first uplink transmission of a transmission layer through M transmit antenna ports of the apparatus at least based on a first transmit precoding vector;receive, from a network device, first transmit precoding information indicative of a reference phase shift increment 0ref;receive, from the network device, second transmit precoding information indicative of one or more phase shifts for the transmission layer associated with one or more respective transmit antenna ports of the apparatus out of the M transmit antenna ports, wherein the one or more phase shifts are integer multiples of the reference phase shift increment 0ref;determine a second transmit precoding vector by applying the one or more phase shifts to one or more respective transmit precoding coefficients of the first transmit precoding vector associated with the one or more respective transmit antenna ports; andperform a second uplink transmission of the transmission layer through the M transmit antenna ports at least based on the second transmit precoding vector.

2. The apparatus of claim 1, wherein the apparatus is further caused to:transmit, to the network device, first capability information indicative of a capability of the apparatus to support differential transmit precoding with enhanced phase-resolution.

3. The apparatus of claim 1 or 2, wherein the apparatus is further caused to :transmit, to the network device, second capability information indicative of a minimum phase shift increment 0min supported by the apparatus for transmit signal precoding,and wherein the reference phase shift increment 0ref is at least based on the minimum phase shift increment 0min.

4. The apparatus of any preceding claim, wherein the reference phase shift increment 0ref is given by 9ref = 2n / Nr with N denoting an integer greater than 1,and wherein applying the one or more phase shifts to the one or more respective transmit precoding coefficients comprises multiplying the one or more transmit precoding coefficients by e^am0ref f with am denoting an integer, and with m e {0, ..., M-l} denoting one or more transmit antenna port indexes of the one or more respective transmit antenna ports.

5. The apparatus of any preceding claim, wherein the second transmit precoding information comprises M phase shift values for the M respective transmit antenna ports.

6. The apparatus of any of claims 1 to 4, wherein the second transmit precoding information comprises:a bitmap for indicating, among the M transmit antenna ports, M* transmit antenna ports associated with a non-null phase shift; andM* non-null phase shift values for the M* respective transmit antenna ports .

7. The apparatus of any preceding claim, wherein the second transmit precoding information is received as part of Downlink Control Information, DCI, or a Medium Access Control Control Element, MAC CE, scheduling the second uplink transmission.

8. The apparatus of any preceding claim, wherein the first transmit precoding information is received as part of Downlink Control Information, DCI, or a Medium Access Control Control Element, MAC CE, scheduling the second uplink transmission, or as part of Radio Resource Control, RRC, signaling.

9. A method comprising, by a terminal device:performing a first uplink transmission of a transmission layerthrough M transmit antenna ports of the terminal device at least based on a first transmit precoding vector;first transmit precodingreceiving, from a network device, information indicative of a reference phase shift increment 0re£;receiving, from the network device, second transmit precoding information indicative of one or more phase shifts for the transmission layer associated with one or more respective transmit antenna ports of the terminal device out of the M transmit antenna ports, wherein the one or more phase shifts are integer multiples of the reference phase shift increment 0ref;determining a second transmit precoding vector by applying the one or more phase shifts to one or more respective transmit precoding coefficients of the first transmit precoding vector associated with the one or more respective transmit antenna ports; andperforming a second uplink transmission of the transmission layer through the M transmit antenna ports at least based on the second transmit precoding vector.

10. An apparatus comprising at least one processor, and at least one memory storing processor instructions that, when executed by the at least one processor, cause the apparatus at least to:receive a first uplink transmission of a transmission layer performed by a terminal device through M transmit antenna ports of the terminal device at least based on a first transmit precoding vector;transmit, to the terminal device, first transmit precoding information indicative of a reference phase shift increment 0re£;transmit, to the terminal device, second transmit precoding information indicative of one or more phase shifts for the transmission layer associated with one or more respective transmit antenna ports of the terminal device out of the M transmit antenna ports, wherein the one or more phase shifts are integer multiples of the reference phase shift increment 0rer; andreceive a second uplink transmission of the transmission layer performed by the terminal device through the M transmit antenna ports at least based on a second transmit precoding vector determined by applying the one or more phase shifts to one or more respective transmit precoding coefficients of the first transmit precoding vector associated with the one or more respective transmit antenna ports.

11. The apparatus of claim 10, wherein the apparatus is further caused to:receive, from the terminal device, first capability information indicative of a capability of the apparatus to support differential transmit precoding with enhanced phase-resolution.

12. The apparatus of claim 10 or 11, wherein the apparatus is further caused to :receive, from the terminal device, second capability information indicative of a minimum phase shift increment 0min supported by the terminal device for transmit signal precoding; anddetermine the reference phase shift increment 0ref at least based on the minimum phase shift increment 0min.

13. The apparatus of any of claims 10 to 12, wherein the apparatus is further caused to:determine or adjust the reference phase shift increment 0rer based on channel measurement information.

14. The apparatus of any of claims 10to 13, whereinthereference phase shift increment 0ref is given by 9ref = 2n / N, with N denoting an integer greater than 1,and wherein applying the one or more phase shifts to the one ormore respective transmit precoding coefficients comprises multiplying the one or more transmit precoding coefficients by e^am0ref, with am denoting an integer, and with m e {0, ..., M-l} denoting one or more transmit antenna port indexes of the one or more respective transmit antenna ports.

15. The apparatus of any of claims 10 to 14, wherein the secondtransmit precoding information comprises M phase shift values for the M respective transmit antenna ports.

16. The apparatus of any of claims 10 to 14, wherein the second35transmit precoding information comprises:a bitmap for indicating, among the M transmit antenna ports, M* transmit antenna ports associated with a non-null phase shift; andM* non-null phase shift values for the M* respective transmit antenna ports.

17. The apparatus of any of claims 10 to 16, wherein the second transmit precoding information is transmitted as part of Downlink Control Information, DCI, or a Medium Access Control Control Element, MAC CE, scheduling the second uplink transmission.

18. The apparatus of any of claims 10 to 17, wherein the first transmit precoding information is transmitted as part of Downlink Control Information, DCI, or a Medium Access Control Control Element, MAC CE, scheduling the second uplink transmission, or as part of Radio Resource Control, RRC, signaling.

19. A method comprising, by a network device:receiving a first uplink transmission of a transmission layer performed by a terminal device through M transmit antenna ports of the terminal device at least based on a first transmit precoding vector;transmitting, to the terminal device, first transmit precoding information indicative of a reference phase shift increment 0re£;transmitting, to the terminal device, second transmit precoding information indicative of one or more phase shifts for the transmission layer associated with one or more respective transmit antenna ports of the terminal device out of the M transmit antenna ports, wherein the one or more phase shifts are integer multiples of the reference phase shift increment 0ref; andreceiving a second uplink transmission of the transmission layer performed by the terminal device through the M transmit antenna ports at least based on a second transmit precoding vector determined by applying the one or more phase shifts to one or more respective transmit precoding coefficients of the first transmit precoding vector associated with the one or more respective transmit antenna ports.45

Images