Apparatus and method for signal precoding

Abstract

Example embodiments of this disclosure relate to apparatus and methods for signal precoding. One method includes acquiring a symbol precoder, the symbol precoder including a first component precoder and a second component precoder that are dependent on each other, wherein the first component precoder and the second component precoder have sizes of N×M and N×K, respectively, and M+K is greater than N, and wherein at least one of the first component precoder and the second component precoder includes at least one of: at least one complex-valued element, or at least two complex-valued or real-valued elements having at least two different non-zero amplitudes affecting at least one precoder output value; determining a precoded signal based on encoding a first symbol vector using the first component precoder and encoding a second symbol vector using the second component precoder; and transmitting a signal including the precoded signal to a second means.

Description

Cross-reference to related applications

[0001] This application claims priority and benefit to European Patent Application No. 25165848.0, filed on March 25, 2025, the entire contents of which are incorporated herein by reference. Technical Field

[0002] Various exemplary embodiments of this disclosure generally relate to the telecommunications field, and particularly to methods, apparatus and computer-readable storage media for signal precoding. Background Technology

[0003] A communication network can serve as a facility that enables communication between two or more communication devices or provides communication devices with access to a data network. A mobile or wireless communication network is one example of a communication network. Communication networks can operate according to standards provided by organizations such as the 3rd Generation Partnership Project (3GPP) or the European Telecommunications Standards Institute (ETSI). Examples of standards provided by 3GPP are the so-called 3GPP standards for cellular technology generations, such as those for 4G, 5G, and 6G technologies. Summary of the Invention

[0004] In a first aspect of this disclosure, a first apparatus is provided. The first apparatus includes at least one processor; and at least one memory storing instructions, which, when executed by the at least one processor, cause the first apparatus to at least: acquire a symbol precoder, the symbol precoder including a first component precoder and a second component precoder that are dependent on each other, wherein the first component precoder corresponds to an N x M first matrix for precoding M symbols, and the second component precoder corresponds to an N x K second matrix for precoding K symbols that are different from the M symbols, and M+K is greater than N, and wherein at least one of the first component precoder and the second component precoder includes at least one of the following: at least one complex-valued element, or having at least two complex-valued or real-valued elements having at least two different non-zero amplitudes that affect the output value of the at least one precoder; determine a precoded signal based on encoding a first symbol vector of the M symbols using the first component precoder and encoding a second symbol vector of the K symbols using the second component precoder; and transmit a signal including the precoded signal to a second apparatus.

[0005] In a second aspect of this disclosure, a second apparatus is provided. The second apparatus includes at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the second apparatus to at least: receive a signal from a first apparatus; and decode the received signal using at least one of a first component precoder and a second component precoder, wherein the first component precoder corresponds to an N-row M-column first matrix for precoding M symbols, and the second component precoder corresponds to an N-row K-column second matrix for precoding K symbols, which are different from the M symbols, and M+K is greater than N, and wherein at least one of the first component precoder and the second component precoder includes at least one of: at least one complex-valued element, or has at least two complex-valued or real-valued elements having at least two different non-zero amplitudes affecting the output value of the at least one precoder.

[0006] In a third aspect of this disclosure, a method is provided. The method includes: acquiring a symbol precoder at a first device, the symbol precoder including a first component precoder and a second component precoder that are dependent on each other, wherein the first component precoder corresponds to an N x M first matrix for precoding M symbols, and the second component precoder corresponds to an N x K second matrix for precoding K symbols, the K symbols being different from the M symbols, and M+K being greater than N, and wherein at least one of the first and second component precoders includes at least one of: at least one complex-valued element, or has at least two complex-valued or real-valued elements having at least two different non-zero amplitudes affecting the output value of at least one precoder; determining a precoded signal based on encoding a first symbol vector of the M symbols using the first component precoder and encoding a second symbol vector of the K symbols using the second component precoder; and transmitting a signal including the precoded signal to a second device.

[0007] In a fourth aspect of the disclosure, a method is provided. The method comprises receiving a signal from a first device at a second device; and decoding the received signal by using at least one of a first component precoder and a second component precoder, wherein the first component precoder corresponds to a first matrix of N rows and M columns for precoding M symbols, and the second component precoder corresponds to a second matrix of N rows and K columns for precoding K symbols, the K symbols being different from the M symbols, and M+K is greater than N, and wherein at least one of the first component precoder and the second component precoder comprises at least one of: at least one complex-valued element, or having at least two complex-valued or real-valued elements with at least two different non-zero amplitudes affecting at least one precoder output value.

[0008] In a fifth aspect of the disclosure, a first device is provided. The first device comprises means for obtaining a symbol precoder comprising a first component precoder and a second component precoder dependent on each other, wherein the first component precoder corresponds to a first matrix of N rows and M columns for precoding M symbols, and the second component precoder corresponds to a second matrix of N rows and K columns for precoding K symbols, the K symbols being different from the M symbols, and M+K is greater than N, and wherein at least one of the first component precoder and the second component precoder comprises at least one of: at least one complex-valued element, or having at least two complex-valued or real-valued elements with at least two different non-zero amplitudes affecting at least one precoder output value; means for determining a precoded signal based on encoding a first symbol vector of the M symbols by using the first component precoder, and encoding a second symbol vector of the K symbols by using the second component precoder; and means for transmitting a signal comprising the precoded signal to a second device.

[0009] In a sixth aspect of the disclosure, a second device is provided. The second device comprises means for receiving a signal from a first device; and means for decoding the received signal by using at least one of a first component precoder and a second component precoder, wherein the first component precoder corresponds to a first matrix of N rows and M columns for precoding M symbols, and the second component precoder corresponds to a second matrix of N rows and K columns for precoding K symbols, the K symbols being different from the M symbols, and M+K is greater than N, and wherein at least one of the first component precoder and the second component precoder comprises at least one of: at least one complex-valued element, or having at least two complex-valued or real-valued elements with at least two different non-zero amplitudes affecting at least one precoder output value.

[0010] In a seventh aspect of the disclosure, a computer readable medium is provided. The computer readable medium comprises instructions stored thereon for causing an apparatus to perform at least the method according to the third aspect.

[0011] In an eighth aspect of the disclosure, a computer readable medium is provided. The computer readable medium comprises instructions stored thereon for causing an apparatus to perform at least the method according to the fourth aspect.

[0012] It is to be understood that the Summary is not intended to identify key or essential features of embodiments of the disclosure, nor is it intended to limit the scope of the disclosure. Other aspects of the disclosure will become readily apparent to those skilled in the art by review of the following description. BRIEF DESCRIPTION OF DRAWINGS

[0013] Some example embodiments will now be described with reference to the accompanying drawings, in which:

[0014] Figure 1 a communication environment in which example embodiments of the disclosure can be implemented is illustrated;

[0015] Figure 2A a signaling flow illustrating an example process for signal precoding according to some example embodiments of the disclosure is illustrated;

[0016] Figure 2B a schematic diagram illustrating an example process for signal encoding and decoding according to some example embodiments of the disclosure is illustrated;

[0017] Figure 3 a schematic diagram illustrating an example precoding-based transmission and estimation system according to some example embodiments of the disclosure is illustrated;

[0018] Figure 4A and Figure 4B a graph illustrating example simulation results according to some example embodiments of the disclosure is illustrated;

[0019] Figures 5A to 5C a matrix for an example symbol precoder according to some example embodiments of the disclosure is illustrated;

[0020] Figure 6 a flow diagram illustrating a method implemented at a first apparatus according to some example embodiments of the disclosure is illustrated;

[0021] Figure 7 a flow diagram illustrating a method implemented at a second apparatus according to some example embodiments of the disclosure is illustrated;

[0022] Figure 8 a simplified block diagram of a device suitable for implementing example embodiments of the disclosure is illustrated; and

[0023] Figure 9 FIG. 1 illustrates a block diagram of an example computer-readable medium, in accordance with some example embodiments of the present disclosure.

[0024] Throughout the drawings, identical or similar reference numerals can designate identical or similar elements throughout the several views. DETAILED DESCRIPTION

[0025] The principles of the present disclosure will now be described with reference to some example embodiments. It should be understood that these embodiments are described for illustrative purposes only and help the skilled person to understand and implement the present disclosure and do not represent any limitation on the scope of the present disclosure. The embodiments described herein can be implemented in various ways other than those described below.

[0026] In the following description and claims, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.

[0027] In the present disclosure, references to “one embodiment”, “an embodiment”, “example embodiments” etc. mean that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment.

[0028] It should be understood that although the terms “first”, “second”, “third” etc. before a noun (or nouns) can 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 and do not limit the order of the noun(s). For example, a first element can be termed as a second element, and similarly, a second element can be termed as a first element, without departing from the scope of the example embodiments. As used herein, the term “and / or” includes any and all combinations of one or more of the listed terms.

[0029] As used herein, “at least one of ” and “one or more of ” and similar phrases, where a list of two or more elements is preceded by “at least one of” or “one or more of”, refers to any one of the elements in the list, or any combination of at least two or more of the elements in the list.

[0030] As used herein, unless expressly stated otherwise, performing a step "in response to A" does not indicate that the step is performed immediately after "A" occurs, but can include one or more intervening steps.

[0031] 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", "has", "having", "includes" and / or "including" when used herein, specify the presence of stated features, elements and / or components etc. but do not preclude the presence or addition of one or more other features, elements, components and / or combinations thereof.

[0032] As used in this application, the term "circuitry" can refer to one or more or all of the following: (a) hardware-only circuit implementations (such as implementations in only analog and / or digital circuitry) and (b) combinations of hardware circuits and software, such as (as applicable): (i) combinations of analog and / or digital hardware circuits with software / firmware (ii) combinations of hardware processors (including digital signal processors) with software software, and memory that work together to make the device, such as a mobile phone or server, carry out various functions) and (c) hardware circuit(s) and or processor(s), such as a microprocessor(s) or a portion of a microprocessor(s), that requires software (e.g., firmware) for operation, but it does not mean that software is required for the hardware circuit or processor to function; it the software can not be present when it is not needed for the hardware circuit or processor to function.

[0033] This definition of circuitry applies to all uses of this term in this application, including in any claims. As a further example, as used in this application the term circuitry also covers an implementation that has a hardware circuit or processor (or multiple processors) and software (or firmware) that works together to make the device carry out various functions described herein, regardless of whether such software is separate from the hardware circuit(s) or processor(s). For example, if a claim recites a computing device, processor, or controller that "has memory", this means that the computer device, processor, or controller has the ability to retain and convey software even if that software is not physically present within the device, processor, or controller. Software can be a simple set of instructions for using the circuitry, or circuitry and / or processor, or it can be more complex, such as an operating system with appropriate application software. Note that just as hardware is not physical software, physical hardware is not to be construed as physically encompassing software unless the claim explicitly states that software is physically encompassed.

[0034] As used herein, the term “communication network” refers to a network that follows any suitable communication standard, such as New Radio (NR), Long Term Evolution (LTE), LTE-Advanced (LTE-A), Wideband Code Division Multiple Access (WCDMA), High-Speed Packet Access (HSPA), Narrow Band Internet of Things (NB-IoT), etc. Further, the communication between terminal devices and network devices in a communication network can be conducted according to any suitable generation communication protocol, including but not limited to, first generation (1G), second generation (2G), 2.5G, 2.75G, third generation (3G), fourth generation (4G), 4.5G, fifth generation (5G), 5.5G, and sixth generation (6G) communication protocols, and / or any other protocols that are currently known or that become developed in the future. Embodiments of the present disclosure can be applied to various communication systems. In view of the rapid development in communications, it is of course possible that future types of communication technologies and systems will be introduced to embody the present disclosure. It should not be considered as limiting the scope of the present disclosure to the above-described systems only.

[0035] As used herein, the term “network device” refers to a node in a communication network via which a terminal device accesses the network and receives services from the network. The network device can refer to a base station (BS) or an access point (AP), e.g., a NodeB (NB), an evolved NodeB (eNodeB or eNB), an NR NB (also known as gNB), a remote radio unit (RRU), a radio head (RH), a remote radio head (RRH), a relay, an integrated access and backhaul (IAB) node, a low power node (such as a femto, pico), a non-terrestrial network (NTN) or non-ground network device, such as a satellite network device, a low earth orbit (LEO) satellite and a geosynchronous earth orbit (GEO) satellite, an airplane network device, etc., depending on the terminology used and technology. In some example embodiments, a radio access network (RAN) split architecture includes a centralized unit (CU) and a distributed unit (DU) at an IAB donor node. An IAB node includes a mobile terminal (IAB-MT) part that behaves like a UE to a parent node, and a DU part of the IAB node that behaves like a base station to a next-hop IAB node.

[0036] The term "terminal device" refers to any terminal device capable of wireless (radio, but not limited to radio), or even wired (e.g., optical) communication, depending on the communication system. By way of example, and without limitation, a terminal device can also be referred to as a communication device, user equipment (UE), subscriber station (SS), portable subscriber station, mobile station (MS), or access terminal (AT). A terminal device can include, but is not limited to, a mobile telephone, a cellular telephone, a smartphone, a voice over Internet Protocol (VoIP) telephone, a wireless local loop (WLL) telephone, a tablet, a wearable terminal device, a personal digital assistant (PDA), a portable computer, a desktop computer, an image capture terminal device, such as a digital camera, a game terminal device, a music storage and playback appliance, a vehicle-mounted wireless terminal device, a wireless endpoint, a mobile station, a laptop-embedded equipment (LEE), a laptop-mounted equipment (LME), a USB dongle, a smart device, a wireless customer-premise equipment (CPE), an Internet of Things (IoT) device, a watch or other wearable device, a head-mounted display (HMD) (e.g., a pair of glasses or other eyewear with a display for virtual reality applications), a vehicle, a drone, a medical device and applications (e.g., remote surgery), industrial devices and applications (e.g., robots and / or other wireless devices operating in an industrial and / or

[0037] As used herein, the terms "resource," "transmission resource," "resource block," "physical resource block" (PRB), "uplink resource," or "downlink resource" can refer to any resource used to perform communication, such as communication between a terminal device and a network device, such as a time-domain resource, a frequency-domain resource, a spatial-domain resource, a code-domain resource, or any other combination of time-domain, frequency-domain, spatial-domain, and / or code-domain resources, etc., that enables the communication. Hereinafter, unless explicitly stated otherwise, resources in the frequency and time domains will be used as an example of transmission resources to describe some example embodiments of the present disclosure. It should be noted that example embodiments of the present disclosure are equally applicable to other resources in other domains.

[0038] Figure 1 An example communication environment 100 in which example embodiments of the present disclosure can be implemented is illustrated. In the communication environment 100, multiple communication devices, including a first apparatus 110 and a second apparatus 120, can communicate with each other. In Figure 1 In an example, the first apparatus 110 can be a UE, and the second apparatus 120 can be a base station serving the UE. A service area of the second apparatus 120 can be referred to as a cell 102.

[0039] It should be understood that Figure 1 The number of devices and their connections shown are for illustrative purposes only and are not meant to be limiting. The communication environment 100 can include any suitable number of devices configured to implement example embodiments of the present disclosure. Although not shown, it is to be understood that one or more additional devices can be located in the cell 102, and one or more additional cells can be deployed in the communication environment 100. Note that while illustrated as a network device, the second apparatus 120 can be another device other than a network device. While illustrated as a terminal device, the first apparatus 110 can be another device other than a terminal device.

[0040] Hereinafter, for illustrative purposes, some example embodiments are described in which the first apparatus 110 operates as a UE and the second apparatus 120 operates as a base station. However, in some example embodiments, operations described in connection with a terminal device can be implemented at a network device or other device, and operations described in connection with a network device can be implemented at a terminal device or other device.

[0041] In some example embodiments, the transmission direction from the second apparatus 120 to the first apparatus 110 is referred to as the downlink (DL), and the transmission direction from the first apparatus 110 to the second apparatus 120 is referred to as the uplink (UL). In the DL, the second apparatus 120 is the transmitting (TX) device (or transmitter), and the first apparatus 110 is the receiving (RX) device (or receiver). In the UL, the first apparatus 110 is the TX device, and the second apparatus 120 is the RX device.

[0042] Communications in the communication environment 100 can be implemented according to any suitable communication protocol(s), including but not limited to cellular communication protocols, wireless local area network communication protocols such as Institute of Electrical and Electronics Engineers (IEEE) 802.11, and / or any other protocol that is presently known or that is hereafter developed. Further, communications can utilize any suitable wireless communication techniques, including but not limited to code division multiple access (CDMA), frequency division multiple access (FDMA), time division multiple access (TDMA), frequency division duplexing (FDD), time division duplexing (TDD), multiple-input multiple-output (MIMO), orthogonal frequency division multiplexing (OFDM), discrete Fourier transform spread OFDM (DFT-s-OFDM), and / or any other techniques that are presently known or that are hereafter developed.

[0043] Multiplexing is a mechanism in a communication network that aims to combine multiple signals for transmission over a shared medium. Various mechanisms have been proposed for signal multiplexing. For example, time or frequency orthogonal sub-channels can be multiplexed. Multiplexing techniques can include time division multiplexing (TDM), frequency division multiplexing (FDM), and code division multiplexing (CDM). However, inefficient allocation of radio resources for multiplexing can result in wastage.

[0044] The operation and performance of multiplexing can be related to channel properties. For example, the multiplexing granularity of pilots (e.g., the frequency at which pilots are introduced) can depend on channel properties such as Doppler, frequency selectivity, etc. Signal multiplexing can impact channel estimation at the receiver side. For example, multiplexed pilots (or any reference symbols) can be used for channel estimation. As another example, channel estimation methods for pilot-less transmission (e.g., via constellation shaping) can also be used.

[0045] Currently, as an example, to enable efficient channel estimation in current wireless systems or 6G systems, methods for designing pilot / reference symbol sequence framework in conjunction with data modulation are proposed. For example, pilots can be multiplexed using orthogonal resources (e.g., in CDM or TDM), or can be independently multiplexed across data and known symbols, as in superposition pilot schemes.

[0046] However, typical superposition pilot schemes can cause interference in the channel estimation process and can result in less accurate data detection. It can require some complex interference cancellation. Furthermore, in different environments, the resources allocated to known symbols and data, e.g., time slots / slots, need to be adjusted and managed to improve overall performance. In many cases, the inaccuracy of channel estimation can cause a bottleneck to overall performance.

[0047] In communication systems such as large-scale multiple-input multiple-output (MIMO) systems, it is necessary to control the pilot overhead in a reasonable way to ensure a conscious trade-off between channel accuracy (via estimation by any method, such as artificial intelligence and machine learning (AIML) or traditional techniques) and data detection performance and / or transmission rate. Increasing the number of reference symbols can generally reduce the number of remaining transmission resources for data. Similarly, in channels with high Doppler spread, the receiver can need higher pilot granularity in the time domain. In MIMO or MISO systems, channel estimation not only plays a key role in decoding data, but also plays a key role in various closed-loop beamforming concepts (such as in closed-loop MIMO), in which CSI-related information (such as beamforming codebook information or channel estimation) is signaled to the transmitting unit for use in some subsequent transmission instances.

[0048] In many cases, it is beneficial to multiplex additional information or additional signals (data and / or pilots) into the transmission such that the effect on some existing impact of the main stream transmission scheme is small. For example, a wireless system can already employ a precoding scheme for different purposes. For example, in 5G systems, symbol precoding is employed for the purpose of peak-to-average ratio reduction for OFDM systems (e.g. DFT-s-OFDM). It can thus be meaningful to consider a multiplexing or precoding solution that causes minimal changes to the DFT-s-OFDM waveform, preferably such that the existing transmission concepts can be preserved to some extent. To this end, in a particular example, it can be beneficial to precode the DFT precoder with a matrix that has dominant amplitude values in each row or at least contains elements with different amplitude values.

[0049] According to some example embodiments of the present disclosure, a solution for signal precoding in signal multiplexing is provided. In the solution, a first apparatus obtains a symbol precoder (dependency can be defined as algorithmic dependency or via algebraic properties like correlation, non-unitarity, etc.), the symbol precoder comprising a first constituent precoder and a second constituent precoder dependent on each other, wherein the first constituent precoder has N rows and M columns for precoding M symbols, and the second constituent precoder has N rows and K columns for precoding K symbols, the K symbols being different from the M symbols, and M+K being greater than N, and wherein at least one of the first constituent precoder and the second constituent precoder comprises at least one of: at least one complex-valued element, or has at least two complex-valued or real-valued elements with at least two different non-zero amplitudes affecting at least one precoder output value. The first apparatus determines a precoded signal based on encoding a first symbol vector of the M symbols by using the first constituent precoder, and encoding a second symbol vector of the K symbols by using the second constituent precoder, and transmits a signal comprising the precoded signal to a second apparatus.

[0050] With the solution, the first constituent precoder and the second constituent precoder dependent on each other can be used for precoding the first symbol vector and the second symbol vector or more generally symbol vectors, respectively. The dependency between the first constituent precoder and the second constituent precoder can provide a transmission scheme that is in between a fully orthogonal scheme and a superposition scheme.

[0051] For example, the proposed solution of the present disclosure can provide an improved and versatile arrangement for multiplexing pilot symbols or data symbols or a combination thereof (e.g., reference symbols) to a transmission chain in a way that combines pilot-free (constellation design) and pilot superposition schemes. As an example, the proposed solution of the present disclosure can enable a transmission scheme in which the interference between superposed pilot and data channels is at one extremum, zero. In a variant, the interference projection or cross-interference between multiplexed signals can be fully controllable. Moreover, for example, the superposed pilot sequence can be spread over multiple data symbols in a way that limits or controls the cross-interference, and can also include other criteria for the sequence of symbols, such as peak-to-average ratio.

[0052] Furthermore, the proposed solution of the present disclosure can enable multiplexing of pilot signals to N-slot block transmissions without the need to clear one of these slots for pilot / reference symbols. Thus, if better channel estimation is needed, there is no need to necessarily modify the frame structure. Moreover, if the data and pilot signals are made substantially orthogonal (at the cost of partially non-orthogonal data ("self-interference") or non-orthogonal pilots, respectively), the power of the pilot signals can be increased if better channel estimation is needed. Furthermore, some receivers can not even want to decode / detect the data, e.g., if it is for a different receiver or a different service. Thus, the ability to effectively decouple the multiplexed streams using a properly designed precoding matrix reduces the complexity of the receiver and, typically, also the energy consumption, since there is no need to process the undesired signals.

[0053] Example embodiments of the present disclosure will be described in detail below with reference to the attached drawings.

[0054] Figure 2A A signaling flow illustrating an example procedure 200 for signal precoding according to some example embodiments of the present disclosure is shown. For the purpose of discussion, reference will be made to Figure 1 The procedure 200 is described. The procedure 200 involves Figure 1 a first device 110 and a second device 120 in Figure 2B A signaling flow illustrating an example procedure 250 for signal encoding and decoding according to some example embodiments of the present disclosure is shown.

[0055] As Figure 2A shown, the first device 110 obtains (205) a symbol precoder comprising a first constituent precoder and a second constituent precoder dependent on each other. The first device 110 determines (210) a precoded signal based on encoding a first symbol vector by using the first constituent precoder and encoding a second symbol vector by using the second constituent precoder. For example, as Figure 2BAs shown, the first apparatus 110 can encode the data symbol vector X with a first constituent precoder and the pilot symbol vector with a second constituent precoder.

[0056] The first and second constituent precoders that are dependent on each other can mean that one of the first and second constituent precoders changes as a function of the other of the first and second constituent precoders. In other words, if the first constituent precoder changes, the second constituent precoder changes accordingly, and vice versa. Each of these first and second constituent precoders is not a unit matrix, which distinguishes it from a typical superposition scheme.

[0057] In the following, various designs of the first constituent precoder (also referred to as precoder A) and the second constituent precoder (also referred to as precoder B) will be described. The precoder A corresponds to a first precoding matrix (also referred to as matrix A), and the precoder B corresponds to a second precoding matrix or vector (also referred to as matrix or vector B). The matrix A has N rows and M columns for precoding M symbols, and the second constituent precoder B has N rows and K columns for precoding K symbols that are different from the M symbols, and the sum of M and K (i.e., M+K) is greater than N. Thus, the symbol precoder can also be referred to as a “fat” matrix.

[0058] At least one of the first and second constituent precoders comprises at least one of: at least one complex-valued element, or has at least two complex-valued or real-valued elements with at least two different non-zero magnitudes affecting at least one precoder output value. For example, at least one of the first and second constituent precoders (which can be precoder A or precoder B in different cases) can comprise at least one complex-valued element, such as a matrix with complex diagonal values. However, it is not limited to a diagonal real-valued projection matrix or a Hadamard matrix.

[0059] To enable the dependency between the first and second constituent precoders, the two precoders can be jointly designed, or they can have interrelated algebraic properties (e.g., via projection or interference energy or correlation with a certain structure)

[0060] In some example embodiments, the dependency between the first and second constituent precoders can be implemented by a correlation between columns of the first and second constituent precoders. The correlation between at least one pair of columns within the first constituent precoder can be higher than the correlation between any column of the first constituent precoder and any column of the second constituent precoder. For example, if a data symbol vector X is precoded via a matrix A, and a pilot symbol vector is precoded via a matrix / vector B, the correlation of a column vector or a column vector in B with a column vector of matrix A can be smaller compared to the correlation of a pair of columns in matrix A. If there is no such correlation, channel estimation can be performed under the assumption that the pilot symbol vector is independent of the data symbol vector.

[0061] In some embodiments, the matrix A can be associated with a first projection matrix, and the matrix B can be a second projection matrix, or associated with basis vectors defining the above-mentioned projection matrices. Alternatively, the first and second matrices can be approximate projection matrices, or at least one of the first or second matrices depends on a projection matrix. The first and second projection matrices can define different subspaces. For example, the precoders A and B can be constructed as (dependent on each other) projection matrices to two different subspaces. In particular, the different subspaces can have different dimensions. The projection matrices can be defined, for example, via an outer product of respective orthogonal basis vectors, which will be described in detail below.

[0062] In some embodiments, a first subspace defined by the matrix A can be orthogonal to a second subspace defined by the matrix B or the basis vector(s) of the above-mentioned subspace. For example, the first subspace defined by the matrix A can be orthogonal to the second subspace defined by the matrix B, denoted as where I denotes an identity matrix.

[0063] Alternatively, in some example embodiments, the first subspace defined by the first matrix A can be orthogonal to a rotated subspace or modified subspace that is rotated from a second subspace defined by the second matrix or vector B. In this scheme, the matrix A can not be a rotation in the strict sense, as a rotation matrix is not necessarily a projection matrix.

[0064] In particular, the first matrix can be obtained by subtracting a scaling matrix from an identity matrix, and the scaling matrix is a matrix that is scaled from the second matrix B based on a rotation or modification factor. For example, it can be denoted as As shown in this equation, the modification or rotation of the rotated subspace from the second subspace defined by the second matrix B can be controlled by a rotation or modification factor where the rotation or modification factor is smaller than 1 and larger than 0. The matrix A can be based on this factor is constructed. It should be noted that the phrase rotation is only used to highlight the modification to the precoder and the phrase projection matrix can also be an approximate projection matrix. In particular, matrix A can be an approximate projection matrix, but the subspace associated with matrix A is still different from the subspace associated with matrix B.

[0065] In some embodiments, matrix B can be determined first based on the sequence, and matrix A can be determined accordingly based on matrix B. The second matrix B can be the Hermitian product of the scaled vectors from the sequence, and the first matrix A can be a matrix scaled from another matrix, which is obtained by subtracting the scaled second matrix B from the identity matrix, the scaled second matrix being based on a rotation factor scaled. As an example, this can be represented as follows. where b N denotes a sequence, denotes matrix A, denotes matrix B, and a and b are non-zero coefficients that affect the amplitudes of the elements in matrix A and matrix B. Note that if the basis matrix is determined by an orthogonal vector u, then the sequence of pilot signals precoded by the second constituent precoder is , or is the corresponding as described above. Thus, it is clear that matrix B does not necessarily need to be explicitly calculated. If more than one auxiliary data or pilot signal is to be used, we can have another basis vector (even possibly a non-orthogonal / unitary basis vector), for example, two basis vectors and determine the projection matrices and , or their approximations, such as , It should be noted that there are also alternative algorithms for calculating the projection matrix. Here, the projection matrix determines the relative weights of the matrix elements, and amplitude or power scaling (power control, etc. known in the art) can be further used.

[0066] the sequence (or ) can be known by one or both of the transmitter and receiver. In some embodiments, the first apparatus 110 and the second apparatus 120 can know the sequence. For example, information identifying the sequence can be determined by the first apparatus 110 and sent to the second apparatus 120, or information identifying the sequence can be determined by the second apparatus 120 and sent to the first apparatus 110. The information can be the sequence itself, or for example an index into a codebook of predefined sequences (such as a DFT row / column index). Furthermore, the sequence can be defined over multiple blocks or channel uses. For example, it can be defined over CDM, TDM, OFDM, and various channel uses. The scope of the present disclosure is not limited in this respect.

[0067] In the example of a pilot-driven design, the sequence can be a pilot sequence. The first apparatus 110 can be provided with the pilot sequence b N In some cases, the pilot sequence can be defined in a standard. Alternatively, the pilot sequence can be signaled from the second apparatus 120 to the first apparatus 110. Alternatively, the pilot sequence can be selected by the first apparatus 110 and signaled to the second apparatus 120.

[0068] The pilot sequence can define a "pilot subspace", and based on the selected sequence b N The first apparatus 110 can determine the matrix B as the Hermitian product of the vector b N scaled by the matrix B, and determine the matrix u based on the scaling from the matrix A N The matrix is obtained by subtracting the scaled matrix B from the identity matrix I .

[0069] In some example embodiments, the matrix A can be determined first, and the matrix B can be determined based on the matrix A accordingly. In the example where the matrix A encodes the data symbol vector, this can be referred to as a data-driven design.

[0070] The matrix B can be defined by the smallest dominant eigenvector of the product of the matrix A and the conjugate transpose of the matrix A. The matrix A can be one of the following matrices: a non-orthogonal matrix, a non-unitary matrix, a square matrix with a rank less than the dimension of the square matrix, or a matrix whose eigenvalues of the product of the matrix and its conjugate transpose are at least partially unequal. For example, The eigenvalues of the product of the matrix A and the conjugate transpose of the matrix A can be at least partially unequal, and the r eigenvectors corresponding to the smallest eigenvalues of the product of the matrix A and the conjugate transpose of the matrix A can define the matrix B. The r eigenvectors of the matrix A can define the matrix B.

[0071] In this case, for example, the matrix A (e.g., N N The matrix A can be defined as It should be noted that when γ = 1, this can be an average transform. It can subtract a total sum signal from the desired signal, which depends on all or multiple signals in the block. When combining in-phase and quadrature (I / Q) samples over the block, the total sum signal can approach a Gaussian distributed interference.

[0072] The matrix B can be defined as The matrix B can be a superimposed pilot which can be jointly designed with or can use a rotation to generate as described above. It should be noted that when equals 1, the all-one pilot sequence ( ) can be deterministically projected to zero, mainly due to the minimum dominant eigenvector property. In this case, the situation can occur. Therefore, the all-one vector can be used as a zero-projection superimposed pilot sequence. Therefore, due to the all-one property, the channel estimation can be formed by summing the I / Q samples over the block of N received symbols. If the definition of the matrix A is different, the channel estimation can be a (complex) weighted combination of the received samples in the block of N received samples.

[0073] In some example embodiments, some specific designs can be considered. The matrix B can be a (normalized) DFT matrix or a column restriction of the DFT matrix. The column restriction can be any selection of columns, subcarriers, etc. The first apparatus 110 can obtain a sequence from a subcarrier or subvector of the matrix B; and can obtain a matrix A based on the sequence, and obtain a rotation of the matrix B based on a rotation factor. In this specific design, the symbol precoding can involve a DFT matrix, such as Discrete Fourier Transform Spread Orthogonal Frequency Division Multiplexing (DFT-s-OFDM) or OFDM in general. Then, one or more (selected) subcarriers / subvectors of B can be used / selected as the pilot sequence, and the matrix A can be defined based on the selection. For example, the matrix A can be offset from B by a rotation. Depending on the selected DFT vector, the matrix A can be real-valued or complex-valued. In this case, the selection of subcarriers can affect the data performance, as each selection can result in a different matrix A, and different matrix A can have different performance in a given channel. In addition, the selection of the rotation factor or coefficient can also affect the performance trade-off between the data and the channel.

[0074] ​In some other embodiments, the matrix B can be other unitary matrices, column restrictions, Hadamard vectors, or wavelet vectors. In some embodiments, the matrix B can have at least two complex- or real-valued elements with at least two different non-zero amplitudes affecting at least one precoder output value. For example, the elements of the matrix B, or the elements of u or b have different amplitudes, i.e., at least one element of the matrix B (or u or b ) has a different amplitude compared to another element.

[0075] After the symbol precoders are obtained, the first apparatus 110 determines (210) a precoded signal based on encoding a first symbol vector by using a first constituent precoder A, and encoding a second symbol vector by using a second constituent precoder B. The first apparatus 110 also transmits (215) a signal comprising the precoded signal to the second apparatus 120.

[0076] In some embodiments, at least one of the first symbol vector or the second symbol vector can comprise a priori known symbols, such as reference symbols or pilot symbols. For channel estimation purposes, in some cases, a suitable known symbol (e.g., a demodulation reference signal (DMRS)) can be input into the precoder B. For example, the first symbol vector can be a data vector, and the second symbol vector can be a pilot vector. Alternatively, the first symbol vector can be a reference vector combining data information and pilot information, and the second symbol vector can be a different reference vector combining data information and pilot information. The data information and the pilot information can be multiplexed in different ways. For example, a pilot i signal (such as a time sequence of pilot symbols or reference symbols) can be partially mapped to A or modulated by A (e.g., as one input vector), and data information symbols can be mapped to B or modulated by B.

[0077] In some embodiments, the first symbol vector and / or the second symbol vector can be for one or more receivers. For example, signal multiplexing can be applied to a point-to-multipoint channel. The first symbol vector or the second symbol vector can have symbols for one or more apparatuses including the second apparatus 120.

[0078] In some example embodiments, the first apparatus 110 can determine the precoded signal by at least partially multiplexing the encoded first symbol vector and the encoded second symbol vector in overlapping resource elements, and the overlapping resource elements can overlap in at least one of a time domain, a frequency domain, or a spatial domain. The precoded signal can be transmitted using a multi-carrier or a single-carrier modulation. As Figure 2BAs shown, in block T, the outputs of the two precoders A and B can be at least partially multiplexed in overlapping time / frequency / space resources by subcarriers, time slots, or beams. For example, the signals can be multiplexed in the frequency domain and transmitted on different subcarriers, or multiplexed into time-frequency resources.

[0079] In some embodiments, the precoded signal determined based on the symbol precoder can be further processed by another symbol precoder, also referred to as a second symbol precoder, to determine a second precoded signal. The second symbol precoder can have a size Z × N and Z ≥ N . The second symbol precoder can be associated with any waveform that can be represented by a matrix of size Z × N . The second symbol precoder can include a DFT precoder, for example, the DFT part of DFT-s-OFDM. Then, the first apparatus 110 can transmit a signal including the second precoded signal to the second apparatus 120. As Figure 2B shown, this transmission can take place over a channel H. During the transmission, some other channel noise, denoted as n, can also be added to the signal.

[0080] At the receiver side, the second apparatus 120 receives (218) the signal from the first apparatus 110. The second apparatus 120 also decodes (220) the received signal using at least one of the precoder A or the precoder B. Depending on the design of the precoder A and the precoder B, various ways can be used to decode the received signal.

[0081] In some embodiments, the second apparatus 120 can decode the signal by performing joint data estimation and channel estimation. Alternatively, the second apparatus 120 can perform channel estimation without data estimation. For example, the data can not be intended for the second apparatus 120, and the second apparatus 120 can only perform channel estimation. Alternatively, the second apparatus 120 can perform data estimation and channel estimation separately. For example, since the interference between the data part and the pilot part is controllable, the data estimation and the channel estimation can be processed separately or sequentially.

[0082] In some embodiments, the second apparatus 120 can first perform channel estimation, and then perform data estimation based on at least one of the precoder A or the precoder B and the channel estimation. If the precoder A encodes the data vector and the precoder B encodes the pilot vector, the second apparatus 120 can perform channel estimation by using the precoder B, and perform data estimation with or without the precoder A.

[0083] This is because the precoder A (i.e., matrix A) tends to diagonalize as the dimension increases, so the receiver can perform data detection without knowing the precoder A (there can be a small loss in dB if matrix A is "approximated" by the identity matrix). The transmitter can also use the precoder A and vector u to decouple the channel estimation from the data detection. Then, the receiver can only need to know the vector u associated with matrix A. Related simulations in this disclosure even show that it can be better to decouple if the receiver does not know the precoder A. However, if the vector u is used together with the precoder A for channel estimation, it can improve the channel estimation for the purpose of data detection or any other use of channel estimation (e.g., it can provide better quality channel state information (CSI) feedback for beamforming). In some embodiments, the second device 120 can also send (225) feedback related to the channel estimation derived at the second device 120 to the first device 110. At the transmitter side, the first device 110 receives (230) the feedback from the second device 120.

[0084] In some embodiments, the second device 120 can demultiplex the channel resources in different operations according to the selected subspace rotation, i.e., based on the rotation or modification factor γ. As shown in FIG. 2B, in the "iT" block, the channel resources can be demultiplexed. If γ is equal to 0, it means that a superposed pilot (with an externally given sequence) can be used. If γ is equal to 1, it means that the precoder A and the precoder B can independently encode the respective symbol vectors, so the decoding can not need nonlinear interference cancellation or joint detection. In the case of γ = 1 and precoder A being diagonal, the decoding operation can be similar to the decoding operation in TDMA. If γ is greater than 0 and less than 1, it means that there is a trade-off between the processing of precoder A and precoder B, i.e., the cross-interference between precoder A and precoder B needs to be considered in the decoding. Figure 2B

[0085] In some examples, assuming (for simplicity) that the channel h is constant over N symbols (e.g., single-carrier modulation, flat-fading OFDM subcarriers, etc.), the received signal can be represented as:

[0086] The received signal can be processed to perform joint data estimation (for data ) and channel estimation (for channel ). Alternatively, a superposed pilot (which assumes the use of t = 1,..., T channels) can be used to estimate the channel h, and the estimated channel h can be used to perform data detection by using the precoder or the precoder B (or​ at least one of the data and the knowledge of the channel estimates .

[0087] It should be noted that the channel can vary (e.g., using different resources such as subcarriers, time slots, beams, etc.) in different channel uses. In some examples, the pilot sequence can be defined over multiple blocks or channel uses. The dimension N can be chosen such that the channel remains constant over its effective time-frequency span. Then, multiple raw estimates can be combined (e.g., averaged) over multiple estimates (as shown in Figure 3 , for example, the average of 20 channel estimates used).

[0088] Referring to FIG. 2, a solution for signal precoding is provided according to embodiments of the disclosure. In this solution, a precoding scheme is proposed that results in different types of re-encoding matrices. For example, in the present invention, various different choices of unitary matrices can result in less PAR than the state of the art. It can also be applied in one subcarrier (e.g., serial transmission), or output to different subcarriers if needed. Moreover, the present invention can be applied to any multiplexing method, not just limited to OFDM. For example, through this solution, the Fourier basis vectors can be chosen as the pilot precoder b, or any scheme for constructing the precoder A based on arbitrary b can be chosen, and vice versa. It should be noted that when N is large enough, this scheme can achieve orthogonalization, which means that the traditional reception does not need to know the precoder A, as it needs to be applied at the transmitter side. Typically, for shorter blocks, the receiver can need to know the matching precoder A and precoder B. To get the best performance, it can need to control N and g based on data detection or channel estimation.

[0089] Figure 3 A schematic diagram of an exemplary precoding-based transmission and estimation system is illustrated in accordance with some example embodiments of the present disclosure. This illustrates example embodiments implemented in a 5G or 6G setting, which can involve multiple UEs or signal streams in the uplink (UL), or different UEs / signal streams in the downlink (DL).

[0090] In the current 5G system, a fast Fourier transform (FFT) or DFT precoding scheme is used. As Figure 3As shown, in response to a data stream being fed into a modulator, it can be modulated using a digital modulation scheme (e.g., QPSK), and a cyclic extension (zero padding or cyclic prefix) can be performed, for example. The processed signal (modulated and cyclically extended, for example) can then be precoded with an FFT / DFT precoding scheme using a precoder P (as shown by the P block) that includes auxiliary signals (as shown by the AUX block). Subsequently, the precoded signal can be performed by an inverse fast Fourier transform (IFFT) and transmitted via a channel. In response to the precoded signal being received by a receiver (e.g., the second apparatus 120), the precoded signal can be subjected to a cyclic extension removal, an FFT, and forwarded to a minimum mean square error (MMSE) equalizer and an IFFT, for example. The signal can then be demodulated to retrieve the original transmitted data stream. The solution of the present disclosure mainly focuses on the precoding process (as shown by the dashed box 305), which is described in detail in FIG. 2 and will be discussed with more examples below.

[0091] For example, in the existing precoding scheme DFT-s-OFDM, an FFT scheme can be employed, which can reduce the peak-to-average ratio (PAR). In this approach, the FFT output can be transmitted directly using OFDM, e.g., via an inverse fast Fourier transform (IFFT) of size N = 2048, where a DFT / FFT precoding of size M is performed to achieve PAR reduction (size M < N). Each user can be allocated a set of subcarriers corresponding to a specific set of columns of the IFFT matrix.

[0092] In contrast, in example embodiments, a precoder (denoted as the P block in Figure 3 here) can be inserted before the M-dimensional FFT precoder. The precoder input can then be M+K-dimensional (K > 0), including K auxiliary signals (e.g., K pilots, data, or any complex symbols, as shown by the AUX block in Figure 3

[0093] The matrices A and B can at least be dependent on each other, which means that changing one affects the other. In addition, the second precoder can also be dependent on the first precoder. For example, in some example embodiments, the precoder matrix B (or the vector u referenced in FIG. 2) can also be dependent on the FFT / DFT precoder. For example, if the vector u is defined as a row z of the DFT precoder matrix, and the auxiliary signals are transmitted using the vector u, then the pilots can be in one column (one subcarrier) of the IFFT matrix. The transmitted signal can then be passed through the IFFT (P​ s) is given. The precoder matrix B (or vector u) can also be a different type of matrix, as described in Figure 2.

[0094] In the solution of the present disclosure, the precoder can typically be complex-valued to feed the existing system precoder to the model (matrix B). This typically results in a complex-valued precoder (notably, the DFT is also complex-valued). This design has a small impact on the PAR, as reducing the PAR is already a core concept of DFT-s-OFDM.

[0095] The solution of the present disclosure has a novel parameterization. In this example embodiment, the result or novel parameterization can be a modified precoder, where the precoder output can have fewer dimensions than the IFFT dimensions. For example, in Figure 3 , only one user / stream can apply the scheme, and this stream can be assigned only a subset of all subcarriers (whereas in the prior art, all subcarriers are used).

[0096] As another example, a DFT-s-OFDM type of system can be used. In the process in the dashed box, in a simplified example embodiment, the transmitted signal can be written as: where , , where the vector is an N-dimensional vector (typically complex-valued with unit norm), is a signal precoding matrix determined by the vector , the coefficients determine the correlation between the columns of A N and , the matrix is a second precoding matrix, is a ZxN wave form matrix (e.g., possibly including a cyclic prefix or zero padding). In DFT-s-OFDM, may be an N x N DFT matrix, and may include specified columns (subcarriers) of a Z x Z dimensional inverse discrete Fourier transform (IDFT) matrix. In DFT-s-OFDM, the IDFT and the DFT have a joint effect of reducing the PAR. For the purposes of the solution of the present disclosure, it can be possible to define a matrix with full dimensions (N x N) but still be able to add b N A specific type of (Or a superimposed signal modulated by known symbols or information symbols; in the above example, it is unmodulated or modulated with a known value of 1) to define in a way that keeps the PAR small. and b N .

[0097] In the above model, u Vectors can usually be used to... Defined as in u In the null space (when γ=1), or it can rotate or modify the matrix. The legi made it far away u (When 0 < γ < 1). When u When it is a reference symbol sequence, it can therefore be used (by connecting it with a subsequent receiver). u (Perform relevant estimations from data symbols) x N Channels with zero interference or only limited interference. Algebraic forms also allow for selection... u In order to, for example, combine with a DFT precoder To maintain the PAR reduction effect. When the matrix This can happen when elements do not have the same magnitude, but for example, their diagonal values ​​(or at least one value in at least one row) can have a larger magnitude than another matrix value in the same row.

[0098] To give another example, if , ,in These are all-one matrices. These matrices can be scaled to have different powers, but this can be omitted simply to simplify the notation. The magnitude of the diagonal values ​​is significantly larger. The example above would correspond to a block of 4 symbols. It will be apparent to those skilled in the art that the diagonal advantage can be further increased as the block size and matrix size increase. Matrices with larger block sizes... It can approach the identity matrix because the magnitude of each off-diagonal value can be 1 / N, and each diagonal value can be 1-1 / N, the first approaching 0, the second approaching 1, and N increasing. Nevertheless, it is possible to send vectors including N-dimensional unit vectors simultaneously. Therefore, the DFT precoder is essentially unaffected by the matrix. The influence of [the event / condition] is negligible, and its properties can remain unchanged. It should be noted that... It lies on a cyclic matrix known to have all-1 vectors (normalized) corresponding to zero eigenvalues. In practice, the smallest dominant eigenvector of the precoding matrix (preferably with zero or near-zero eigenvalues) can be used as an auxiliary basis vector.

[0099] As another example of a DFT-s-OFDM type system According to and Choose from any one of them. For example, if Corresponding to the DFT matrix If the specified row / column is specified, the matrix can be obtained via... Defined by this, and through direct calculation, it can typically have complex-valued elements in each row, while still having higher magnitudes on the diagonal. In this case, the product... It can have only one non-zero value, and therefore can only be in the matrix. Known symbols are transmitted on the corresponding column (e.g., subcarrier). However, this is generally not mandatory in the solution disclosed herein. With proper selection, the reference signal can be distributed across On any selected column. Then, the receiver can efficiently estimate Aggregation channels on multiple columns (by (Weighted calculation). Similarly, data can often be distributed across multiple columns. It should be noted that columns can represent subcarriers, time slots (e.g., in single-carrier transmission, if...). It is the identity matrix.

[0100] Nevertheless, vector (second component pre-encoder) The elements can be complex values, but at least two elements can have different magnitudes. This again leads to a first precoder composed of different structures. A N exist A N Different amplitudes can also be found on the diagonal.

[0101] Figure 4A and Figure 4B The figure illustrates example simulation results according to some example embodiments of the present disclosure. Figure 4A and Figure 4B The diagram specifically illustrates a comparison of the bit error rate (BER) for different precoding schemes with quadrature phase shift keying (QPSK) modulation.

[0102] Figure 4A The diagram illustrates the joint effect of using a linear receiver on data and channel estimation, although this may not be optimal without complexity constraints. Figure 4A In this context, the projected nonzero mean (denoted as P-NZM) refers to an example embodiment of the solution of this disclosure (as described above), where the cyclic N-dimensional (with an "average" matrix) ) can be used as precoder and the sequence of all ones pilots can be transmitted as superimposed pilots. The figure shows the performance (expressed as QPSK BER) of channel estimation for different block sizes N, which can be processed by simply averaging over a prescribed number of samples. As an example, if performed as a long term average, the transmitted signal can be expressed as which means that the average value of all symbols is subtracted from the data symbols If γ = 0, the precoder A can become a diagonal matrix, which is similar to the design of the prior art. In this special case, the pilot sequence can be a vector of all ones, which is the smallest eigenvector of , representing .

[0103] Furthermore, the theoretical BER for QPSK in an orthogonal channel is provided as a reference, as shown by the bottom curve with circular symbols. The figure demonstrates that the P-NZM outperforms the conventional superimposed pilot scheme significantly when the block size is realistic (e.g. block size 20 in the figure). However, in the case of a perfect channel, the performance is similar, since the P-NZM can inherently reduce the minimum distance due to the non-unitary precoding of the data part.

[0104] Figure 4A It is also illustrated that the loss due to non-unitary precoding can disappear as the block size increases. This is because the effect of the precoder can be to let room for one (or several) additional pilot channel(s) by compressing the data basis vectors a little closer to each other. However, as the block size N increases, the interference, effect or Gaussianization effect can become almost indistinguishable. Therefore, the solution of the present disclosure is particularly useful if N is large enough. For smaller N values, a more suitable receiver can be needed, such as a maximum likelihood receiver or an approximation thereof (e.g. iterative interference cancellation) known in the art.

[0105] Non-zero mean (denoted as NZM) was also tested. Figure 4A The simulation results for NZM projection for N = 32 and N = 128 are shown in the figure. It demonstrates that N = 32 can prove to be an acceptable performance for keeping non-orthogonality small. However, an improvement in performance can be achieved when γ = 1 / 2, which corresponds to approximately 50% of the interference being projected into the null subspace. In the conventional scheme, which means an independent design of a random projection based purely on data.

[0106] Figure 4B The impact on channel estimation of the conventional non-zero mean versus P-NZM with the same block size N is illustrated. The impact is expressed by the mean square error (MSE). As Figure 4BAs shown, due to interference avoidance, the number of symbols (e.g., the number of consecutive channel uses) required given a channel estimation error is significantly smaller. This can be relevant in fast fading channels and in applications where the estimated channel controls other resources (e.g., CSI for a beamforming codebook) and fast feedback is critical.

[0107] Figures 5A to 5C Figures illustrating matrices for an example symbol precoder (denoted P) in accordance with some example embodiments of the present disclosure. Figure 5A The matrix in Figure 505 (which is the first 8 columns of 9 columns of 8-dimensional vectors) represents the data precoder A. The last column of 510 (which is the last column of 9 columns of 8-dimensional vectors) is the superimposed pilot. The last column can correspond to the smallest dominant eigenvector (smallest eigenvalue equal to 0). The symbol precoder is generated by the first 8 columns, i.e., P = [A b].

[0108] Figure 5B Figure illustrates another example symbol precoder P when the data precoder A is a complex precoder with N = 4 (γ = 1) generated by a DFT. Note that, as shown in region 515 in Figure Figure 5B As shown in region 515 in Figure Figure 5C As a result of the It should be noted that, as a result of the

[0109] With the solution of the present disclosure, derivation of a projection or an approximate projection matrix as a precoder and a corresponding precoding method, and a fully general method for defining a pilot sequence and matching a data precoder are proposed. The definition of the pilot precoder (e.g., precoder B) and the data precoder (e.g., precoder A) can depend on each other, so precoder A is neither a unitary matrix (or a matrix with only zeros as non-diagonal values) nor a matrix with all column elements having the same power (excluding CDMA and TDMA schemes). For example, precoder B can be a conventional superimposed pilot sequence, and precoder A can be different from a unitary matrix. Preferably, if the column vectors in precoder B have a small correlation with the column vectors of precoder A, for example, data can be projected via precoder A, and pilots can be projected via precoder B. Furthermore, if there is no correlation between the column vectors in precoder B and the column vectors in precoder A, channel estimation can use pilots independent of data.

[0110] In some example embodiments, simulations can have been performed with different values of gamma, and the results were consistent with expectations. The best channel estimation can occur at gamma = 1, and the best data decoding (assuming perfect channel) also requires gamma = 1. Realistic scenarios can be somewhere in between, which is where the solution of the present disclosure can be applicable. For example, in time-varying or frequency-selective channels, the samples used for channel estimation can be only 20. Therefore, the design of the data precoding matrix should be performed under the assumption of imperfect channel knowledge. It should be noted that in simulations (e.g., as shown in Figure 4A and Figure 4B The number 20 can refer to the number of blocks used in channel estimation, which is different from the matrix dimension N. If the channel changes, in example embodiments, channel estimation can be performed every P blocks of symbols. The gist of this scheme is that for shorter blocks (e.g., number of OFDM symbols), the noise of channel estimation can also be smaller. This is the same granularity as TDM multiplexed pilots in a fading channel.

[0111] In some example embodiments, if the precoders A and B are orthogonal (e.g., gamma = 1), the system can perform channel estimation in a similar way to TDMA pilot symbols. However, unlike a conventional TDMA-based system that transmits N-1 symbols, in the present invention, N symbols can be transmitted, effectively solving the problem of self-interference caused by precoding.

[0112] In some example embodiments, the precoders can also be a truncated Hadamard matrix family, which corresponds to removing one row from a Hadamard matrix. It should be noted that this way is explicitly excluded in the prior art, which has zeros or gamma = 1 in the selected rows. Furthermore, compared to the prior art, the present invention proposes a completely decoupled approach.

[0113] In some example embodiments, it can be clear how this can be applied to MIMO settings. For example, additional multiplexing can be used in different MIMO channel usage. The solution of the present disclosure can be well matched with, for example, 5G and 6G air interfaces, basically only requiring modification of the precoding of the transmitted symbols or waveforms. For example, if the proposed concept is applied to OFDM, the transmitted waveforms can only be slightly modified when N is large. In fact, the transmitted symbols, which are originally QPSK, will exhibit some transmitter Gaussian noise due to the precoder. Furthermore, the present disclosure can also be applied when the data needs a higher modulation order than QPSK for performance reasons.

[0114] Figure 6 A flowchart illustrating an example method 600 implemented at a first device, in accordance with some example embodiments of the present disclosure, is shown. For purposes of discussion, the method 600 will be described from the perspective of the first device 110 in Figure 1 the system 100 of FIG. 1.

[0115] At block 610, the first apparatus 110 obtains a symbol precoder, the symbol precoder comprising a first constituent precoder and a second constituent precoder dependent on each other, wherein the first constituent precoder corresponds to a first matrix of N rows and M columns for precoding M symbols, and the second constituent precoder corresponds to a second matrix of N rows and K columns for precoding K symbols, the K symbols being different from the M symbols, and M+K being greater than N, and wherein at least one of the first constituent precoder and the second constituent precoder comprises at least one of: at least one complex-valued element, or at least two complex-valued or real-valued elements having at least two different non-zero amplitudes affecting at least one precoder output value.

[0116] At block 620, the first apparatus 110 determines a precoded signal based on encoding a first symbol vector of M symbols by using the first constituent precoder, and encoding a second symbol vector of K symbols by using the second constituent precoder.

[0117] At block 630, the first apparatus 110 transmits a signal comprising the precoded signal to a second apparatus.

[0118] In some example embodiments, the method 600 further comprises determining a second precoded signal based on processing the precoded signal by using a second symbol precoder of size ZxN, Z being greater than or equal to N; and wherein transmitting the signal comprising the precoded signal comprises transmitting a signal comprising the second precoded signal.

[0119] In some example embodiments, the second symbol precoder comprises a Discrete Fourier Transform (DFT) precoder. In some example embodiments, the precoded signal is transmitted using multi-carrier or single-carrier modulation. In some example embodiments, at least one of the first symbol vector or the second symbol vector comprises a priori known symbols, the a priori known symbols comprising reference symbols or pilot symbols.

[0120] In some example embodiments, a correlation between at least one pair of columns within the first constituent precoder is higher than a correlation between any column of the first constituent precoder and any column of the second constituent precoder.

[0121] In some example embodiments, the first matrix and the second matrix are projection matrices, approximate projection matrices, or at least one of the first matrix or the second matrix depends on a projection matrix.

[0122] In some example embodiments, the first subspace defined by the first matrix is orthogonal to the second subspace defined by the second matrix. In some example embodiments, the first subspace defined by the first matrix is orthogonal to a rotated subspace or a modified subspace rotated from the second subspace defined by the second matrix. In some example embodiments, the modification or rotation from the rotated subspace of the second subspace defined by the second matrix is controlled by a modification factor or a rotation factor, the modification factor or the rotation factor being less than 1 and greater than 0.

[0123] In some example embodiments, the first matrix is obtained by subtracting a scaled matrix from an identity matrix, the scaled matrix being a matrix scaled from the second matrix based on a rotation factor.

[0124] In some example embodiments, the second matrix is a Hermitian product of vectors scaled from a sequence, and the first matrix is a matrix scaled from another matrix, the other matrix being obtained by subtracting the scaled second matrix from an identity matrix, the scaled second matrix being scaled based on a rotation factor. In some example embodiments, the sequence is known to the first device and the second device.

[0125] In some example embodiments, the information identifying the sequence is determined by the first device and transmitted to the second device, or the information identifying the sequence is determined by the second device and transmitted to the first device. In some example embodiments, the sequence is defined over a plurality of blocks or channel uses.

[0126] In some example embodiments, the first matrix and the second matrix define different subspaces with different dimensions. In some example embodiments, the second matrix is defined by a smallest dominant eigenvector of a product of the first matrix and a conjugate transpose of the first matrix.

[0127] In some example embodiments, the first matrix is one of: a non-orthogonal matrix, a non-unitary matrix, a square matrix with a rank less than a dimension of the square matrix, or a matrix whose eigenvalues of a product of the matrix and a conjugate transpose of the matrix are at least partially unequal.

[0128] In some example embodiments, the first matrix is a cyclic matrix or a circular matrix, and the second matrix is defined by an all-one vector as a zero-power eigenvalue of the first matrix.

[0129] In some example embodiments, the second matrix is a discrete Fourier transform (DFT) matrix or a column restriction of the DFT matrix, and obtaining a symbol precoder comprising a first constituent precoder and a second constituent precoder comprises: obtaining a sequence from subcarriers or subvectors of the second matrix; and obtaining a first matrix based on the sequence and a rotation of the second matrix based on a rotation factor.

[0130] In some example embodiments, the second matrix is one of: a unitary matrix, a column restriction, a Hadamard vector, or a wavelet vector.

[0131] In some example embodiments, the second matrix has at least two complex- valued or real-valued elements having at least two different non-zero magnitudes affecting at least one precoder output value.

[0132] In some example embodiments, the method 600 further comprises determining a precoded signal by at least partially multiplexing the encoded first symbol vector and the encoded second symbol vector in overlapping resource elements, the overlapping resource elements overlapping in at least one of a time domain, a frequency domain, or a spatial domain.

[0133] In some example embodiments, the first symbol vector is a data vector and the second symbol vector is a pilot vector. In some example embodiments, the first symbol vector is a reference vector combining data information and pilot information and the second symbol vector is a different reference vector combining data information and pilot information. In some example embodiments, the first symbol vector or the second symbol vector has a symbol for one or more devices including the second device.

[0134] Figure 7 A flowchart of an example method 700 implemented at a second device is shown in accordance with some example embodiments of the present disclosure. For purposes of discussion, the method 700 will be described from the perspective of the second device 120 in Figure 1 The method 700 will be described from the perspective of the second device 120 in

[0135] At block 710, the second device 120 receives a signal from a first device.

[0136] At block 720, the second device 120 decodes the received signal by using at least one of a first constituent precoder and a second constituent precoder, wherein the first constituent precoder corresponds to a first matrix of N rows and M columns used to precode M symbols, and the second constituent precoder corresponds to a second matrix of N rows and K columns used to precode K symbols, the K symbols being different from the M symbols, and M + K being greater than N, and wherein at least one of the first constituent precoder and the second constituent precoder includes at least one of: at least one complex-valued element, or at least two complex-valued or real-valued elements having at least two different non-zero magnitudes affecting at least one precoder output value.

[0137] In some example embodiments, decoding the received signal includes performing joint data estimation and channel estimation. In some example embodiments, decoding the received signal includes performing channel estimation without data estimation.

[0138] In some example embodiments, decoding the received signal comprises performing data estimation and channel estimation separately.

[0139] In some example embodiments, performing data estimation and channel estimation separately comprises performing channel estimation and performing data estimation based on at least one of the first constituent precoder or the second constituent precoder and the channel estimation.

[0140] In some example embodiments, the first constituent precoder encodes a data vector and the second constituent precoder encodes a pilot vector, and performing data estimation based on at least one of the first constituent precoder or the second constituent precoder and the channel estimation comprises performing data estimation with or without the first constituent precoder.

[0141] In some example embodiments, the method 700 further comprises sending feedback related to the channel estimation derived at the second device to the first device.

[0142] In some example embodiments, a first device (e.g., the first device 110 in Figure 1 ) capable of performing any of the steps of the method 600 can comprise means for performing the corresponding operations of the method 600 and any of its embodiments. The means can be implemented in any suitable form. For example, they can be implemented in circuitry or software modules. The first device can be implemented as or included in the first device 110 in Figure 1 .

[0143] In some example embodiments, a second device (e.g., the second device 120 in Figure 1 ) capable of performing any of the steps of the method 700 can comprise means for performing the corresponding operations of the method 700 and any of its embodiments. The means can be implemented in any suitable form. For example, they can be implemented in circuitry or software modules. The second device can be implemented as or included in the second device 120 in Figure 1 .

[0144] Figure 8 is a simplified block diagram of a device 800 suitable for implementing example embodiments of the present disclosure. The device 800 can be provided to implement a communication device, e.g., the first device 110 or the second device 120 as shown in Figure 1 . As shown, the device 800 includes one or more processors 810, one or more memories 820 coupled to the processor(s) 810, and one or more communication modules 840 coupled to the processor(s) 810.

[0145] The communication module 840 is for bidirectional communication. The communication module 840 has one or more communication interfaces to facilitate communication with one or more other modules or devices. The communication interface can represent any interface needed for communication with other network elements. In some example embodiments, the communication module 840 can include at least one antenna.

[0146] The processor 810 can be of any type suitable to the local technical network, and can include, by way of non-limiting example, one or more of general purpose computers, special purpose computers, microprocessors, digital signal processors (DSPs) and processors based on multi-core processor architectures, as non-limiting examples. The device 800 can have multiple processors such as a dedicated integrated circuit chip that is time-slaved to a clock that is synchronized with a master processor.

[0147] The memory 820 can include one or more non-transitory memories and one or more transitory memories. Examples of non-transitory memories include, but are not limited to, read-only memory (ROM) 824, electrically programmable read only memory (EPROM), flash memory, a hard disk, a compact disc (CD), a digital video disc (DVD), an optical disc, a laser disc, and other magnetic storage and / or optical storage. Examples of transitory memories include, but are not limited to, random access memory (RAM) 822 and other volatile memories that do not persist during power down.

[0148] The computer program 830 includes computer executable instructions executed by the associated processor 810. The instructions of the program 830 can include instructions for performing the operations / actions of some example embodiments of the present disclosure. The program 830 can be stored in a memory (e.g., ROM 824). The processor 810 can perform any suitable actions and processes by loading the program 830 into the RAM 822.

[0149] Example embodiments of the present disclosure can be implemented by the program 830 such that the device 800 can perform any process of the present disclosure discussed with reference to FIGS. 2 to Figure 7 Example embodiments of the present disclosure can be implemented by the program 830 such that the device 800 can perform any process of the present disclosure discussed with reference to FIGS. 2 to

[0150] In some example embodiments, the program 830 can be tangibly embodied in a computer readable medium, which can be included in the device 800 (such as in the memory 820) or other storage accessible to the device 800. The device 800 can load the program 830 from the computer readable medium into the RAM 822 for execution by the device 800. In some example embodiments, the computer readable medium can include any type of non-transitory storage medium, such as a ROM, an EPROM, a flash memory, a hard disk, a CD-ROM, a DVD, and the like. The term "non-transitory" as used herein is a limitation of the medium itself (i.e., tangible, rather than a signal), rather than a limitation of the durability of the data stored thereon (e.g., RAM vs. ROM).

[0151] Figure 9 An example of a computer readable medium 900, which can be in the form of a CD, DVD, or other optical storage disk, is shown. The computer readable medium 900 has the program 830 stored thereon.

[0152] In general, the various embodiments of the disclosure can be implemented using hardware or special-purpose circuits, software, logic or any combination thereof. Some aspects can be implemented using hardware, while other aspects can be implemented using software or firmware that is executed by a controller, microprocessor or other computing device. Although the various aspects of the disclosure are illustrated and described as block diagrams, flow charts, or using some other pictorial representation, it is well understood that these descriptions are by way of non-limiting example only, and that the block, device, system, techniques or methods described herein can be implemented using hardware, software, firmware, special-purpose circuits or logic, general purpose hardware or controller or other computing device, or some combination thereof.

[0153] Some example embodiments of the disclosure also provide at least one computer program product, which is tangibly stored on a computer readable medium, such as a non-transitory computer readable medium. The computer program product includes instructions that are executable by a device having a processor or virtual processor to execute any of the methods described above. Generally, program modules include routines, programs, libraries, objects, classes, components, data structures, or the like that perform particular tasks or implement particular abstract data types. The functionality of the program modules can be combined or split between program modules as desired in various embodiments. Machine executable instructions for program modules can be executed within a local or distributed device. In a distributed device, program modules can be located in both local and remote storage media.

[0154] Program code for carrying out methods of the present disclosure can be written in any combination of one or more programming languages. The program code can be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus, such that the program code, when executed by the processor or controller, causes the functions / operations specified in the flow diagrams and / or block diagrams to be implemented. The program code can be entirely on the machine, partially on the machine, as a stand-alone software package, partially on the machine and partially on a remote machine or entirely on a remote machine or server.

[0155] In the context of the present disclosure, computer program code or related data can be carried by any suitable carrier to enable a device, apparatus, or processor to perform the various processes and operations as described above. Examples of carriers include signals, computer readable media, and the like.

[0156] The computer readable medium can be a computer readable signal medium or a computer readable storage medium. The computer readable medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of the computer readable storage medium would include one or more of an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0157] Moreover, while operations can be described as following a specific sequence, this should not be understood as requiring such a specific sequence, or that all operations be performed in the order presented, or that all operations be performed. In certain circumstances, multitasking and parallel processing can be advantageous. Likewise, the various steps previously outlined are described in flow chart form but could also be implemented individually or in various orders as commands or software loops or in concurrency or in any suitable form not specifically presented. Also, descriptions of the various embodiments have been presented for purposes of clarity and understanding. It is not intended to be an exhaustive list of all possible implementations. Further, it will be appreciated by one skilled in the art that those elements and / or operations expressed as discrete steps in the above descriptions can in fact be combined with one another in a single step. Similarly, those elements and / or operations expressed as discrete steps can be implemented at other times, in other sequences, or in other manners.

[0158] Although the present disclosure has been described in language specific to structural features and / or methodological acts, it is to be understood that the present disclosure defined in the appended claims is not necessarily limited to the specific features or acts described. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims.

[0159] Some additional examples:

[0160] Example 1. A first apparatus for communication, comprising: at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the first apparatus at least to: obtain a symbol precoder, the symbol precoder comprising a first constituent precoder and a second constituent precoder dependent on each other, wherein the first constituent precoder corresponds to a first matrix of N rows and M columns for precoding M symbols, and the second constituent precoder corresponds to a second matrix of N rows and K columns for precoding K symbols, the K symbols being different from the M symbols, and M+K being greater than N, and wherein at least one of the first constituent precoder and the second constituent precoder comprises at least one of: at least one complex-valued element, or at least two complex-valued or real-valued elements having at least two different non-zero amplitudes affecting at least one precoder output value; determine a precoded signal based on encoding a first symbol vector of the M symbols by using the first constituent precoder, and encoding a second symbol vector of the K symbols by using the second constituent precoder; and transmit, to a second apparatus, a signal comprising the precoded signal.

[0161] Example 2. The first apparatus according to example 1, wherein the first apparatus is further caused to: determine a second precoded signal based on processing the precoded signal by using a second symbol precoder of size ZxN, Z being greater than or equal to N; and wherein transmitting the signal comprising the precoded signal comprises transmitting a signal comprising the second precoded signal.

[0162] Example 3. The first apparatus according to example 2, wherein the second symbol precoder comprises a Discrete Fourier Transform, DFT, precoder.

[0163] Example 4. The first apparatus according to example 1, wherein at least one of the first symbol vector or the second symbol vector comprises an a priori known symbol, the a priori known symbol comprising a reference symbol or a pilot symbol.

[0164] Example 5. The first apparatus according to example 1, wherein a correlation between at least one pair of columns within the first constituent precoder is higher than a correlation between any column of the first constituent precoder and any column of the second constituent precoder.

[0165] Example 6. The first apparatus according to example 1, wherein the first matrix and the second matrix are projection matrices, approximate projection matrices, or at least one of the first matrix or the second matrix is dependent on a projection matrix.

[0166] Example 7. The first apparatus of Example 1, wherein the first subspace defined by the first matrix is orthogonal to a second subspace defined by a second matrix; or wherein the first subspace defined by the first matrix is orthogonal to a rotated subspace or a modified subspace rotated from a second subspace, the second subspace defined by a second matrix.

[0167] Example 8. The first apparatus of Example 8, wherein the first matrix is obtained by subtracting a scaled matrix from an identity matrix, the scaled matrix being a matrix scaled from the second matrix based on a rotation factor.

[0168] Example 9. The first apparatus of Example 8, wherein the second matrix is a Hermitian product of vectors scaled from a sequence, and the first matrix is a matrix scaled from another matrix, the other matrix obtained by subtracting a scaled second matrix from an identity matrix, the scaled second matrix scaled based on a rotation factor; or wherein the first matrix and the second matrix define different subspaces with different dimensions; or wherein the second matrix is defined by a smallest dominant eigenvector of a product of the first matrix and a conjugate transpose of the first matrix.

[0169] Example 10. The first apparatus of Example 1, wherein the second matrix is a Discrete Fourier Transform, DFT, matrix or a column restriction of the DFT matrix, and obtaining the symbol precoder comprising a first constituent precoder and a second constituent precoder comprises: obtaining the sequence from subcarriers or subvectors of the second matrix; and obtaining a rotation based on the sequence of the first matrix and the second matrix based on the rotation factor.

[0170] Example 11. The first apparatus of any of Examples 1 to 10, wherein the first apparatus is further caused to: determine the precoded signal by at least partially multiplexing the encoded first symbol vector and the encoded second symbol vector in overlapping resource elements, the overlapping resource elements overlapping in at least one of a time domain, a frequency domain, or a spatial domain.

[0171] Example 12. The first apparatus of any of Examples 1 to 10, wherein the first symbol vector is a data vector and the second symbol vector is a pilot vector; or wherein the first symbol vector is a reference vector combining data information and pilot information, and the second symbol vector is a different reference vector combining data information and pilot information.

[0172] Example 13. A second apparatus for communication, comprising: at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the second apparatus at least to: receive a signal from the first apparatus; and decode the received signal by using at least one of a first component precoder and a second component precoder, wherein the first component precoder corresponds to a first matrix of N rows and M columns used to precode M symbols, and the second component precoder corresponds to a second matrix of N rows and K columns used to precode K symbols, the K symbols being different from the M symbols, and M+K being greater than N, and wherein at least one of the first component precoder and the second component precoder comprises at least one of: at least one complex-valued element, or at least two complex-valued or real-valued elements having at least two different non-zero magnitudes affecting at least one precoder output value.

[0173] Example 14. A method for communication, comprising: obtaining, at a first apparatus, a symbol precoder comprising a first component precoder and a second component precoder dependent on each other, wherein the first component precoder corresponds to a first matrix of N rows and M columns used to precode M symbols, and the second component precoder corresponds to a second matrix of N rows and K columns used to precode K symbols, the K symbols being different from the M symbols, and M+K being greater than N, and wherein at least one of the first component precoder and the second component precoder comprises at least one of: at least one complex-valued element, or at least two complex-valued or real-valued elements having at least two different non-zero magnitudes affecting at least one precoder output value; determining a precoded signal based on encoding a first symbol vector of the M symbols by using the first component precoder and encoding a second symbol vector of the K symbols by using the second component precoder; and transmitting, to a second apparatus, a signal comprising the precoded signal.

[0174] Example 15. A method for communication, comprising: receiving, at a second apparatus, a signal from a first apparatus; and decoding the received signal by using at least one of a first constituent precoder and a second constituent precoder, wherein the first constituent precoder corresponds to a first matrix of N rows and M columns used for precoding the M symbols, and the second constituent precoder corresponds to a second matrix of N rows and K columns used for precoding the K symbols, the K symbols being different from the M symbols, and M+K being greater than N, and wherein at least one of the first constituent precoder and the second constituent precoder comprises at least one of: at least one complex-valued element, or at least two complex-valued or real-valued elements having at least two different non-zero amplitudes affecting at least one precoder output value.

Claims

1. A first apparatus for communication, comprising: at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the first apparatus at least to: obtain a symbol precoder, the symbol precoder comprising a first constituent precoder and a second constituent precoder dependent on each other, wherein the first constituent precoder corresponds to a first matrix of N rows and M columns for precoding M symbols, and the second constituent precoder corresponds to a second matrix of N rows and K columns for precoding K symbols, the K symbols being different from the M symbols, and M + K being greater than N, and wherein at least one of the first constituent precoder and the second constituent precoder comprises at least one of: at least one complex-valued element, or at least two complex-valued or real-valued elements having at least two different non-zero amplitudes affecting at least one precoder output value; determine a precoded signal based on encoding a first symbol vector of the M symbols by using the first constituent precoder, and encoding a second symbol vector of the K symbols by using the second constituent precoder; and transmit a signal comprising the precoded signal to a second apparatus.

2. The first apparatus of claim 1, wherein the first apparatus is further caused to: determine a second precoded signal based on processing the precoded signal by using a second symbol precoder of size Z x N, Z being greater than or equal to N; and wherein transmitting the signal comprising the precoded signal comprises: transmit the signal comprising the second precoded signal.

3. The first apparatus of claim 1, wherein at least one of the first symbol vector or the second symbol vector comprises a priori known symbols, the a priori known symbols comprising reference symbols or pilot symbols.

4. The first apparatus of claim 1, wherein a correlation between at least one pair of columns within the first constituent precoder is higher than a correlation between any column of the first constituent precoder and any column of the second constituent precoder.

5. The first apparatus of claim 1, wherein a first subspace defined by the first matrix is orthogonal to a second subspace defined by the second matrix; or wherein a first subspace defined by the first matrix is orthogonal to a rotated subspace or a modified subspace rotated from a second subspace, the second subspace being defined by the second matrix.

6. The first apparatus of claim 5, wherein the first matrix is obtained by subtracting a scaled matrix from an identity matrix, the scaled matrix being a matrix scaled from the second matrix based on a rotation factor.

7. The first apparatus of claim 6, wherein the second matrix is a Hermitian product of a vector scaled from a sequence, and the first matrix is a matrix scaled from another matrix, the other matrix being obtained by subtracting a scaled second matrix from an identity matrix, the scaled second matrix being scaled based on the rotation factor; or wherein the first matrix and the second matrix define different subspaces having different dimensions; or wherein the second matrix is defined by a smallest dominant eigenvector of a product of the first matrix and a conjugate transpose of the first matrix.

8. The first apparatus of claim 1, wherein the second matrix is a Discrete Fourier Transform, DFT, matrix or a column restriction of the DFT matrix, and obtaining the symbol precoder comprising the first constituent precoder and the second constituent precoder comprises: obtaining a sequence from subcarriers or subvectors of the second matrix; and obtaining a rotation of the first matrix based on the sequence and the second matrix based on a rotation factor.

9. The first apparatus of any one of claims 1-8, wherein the first apparatus is further caused to: determine the precoded signal by at least partially multiplexing an encoded first symbol vector and an encoded second symbol vector in overlapping resource elements, the overlapping resource elements overlapping in at least one of a time domain, a frequency domain, or a spatial domain.

10. A second apparatus for communication, comprising: at least one processor; and at least one memory storing instructions that, when executed by the at least one processor, cause the second apparatus to at least: receive a signal from a first apparatus; and decode the received signal by using at least one of a first constituent precoder and a second constituent precoder, wherein the first constituent precoder corresponds to a first matrix of N rows and M columns used to precode M symbols, and the second constituent precoder corresponds to a second matrix of N rows and K columns used to precode K symbols, the K symbols being different from the M symbols, and M + K being greater than N, and wherein at least one of the first constituent precoder and the second constituent precoder comprises at least one of: at least one complex-valued element, or at least two complex-valued or real-valued elements having at least two different non-zero magnitudes affecting at least one precoder output value.

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