CN117397215A - Generation and reception of pre-coded signals based on codebook linearization - Google Patents

Abstract

Embodiments relate to generation and reception of a precoding signal based on codebook linearization. A device may obtain a antipodal input sequence and a precoding matrix. The precoding matrix may be based on a multiplication of a codebook matrix comprising M codewords of complex symbols with a antipodal matrix comprising M different antipodal vectors. The device may generate a precoded codeword by multiplying the antipodal input sequence with the precoding matrix. Another device may receive and demodulate the signal and perform linear equalization on the demodulated signal.

Description

Generation and reception of pre-coded signals based on codebook linearization

Technical Field

The present invention relates generally to the field of wireless communications. In particular, some embodiments of the invention relate to the generation and reception of a pre-coded signal based on codebook linearization (codebook linearization).

Background

In wireless communication systems, e.g. by the third generation partnership project (3 ^rd generation partnership project,3 GPP) specified fifth generation (5G) systems may require a large number of terminal devices to be connected together to support various applications and service classes running in a wide range of frequency and deployment scenarios. To meet the needs of a large number of users, non-orthogonal multiple access (non-orthogonal multiple access, NOMA) techniques involving sharing resource blocks among users may be applied to improve spectral efficiency.

Disclosure of Invention

This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.

The invention aims to improve the frequency spectrum efficiency and reduce the complexity of a receiver, thereby improving the energy efficiency of signal transmission. The above-mentioned and other objects are achieved by the features of the independent claims. Other implementations are apparent from the dependent claims, the description and the drawings.

According to a first aspect, there is provided an apparatus for generating a signal. The device may be for: acquiring antipodal input sequences (antipodal input sequence); acquiring a precoding matrix based on multiplication of a codebook matrix (codebook matrix) and an antipodal matrix (antipodal matrix), wherein the codebook matrix comprises M code words of complex symbols (complex symbols), and the antipodal matrix comprises M different antipodal vectors; a precoded codeword is generated by multiplying the antipodal input sequence with the precoding matrix. This scheme improves transmission performance and reduces receiver complexity by linearizing the codebook matrix.

According to an implementation form of the first aspect, the antipodal matrix may comprise M different antipodal vectors corresponding to binary representations of values 0 to M-1 arranged in ascending order. The scheme provides an implementation for determining the antipodal matrix to improve transmission performance and linearize the codebook matrix.

According to an implementation form of the first aspect, the precoding matrix S of the kth user _k May includeWherein X is _k Is the codebook matrix, B ^T Is the antipodal matrix. The scheme provides an implementation of generating the precoding matrix to improve transmission performance and reduce complexity at the receiver by codebook linearization.

According to an implementation form of the first aspect, the apparatus may be further configured to: acquiring a plurality of antipodal input sequences corresponding to a plurality of users, wherein the plurality of users are associated with a plurality of codebook matrixes; acquiring a plurality of precoding matrixes corresponding to the plurality of users, wherein the precoding matrix of the kth user is based on multiplication operation of the codebook matrix of the kth user and the antipodal matrix; generating a plurality of precoding codewords for each of the plurality of users, wherein each precoding codeword for the kth user is based on a multiplication of a different subset of the antipodal input sequences for the kth user with the precoding matrix for the kth user; the signal is generated based on the concatenation of the plurality of precoded codewords for each of the plurality of users, wherein a number of the plurality of users is greater than a number of complex symbols of codewords for the plurality of codebook matrices. The scheme may generate a plurality of signals to improve transmission performance for a plurality of users sharing transmission resources according to the NOMA scheme.

According to an implementation form of the first aspect, the apparatus may be further configured to: by combining the concatenated plurality of precoding codewords of the kth user with a modulation matrix G of the kth user _k Multiplying to generate a modulation symbol, wherein

Wherein the signature root ρ of the modulation matrix of the kth user _n,k Meets the following conditions thatWherein a is _k Is the radius of the kth user, and wherein κ _k Is a normalization factor for the kth user; zero-padding (also called zero padding) is inserted at the end of the modulation symbol. This scheme improves transmission performance by combining vandermonde-lagrangian division multiplexing (lagranger-Vandermonde division multiplexing, LVDM) with the codebook linearization. In conjunction with the codebook linearization, this approach improves the performance of the linear receiver in the dual selective channel (doubly selective channel).

According to an implementation form of the first aspect, the apparatus may be further configured to: receiving said radius a of said kth user from a receiver _k Or the signature root ρ of the modulation matrix of the kth user _n,k Is an indication of (a). The scheme can dynamically optimize LVDM modulation of each user independently so as to improve transmission performance.

According to an implementation form of the first aspect, the apparatus may be further configured to: based on the radius a of the kth user _k To determine the normalization factor k of the kth user _k . In a practical implementation, the normalization factor may avoid increasing or decreasing the transmitted symbol energy. The scheme can also be implemented efficiently using unitary energy filters, where the coefficients of the filters comprise an LVDM modulation matrix G _k Is a column of (c).

According to an implementation form of the first aspect, the apparatus may be further configured to: generating a plurality of said modulation symbols for said kth user; inserting the zero padding at the end of each of the plurality of modulation symbols; a plurality of training sequences including L zeros at the end of each training sequence are periodically inserted within the plurality of modulation symbols. This scheme may improve channel estimation of LVDM signals at the receiver.

According to an implementation form of the first aspect, the plurality of training sequences may be different for each of the plurality of users. This scheme improves the separation of the channel impulse responses of different users at the receiver.

According to an implementation form of the first aspect, the apparatus may be further configured to: the plurality of training sequences is transmitted for each of the plurality of users with a time shift between the training sequences of the plurality of users. This scheme improves the separation of the channel impulse responses of different users at the receiver.

According to a second aspect, there is provided an apparatus for receiving a signal. The device may be for: receiving the signal, the signal comprising at least one precoding codeword generated based on a multiplication of a antipodal input sequence with a precoding matrix, the precoding matrix being based on a multiplication of a codebook matrix comprising M codewords of complex symbols and an antipodal matrix comprising M different antipodal vectors; demodulating the signal and performing linear equalization on the demodulated signal. This scheme improves reception performance and allows the use of linear equalization to reduce receiver complexity.

According to an implementation form of the second aspect, the antipodal matrix may comprise M different antipodal vectors corresponding to binary representations of values 0 to M-1 arranged in ascending order. This scheme provides an implementation of the antipodal matrix to improve the reception performance and achieve linear equalization.

According to an implementation manner of the second aspect, the apparatus may further be configured to: adding L first columns of the discrete fourier transform matrix to a discrete fourier transform matrix, wherein the demodulation of the signal is based on the added discrete fourier transform matrix. The scheme may demodulate the received signal to utilize zeros inserted at the end of the LVDM symbol.

According to an implementation manner of the second aspect, the signal may include a plurality of modulation symbols of a kth user of a plurality of users, the plurality of modulation symbols being based on a plurality of the pre-amblesCoding codeword and modulation matrix G of the kth user _k Generated by multiplication of (a) wherein

Wherein the signature root ρ of the modulation matrix of the kth user _n,k Meets the following conditions thatWherein a is _k Is the radius of the kth user, and κ _k Is a normalization factor for the kth user. This scheme further improves the reception performance by combining vandermonde-lagrangian division multiplexing (Lagrange-Vandermonde division multiplexing, LVDM) with the codebook linearization. In combination with the codebook linearization, this approach improves the performance of the linear receiver in the dual selective channel.

According to an implementation manner of the second aspect, the apparatus may further be configured to: receiving a plurality of training sequences periodically located within the plurality of modulation symbols of the kth user, the plurality of training sequences comprising L zeros at the end of each training sequence; an estimate of a wireless channel of the plurality of modulation symbols is determined based on the received plurality of training sequences, wherein the linear equalization of the demodulated signal is based on the estimate of the wireless channel. The scheme can improve channel estimation of LVDM signals.

According to an implementation manner of the second aspect, the apparatus may further be configured to: stacking the received plurality of training sequences into a vector of received training sequencesWherein the vector of the received training sequence is in the form ofWherein eta _m Is additive noise, < >>Wherein->The q coefficient, matrix phi, of the kth delay tap comprising the fourier base spread of the wireless channel _m Included

Wherein the method comprises the steps ofWherein->Wherein N is _c Is the coherence time of the radio channel, J is the length of the plurality of training sequences, < >>Is the first column +.>Is a lower triangular toeplitz matrix (lower triangular Toeplitz matrix), wherein +.>Is the training sequence of the kth user, N _p Is the number of the plurality of training sequences, M _s -1 is the number of modulation symbols between training sequences; according to being based on the matrix phi _m To determine said estimate of said wireless channel. According to the scheme, efficient MMSE-based channel estimation can be performed according to the training sequence, so that the receiving performance is improved.

According to an implementation manner of the second aspect, the apparatus may further be configured to: determining a predicted estimate of the wireless channel for at least one subsequent modulation symbol based on the received plurality of training sequences Counting; determining an updated signature root ρ of the modulation matrix of the kth user based on the predictive estimate of the wireless channel _n,k The method comprises the steps of carrying out a first treatment on the surface of the Transmitting said updated signature root ρ of said modulation matrix of said kth user to a transmitter _n,k Is an indication of (a). The scheme provides an implementation for optimizing LVDM modulation for each user individually to improve reception performance.

According to an implementation manner of the second aspect, the apparatus may further be configured to: determining a predictive estimate of the wireless channel for at least one subsequent modulation symbol based on the received plurality of training sequences; determining an updated radius a of the kth user based on the predictive estimate of the wireless channel _k,opt The method comprises the steps of carrying out a first treatment on the surface of the Transmitting the updated radius a of the kth user to a transmitter _k,opt Is an indication of (a). The scheme provides an implementation for optimizing LVDM modulation for each user individually to improve reception performance.

According to an implementation manner of the second aspect, the apparatus may further be configured to: determining the updated radius a of the kth user based on the following equation _k,opt

Wherein the method comprises the steps of

Wherein the method comprises the steps ofIs a frequency domain coefficient of the predictive estimate of the wireless channel of the kth user on subcarrier n, and wherein PN is the size of the discrete fourier transform matrix. The solution provides an implementation for determining the updated radius of the LVDM modulation for each user individually to improve reception performance.

According to a third aspect, a method for generating a signal is provided. The method may include: acquiring antipodal input sequences; acquiring a precoding matrix, wherein the precoding matrix is based on multiplication operation of a codebook matrix and an antipodal matrix, the codebook matrix comprises M code words of complex symbols, and the antipodal matrix comprises M different antipodal vectors; a precoded codeword is generated by multiplying the antipodal input sequence with the precoding matrix. This scheme improves transmission performance and reduces receiver complexity by linearizing the codebook matrix.

According to a fourth aspect, a method for receiving a signal is provided. The method may include: receiving the signal, the signal comprising at least one precoding codeword generated based on a multiplication of a antipodal input sequence with a precoding matrix, the precoding matrix being based on a multiplication of a codebook matrix comprising M codewords of complex symbols and an antipodal matrix comprising M different antipodal vectors; demodulating the signal and performing linear equalization on the demodulated signal. This scheme improves reception performance and allows the use of linear equalization to reduce receiver complexity.

According to a fifth aspect, a computer program is provided. The computer program may comprise program code for performing any implementation of the method of the third aspect when the computer program is executed on a computer.

According to a sixth aspect, a computer program is provided. The computer program may comprise program code for performing any implementation of the method of the fourth aspect when the computer program is executed on a computer.

Any implementation may be combined with one or more other implementations. Accordingly, implementations of the present invention may provide an apparatus, method, and computer program for generating or receiving a chirp waveform (chirp waveform). These and other aspects of the invention are apparent from and will be elucidated with reference to one or more of the exemplary embodiments described hereinafter.

Drawings

The accompanying drawings, which are included to provide a further understanding of the exemplary embodiments and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments and together with the description serve to explain the exemplary embodiments. In the drawings:

fig. 1 shows an example of a communication system provided by an embodiment of the present invention;

FIG. 2 illustrates an example of an apparatus for practicing one or more embodiments of the invention;

fig. 3 shows an example of a sparse code multiple access (sparse code multiple access, SCMA) scheme provided by an embodiment of the invention;

fig. 4 shows an example of a factor graph representation (factor graph representation) of a sparse code multiple access (sparse code multiple access, SCMA) scheme provided by an embodiment of the present invention;

FIG. 5 shows a Doppler frequency f provided by an embodiment of the present invention _D =0khz and f _D An example of an effective channel of =1 KHz;

FIG. 6 shows a Doppler frequency f provided by an embodiment of the present invention _D =5khz and f _D An example of an effective channel of =2khz;

FIG. 7 illustrates an example of a multi-dimensional SCMA map with 8-point codebook provided by embodiments of the invention;

FIG. 8 illustrates an example of a multi-dimensional SCMA map with 16-point codebook provided by embodiments of the invention;

fig. 9 illustrates an example of an LVDM transmitter application linearization codebook of a kth user provided by an embodiment of the invention;

FIG. 10 illustrates an example of a LVDM-based NOMA system provided by an embodiment of the invention;

FIG. 11 illustrates an example of a pilot pattern for use with LVDM-NOMA symbols provided by embodiments of the invention;

Fig. 12 shows an example of applying training sequences for channel estimation and prediction provided by an embodiment of the present invention;

fig. 13 shows an example of average Bit Error Rate (BER) of SCMAMPA and LVDM-based NOMA in a frequency selective channel provided by an embodiment of the present invention;

fig. 14 shows an example of BER of NOMA based on OFDM and LVDM in a dual selective channel provided by an embodiment of the present invention;

fig. 15 shows an example of average BER of NOMA based on OFDM and LVDM in a 3GPP extended vehicle (Extended Vehicular, EVB) channel provided by an embodiment of the present invention;

FIG. 16 shows an example of the average BER of NOMA based on OFDM and LVDM in a 3GPP tap delay line C (Tapped Delay Line C, TDL-C) channel provided by an embodiment of the present invention;

fig. 17 shows an example of pilot patterns of a plurality of users provided by an embodiment of the present invention;

FIG. 18 shows an example of sensitivity of LVDM based NOMA to channel estimation and radius estimation errors provided by an embodiment of the present invention;

FIG. 19 shows an example of a method for generating a signal provided by an embodiment of the invention; and

fig. 20 shows an example of a method for receiving a signal provided by an embodiment of the present invention.

In the drawings, like reference numerals are used to designate like parts.

Detailed Description

Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. The detailed description provided below in connection with the appended drawings is intended as a description of embodiments of the present invention and is not intended to represent the only manner in which an embodiment of the present invention may be constructed or utilized. The detailed description sets forth the functions of the examples of the invention and the sequence of operations for constructing and operating the examples. However, the same or equivalent functions and sequences may be accomplished by different examples.

The 5G system provides three classes of service: enhanced mobile broadband (enhanced mobile broadband, emmbb), ultra-reliable low-latency communication (URLLC), and large-scale machine communication (massive machine type communications, mctc). In an mctc scenario, a large number of terminal devices may need to be connected together, which means that a large number of connections may need to be supported. Orthogonal frequency division multiple access (Orthogonal Frequency Division Multiple Access, OFDMA) and other orthogonal multiple access (orthogonal multiple access, OMA) techniques may not support large-scale connection requirements due to spectrum scarcity.

NOMA technology involves the concept of user overload, which may involve sharing resource blocks among users, thereby improving spectral efficiency. Different NOMA schemes can be designed to take into account time-varying channels in a 5G network. However, a maximum likelihood (maximum likelihood, ML) based scheme such as message passing algorithms (message passing algorithm, MPA) may be used to attempt to achieve adequate performance while maintaining low complexity compared to a full ML scheme. However, such schemes may target low speeds (e.g., 3 km/h), and thus inter-carrier interference caused by higher mobility may damage MPA-based schemes.

One MPA-based approach is to use MPA to jointly detect superimposed user data. By exploiting sparsity in SCMA, a decoder can benefit from a strong iterative decoding scheme that provides near ML detection performance. However, even for small SCMA codes, such MPA algorithms may require excessive computational complexity. For example, the computation of soft information sent from a resource node to a user node may have an exponential complexityWherein d is _f Is the MPA layer threshold to enumerate all possible input combinations of collision symbols (collision symbols).

MPA can be enhanced by a desired propagation algorithm (expectation propagation algorithm, EPA) to reduce the complexity of the receiver. EPA may include approximating one distribution with another distribution as a simple family of distributions by distribution projection. By selecting projections to complex gaussian distributions, messaging is reduced to updating mean and variance parameters. Furthermore, messages between nodes (complex vector gaussian distribution) are reduced to scalar complex gaussian distribution. However, while EPA-MPA reduces complexity to O (INPD _f 2 ^μ ) But the error performance of the EPA-MPA receiver may be similar to the full MPA receiverAnd a receiver. Thus, under high mobility mechanisms, performance degradation may result.

To reduce complexity, a gaussian approximation based MPA (Gaussian approximation based MPA, GA-MPA) algorithm may be used. In GA-MPA, the discrete information exchanged between users and resource nodes can be approximated as a continuous gaussian function, avoiding high complex marginalization operations of MPA. GA-MPA has lower complexity compared to MPA, with a complexity scale of O (IKP μ2 ^μ ). However, in case of high mobility, GA-MPA may not bring any additional performance improvement.

Another option is to apply MPA (SIC-MPA) based on successive interference cancellation (successive interference cancellation, SIC), where the features of SIC and MPA can be combined to achieve a good balance between performance improvement and implementation complexity. In a SIC-MPA receiver, MPA may be applied to a limited number of users first, such that the number of collision layers per Resource Element (RE) does not exceed MPA layer d _f . The successfully decoded MPA layer may then be deleted by SIC and the process may continue until all users are successfully decoded. In a SIC-MPA receiver, the complexity level is Which is comparable to MPA. The additional boost is achieved at the cost of high complexity. Embodiments of the present invention thus provide NOMA communication schemes that can improve communication performance over dual selective channels while reducing complexity.

According to one embodiment, an apparatus for generating a signal is disclosed. The device may obtain a antipodal input sequence and a precoding matrix. The precoding matrix may be based on a multiplication of a codebook matrix comprising M codewords of complex symbols with a antipodal matrix comprising M different antipodal vectors. The device may generate a precoded codeword by multiplying the antipodal input sequence with the precoding matrix. This may linearize the codebook so that linear equalization may be applied at the receiver. Another device may receive and demodulate the signal and perform linear equalization on the demodulated signal. Thus, the computational complexity is reduced.

Fig. 1 shows an example of a communication system 100 provided by an embodiment of the present invention. The communication system 100 may include a transmitter (Tx) 110 and a receiver (Rx) 130, and the transmitter (Tx) 110 and the receiver (Rx) 130 may communicate over a wireless channel 120. Transmitter 110 may be based on bit vector b for the kth user _k A transmission signal is generated. There may be one or more users K, so that the number of users K.gtoreq.1. The transmitter 110 may be based on applying a user-specific precoding matrix S _k To generate a signal as will be described further below. The transmit signal may be fed through a wireless channel 120, which wireless channel 120 may be modeled by a channel matrix H. The noise η may be modeled by additive white gaussian noise added after the wireless channel 120. Receiver 130 may determine an estimate of the transmitted bit vector based on demodulation and linear equalization of the received signal yAs will be described further below.

FIG. 2 illustrates an example of a device for implementing one or more embodiments. For example, the apparatus 200 may be configured to generate or receive signals according to a NOMA scheme. The device 200 may include at least one processor 202. For example, the at least one processor 202 may include one or more of a variety of processing devices (e.g., coprocessors, microprocessors, controllers, digital signal processors (digital signal processor, DSPs), processing circuitry with or without DSPs), or a variety of other processing devices including integrated circuits (e.g., application specific integrated circuits (application specific integrated circuit, ASICs), field programmable gate arrays (field programmable gate array, FPGAs), microcontroller units (microcontroller unit, MCUs), hardware accelerators, special purpose computer chips, etc.).

The device 200 may also include at least one memory 204. Memory 204 may be used to store, for example, computer program code, such as operating system software and application software. The memory 204 may include one or more volatile memory devices, one or more non-volatile memory devices, and/or combinations thereof. For example, the memory may be implemented as a magnetic storage device (e.g., hard disk drive, magnetic tape, etc.), an opto-magnetic storage device, or a semiconductor memory (e.g., mask ROM, programmable ROM, PROM, erasable PROM, EPROM), flash ROM, random access memory (random access memory, RAM), etc.).

The device 200 may also include a communication interface 208, the communication interface 208 for enabling the device 200 to send and/or receive information. The communication interface 208 may include an internal communication interface, such as an interface between baseband circuitry and Radio Frequency (RF) circuitry of a transmitter, receiver, or transceiver device. Alternatively or additionally, the communication interface 208 may be used to provide at least one external radio station connection, such as a 3GPP mobile broadband connection (e.g., 3G, 4G, 5G, or offspring); a wireless local area network (wireless local area network, WLAN) connection, for example standardized by the IEEE 802.11 family or Wi-Fi alliance; a short-range wireless network connection, such as a bluetooth connection. Accordingly, the communication interface 208 may include one or more antennas to enable over-the-air transmission and/or reception of radio frequency signals.

The device 200 may also include other components and/or functionality, such as a user interface (not shown) including at least one input device and/or at least one output device. The input device may take various forms, such as a keyboard, a touch screen, or one or more embedded control buttons. The output device may include, for example, a display, a speaker, a vibration motor, etc.

When the device 200 is used to implement a certain function, certain and/or certain components of the device (e.g., the at least one processor 202 and/or the at least one memory 204) may be used to implement the function. Further, when the at least one processor 202 is used to implement a certain function, the function may be implemented using program code 206 included in the at least one memory 204 or the like.

The functions described herein may be performed, at least in part, by one or more computer program product components (e.g., software components). According to one embodiment, the device 200 includes a processor or processor circuit (e.g., a microcontroller) that, when executing the program code 206, is configured by the program code 206 to perform embodiments of the operations and functions described herein. Alternatively or additionally, the functions described herein may be performed, at least in part, by one or more hardware logic components. For example, but not limited to, exemplary types of hardware logic components that can be used include field-programmable gate arrays (FPGA), application-specific integrated circuits (ASIC), application-specific standard products (application-specific standard product, ASSP), system-on-a-chip Systems (SOC), complex programmable logic devices (complex programmable logic device, CPLD), graphics processing units (graphics processing unit, GPU), and the like.

The apparatus 200 may be used to perform or include means for performing one or more of the methods described herein. In one example, the apparatus includes at least one processor 202, at least one memory 204 including program code 206, the program code 206 to, when executed by the at least one processor 202, cause the device 200 to perform the one or more methods.

Device 200 may include, for example, a computing device such as a modulator chip, a demodulator chip, a baseband chip, a mobile phone, a tablet, a notebook, an internet of things device, a base station, etc. Although device 200 is shown as a single device, it should be understood that the functionality of device 200 may be distributed to multiple devices, such as between components of a transmitter, receiver, or transceiver, where applicable.

Fig. 3 shows an example of a sparse code multiple access (sparse code multiple access, SCMA) scheme provided by an embodiment of the present invention. In various NOMA technologies, exemplary embodiments have been described in the context of SCMA. It should be noted, however, that the exemplary embodiments may be applied to any suitable transmission scheme. SCMA may be based on low density spread spectrum code division multiple access (low-density spreading code division multiple access, LDS-CDMA) as shown in fig. 3. Examination paper K users are considered, each of which may have a user-specific codebook with m=2 of size N ^μ Each codeword (complex vector). In this context, the parameter M represents the modulation order, and N is the number of modulation orders used by each user to transmit μ=log ₂ Number of Resource Elements (REs) or subcarriers of M bits. A Resource Block (RB) may include a set of N consecutive REs in a time and/or frequency direction.

The kth user's binary vector of size μCan be mapped to codeword x of size N _k . Codeword x _k N complex symbols from a constellation, for example a phase-shift keying (PSK) or quadrature amplitude modulation (quadrature amplitude modulation, QAM) constellation, with an order of M, may be included. In the example of fig. 3, each user has m=8=2 with a size of n=4 ³ And code words. Each user binary vector (μ=3 bits) can be mapped to a codeword consisting of four complex symbols to be transmitted on four physical layer resource elements (e.g., subcarriers). The mapping function may add the binary vector of user 1>Mapping into layer 1 to be x ₁ A fourth codeword to send, and so on. Therefore, the codeword can be transmitted by using a multicarrier waveform such as an orthogonal frequency division multiplexing (orthogonal frequency division multiplexing, OFDM) waveform. In orthogonal multiple access (orthogonal multiple access, OMA), at least 6 REs are required for 6 users to transmit the same data. The user may be understood as a human user, or the user may be an application, an information stream, a layer, etc. In general, a user may be a data source, and the system may include K data sources.

Fig. 4 shows an example of a factor graph representation of a sparse code multiple access (sparse code multiple access, SCMA) scheme provided by an embodiment of the invention. The example also applies to k=6 and n=4. At the receiver 130, a vector of size N of received signals from K users sharing the same RB may be represented as

Wherein h is _n,k Is the channel coefficient at the nth RE of the kth user, η is the channel coefficient with covariance matrix σ ² I _N Additive Gaussian noise vector of I _N Is an N x N identity matrix. In the factor graph representation, each codebook layer may be represented by a variable node u _k And (3) representing. Each RE may be defined by a functional node c _n And (3) representing. Wherein a variable node u is given if and only if the corresponding element in the SCMA N x K signature matrix (signature matrix) S is non-zero _k Can be connected to the functional node c by a factor graph edge _n . The signature matrix may include

Will beDefined as the user index set constituting the nth RE and will +.>Defined as the set of RE indices used by the kth user, the received signal at the nth RE can be expressed as

Wherein x is _n,k Is the symbol transmitted by the kth user on the nth RE. The sparsity of the SCMA signature matrix allows the use of a message passing algorithm (message passing algorithm, MPA) that gives a near optimal solution for joint optimal maximum a posteriori probability (maximum a posteriori probability, MAP) detection by the following equation

Wherein the X vector stacks codewords for the user as x= [ X ₁ ,…,x _K ]Wherein χ=χ ₁ ×χ ₂ ×…×χ _K And χ _k Is the kth codebook.

The MPA detector can alternatively calculate the slave function node c _n (nth RE) sent to variable node u _k Information vector of (kth user)And slave variable node u _k To the functional node c _n Information vector +.>Vector->Andboth may have a size M and contain each possible codeword x _k Reliability values of (2). For i ε {1, …, M }, ->Can be calculated according to the following equation

Can be calculated according to the following equation

In the above expression, p _k (i) Is the kth user prior probability of the ith codeword. In addition, X _n,l Is the (n, l) th element of X, X _k Is the kth column vector of X.

FIG. 5 shows a Doppler frequency f provided by an embodiment of the present invention _D =0khz and f _D An example of an effective channel of =1 KHz. In this simulation scenario, each SCMA-encoded data is mapped to a resource block and MPA is performed for detection while exploiting channel sparsity. In frequency selective channels, especially where the effective channel is a block diagonal channel and the MPA detector can utilize this structure shown in the left-hand diagram (no mobility, f _D =0 KHz), MPA performs well. However, when the channel becomes time-varying due to mobility, orthogonality of Subcarriers (REs) is broken and inter-carrier interference (intercarrier interference, ICI) occurs, as shown in the right figure, where f _D =1khz. Notably, at f _D In the case of =1khz, off-block diagonal elements may occur in the effective channel and may not be considered by the MPA detector.

FIG. 6 shows a Doppler frequency f provided by an embodiment of the present invention _D =5khz and f _D An example of an effective channel of =2khz. The simulated scenario is similar to that of fig. 5, but the doppler frequency is higher. In this example of a high mobility mechanism, doppler frequency expansion makes the MPA scheme inefficient. It was observed that the off-block diagonal elements become more prominent due to ICI.

Exemplary embodiments of the present invention may be applied to NOMA transmission and reception over fast time-varying channels. This is beneficial because the key performance indicator of a Beyond 5G network is high mobility. Each coded data may be mapped to a resource block for which an MPA detector is applied at the receiving end by exploiting codebook sparsity, using a NOMA scheme such as SCMA. However, as noted above, doppler frequency spreading caused by mobility may break the sparsity of SCMA and make MPA detection impractical in certain applications. Furthermore, ICI may occur between several resource blocks, so performing MPA detection on all subcarriers (by considering the entire effective channel matrix, not just the block diagonal elements) may be very expensive in terms of implementation complexity and energy efficiency. To overcome these problems, embodiments of the present invention provide NOMA schemes that are suitable for dual selective channels (frequency selective and time selective) and maintain acceptable receiver complexity. Furthermore, flexible transmitter, receiver and transceiver implementations are disclosed that can improve performance while maintaining low implementation costs compared to MPA-based schemes.

According to one embodiment, a linear codebook dependent NOMA scheme is provided that may use a linear receiver. This significantly reduces implementation costs. Furthermore, flexible transmitter, receiver or transceiver implementations based on LVDM are disclosed. This would improve the performance of the linear codebook based NOMA scheme while keeping its implementation costs low compared to maximum likelihood (maximum likelihood, ML) based schemes (e.g., MPA). Thus, an LVDM transmitter, receiver and transceiver that handles dual selective channels are disclosed. The receiver 130 may calculate an optimal or improved value a of the LVDM signature root radius for each user, for example, with reference to a particular metric such as mean square error (mean squared error, MSE) _opt . The receiver 130 may feed back the determined radius to the transmitter 110 during the training phase to construct a precoder and modulator block. However, in time-varying channels, the following phenomena may degrade performance: 1) Outdated feedback signaling breaks the optimization of signature root; 2) ICI makes MPA inadequate. It is therefore desirable to be able to implement receiver implementations that take these factors into account with acceptable implementation complexity.

Fig. 7 shows an example of a multi-dimensional SCMA map with 8-point codebook provided by an embodiment of the present invention. Linearization of the codebook may be performed according to symmetry of the codebook. In a symmetric codebook, complementary (bit-wise reversed) binary words (e.g., 100 and 011) can be mapped to opposite codewords. Fig. 7 shows two examples of such codebooks corresponding to a first non-zero entry and a second non-zero entry. Similarly, fig. 8 shows an example of a symmetric codebook, e.g., mapping complementary binary words 1101 and 0010 to opposite codewords of a 16-point codebook.

May be achieved by having M different logs of antipodal entries (e.g., + -1) ₂ (M) linear transformation of the vector (matrix multiplication) to generate a codebook of M codewords. Thus, the transmitter 110 may obtain the antipodal input sequence for the kth user. For example, b can be given based on the passage _k ＝2b _k The linear transformation of-1 takes the size of the kth user to be log ₂ Binary input vector b of (M) _k Mapping is antipodal binary phase shift keying (binary shift phase keying, BPSK) modulation to obtain the antipodal input sequence, where 1 is an all 1 vector. The generated (pre-encoded) codeword x to be transmitted may be determined according to the following equation _k

x _k ＝S _k b _k

Wherein s is _k N x log of the kth user ₂ (M) precoding matrix. Thus, the transmitter 110 may input the sequence b by inputting the antipodal _k And the precoding matrix s _k Multiplication generates a precoded codeword.

The precoding matrix s _k May be based on a matrix B, which may have a size log ₂ (M). Times.M. The columns of matrix B may include M different antipodal vectors. Thus, matrix B may be a antipodal matrix. For example, columns of matrix B given in ascending order may include BPSK vectors corresponding to an M binary representation of 0, 1. Herein, the first row of B may represent the least significant bit (least significant bit, LSB). For example, for m=4, the corresponding matrix B may be expressed as

Wherein the columns from left to right represent antipodal binary vectors corresponding to the values 0,1, 2 and 3, respectively.

In addition, X is _k Let N x M matrix (codebook matrix) representing the codebook of the kth user, whose columns correspond to M different antipodal vectors. Codebook matrix x _k May include complex symbolsIs a single code word. For example, X is given in ascending order _k May include codeword vector x corresponding to an M binary representation of 0,1, …, M-1 _k . Thus, the first and second substrates are bonded together,

X _k ＝S _k B。

according to the definition of B,this follows X _k B ^T ＝M S _k . Therefore, the precoding matrix S can be determined according to the following equation _k

Thus, the precoding matrix S _k May be based on codebook matrix X _k And antipodal matrix B ^T Is a multiplication of (a) by (b). The elements of the precoding matrix may also be inversely proportional to the number M of codewords in the codebook. The transmitter 110 may apply a pre-configured precoding matrix S _k . For example, the transmitter 110 may retrieve the precoding matrix S from the memory of the transmitter 110 _k . Alternatively, the transmitter 110 may receive the precoding matrix S from another device _k For example as part of the signalling information. The transmitter 110 may also be based on a pre-configured or received codebook matrix X _k To determine the precoding matrix S _k . These examples may be generalized to applications with multiple users and corresponding codebook matrices and/or precoding matrices.

Since there may be a plurality of users, the transmitter 110 may acquire a plurality of antipodal input sequences b corresponding to the plurality of users _k . Different users may be associated with different codebook matrices. The transmitter 110 may also obtain a plurality of precoding matrices s corresponding to the plurality of users _k . The precoding matrix of the kth user may be based on a multiplication of the codebook matrix of the kth user with the antipodal matrix. The antipodal matrix may be the same for K users. A plurality of precoded codewords may then be generated for each of the plurality of users. The kthEach pre-encoded codeword of a user may be based on the antipodal input sequence b of the kth user _k And the precoding matrix s of the kth user _k Is a multiplication of (a) by (b). A signal may then be generated based on the concatenation of the precoded codewords for each of the K users. It should also be noted that the number of users may be greater than the complex symbols of the codewords of the plurality of codebook matrices. This may overload information to available resource units according to the NOMA scheme.

The received signal y can be generally expressed as

Wherein the method comprises the steps ofOne or more BPSK words, s comprising the kth user _k Is the kth user precoding matrix. Kth user diagonal channel matrix diag { h _1,k ，…，h _N，k May be expressed as H _k . Receiver 130 may convert vector b _k Concatenated into a size K log ₂ Vector b of (M). Thus, the received signal can be rewritten as

y＝[H ₁ S ₁ ，...，H _K S _K ]b+η

＝Hb+η。

Whole NxK log ₂ The (M) channel matrix H may comprise

H＝[H ₁ S ₁ ,…,H _K S _K ]。

K users may be used, for example, to transmit successively over P RBs of size N. Thus b _k Becomes P log in size ₂ (M) and b _k Each log of (1) ₂ The (M) symbol may be represented by S _k Converted into SCMA codewords of size N to form together concatenated vector x of size NP _k Comprises

Wherein the method comprises the steps ofRepresents the Cronecker product (Kronecker product), I _P Is a P x P identity matrix,>is the kth block diagonal precoding matrix. Linearization of the codebook enables the receiver 130 to perform linear equalization on the received signal. This may significantly reduce complexity at the receiver 130.

Fig. 9 shows an example of an LVDM transmitter application linearization codebook of a kth user provided by an embodiment of the invention. LVDM will generalize the OFDM waveform while providing a more flexible implementation. The LVDM transmitter 900 may receive a binary (antipodal) vector b _k As input. Alternatively, binary vector b _k May be divided into a plurality of subsets (sub-vectors) that may be provided as inputs to a corresponding one or more precoders 902. Thus, it can be based on the binary vector b _k And the precoding matrix S of the kth-user _k To obtain each pre-encoded codeword for said kth user. LVDM transmitter 900 may further include LVDM modulator 904, which may apply modulation matrix G to one or more outputs of one or more precoders 902 _k . The output of precoder 902 may comprise a precoded codeword. The output of the LVDM modulator 904 may include LVDM modulation symbols. Thus, the LVDM transmitter 900 may concatenate the precoded codewords of the kth user and based on concatenating the concatenated precoded codewords with the modulation matrix G _k The multiplication generates a modulation symbol. The modulation matrix may be user specific. Thus, one or more of the K users may be associated with different modulation matrices.

Modulation matrix G _k May include

Wherein the signature root ρ of the modulation matrix of the kth user _n,k Meets the following conditions thatWherein a is _k Is the radius of the kth user, and wherein κ _k Is a normalization factor for the kth user. Normalization factor kappa can be applied _k To conform to the passing->The resulting kth user transmits a power limit. For example, the radius a of the kth user can be determined _k The normalization factor κ is determined, for example, according to the following equation _k

L zeros may be used to fill each modulation symbol s prior to transmission _k . For example, zero padding may be inserted at the end of the modulation symbol, as shown in fig. 9. The LVDM transmitter 900 may also apply a parallel-to-serial transform 906 to the generated modulation symbols.

Fig. 10 shows an example of a LVDM-based NOMA system provided by an embodiment of the present invention. The system includes a receiver 130 and K transmitters 110. The transmitter 110 may be located within a single device 1010, which device 1010 may alternatively be implemented as a system comprising multiple transmitters 110. The transmitter 110 may also be implemented at a separate device, for example at a plurality of User Equipment (UE). The receiver 130 may also be located at a separate device such as a base station. However, a transceiving device or system may include a receiver 130 and one or more transmitters 110. For example, the transmitter 110 may include in its memory 204 a NOMA codebook 1 … K, e.g., codebook matrix x, for a corresponding user 1 … K _k . The transmitter 110 may apply one or more NOMA codebooks at the corresponding precoders 1012 to input a sequence b for K users' binary _k Precoding is performed. As described above, one or more precoding codewords per user may be based on a user-specific modulation matrix G _k Processed at a corresponding LVDM modulator 1014, and transmitted separately, e.g., through multiple antennas.

Considering that each user is provided with an LVDM modulator 1014, the number of the LVDM modulators can be reduced by s _k ＝x _kk To obtain the modulated signal of the kth user. The received signal at receiver 130, such as a base station, may include

Wherein C is _k Is a (np+l) x NP matrix with up to l+1 non-zero first sub-diagonals (including the main diagonal) representing a convolution with the kth user time-varying channel impulse response including the transceiver filter, and η is the corresponding AWGN noise as described above. The received signal may be processed by a receive filter 1030.

If the receiver 130 includes an OFDM demodulator, the frequency domain received signal at the receiver 130 may be represented as

Wherein the method comprises the steps ofIs an NP× (NP+L) matrix obtained by appending its L first columns to an NP DFT matrix F, where

Thus, the receiver 130 may include a DFT module 1032, the DFT module 1032 for calculating a DFT of the received signal with the added DFT matrix. The frequency domain received signal at the base station may be rewritten as

Since the codebook is already linearized, a low complex linearity based detection may be applied at the receiver 130. However, in case of NOMA overload, for example, zero-forcing (ZF) and MMSE etc. linear equalizers may not be optimal, as the number of unknown variables may be larger than the observed values in the system. However, by applying a linear based successive interference cancellation receiver, such as an ordered successive interference cancellation (ordered successive interference cancellation, OSIC), in an LVDM/OFDM based NOMA system, detection performance can be improved. Hereinafter, a precoding matrix S including NOMA is derived _k (k=1, …, K). Furthermore, an osc receiver based on minimum mean square error (minimum mean squared error, MMSE) is disclosed, which receiver can address NOMA coding and ICI terms simultaneously. The frequency domain received signal may include

By log in size PK ₂ (M)Middle stacked BPSK vector b _k K=1, …, K, the frequency domain received signal y can be rewritten as

Wherein NP× (KP log ₂ (M)) matrix Q is the effective overall frequency domain channel matrix. Will (z) ₁ ,z ₂ ,…,z _i-1 ) Let (i-1) be the order of indexes of the symbols detected in vector b by MMSE-OSIC equalization after the iterations. In the ith iteration, i=1, …, PK log ₂ (M) the linear system of the solution of the requirement may include

Herein, delete the data detected by z that has been detected in (i-1) previous iterations ₁ ,…,z _i-1 After the entry of the index is made,may include a Binary (BPSK) vector b. The matrix can be determined by deleting the corresponding column of Q>Vector->Is to delete +.>Is a vector y received after the construction of (b), b _l Is the first element of b.

Notably, to be estimatedMay be a real-valued vector, and a Wide Linear (WL) MMSE may be applied, which is at +.>Satisfy->And then reduced to linear MMSE equalization. Thus, linear equalization may include linear MMSE equalization. In the following example, - >And WL-MMSE equalization processing may include one or more of:

a) In the ith iteration, i=1:pk log ₂ (M) can be obtained by using the following equationTo perform WL-MMSE

Matrix arrayA noise covariance matrix in the frequency domain may be included.

b) During the ith iteration, the index z of the selected symbol to be detected may be determined according to the following equation _i

z _i ＝Ω _i (t)

Wherein t comprises

Herein, Ω _i May include omega _i ＝{1,…,PK log ₂ (M)}\{z ₁ ,…,z _i-1 }，w _l Can be derived from the following equation

q _l Can be derived from the following equation

c) The hard decision can be determined by the following equation

Wherein the method comprises the steps of

The complexity level of the disclosed MMSE-OSIC detector performing WL-MMSE equalization may be evaluated based on the complexity during each iteration. Receiver 130 may perform PK log ₂ (M) th order matrixCan perform the passing off lineCalculation of derived noise covariance matrix and inverse R thereof ^-1 Calculation, R and R can therefore be omitted in complexity analysis ^-1 Is calculated by the computer.

In the ith iteration, the matrix Q has a size of (np× (KP log ₂ (M) -i+1)), the WL-MMSE operation cost is O ((KP log) ₂ (M)-i+1) ³ ). Since the number of OSIC iterations is (KP log ₂ (M)), the complexity level of the disclosed MMSE-OSIC detector can be determined by the following equation

Thus, through O ((KPμ) ⁴ ) Deriving a complexity level of the disclosed MMSE-OSIC assay, where μ = log ₂ (M) is the binary word size.

The following table summarizes the complexity of different types of receivers. Complexity level has been taken as codebook size m=2 ^μ Rather than μ. To provide a fair comparison, the complexity level based on non-LVDM receivers has been multiplied by the number P of SCMA codes.

In conjunction with the codebook linearization, LVDM may improve the performance of a linear receiver in a dual selective channel. Unlike MPA-based receivers, the linear receiver will scan the entire effective channel matrix and thus provide better performance than MPA in dual selective channels. In addition, LVDM can avoid using high complexity maximum likelihood (maximum likelihood, ML) receivers and using less complex but energy efficient receivers to improve performance and overcome its loss.

Fig. 11 illustrates an example of a pilot pattern provided by an embodiment of the present invention for use with LVDM-NOMA symbols. The pilot pattern may be used to estimate the transmission channel 120 of the LVDM-NOMA symbol. The LVDM-NOMA frame may include one or more LVDM-NOMA symbols 1101, shown in white. The LVDM-NOMA frame may also include one or more training sequences (pilot vectors) 1102 inserted within the LVDM-NOMA symbols 1101, shown in phantom. Training sequence 1102 may be periodically inserted within LVDM-NOMA symbol 1101, e.g., in M _s Each symbol is one period. Fig. 11 shows an example of pilot patterns for k=6 users using dedicated LVDM-NOMA symbols, where M _s ＝N _p =4, and each pilot symbol vector heel (M _s -1) LVDM-NOMA symbols (vectors). Can be every other M _s The transmitted symbol vectors are inserted into training sequence 1102. For example, one training sequence vector 1102 may be followed by (M _s -1) LVDM-NOMA symbols 1101. Thus, each user k can periodically transmit PN log ₂ Training sequence u of (M) samples _k . The training sequences of the users may be transmitted simultaneously, as shown in the example of fig. 11; alternatively, the pilot sequences 1102 of the users are made non-overlapping in time, as shown in the example of fig. 17. Thus, the length of the LVDM-NOMA frame or the training sequence and modulation symbol sequence commonly used for channel estimation and prediction (channel estimation and prediction, CEP) may be N _p M _s . The training sequence may be followed by L zeros. Thus, training sequences 1102 may include L zeros at the end of each training sequence 1102. The training sequence 1102 may be different for different users. This enables separation of the user at the receiver 130.

Due to movementThe channel impulse response (channel impulse response, CIR) of each user can even vary within one LVDM symbol, making the feedback signaling exchange and detection process challenging. Thus, the receiver 130 may apply a joint channel estimation and prediction (channel estimation and prediction, CEP) algorithm, where the radius a _k,opt May be predicted at the receiver 130. The receiver 130 may transmit the predicted values to one or more transmitters 110. The transmitter 110 may use the predicted radius to generate a subsequent LVDM symbol or symbols for the kth user. The receiver 130 may also use channel estimation to detect received symbols of LVDM users using advanced processing to overcome ICI, as will be described further below.

Will tau _max And f _D Set to the delay spread and doppler spread of the wireless channel 120, respectively. The sampling period (sampling time) of the receiver 130 may be denoted as T _s . It should be noted that receiver 130 may measure τ experimentally in practice _max And f _D Both of which are located in the same plane.

The channel estimation may be based on a base extended channel model (basis expansion channel model, BEM) in which the channel impulse response h of the kth user _p,k (t, τ) is for t ε [ ζN ] using the following _c t _s ,(ζ+1)N _c T _s ) Presented (within the zeta channel coherence time)

a.Q +1 coefficientsEach block remains unchanged but is allowed to change with ζ, an

b.Q +1 Fourier basesThe capture time varies but is common to all zeta,

wherein the method comprises the steps of Representing integer upper bound operator, ">Thus, h _p,k (t, τ) can be approximated as

Wherein (L, p) ε {0, …, L } × [0, …, N _C -1]

Wherein the method comprises the steps of Representing an integer lower bound operator. In this example, the number of channel taps is l+1. Each channel impulse response h _p,k [l]The number of samples in (a) may be equal to N _c (across the entire frame duration in the time domain).

Receiver 130 may receive training sequence 1102. Receiver 130 may then transmit the signal to N _p The received training sequences perform CEP algorithms. The number of training sequences may satisfy N _p M _s J<N _c Wherein N is _c Is the coherence period of the wireless channel 120. When the received p-th LVDM-NOMA symbol r _p Corresponds to the mth training sequence (p=mm _s ，) In this case, the CEP module may utilize N _p The received training sequence->To predict the back (M) _s -1) channel time evolution over LVDM-NOMA symbols to determine a that the receiver 130 can feed back to the transmitter 110 _k,opt . The transmitter 110 may configure the precoding and modulation blocks based on the received feedback. The receiver 130 may also estimate the time period after the last (M _s -1) channels during LVDM-NOMA symbolsAnd (3) tapping. The estimate may be provided to feed an equalizer for detection.

Fig. 12 shows an example of applying training sequences for channel estimation and prediction provided by an embodiment of the present invention. The channel estimation and prediction may be performed at CEP module 1034 of receiver 130. The received training sequence may be expressed as

Wherein the method comprises the steps ofComprising capturing a J x C matrix of kth time-varying CIR evolution during an nth transmitted symbol, derived by the following equation

Wherein the method comprises the steps of

Wherein the method comprises the steps ofWherein N is _c Representing the coherence time of the wireless channel 120. Matrix->May comprise a lower triangular toeplitz matrix, the first column of which comprises [ c ] _q,k [0],…,c _q,k [L],0,…,0] ^T . From algebraic operations, the received sequence can be expressed as +.>

Matrix arrayIs a J× (L+1) lower triangular toeplitz matrix, the first column of which is +.>Andvector->An mth training sequence for a kth user may be included. Vector->May include coefficients->The parameter J may be equal to the length of the training sequence. Thus, each training sequence may have the same length J.

CEP module 1034 may use BEM approximation, for example, to estimate and predict wireless channel 120.CEP module 1034 can convert N _p Stacking the received training sequences into a vector of received training sequencesThe size of which may be (N) _p J×1) and is expressed as

In the example of fig. 12, the receiver 130 may stack four training sequences 1102 indicating participation in channel estimation/prediction. The stacked vectors may include a currently received multi-carrier (MC) symbol and N _p -1 previously received multicarrier symbol. The received signal may take the form of

Wherein the method comprises the steps ofIncluding additive noise. Additive noise vector->May include->Matrix phi _m May include

Then, a matrix-based φ may be used _m To estimate the estimate of wireless channel 120. Can be matched withApplying the linear MMSE estimator to derive

Wherein R is _c ＝E{cc ^H The channel covariance matrix is represented by Trace { R }, where _c } =k. It should be noted that R _c Depending on the power delay profile (power delay profile, PDP) of the channel model, this is known at the receiver 130.

From coefficients estimated, for example, by MMSE as described aboveCEP module 1034 can predict the radio channel 120 for subsequent (e.g., subsequent) one or more LVDM-NOMA symbols as shown in fig. 12. The predicted time-varying CIR of the user may be determined for (L, K) ε {0, …, L } × {1, …, K } according to the following equation, which may be provided to the senderThe transmitter 110 is used to construct one or more LVDM-NOMA symbols in succession

Wherein P.epsilon { (mM) _s +1)J,…,(m+1)M _s J-1}. The estimated time-varying CIR of the user may be determined for (L, K) e {0, …, L } × {1, …, K } according to the following equation, which may be provided to an equalizer of detector 1038 to detect the last received (M _s -1) LVDM-NOMA symbols

Wherein P.epsilon. { ((M-1) M _s +1)J,…,mM _s J-1}. Accordingly, CEP module 1034 may determine an estimate and a predictive estimate of wireless channel 120 for subsequent one or more modulation symbols based on the received training sequence. The determined channel estimate (denoted as H in fig. 10 _Det ) And predictive estimation (H) of wireless channel 120 _Pred ) May be provided to an optimization block 1036.

The optimization block 1036 may use the estimates and/or predictions of the wireless channel 120 to determine one or more LVDM parameters for the subsequent one or more symbols. For example, the optimization block 1036 may determine the update radius a of the kth user based on the predictive estimate of the wireless channel 120 _k,opt . The optimization block or in general the receiver 130 may send said updated radius a of the kth user to the sender 110 _k,opt Is an indication of (a).

According to one embodiment, the update (optimization) radius may be determined using a metric such as erfc. Thus, the update radius may be determined, for example, according to the following equation

Wherein the method comprises the steps of

Is the kth user frequency domain channel coefficient on subcarrier n. The parameter PN may be equal to the size of the DFT matrix. Alternatively, a machine learning algorithm may be used to determine the update radius a _k,opt For example according to a random gradient descent method.

Thus, upon receiving the training sequence, a channel estimation and prediction (channel estimation and prediction, CEP) module 1034 may determine an estimate of the wireless channel 120 for the modulation symbols from the received training sequence. Detector 1038 may then demodulate the received signal and perform linear equalization on the demodulated signal based on the determined channel estimate. The linear equalization is achieved by linearization of the codebook.

Thus, embodiments of the present invention provide a NOMA scheme that uses a linear codebook to enable a linear receiver to handle dual selective channels with high mobility. In one embodiment, LVDM may be used on the transmitter side to allow flexible implementation while improving performance compared to OFDM-based schemes. Frequency domain equalization may be used to reduce receiver complexity. Wherein joint channel estimation and prediction may be applied. The channel estimation portion may feed the detector (equalization) and the channel prediction output may be used to configure the transmitter block for each user for the following LVDM symbols. However, the complexity of the transmitter, receiver or transceiver implementation remains at an acceptable level.

In a first step, joint channel estimation and prediction (channel estimation and prediction, CEP) may be performed, e.g. as shown in fig. 10, wherein the dashed arrow shows the radius value a to be updated _k，opt As feedback to each transmitter 110. A joint channel estimation and prediction method may be applied, wherein the channel estimation entity feeds a frequency domain equalizer to detect the symbols of the (actually) received LVDM users and configures the following transmission slots with the prediction entity Transmitter blocks (e.g., precoders and modulators). The radius value a may be performed based on channel state information (from channel estimation) and an optimization metric (e.g., MSE as described above) _k，opt Is described. Furthermore, the determined radius value a may be applied _k，opt Is a refinement of (2).

Signaling feedback (a) derived from the predictive entity to the kth sender 110 _k，opt Or refined signature root) enables the modulation and precoding block to adapt to transmitter specific radio channel conditions. Further, the disclosed training sequence enables separation of the user's channel impulse response at the receiver 130.

In a second step, detection may be performed on the transmitted signal. For example, the receiver 130 may apply a fast fourier transform (fast Fourier transform, FFT) for demodulation to keep implementation costs low. Frequency domain equalization (method) may be used to process the dual selective wireless channel. Wherein a linear detector may be used and optionally enhanced by an iterative process.

Performance results of the disclosed embodiments are discussed below. First, performance results for frequency selective channels and dual selective channels are provided. Since analysis is performed for multi-user schemes as a function of signal-to-noise ratio (SNR), LVDM based and OFDM based NOMA performance is discussed in terms of Bit Error Rate (BER). In addition, the sum of channel estimation a is presented _opt The sensitivity of the estimation error.

Fig. 13 shows an example of the average Bit Error Rate (BER) of SCMA MPA and LVDM-based NOMA in a frequency selective channel provided by an embodiment of the present invention. Comparison between SCMA and LVDM-based NOMA is performed on a frequency selective channel (f _D =0 Hz). The NOMA scheme based on LVDM is significantly better than SCMA, which reaches saturation at high SNR (lower BER limit).

Fig. 14 shows an example of the average BER of NOMA based on OFDM and LVDM in a dual selective channel provided by an embodiment of the present invention. It was observed that LVDM based NOMA was still significantly better than OFDM based NOMA at high SNR. Furthermore, by using the proposed WL-MMThe SE-OSIC detector has improved NOMA (SCMA) performance over OFDM even in dual selective channels. However, LVDM based NOMA still achieves frequency diversity in the channel and is superior to OFDM based NOMA. For example, performance results indicate that at ber=10 ^-5 LVDM performs 5dB higher than OFDM.

In the simulations of fig. 13 and 14, the number of resource units (subcarriers) is c=64, l=16. Each Resource Block (RB) contains four resource units, and thus the number of resource blocks is 16. Thus, there are also 16 NOMA codewords. For the dual selective channel of fig. 14, the maximum doppler spread is f _D =1khz. The subcarrier spacing is Δf=30khz. For both simulations, a quadratic phase-shift keying (QPSK) modulation was used, and thus m=4.

Fig. 15 shows an example of average BER of NOMA based on OFDM and LVDM in a 3GPP extended vehicle (Extended Vehicular, EVB) channel provided by an embodiment of the present invention. The results show that LVDM based NOMA is superior to OFDM based NOMA. For example, at ber=10 ^-5 At this point, the SNR gain has almost reached 8dB. In this simulation, l=39.

Fig. 16 shows an example of average BER of NOMA based on OFDM and LVDM in a 3GPP tap-delay line C (Tapped Delay Line C, TDL-C) channel provided by an embodiment of the present invention. The results show that the LVDM based NOMA is again superior to the OFDM based NOMA. For example, at ber=10 ^-5 At this point, the SNR gain has almost reached 7dB. In this simulation, l=20.

In the simulations of fig. 15 and 16, the following set of simulation parameters was used: c=64, carrier frequency f _c =3.5 GHz, velocity v=200 Km/h, doppler spread f _D =648 Hz, subcarrier spacing Δf=30 KHz. QPSK modulation and the same NOMA configuration are considered.

Fig. 17 shows an example of pilot patterns of a plurality of users provided by an embodiment of the present invention. As described above, multiple training sequences may be periodically inserted within multiple modulation symbols. In addition, as shown in FIG. 17, a time shift between training sequences of the plurality of users may be transmitted for each of the users Training sequences. Between consecutive bursts of non-zero symbols for any two of the k users, a gap of zero symbols may be provided for each of the users. In this example, N _p ＝6，M _s =5. In order for CEP algorithm 1034 to separate the user's channels, (k=6) users may send different training sequences, for example as given by the pattern of fig. 17. Thus, each user may have a contiguous portion of non-zero symbols within the training sequence. Furthermore, the non-zero symbols of different users may not overlap in time. This may be achieved, for example, by shifting the position of the non-zero symbols for each user by a predetermined (user-specific) symbol amount within its training sequence. In the example of fig. 17, each of users 1 to 6 has four non-zero consecutive symbols among 64 symbols of the training sequence in the time domain. For example, the value of the non-zero samples may be determined as follows:

in general, the values of the non-zero samples may be selected such that the non-zero samples are orthogonal or have low cross-correlation among a group of users. For example, the values of the non-zero samples may be extracted from a hadamard sequence (Hadamard sequence) that provides code orthogonality or a Zadoff-Chu sequence with good correlation properties.

Fig. 18 shows an example of sensitivity of a LVDM based NOMA to channel estimation and radius estimation errors provided by an embodiment of the present invention. It should be noted that although the simulation results of fig. 13-16 have been obtained at the receiver 130 using the full channel state information (channel state information, CSI), the figure provides performance results at the receiver 130 using the disclosed CEP algorithm. The performance results of the pilot pattern of fig. 17 are provided for an extended typical city (Extended Typical Urban, ETU) channel. In this simulation, c=64, carrier frequency f _c =3.5 GHz, velocity v=200 Km/h, doppler spread f _D =648 Hz, subcarrier spacing Δf=30 KHz. Likewise, QPSK modulation and the same NOMA configuration are considered. Notably, the performance of OFDM depends only onWhereas the performance of LVDM depends on channel estimation and prediction quality. However, fig. 18 shows that even in the case of non-ideal channel estimation, the LVDM based NOMA is still superior to the OFDM based NOMA. The LVDM scheme exploits the flexibility of helping the equalizer to overcome mismatch. Thus, simulation results indicate that embodiments of the present invention improve transmission performance in frequency selective channels and dual selective channels.

Fig. 19 illustrates an example of a method 1900 for generating a signal provided by an embodiment of the invention.

At 1901, the method may include obtaining a antipodal input sequence.

At 1902, the method may include acquiring a precoding matrix. The precoding matrix may be based on a multiplication of a codebook matrix comprising M codewords of complex symbols with a antipodal matrix comprising M different antipodal vectors.

At 1903, the method may include generating a precoded codeword by multiplying the antipodal input sequence with the precoding matrix.

Fig. 20 shows an example of a method 2000 for receiving a signal provided by an embodiment of the present invention.

At 2001, the method may include receiving the signal. The signal may include at least one precoding codeword generated based on a multiplication of the antipodal input sequence with a precoding matrix. The precoding matrix may be based on a multiplication of a codebook matrix comprising M codewords of complex symbols with a antipodal matrix comprising M different antipodal vectors.

At 2002, the method may include demodulating the signal and performing linear equalization on the demodulated signal.

Other features of the method are directly derived from the functions and parameters of the method and the device (e.g., transmitters 110 and 900, receiver 130 or device 200) as described in the appended claims and throughout the specification and are therefore not described in further detail herein.

The apparatus or system may be used to perform or cause to be performed any aspect of one or more methods described herein. Furthermore, a computer program may comprise program code for performing one aspect of one or more methods described herein when the computer program is executed on a computer. Furthermore, a computer program product may comprise a computer readable storage medium storing program code comprising instructions for performing any aspect of one or more methods described herein. Furthermore, an apparatus may comprise means for performing any aspect of one or more methods described herein. According to an exemplary embodiment, the apparatus comprises at least one processor and at least one memory including program code, the at least one processor and the program code, when executed by the at least one processor, are to cause performance of any aspect of the one or more methods.

Any range or device value given herein may be extended or altered without losing the effect sought. Moreover, any embodiment may be combined with other embodiments unless explicitly disabled.

Although the subject matter has been described in language specific to structural features and/or acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims, and other equivalent features and acts are intended to be included within the scope of the claims.

It should be understood that the advantages and advantages described above may relate to one embodiment or may relate to several embodiments. The embodiments are not limited to embodiments that solve any or all of the problems, nor to embodiments that have any or all of the advantages and benefits. Furthermore, it should also be understood that references to "an" item may refer to one or more of those items. Further, reference to "at least one" item or "one or more" items may refer to one or more of those items.

The operations of the methods described herein may be performed in any suitable order, or concurrently where appropriate. Additionally, individual blocks may be deleted from any of the methods without departing from the scope of the subject matter described herein. Aspects of any of the embodiments described above may be combined with aspects of any of the other embodiments described to form further embodiments without loss of the effect sought.

The term "comprising" is used herein to mean including the identified method, block or element, but such block or element does not include an exclusive list, and the method or apparatus may include additional blocks or elements.

It should be understood that the above description is provided by way of example only and that various modifications may be made by one skilled in the art. The above specification, examples and data provide a complete description of the structure and application of the exemplary embodiments. Although embodiments have been described above with a certain degree of particularity, or in connection with one or more individual embodiments, those skilled in the art could make numerous alterations to the disclosed embodiments without departing from the scope of this disclosure.

Claims (22)

1. A device (110, 200, 900, 1010) for generating a signal, characterized in that the device (110, 200, 900, 1010) is adapted to:

acquiring antipodal input sequences;

acquiring a precoding matrix, wherein the precoding matrix is based on multiplication operation of a codebook matrix and an antipodal matrix, the codebook matrix comprises M code words of complex symbols, and the antipodal matrix comprises M different antipodal vectors; and

a precoded codeword is generated by multiplying the antipodal input sequence with the precoding matrix.

2. The device (110, 200, 900, 1010) of claim 1, wherein the antipodal matrix comprises M different antipodal vectors corresponding to binary representations of values 0 to M-1 arranged in ascending order.

3. The apparatus (110, 200, 900, 1010) according to claim 1 or 2, wherein the precoding matrix S of the kth user _k Included

Wherein X is _k Is the codebook matrix, B ^T Is the antipodal matrix.

4. A device (200, 1010) according to any one of claims 1 to 3, further configured to:

acquiring a plurality of antipodal input sequences corresponding to a plurality of users, wherein the plurality of users are associated with a plurality of codebook matrixes;

Acquiring a plurality of precoding matrixes corresponding to the plurality of users, wherein the precoding matrix of the kth user is based on multiplication operation of the codebook matrix of the kth user and the antipodal matrix;

generating a plurality of precoding codewords for each of the plurality of users, wherein each precoding codeword for the kth user is based on a multiplication of a different subset of the antipodal input sequences for the kth user with the precoding matrix for the kth user; and

the signal is generated based on a concatenation of the plurality of precoded codewords for each of the plurality of users, wherein a number of the plurality of users is greater than a number of complex symbols of codewords for the plurality of codebook matrices.

5. The apparatus (200, 1010) of claim 4, further configured to:

by concatenating the plurality of precoding codewords of the kth user with a modulation matrix G of the kth user _k Multiplying to generate modulation symbols (1101), wherein

Wherein the signature root ρ of the modulation matrix of the kth user _n,k Meets the following conditions thatWherein a is _k Is the radius of the kth user, and wherein κ _k Is a normalization factor for the kth user; and

Zero padding is inserted at the end of the modulation symbol (1101).

6. The apparatus (200, 1010) of claim 5, further configured to: receiving said radius a of said kth user from a receiver (130) _k Or the signature root ρ of the modulation matrix of the kth user _n,k Is an indication of (a).

7. The apparatus (200, 1010) of claim 6, further configured to: based on the radius a of the kth user _k To determine the normalization factor k of the kth user _k 。

8. The apparatus (200, 1010) of any of claims 5 to 7, further configured to:

-generating a plurality of said modulation symbols (1101) for said kth user;

inserting the zero padding at an end of each of the plurality of modulation symbols (1101); and

a plurality of training sequences (1102) are periodically inserted within the plurality of modulation symbols (1101), the plurality of training sequences (1102) including L zeros at the end of each training sequence (1102).

9. The apparatus (200, 1010) of claim 8, wherein the plurality of training sequences (1102) are different for each of the plurality of users.

10. The apparatus (200, 1010) of claim 8 or 9, further configured to: the plurality of training sequences (1102) are transmitted for each of the plurality of users with a time shift between the training sequences (1102) of the plurality of users.

11. An apparatus (130, 200) for receiving a signal, characterized in that the apparatus is adapted to:

receiving the signal, the signal comprising at least one precoding codeword generated based on a multiplication of a antipodal input sequence with a precoding matrix, the precoding matrix being based on a multiplication of a codebook matrix comprising M codewords of complex symbols and an antipodal matrix comprising M different antipodal vectors; and

demodulating the signal and performing linear equalization on the demodulated signal.

12. The device (130, 200) of claim 11, wherein the antipodal matrix comprises M different antipodal vectors corresponding to binary representations of values 0 to M-1 arranged in ascending order.

13. The apparatus (130, 200) of claim 11 or 12, further configured to: adding L first columns of the discrete fourier transform matrix to a discrete fourier transform matrix, wherein the demodulation of the signal is based on the added discrete fourier transform matrix.

14. The apparatus (130, 200) of claim 13, wherein the signal comprises a plurality of modulation symbols (1101) for a kth user of a plurality of users, the plurality of modulation symbols (1101) being based on a plurality of the precoding codewords and a modulation matrix G for the kth user _k Generated by multiplication of (a) wherein

Wherein the signature root ρ of the modulation matrix of the kth user _n,k Meets the following conditions thatWherein a is _k Is the radius of the kth user, and κ _k Is a normalization factor for the kth user.

15. The apparatus (130, 200) of claim 14, further configured to:

-receiving a plurality of training sequences (1102) periodically located within the plurality of modulation symbols (1101) of the kth user, the plurality of training sequences (1102) comprising L zeros at the end of each training sequence (1102); and

an estimate of a wireless channel of the plurality of modulation symbols (1101) is determined based on a received plurality of training sequences (1102), wherein the linear equalization of the demodulated signal is based on the estimate of the wireless channel.

16. The apparatus (130, 200) of claim 15, further configured to:

stacking the received plurality of training sequences (1102) into a vector of received training sequencesWherein the vector of the received training sequence is in the form of +.>Wherein eta _m Is an additive noise that is added to the noise,wherein->The q coefficient, matrix phi, of the kth delay tap comprising the fourier base spread of the wireless channel _m Included

Wherein the method comprises the steps ofWherein->Wherein N is _c Is the coherence time of the radio channel, J is the length of the plurality of training sequences, < >>Is the first column +.>Lower triangular toeplitz matrix of (2), wherein +.>Is the training sequence (1102), N of the kth user _p Is the number, M, of the plurality of training sequences (1102) _s -1 is the number of modulation symbols (1101) between training sequences (1102); and

according to being based on the matrix phi _m To determine said estimate of said wireless channel.

17. The apparatus (130, 200) of claim 15 or 16, further configured to:

determining a predicted estimate of the wireless channel for at least one subsequent modulation symbol based on the received plurality of training sequences (1102);

estimating the prediction based on the wireless channelTo determine an updated signature root ρ of the modulation matrix of the kth user _n,k The method comprises the steps of carrying out a first treatment on the surface of the And

transmitting said updated signature root ρ of said modulation matrix of said kth user to a transmitter (110, 1010) _n,k Is an indication of (a).

18. The apparatus (130, 200) of any one of claims 15 to 17, further configured to:

determining a predicted estimate of the wireless channel for at least one subsequent modulation symbol based on the received plurality of training sequences (1102);

Determining an updated radius a of the kth user based on the predictive estimate of the wireless channel _k,opt The method comprises the steps of carrying out a first treatment on the surface of the And

transmitting the updated radius a of the kth user to a transmitter (110, 1010) _k,opt Is an indication of (a).

19. The apparatus (130, 200) of claim 18, further configured to: determining the updated radius a of the kth user based on the following equation _k,opt

Wherein the method comprises the steps of

Wherein the method comprises the steps ofIs a frequency domain coefficient of the predictive estimate of the wireless channel of the kth user on subcarrier n, and wherein PN is the size of the discrete fourier transform matrix.

20. A method (1900) for generating a signal, the method comprising:

acquiring antipodal input sequences;

acquiring a precoding matrix, wherein the precoding matrix is based on multiplication operation of a codebook matrix and an antipodal matrix, the codebook matrix comprises M code words of complex symbols, and the antipodal matrix comprises M different antipodal vectors; and

a precoded codeword is generated by multiplying the antipodal input sequence with the precoding matrix.

21. A method (2000) for receiving a signal, the method comprising:

receiving the signal, the signal comprising at least one precoding codeword generated based on a multiplication of a antipodal input sequence with a precoding matrix, the precoding matrix being based on a multiplication of a codebook matrix comprising M codewords of complex symbols and an antipodal matrix comprising M different antipodal vectors; and

Demodulating the signal and performing linear equalization on the demodulated signal.

22. A computer program comprising a program code (206), characterized in that the program code (206) is for performing the method according to claim 20 or 21 when the computer program is executed on a computer.