CN108631829B - Joint power distribution, precoding and decoding method and base station thereof - Google Patents

Joint power distribution, precoding and decoding method and base station thereof Download PDF

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CN108631829B
CN108631829B CN201710153444.2A CN201710153444A CN108631829B CN 108631829 B CN108631829 B CN 108631829B CN 201710153444 A CN201710153444 A CN 201710153444A CN 108631829 B CN108631829 B CN 108631829B
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CN108631829A (en
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王晋良
郑竣哲
陈俊宇
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract

The invention provides a joint power distribution, precoding and decoding method and a base station thereof, which are suitable for a multiple-input multiple-output-non-orthogonal multiple access (MIMO-NOMA) system. The method of the invention comprises the following steps: (1) decomposing the precoders corresponding to each group into a first precoder multiplied by a second precoder; (2) obtaining mean-squared error (MSE) functions of decoded signals of all the ues in each group; (3) calculating a power allocation factor for each group while minimizing a maximum of all MSE functions in a group; and (4) obtaining the second precoders and decoders of all the groups by minimizing the sum of the MSE functions of the decoded signals of all the user devices in all the groups under the condition of the total transmission power limitation according to the calculated power allocation factors.

Description

Joint power distribution, precoding and decoding method and base station thereof
Technical Field
The present invention relates to a joint power allocation, precoding and decoding method suitable for a downlink multiple input multiple output-non-orthogonal multiple access (MIMO-NOMA) system and a base station using the same.
Background
With the development of technology, the NOMA system has become a promising technology for the development of next-generation communication systems due to the significant improvement in capacity.
In the NOMA system, user multiplexing can be performed in the power domain of the transmission end, and then the multi-user signals are separated by using a Successive Interference Cancellation (SIC) technique at the receiving end. Thus, the base station will configure more transmit power for user signals with poor channel conditions and less transmit power for user signals with better channel conditions to facilitate successful decoding for both users.
On the other hand, since the MIMO technology can significantly improve the system performance by utilizing the advantages of spatial multiplexing (spatial multiplexing) and diversity gains (diversity gains), a technology combining MIMO and NOMA (i.e., a MIMO-NOMA system) is currently available to further improve the system performance.
Although MIMO-NOMA systems are known to improve system performance, the current art directly decomposes the transmission channel of a MIMO-NOMA system into multiple parallel single-input single-output (SISO) NOMA transmission channels, without taking into account the spatial multiplexing and diversity gains of MIMO techniques.
Therefore, it is one of the issues that those skilled in the art are concerned about how to provide better system performance by utilizing the advantages of spatial multiplexing and diversity gain in MIMO-NOMA systems.
Disclosure of Invention
In view of the above, the present invention provides a joint power allocation, precoding and decoding method, which considers mean-squared error (MSE) performance of a system in a multiple-input multiple-output-non-orthogonal multiple access (MIMO-NOMA) system to provide a design for power allocation, precoder and decoder.
The invention provides a joint power allocation, precoding and decoding method, which is suitable for a base station transmitting messages to 2K user devices in a MIMO-NOMA system, wherein the 2K user devices are divided into K groups, each group comprises two user devices, one of the two user devices is a strong user, and the other one is a weak user. The method comprises the following steps: (1) decomposing the precoders corresponding to each group into a first precoder multiplied by a second precoder, wherein the first precoder is generated by a block diagonalization precoding technique; (2) obtaining a first MSE function associated with a strong user decoding a first signal through a first decoder, a second MSE function associated with a second signal through a second decoder, and a third MSE function associated with a weak user decoding a second signal through a third decoder in each group; (3) calculating, for each group, a power allocation factor α corresponding to each group on a condition that a maximum value among the first MSE function, the second MSE function, and the third MSE function is minimized, given the second precoderkWherein
Figure GDA0002744818460000021
And (4) according to the power allocation factors, under the condition of total transmission power limitation, obtaining the sum of all first MSE functions and all third MSE functions of the K groups to obtain the MSE function corresponding to each groupA second precoder, a first decoder, and a third decoder.
In an embodiment of the invention, after the step (4), repeating the steps (3) and (4) according to the newly obtained second precoder until a sum of all the first MSE functions and all the third MSE functions of the K groups converges to obtain an optimal solution of the power allocation factor, the second precoder, the first decoder, the second decoder, and the third decoder.
In an embodiment of the present invention, the number of antennas of the base station is greater than a sum of dimensions of eigenvector spaces of K-1 interference channel matrices corresponding to any one of the K groups.
In an embodiment of the invention, the first signal and the second signal include a plurality of parallel data symbols transmitted synchronously.
In an embodiment of the present invention, the above "calculating, for each group, the power allocation factor a corresponding to each group under the condition of minimizing the maximum value among the first MSE function, the second MSE function, and the third MSE function given the second precoderk"comprises the following steps: calculating, for each group, a power allocation factor α corresponding to each group under a condition that a maximum value of the first MSE function and the second MSE function is minimizedk(ii) a And calculating, for each group, a power allocation factor α corresponding to each group under the condition that a maximum value of the first MSE function and the third MSE function is minimizedk。
In an embodiment of the present invention, the above "calculating, for each group, the power allocation factor α corresponding to each group under the condition of minimizing the maximum value among the first MSE function, the second MSE function, and the third MSE function given the second precoderk"further comprising the steps of: limiting the first MSE function to be equal to the second MSE function, and limiting the first MSE function to be equal to the third MSE function, so as to obtain the relation between the power distribution factor alphakThe quadratic equation of (a); solving the quadratic equation to obtain a power distribution factor alphakTwo solutions of (a); and selecting the larger of the two solutions as the power allocation factor alphakBest solution of。
In an embodiment of the invention, the first MSE function and the second MSE function are limited to be equal, and the first MSE function and the third MSE function are limited to be equal, so as to obtain the value associated with the power division factor αkThe step of "the quadratic equation" further comprises: will have an included power division factor alphakThe inverse matrix of (c) is approximated by Taylor expansion (Taylor expansion).
In an embodiment of the present invention, the above "calculating, for each group, the power allocation factor α corresponding to each group under the condition of minimizing the maximum value among the first MSE function, the second MSE function, and the third MSE function given the second precoderk"further comprising the steps of: dividing power by a factor of alphakIs substituted into the inverse matrix to check whether the corresponding inverse matrix satisfies a convergence condition of the taylor approximation, and sets the power division factor α if the condition is not satisfiedkIs a fixed value.
In an embodiment of the present invention, the step of obtaining the second precoder, the first decoder and the third decoder corresponding to each group by minimizing a sum of all first MSE functions and all third MSE functions of the K groups under the condition of the total transmission power limitation according to the power allocation factors includes: under the condition of giving a second precoder, obtaining a first decoder and a third decoder corresponding to strong users and weak users in each group by minimizing the sum of all first MSE functions and all third MSE functions of K groups; and according to the first decoders and the third decoders, under the condition of the total transmission power limitation, the second precoder corresponding to each group is obtained by minimizing the sum of all the first MSE functions and all the third MSE functions of the K groups.
In an embodiment of the present invention, the above "obtaining the second precoder method corresponding to each group by minimizing the sum of all the first MSE functions and all the third MSE functions of the K groups under the condition of the total transmission power constraint according to the first decoder and the third decoder" includes: and obtaining a second precoder corresponding to each group which minimizes the sum of all first MSE functions and all third MSE functions of the K groups by adopting a Karush-Kuhn-Tucker (KKT) condition.
The invention provides a base station, which is suitable for an MIMO-NOMA system; the base station comprises a transceiver circuit, a storage circuit and a processing circuit. The transceiver circuit includes a plurality of antennas for transmitting messages to 2K user devices, wherein the 2K user devices are divided into K groups and each group includes two user devices, and one of the two user devices is a strong user and the other is a weak user. The memory circuit stores a plurality of program codes. The processing circuit is coupled with the transceiver circuit and the storage circuit and is configured to execute: (1) decomposing the precoders corresponding to each group into a first precoder multiplied by a second precoder, wherein the first precoder is generated by a block diagonalization precoding technique; (2) obtaining a first MSE function associated with a strong user decoding a first signal through a first decoder, a second MSE function associated with a second signal through a second decoder, and a third MSE function associated with a weak user decoding a second signal through a third decoder in each group; (3) calculating, for each group, a power allocation factor α corresponding to each group on a condition that a maximum value among the first MSE function, the second MSE function, and the third MSE function is minimized, given the second precoderkWherein
Figure GDA0002744818460000041
And (4) according to the power allocation factor alphakUnder the condition of limiting the total transmission power, the sum of the first MSE function and the third MSE function of the K groups is minimized to obtain the second precoder, the first decoder and the third decoder corresponding to each group.
In an embodiment of the invention, the processing circuit is further configured to perform: repeating steps (3) and (4) according to the newly obtained second precoder until the sum of all the first MSE functions and all the third MSE functions of the K groups converges to find the optimal solution of the power allocation factor, the second precoder, the first decoder, the second decoder and the third decoder.
In an embodiment of the present invention, the number of antennas of the transceiver circuit is greater than the sum of dimensions of eigenvector spaces of K-1 interference channel matrices corresponding to any one of the K groups.
In an embodiment of the invention, the first signal and the second signal include a plurality of parallel data symbols transmitted synchronously.
In an embodiment of the invention, the processing circuit is further configured to perform: calculating, for each group, a power allocation factor α corresponding to each group under a condition that a maximum value of the first MSE function and the second MSE function is minimizedk(ii) a And calculating, for each group, a power allocation factor α corresponding to each group under the condition that a maximum value of the first MSE function and the third MSE function is minimizedk。
In an embodiment of the invention, the processing circuit is further configured to perform: limiting the first MSE function to be equal to the second MSE function, and limiting the first MSE function to be equal to the third MSE function, so as to obtain the relation between the power distribution factor alphakThe quadratic equation of (a); solving the quadratic equation to obtain a power distribution factor alphakTwo solutions of (a); and selecting the larger of the two solutions as the power allocation factor alphakThe best solution of (1).
In an embodiment of the invention, the processing circuit is further configured to perform: will be associated with a power allocation factor alphakThe inverse matrix of (d) is approximated by a taylor expansion.
In an embodiment of the invention, the processing circuit is further configured to perform: dividing power by a factor of alphakIs substituted into the inverse matrix to check whether the corresponding inverse matrix satisfies a convergence condition of the taylor approximation, and sets the power division factor α if the condition is not satisfiedkIs a fixed value.
In an embodiment of the invention, the processing circuit is further configured to perform: under the condition of giving a second precoder, obtaining a first decoder and a third decoder corresponding to strong users and weak users in each group by minimizing the sum of all first MSE functions and all third MSE functions of K groups; and according to the first decoders and the third decoders, under the condition of the total transmission power limitation, the second precoder corresponding to each group is obtained by minimizing the sum of all the first MSE functions and all the third MSE functions of the K groups.
In an embodiment of the invention, the processing circuit is further configured to perform: and adopting a Carlo-Cohn-Tack (KKT) condition to obtain a second precoder corresponding to each group which minimizes the sum of all first MSE functions and all third MSE functions of the K groups.
Based on the above, the embodiment of the present invention provides a combined power allocation, precoding and decoding method and a base station thereof; firstly, a precoder capable of eliminating interference among groups is obtained through a block diagonalization technology, and MIMO-NOMA channels of a plurality of groups are decomposed into a plurality of parallel single group MIMO-NOMA channels; the invention also considers the MSE performance of the MIMO-NOMA system, and two optimization problems are formed for the power allocation factor, the precoder and the decoder in sequence so as to obtain the MSE performance of a certain level; in addition, the invention further obtains the final optimal power allocation factor, the optimal precoder and the optimal decoder through an iterative algorithm so as to further improve the MSE performance. In summary, the present invention can effectively improve the performance of the MIMO-NOMA system and provide better transmission quality.
In order to make the features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
Drawings
Fig. 1 is a schematic diagram of a downlink multi-group MIMO-NOMA system according to an embodiment of the present invention.
Fig. 2 is a flowchart illustrating a method for joint power allocation, precoding and decoding according to an embodiment of the invention.
FIG. 3 is a diagram of equivalent K parallel single group MIMO-NOMA channels according to FIG. 1.
[ notation ] to show
1_1, 1_2, 2_1, 2_2, …, K _1, K _ 2: user device
100: downlink multi-group massive MIMO-NOMA system
110: base station
C _1, C _2, …, C _ K: group of groups
S210, S220, S230, S240: step (ii) of
Detailed Description
Fig. 1 is a diagram of a downlink multi-group MIMO-NOMA system according to an embodiment of the present invention. In an embodiment of the present invention, the downlink massive MIMO-NOMA system 100 includes a base station 110 and 2K user devices divided into K groups (i.e., groups C _1, C _2, …, C _ K and user devices 1_1, 1_2, …, K _1, K _2), where K ≧ 1. The transmission ranges of different groups do not overlap with each other, and each group includes two user devices sharing the same transmit-side spatial correlation matrix. The present invention assumes that global channel state information (channel state information) is known, i.e. the channel matrix H between the bs 110 and the 2K ues can be obtainedk,i(K1., K, i 1,2) information. In addition, base station 110 is configured with NTA root antenna, and each of the user devices 1_1, 1_2, …, K _1, K _2 is configured with NRA root antenna, wherein NT＞＞NR。
In the present embodiment, the user devices 1_1, 1_2, …, K _1, and K _2 may be implemented as, but not limited to, a mobile station, an advanced mobile station (advanced mobile station), a server, a user terminal, a desktop computer, a laptop computer, a network computer, a workstation, a personal digital assistant (personal digital assistant), a tablet computer (tablet personal computer), a scanner, a telephone device, a pager, a camera, a television, a palmtop video game device, a music device, a wireless sensor, and the like, for example, and the invention is not limited thereto.
In this embodiment, the base station 110 may include (but is not limited to): for example, an eNB, a home eNB (home eNB), an advanced base station (advanced base station), a base transceiver system (base transceiver system), an access point, a home base station (home base station), a relay, an intermediate node, an intermediate device, and/or a satellite-based communication base station, but the implementable embodiments of the present invention are not limited thereto.
From a hardware perspective, the base station 110 may include at least, but is not limited to, transceiver circuitry, processing circuitry, and optionally memory circuitry. The transceiver circuit may include, but is not limited to, a transmitter circuit, a receiver circuit, an analog-to-digital (a/D) converter, a D/a converter, low noise amplification, mixing, filtering, impedance matching, transmission line, power amplification, one or more antenna circuits, and a local storage medium element. The storage circuit is, for example, a memory, a hard disk, or any other element to store data, and may be configured to record a plurality of program codes or modules.
The processing circuitry is configured to process the digital signals and perform the functions, processes, or method steps of the methods set forth in the exemplary embodiments of the invention. The processing circuit may optionally be coupled to a memory circuit to store program code, device configurations, code books, buffered or persistent data, and the like. The functions of the processing circuit may be implemented using programmable units such as microprocessors, microcontrollers, DSP chips, FPGAs, etc. The functions of the processing circuitry may also be implemented in stand-alone electronic devices or ICs, and the processing circuitry may also be implemented in hardware or software.
In the present embodiment, it is assumed that the channel of the downlink massive MIMO-NOMA system 100 is a geometric single-ring (one-ring) scattering model, and the antennas at the base station 110 are set to be a uniform linear array (uniform linear array). Since two user devices in each group share the same channel resources, it is considered herein that two user devices in the kth group also share the same spatial correlation matrix RkK is equal to { 1. Based on the above, at the angle of incidence (angle of arrival) θkAnd the (m, p) th element of the channel covariant matrix (covariance matrix) corresponding to the kth group with angular spread (Δ) can be represented as:
Figure GDA0002744818460000071
where λ D is the minimum distance between antennas at the base station 110.
According to equation (1), the channel matrix H corresponding to the ith UE in the kth groupk,iCan be expressed as:
Figure GDA0002744818460000072
where i belongs to {1,2}, K belongs to { 1.
Figure GDA0002744818460000073
To follow
Figure GDA0002744818460000074
Distributed fast-fading (fast-fading) complex Gaussian (Gaussian) matrix, IMRepresenting an identity matrix of M x M,
Figure GDA0002744818460000075
representing a spatial correlation matrix RkHas rkA diagonal matrix of non-0 eigenvalues, and
Figure GDA0002744818460000076
is a spatial correlation matrix RkA matrix formed by the feature vectors of (a); herein, r iskAlso called channel matrix Hk,iThe dimension of the feature vector space of (2).
It should be noted that the embodiments of the present invention define the ue with the channel matrix with larger Frobenius norm square (i.e. ue 1_1, 2_1, …, K _1) as the strong user, and the ue with the channel matrix with smaller Frobenius norm square (i.e. ue 1_2, 2_2, …, K _2) as the weak user
Figure GDA0002744818460000077
For the kth group, the base station 110 will have a power allocation factor αkOf strong users
Figure GDA0002744818460000081
And has a power division factor of 1-alphakOf weak users
Figure GDA0002744818460000082
The signal vectors are combined into a multiplexed (multiplexed) signal vector in the power domain as follows:
Figure GDA0002744818460000083
wherein s isk,1And sk,2Is the vector dimension LkRepresenting the number of parallel data symbols transmitted synchronously.
Vector x of signalskMultiplying precoder
Figure GDA0002744818460000084
The signal vector transmitted at the base station 110 can be represented as:
Figure GDA0002744818460000085
and the received signal vector of the ith ue in the kth group can be expressed as:
Figure GDA0002744818460000086
wherein
Figure GDA0002744818460000087
For example, Additive White Gaussian Noise (AWGN), but the present invention is not limited thereto.
If the received signal vector is expanded, it can be expressed as:
Figure GDA0002744818460000088
where the third term on the right of equation (6) is the inter-cluster interference caused by the signal vectors of other clusters, the first term on the right is the signal vector of the strong user (i.e., intra-cluster interference for weak users), and the second term on the right is the signal vector of the weak user (i.e., intra-cluster interference for strong users).
To exploit the spatial multiplexing and diversity gain potential of MIMO-NOMA systems, the present invention considers the MSE performance of MIMO-NOMA systems and proposes a power allocation, precoder and decoder dependent system design for user devices.
Fig. 2 is a flowchart illustrating a joint power allocation, precoding and decoding method according to an embodiment of the invention, which may be performed by the base station 110, and the steps thereof will be described with reference to the system architecture of fig. 1.
In step S210, precoders F corresponding to the respective groups are assigned to respective groupskThe decomposition is into a first precoder multiplied by a second precoder, where the first precoder is generated with a block diagonalization (block diagonalization) precoding technique.
In the present embodiment, the proposed precoder FkIncluding a first precoder for canceling inter-group interference
Figure GDA0002744818460000091
And a second precoder to enhance MSE performance
Figure GDA0002744818460000092
Can be expressed as:
Fk＝QkWkk is equal to { 1.,. K } equation (7)
Where N represents the dimension of the null space of an equivalent channel matrix, this parameter will be the first precoder Q belowkThe design of (1).
The interference of the signal of the kth group to the ith user equipment of the ith group can be expressed as equation (6) and equation (7)
Figure GDA0002744818460000093
In order to eliminate the inter-group interference, the first precoder Q of the kth group of the present inventionkThe design will be such that the corresponding signal vector xkIn the channel matrix Hl,i0 when the receiving ends of the two user devices of the first group are reached; that is, QkWill meet the following zero interference condition: hl,iQk0 (i.e. 1)
Figure GDA0002744818460000094
)，l,k∈{1,...,K},l≠k。
Based on the above, the base station 110 will employ the block diagonalization precoder design technique to generate the first precoder Qk. Specifically, in the block diagonalization procedure, the k-th group of signal vectors x is collected firstkK-1 interference channel matrixes (H) corresponding to interference items generated by other groupsl,iAll eigenvectors of l ∈ { 1.,. K }, l ≠ K), and are represented as a matrix
Figure GDA0002744818460000095
Figure GDA0002744818460000096
Has the dimension of
Figure GDA0002744818460000097
Wherein
Figure GDA0002744818460000098
When in use
Figure GDA0002744818460000099
When the temperature of the water is higher than the set temperature,
Figure GDA00027448184600000910
n (equal to)
Figure GDA00027448184600000911
) The 0 singular value and the corresponding null space (null space) can be passed through the pair
Figure GDA00027448184600000912
Obtained by performing Singular Value Decomposition (SVD) as follows:
Figure GDA00027448184600000913
wherein
Figure GDA00027448184600000914
Is composed of
Figure GDA00027448184600000915
A diagonal matrix of non-zero singular values,
Figure GDA00027448184600000916
and
Figure GDA00027448184600000917
are respectively the matrix formed by the corresponding left singular vector and right singular vector, and
Figure GDA00027448184600000918
can be further provided with
Figure GDA00027448184600000919
And
Figure GDA00027448184600000920
is shown as
Figure GDA00027448184600000921
The matrix is
Figure GDA00027448184600000922
The vector space (spread vector space) formed by N row vectors is the matrix
Figure GDA00027448184600000923
The null space of (a).
Notably, to guarantee a matrix
Figure GDA00027448184600000924
The null space exists and can completely eliminate the interference among the groups, and the number of the antennas at the transmitting end must satisfy the following conditions:
Figure GDA00027448184600000925
wherein r islFor interfering with the channel matrix Hl,iOf the feature vector space, and LkRepresenting the number of parallel data symbols synchronously transmitted to any user of the kth group; due to LkThe inequality (9) means that the number of antennas at the transmitting end must be greater than the sum of dimensions of the eigenvector space of the K-1 interference channel matrices corresponding to any one of the K groups.
When the equal sign in the inequality (9) is established, the matrix
Figure GDA0002744818460000101
The dimension of the null space of (A) is
Figure GDA0002744818460000102
In the present embodiment, the matrix V is derived from the equations (8) and (9)kThe first precoder Q to be the k-th groupkThat is:
Figure GDA0002744818460000103
as such, the base station 110 can determine the first precoder Q by using equation (10)k(K ∈ { 1.,. K }) eliminates the inter-group interference in equation (6). Thus, multiple groups of MIMO-NOMA channels of the downlink massive MIMO-NOMA system 100 may be decomposed into K parallel single groups of MIMO-NOMA channels.
FIG. 3 is a diagram of equivalent K parallel single group MIMO-NOMA channels according to FIG. 1. In this case, the received signal vector of the ith user device in the kth group can be represented as:
Figure GDA0002744818460000104
according to equation (11), for intra-group interference of two user devices in the kth group, the strong user may remove the signal vector of the weak user by performing SIC, and the weak user may directly decode the received signal vector considering the signal vector of the strong user as noise. Based on the above, in the following description, the design of the proposed downlink multi-group MIMO-NOMA system 100 will focus mainly on the MSE performance of two user equipments in a single group.
In step S220, a first MSE function associated with the strong user decoding the first signal through the first decoder and a second MSE function associated with the weak user decoding the second signal through the second decoder in each group are obtained, and a third MSE function associated with the weak user decoding the second signal through the third decoder.
In this embodiment, if the first decoder D is applied in the kth groupk,11A second decoder Dk,12And a third decoder Dk,22To restore the signal vector of the strong user (i.e. the first signal s)k,1) With the signal vector of the weak user (i.e. the second signal s)k,2) Then, the MSE of the received signal vector at the strong ue and the weak ue can be expressed as:
Figure GDA0002744818460000105
Figure GDA0002744818460000106
Figure GDA0002744818460000107
equation (12) indicates that the strong users in the kth group are first decoded by the second decodingDevice Dk,12Decoding weak user's signal sk,2Corresponding second MSE function Jk,12Equation (13) indicates that the strong users in the kth group are under the assumption of perfect SIC (i.e., with perfect SIC)
Figure GDA0002744818460000111
) By means of a first decoder Dk,11Decoding its own signal sk,1Corresponding first MSE function Jk,11And equation (14) indicates that the weak users in the kth group pass through the third decoder Dk,22Decoding its own signal sk,2Corresponding third MSE function Jk,22。
In one embodiment of the invention, a first decoder D is soughtk,11A second decoder Dk,12And a third decoder Dk,22Substituting equation (11) into equations (12) - (14) and developing the result as follows:
Figure GDA0002744818460000112
Figure GDA0002744818460000113
Figure GDA0002744818460000114
wherein
Figure GDA0002744818460000115
And
Figure GDA0002744818460000116
the channel matrixes are equivalent channel matrixes corresponding to the strong user and the weak user respectively.
In the present embodiment, the second decoder D can be derived by using the matrix partial differential rule for equations (15) to (17)k,12A first decoder Dk,11And a third decoder Dk,22Is closedThe best solutions of the formula (closed-form) are respectively shown as the following
Figure GDA0002744818460000117
And
Figure GDA0002744818460000118
Figure GDA0002744818460000119
Figure GDA00027448184600001110
Figure GDA00027448184600001111
note that the second decoder Dk,12A first decoder Dk,11And a third decoder Dk,22The best solution may be obtained in other ways, which the present invention does not limit. It should be noted that the present invention assumes that global channel state information is available, so the second decoder Dk,12A first decoder Dk,11And a third decoder Dk,22The best solution of (a) can be obtained by the base station 110 and then transmitted to the ue, or can be directly calculated by the ue, which is not limited by the invention.
The second decoder Dk,12A first decoder Dk,11And a third decoder Dk,22The optimal solutions of (a) are substituted into equations (15) - (17), respectively, relating the MSE J of the signal vectors for strong and weak usersk,12、Jk,11And Jk,22(i.e., the second, first, and third MSE functions) may be rewritten as:
Figure GDA0002744818460000121
Figure GDA0002744818460000122
Figure GDA0002744818460000123
in step S230, given the second precoder, power allocation factors corresponding to the respective groups are calculated for the respective groups on the condition that the maximum value among the first MSE function, the second MSE function, and the third MSE function is minimized.
In this embodiment, two user devices in a single group are not only able to decode their own signal vectors, but the strong user can also recover the signal vectors of the weak user during SIC in NOMA transmission. Thus, the present invention sets an optimization problem for the power allocation factors associated with two user devices in each group-for the kth group, at a given second precoder WkBased on the above-mentioned MSE
Figure GDA0002744818460000124
And
Figure GDA0002744818460000125
to calculate the power division factor alphak(ii) a The goal of this optimization is to minimize the maximum MSE of the received signal vector in all decoding processes, as shown below:
Figure GDA0002744818460000126
Figure GDA0002744818460000127
wherein the constraint of equation (24) indicates that the optimization problem follows the NOMA principle, i.e., the transmission power of the signal vector of the weak user must be greater than the transmission power (1- α) of the signal vector of the strong userk＞αk)。
To find a solution to the above optimization problem, MSE will be used herein
Figure GDA0002744818460000128
And
Figure GDA0002744818460000129
to the power distribution factor alphakThe partial differential of (a) is expressed as follows:
Figure GDA00027448184600001210
Figure GDA00027448184600001211
wherein
Figure GDA00027448184600001212
Since the derivative of equation (25) always has a positive value, MSE
Figure GDA00027448184600001213
And
Figure GDA00027448184600001214
allocating a factor alpha to the powerkA strictly increasing function of; in addition, according to
Figure GDA00027448184600001215
Is a negative definite (negative definite) matrix, which also causes the derivative in equation (26) to always have a negative value and results in MSE
Figure GDA0002744818460000131
Allocating a factor alpha to the powerkIs strictly decreasing function. Thus, in
Figure GDA0002744818460000132
In the case of (3), MSE
Figure GDA0002744818460000133
And
Figure GDA0002744818460000134
there will be two crossover points.
Based on the above results, in the present embodiment, the base station 110 can decompose the optimization problem of equation (24) into minimizing MSE
Figure GDA0002744818460000135
And
Figure GDA0002744818460000136
maximum value of (i.e. of)
Figure GDA0002744818460000137
) And minimizing MSE
Figure GDA0002744818460000138
And
Figure GDA0002744818460000139
(i.e. the
Figure GDA00027448184600001310
) Two subproblems of maximum value in (1).
In this case, the base station 110 may also set the MSE by setting the MSE separately
Figure GDA00027448184600001311
And MSE
Figure GDA00027448184600001312
To obtain the power division factor alphakAs shown below:
Figure GDA00027448184600001313
Figure GDA00027448184600001314
note that, the terms of equations (27) and (28) have the following characteristic value characteristics:
Figure GDA00027448184600001315
Figure GDA00027448184600001316
Figure GDA00027448184600001317
wherein
Figure GDA00027448184600001318
Based on the above-described characteristic feature characteristics, equations (27) and (28) can be rewritten as:
Figure GDA00027448184600001319
Figure GDA00027448184600001320
however, equations (32) and (33) show the power division factor αkBit-in-inverse matrix
Figure GDA00027448184600001321
Within this, this will result in a power division factor αkThe optimal solution of (a) is not easy to find. To address this challenge, the present invention employs Taylor expansion (Taylor expansion) to approximate the relationship to the power division factor αkWherein the Taylor approximation corresponding to the inverse matrix can be expressed as
Figure GDA00027448184600001322
It is noted that the inverse matrix satisfies the Taylor approximationSimilar conditions are as follows: | BA-1< 1 (or A |)-1B | < 1), the convergence of the corresponding Taylor expansion is ensured.
In the present embodiment, the base station 110 is provided
Figure GDA00027448184600001323
And is
Figure GDA00027448184600001324
To obtain the following taylor approximation:
Figure GDA00027448184600001325
substituting equation (34) into equations (32) and (33) may result in:
Figure GDA0002744818460000141
Figure GDA0002744818460000142
based on equations (35) and (36) and
Figure GDA0002744818460000143
Figure GDA0002744818460000144
and
Figure GDA0002744818460000145
Figure GDA0002744818460000146
base station 110 obtains power allocation factor α via quadratic equation solutionkTwo solutions of
Figure GDA0002744818460000147
And
Figure GDA0002744818460000148
as shown below:
Figure GDA0002744818460000149
Figure GDA00027448184600001410
it should be noted that, according to the MSE characteristics in equations (25) and (26), the power allocation factor with the larger solution has a smaller MSE value than the other, so that the base station 110 selects the power allocation factor with the larger solution as the power allocation factor α in equations (37) and (38)kAs shown below:
Figure GDA00027448184600001411
it should be noted that the power division factor obtained according to the Taylor expansion described above
Figure GDA00027448184600001412
The taylor approximation condition of the corresponding inverse matrix must be satisfied. Therefore, the base station 110 needs to further allocate this power factor
Figure GDA00027448184600001413
And substituting the Taylor approximation condition of the corresponding inverse matrix to check whether convergence occurs. When in use
Figure GDA00027448184600001414
(or
Figure GDA00027448184600001415
) The solution obtained in equation (39) is not available, which also implies that the corresponding channel conditions are rather poor; in this case, the base station 110 will set the power allocation factor
Figure GDA00027448184600001416
Is a fixed value, e.g.
Figure GDA00027448184600001417
In light of the above, in the present embodiment, the base station 110 allocates the power factors for the two user devices in the kth group
Figure GDA00027448184600001418
Can be expressed as:
Figure GDA00027448184600001419
notably, the power division factor of equation (40)
Figure GDA00027448184600001420
Meaning that the MSE performance of all decoding procedures in the kth group can reach at least a certain level.
In step S240, according to the obtained power allocation factor, the second precoder, the first decoder, and the third decoder corresponding to each group are obtained by minimizing the sum of the first MSE function and the third MSE function of all groups under the condition of total transmission power limitation.
In the present embodiment, the base station 110 allocates the factors according to the power obtained in step S230
Figure GDA0002744818460000151
Form a second precoder WkA first decoder Dk,11And a third decoder Dk,22Where K e { 1. The optimization problem is given a total transmit power limit PTIn the case of (2), minimizing the MSE J described in equations (16) and (17) for all groupsk,11And Jk,22To obtain the best second precoder W corresponding to each group K e {1kThe best first decoder Dk,11And an optimal third decoder Dk,22As shown below:
Figure GDA0002744818460000152
Figure GDA0002744818460000153
it is to be noted that the constraint of equation (41) does not relate to the first decoder Dk,11And a third decoder Dk,22Thus, given the second precoder WkIn this case, the optimization problem can be expressed as:
Figure GDA0002744818460000154
by making the gradient corresponding to the objective function of equation (42) equal to zero (or by using the method in step S220), the optimal solution of the first decoder as described by equations (19) and (20), respectively, can be obtained directly
Figure GDA0002744818460000155
Optimal solution to third decoder
Figure GDA0002744818460000156
Then, given the best solution of the first decoder
Figure GDA0002744818460000157
Optimal solution to third decoder
Figure GDA0002744818460000158
In the case of (2), the above minimizes the MSE J described in equations (16) and (17) for all groupsk,11And Jk,22To obtain the best second precoder W corresponding to each group K e {1kThe optimization problem of (a) can be expressed as:
Figure GDA0002744818460000159
Figure GDA00027448184600001510
to solve this optimization problem, the karo-kunn-tower (KKT) condition can be used, and the corresponding Lagrangian function can be expressed as:
Figure GDA00027448184600001511
wherein λ ≧ 0 is the Lagrangian multiplier (Lagrangian multiplier) of the constraint in equation (43). Therefore, the KKT condition for the optimization problem described above can be expressed as:
Figure GDA0002744818460000161
Figure GDA0002744818460000162
Figure GDA0002744818460000163
wherein H'k,1＝Hk,1QkAnd H'k,2＝Hk,2Qk(excluding the second precoder Wk) Are equivalent channel matrices associated with strong and weak users, respectively.
Based on equation (45a), the second precoder
Figure GDA0002744818460000164
The best solution of (c) can be expressed as:
Figure GDA0002744818460000165
as can be seen from equation (46), the second precoder
Figure GDA0002744818460000166
Power (i.e. of
Figure GDA0002744818460000167
) Strictly decreasing corresponding to λ; thus, the upper bound for optimum λ is as follows:
Figure GDA0002744818460000168
wherein
Figure GDA0002744818460000169
And is
Figure GDA00027448184600001610
According to inequality (47), total transmission power limit P satisfying equation (43)TThe optimal lambda of (b) can be obtained by binary search.
Briefly, according to the joint power allocation, precoding and decoding method of fig. 2, the downlink multi-group massive MIMO-NOMA system 100 can obtain the preliminary optimal power allocation factor, optimal precoder and optimal decoder to reduce the MSE of the system. However, in other embodiments of the present invention, the optimal solution of the second precoder obtained in step S240 may also be used
Figure GDA00027448184600001611
Iteratively executing steps S230 to S240 until the sum of the first MSE function at the strong ue and the third MSE function at the weak ue converges for obtaining the final power allocation factor α that minimizes the system MSEkA second precoder WkA first decoder Dk,11A second decoder Dk,12And a third decoder Dk,22The best solution of (1).
In the present embodiment, the second pre-editing is performed according to the second pre-editing obtained in step S240Code device WkThe optimal solution of (a) can be directly updated by using the equations (37), (38) and (40) obtained in step S230 to update the power distribution factor αkSo that two user devices in the kth group have reasonable MSE performance. Then, the updated power allocation factor αkThe first decoder D may also be updated directly using equations (18) - (20) and (46) obtained in step S240k,11A second decoder Dk,12A third decoder Dk,22And a second precoder WkTo further reduce the MSE of the system. The iterative process is repeated until the sum of the MSEs for all users in the system converges to obtain the final optimal power allocation factor, optimal precoder and optimal decoder that minimizes the MSE for the system.
In summary, the embodiments of the present invention provide a joint power allocation, precoding and decoding method and a base station thereof; firstly, a precoder capable of eliminating interference among groups is obtained through a block diagonalization technology, and MIMO-NOMA channels of a plurality of groups are decomposed into a plurality of parallel single group MIMO-NOMA channels; the invention also considers the MSE performance of the MIMO-NOMA system, and two optimization problems are formed for the power allocation factor, the precoder and the decoder in sequence so as to obtain the MSE performance of a certain level; in addition, the invention further obtains the final optimal power allocation factor, the optimal precoder and the optimal decoder through an iterative algorithm so as to further improve the MSE performance. In summary, the present invention can effectively improve the performance of the MIMO-NOMA system and provide better transmission quality.
Although the present invention has been described with reference to the above embodiments, it is not intended to limit the present invention. Those skilled in the art can make appropriate changes and modifications without departing from the spirit and scope of the invention, which should be construed as broadly as the invention pertains.

Claims (20)

1. A joint power allocation, precoding and decoding method for a base station transmitting messages to 2K user equipments in a multiple-input multiple-output-non-orthogonal multiple access (MIMO-NOMA) system, wherein the 2K user equipments are divided into K groups and each group includes two user equipments, and one of the two user equipments is a strong user and the other is a weak user, the method comprising:
(1) decomposing the precoders corresponding to the groups into a first precoder multiplied by a second precoder, wherein the first precoder is generated by a block diagonalization precoding technique;
(2) obtaining a first Mean Square Error (MSE) function associated with the strong user decoding a first signal via a first decoder and a second MSE function associated with the weak user decoding a second signal via a second decoder in each group, and a third MSE function associated with the weak user decoding the second signal via a third decoder;
(3) calculating, for each group, a power allocation factor α corresponding to the each group on a condition that a maximum value among the first MSE function, the second MSE function, and the third MSE function is minimized, given the second precoderkWherein
Figure FDA0002561923770000011
And
(4) according to the power distribution factor alphakAnd obtaining the second precoder, the first decoder and the third decoder corresponding to each group by minimizing the sum of all the first MSE functions and all the third MSE functions of the K groups under the condition of total transmit power limitation.
2. The method of claim 1, further comprising, after step (4):
repeating steps (3) and (4) according to the optimal solution of the second precoder until the sum of all the first MSE functions and all the third MSE functions of the K groups converges to obtain the optimal solutions of the power allocation factor, the second precoder, the first decoder, the second decoder and the third decoder.
3. The method of claim 1, wherein the number of antennas of the base station is greater than the sum of dimensions of the eigenvector space of the K-1 interference channel matrices corresponding to any one of the K groups.
4. The method of claim 1 wherein the first signal and the second signal comprise a plurality of synchronously transmitted parallel data symbols.
5. The method of claim 1, wherein the power allocation factor α corresponding to the respective group is calculated for the respective group with a condition that minimizes a maximum of the first MSE function, the second MSE function, and the third MSE function given the second precoderkComprises the following steps:
calculating the power allocation factor α corresponding to each group under the condition of minimizing the maximum value of the first MSE function and the second MSE function for each groupk(ii) a And
calculating the power allocation factor α corresponding to each group under the condition of minimizing the maximum value of the first MSE function and the third MSE function for each groupk。
6. The method of claim 5, wherein the power allocation factor α corresponding to the respective group is calculated for the respective group with a condition that minimizes a maximum of the first MSE function, the second MSE function, and the third MSE function, given the second precoderkFurther comprising the steps of:
limiting the first MSE function to be equal to the second MSE function and limiting the first MSE function to be equal to the third MSE function to obtain a value associated with the power allocation factor αkThe quadratic equation of (a);
solving the quadratic equation to obtain the power distribution factor alphakTwo solutions of (a); and
selecting the larger of the two solutions as the power allocation factor alphakThe best solution of (1).
7. The method of claim 6Wherein the first MSE function and the second MSE function are constrained to be equal, and the first MSE function and the third MSE function are constrained to be equal, to obtain a value associated with the power allocation factor αkThe step of the quadratic equation of (a) further comprises:
will be associated with the power allocation factor alphakIs approximated by Taylor expansion (Taylor expansion).
8. The method of claim 7, wherein the power allocation factor α corresponding to the respective group is calculated for the respective group with a condition that minimizes a maximum of the first MSE function, the second MSE function, and the third MSE function, given the second precoderkFurther comprising the steps of:
dividing the power by a factor of alphakIs substituted into the inverse matrix to check whether the inverse matrix satisfies a convergence condition of the taylor expansion approximation, and sets the power division factor alpha if the condition is not satisfiedkIs a fixed value.
9. The method of claim 1 wherein the power allocation factor α is based onkThe step of obtaining the second precoder, the first decoder and the third decoder corresponding to each group by minimizing the sum of all the first MSE functions and all the third MSE functions of the K groups under the condition of the total transmit power limitation includes:
obtaining the first decoder and the third decoder corresponding to each group by minimizing the sum of all the first MSE functions and all the third MSE functions of the K groups given the second precoder; and
according to the first decoder and the third decoder, the second precoders corresponding to the groups are obtained by minimizing the sum of all the first MSE functions and all the third MSE functions of the K groups under the condition of the total transmission power limitation.
10. The method of claim 9, wherein the second precoder method according to the first decoder and the third decoder for each group by minimizing a sum of all the first MSE functions and all the third MSE functions for the K groups under the total tx power constraint comprises:
obtaining the second precoders corresponding to the respective groups that minimize the sum of all of the first MSE functions and all of the third MSE functions of the K groups using a karo-kun-tower (KKT) condition.
11. A base station adapted for use in a multiple-input multiple-output-non-orthogonal multiple access (MIMO-NOMA) system, the base station comprising:
a transceiver circuit comprising a plurality of antennas for transmitting messages to 2K user devices, wherein the 2K user devices are divided into K groups and each group comprises two user devices, and one of the two user devices is a strong user and the other is a weak user;
a storage circuit storing a plurality of program codes; and
a processing circuit coupled to the transceiver circuit and the storage circuit and configured to perform operations comprising:
(1) decomposing the precoders corresponding to the groups into a first precoder multiplied by a second precoder, wherein the first precoder is generated by a block diagonalization precoding technique;
(2) obtaining a first MSE function associated with the strong user decoding a first signal through a first decoder, a second MSE function associated with the weak user decoding a second signal through a second decoder, and a third MSE function associated with the weak user decoding the second signal through a third decoder in each group;
(3) calculating, for each group, a power allocation factor α corresponding to the each group on a condition that a maximum value among the first MSE function, the second MSE function, and the third MSE function is minimized, given the second precoderkWherein
Figure FDA0002561923770000031
(4) According to the power distribution factor alphakThe second precoder, the first decoder and the third decoder corresponding to each group are obtained by minimizing the sum of all the first MSE functions and all the third MSE functions of the K groups under the condition of total transmit power limitation.
12. The base station of claim 11, wherein the processing circuitry is further configured to perform:
repeating the above (3) and (4) according to the optimal solution of the second precoder until the sum of all the first MSE functions and all the third MSE functions of the K groups converges to obtain the optimal solutions of the power allocation factor, the second precoder, the first decoder, the second decoder and the third decoder.
13. The base station of claim 11, wherein the number of antennas of the transceiver circuit is greater than the sum of dimensions of the eigenvector space of the K-1 interference channel matrices corresponding to any one of the K groups.
14. The base station of claim 11 wherein the first signal and the second signal comprise a plurality of synchronously transmitted parallel data symbols.
15. The base station of claim 11, wherein the processing circuitry is further configured to perform:
calculating the power allocation factor α corresponding to each group under the condition of minimizing the maximum value of the first MSE function and the second MSE function for each groupk(ii) a And
calculating the power allocation factor α corresponding to each group under the condition of minimizing the maximum value of the first MSE function and the third MSE function for each groupk。
16. The base station of claim 15, wherein the processing circuitry is further configured to perform:
limiting the first MSE function to be equal to the second MSE function and limiting the first MSE function to be equal to the third MSE function to obtain a value associated with the power allocation factor αkA first order equation of (a);
solving the quadratic equation to obtain the power distribution factor alphakTwo solutions of (a); and
selecting the larger of the two solutions as the power allocation factor alphakThe best solution of (1).
17. The base station of claim 16, wherein the processing circuit is further configured to perform:
will be associated with the power allocation factor alphakIs approximated by taylor expansion.
18. The base station of claim 17, wherein the processing circuit is further configured to perform:
dividing the power by a factor of alphakIs substituted into the inverse matrix to check whether the inverse matrix satisfies a convergence condition of the taylor expansion approximation, and sets the power division factor alpha if the condition is not satisfiedkIs a fixed value.
19. The base station of claim 11, wherein the processing circuitry is further configured to perform:
obtaining the first decoder and the third decoder corresponding to each group by minimizing the sum of all the first MSE functions and all the third MSE functions of the K groups given the second precoder; and
according to the first decoder and the third decoder, the second precoders corresponding to the groups are obtained by minimizing the sum of all the first MSE functions and all the third MSE functions of the K groups under the condition of the total transmission power limitation.
20. The base station of claim 19, wherein the processing circuitry is further configured to perform:
obtaining the second precoders corresponding to the respective groups that minimize the sum of all of the first MSE functions and all of the third MSE functions of the K groups using a karo-kun-tower (KKT) condition.
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