CN110401476B - Codebook-based millimeter wave communication multi-user parallel beam training method - Google Patents

Codebook-based millimeter wave communication multi-user parallel beam training method Download PDF

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CN110401476B
CN110401476B CN201910715824.XA CN201910715824A CN110401476B CN 110401476 B CN110401476 B CN 110401476B CN 201910715824 A CN201910715824 A CN 201910715824A CN 110401476 B CN110401476 B CN 110401476B
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CN110401476A (en
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戚晨皓
陈康建
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Southeast University
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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
    • H04B7/0452—Multi-user 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
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • 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
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • 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
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming
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    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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Abstract

The invention discloses a millimeter wave communication multi-user parallel beam training method based on a codebook. The method carries out parallel beam training on a multi-user system by designing beam forming of a sending end. Compared with the existing multi-user serial layered beam training, the method can approach the performance of the existing multi-user serial layered beam training method on the premise of greatly reducing the training overhead.

Description

Codebook-based millimeter wave communication multi-user parallel beam training method
Technical Field
The invention belongs to the field of millimeter wave wireless communication, and relates to a codebook-based millimeter wave communication multi-user parallel beam training method.
Background
With the popularity of mobile terminal devices, the demand for wireless communication is increasing. In order to meet the increasing demand for data traffic, millimeter wave communication (30GHz-300GHz) is receiving much attention due to its abundant spectrum resources and extremely high transmission rate.
Due to the fact that the carrier frequency is higher than that of existing conventional frequency band communication, millimeter wave communication has larger path loss when being spread in space. On the other hand, higher carrier frequencies enable millimeter wave communications with smaller antenna sizes. This allows a larger antenna array to be packaged in a limited area and compensates for channel path loss using the gain of the antenna array. Current microwave band communications typically assign a dedicated radio frequency link to each antenna. However, millimeter wave communication generally employs large-scale antenna arrays, and assigning a dedicated rf link to each antenna would result in high rf link cost. In order to save radio frequency link resources, a hybrid precoding structure using a small number of radio frequency links is widely adopted in millimeter wave communication. In a hybrid precoding structure, each radio frequency link is linked to all antennas by a number of antenna phase shifters.
In order to obtain information of a millimeter wave communication channel, beam training based on a preset codebook, i.e., beam scanning, is widely adopted. The method traverses all beam possibilities in the codebook to obtain codeword combinations of the best matching channels (document [1 ]: A. Alkhateeb, G.Leus, and R.W.Heath, "Limited feedback hybrid decoding for multi-user millimeter wave systems," IEEE trans. Wireless Commun., vol.14, No.11, pp.6481-6494, Nov.2015.). In order to further increase the beam scanning speed, a hierarchical beam training mode based on a hierarchical codebook is proposed. In the hierarchical codebook, each codeword is a beam covering a certain spatial range, and the beam coverage of the upper codeword is the superposition of the corresponding two codeword beam coverage of the bottom layer. The beam training usually finds the codeword with the largest energy among the codewords to be tested for beamforming. The use of hierarchical codebooks in multi-user communication systems has attracted considerable interest due to the advantages of hierarchical codebooks. The conventional beam training method usually performs sequential estimation for multiple users, i.e. a hierarchical codebook training method of Time Division Multiplexing (TDMA). Although the performance of TDMA codebook training successfully applies a layered codebook to multi-user beam training, its training overhead grows linearly with the number of users. Document [2] proposes a layered codebook training scheme for parallel operation of multiple radio frequency links (document [2 ]: R.Zhang, H.Zhang, W.Xu, and C.ZHao, "A code book based multiple beamforming for mmwave multi-user MIMO systems with space structure," in 2018IEEE Global Commun.Conf. (GLOBECOM), Abu Dhabi, UAE, Dec.2018, pp.1-6.). However, this scheme is only applicable to partially connected architectures, and there will be a significant performance penalty in applying it to the hybrid precoding architecture.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems, the invention provides a millimeter wave communication multi-user parallel beam training method based on a codebook. The method comprises three stages: in the first stage, the base station sends 2 spatial beams, and the user feeds back the index of the spatial beam corresponding to the user. In the second stage, the base station forms two code words to perform simultaneous beam training on multiple users according to the space position of the last detection. In the third phase, the users send signals to the base station in sequence, so that the base station obtains an equivalent channel matrix to eliminate the interference among the multiple users.
The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a millimeter wave communication multi-user parallel beam training method based on a codebook comprises the following steps:
(1) establishing a signal transmission model of millimeter wave multi-user communication;
(2) establishing a millimeter wave communication channel model of a base station and multiple users;
(3) designing a user terminal hierarchical codebook for estimating the channel model channel path arrival angle;
(4) designing a base station end codebook for estimating the channel path transmitting angle of the channel model, implementing multi-user parallel beam training by using the user-side hierarchical codebook and the base station end codebook, and designing a new base station end codebook according to a beam training result for next multi-user parallel beam training until the beam training is finished;
(5) designing digital precoding of a transmitting end on the basis of the steps (1) to (4).
Further, in step (1), a signal transmission model of millimeter wave multi-user communication is established as follows:
setting a base station for communication with K users, wherein the base station adopts a mixed pre-coding structure comprising digital pre-coding and analog pre-coding; each user only adopts analog pre-coding; the number of radio frequency links of the base station and the user is N respectivelyRFAnd 1, the antenna arrays of the sending end and the receiving end are uniform linear arrays with the interval of half-wavelength and respectively have NBSAnd NUEThe signal is sent out through the antenna array after being subjected to digital pre-coding, radio frequency link and analog pre-coding at a sending end, the signal reaches the kth user after being transmitted in a wireless channel, the signal received by the antenna array of the kth user is subjected to analog combination and radio frequency link to obtain a final received signal, and the received signal can be expressed as:
Figure BDA0002155394170000021
wherein K is 1, 2BB、FRF、HkAnd wkRespectively representing a digital precoding matrix, an analog precoding matrix, a channel matrix between the base station and the kth user, an analog combining vector, ykS and nkRespectively representing the received signal, the transmitted signal and the additive white Gaussian noise vector of the kth user-HThe representation is subjected to conjugate transposition.
Further, in step (2), the millimeter wave multi-user communication channel model is established as follows:
l is set to be shared between the base station and the k userkInformation of each transmission path is expressed by a transmission angle, a reception angle and a channel gain, and a channel of the millimeter wave communication system is modeled as follows:
Figure BDA0002155394170000031
wherein N isBS、NUE、Lk、λl、
Figure BDA0002155394170000032
And
Figure BDA0002155394170000033
respectively representing the number of base station antennas, the number of user antennas, the number of paths, the channel gain of the ith path, the arrival angle of a channel and the transmission angle of the channel, wherein alpha (N, theta) represents a channel steering vector and is defined as:
Figure BDA0002155394170000034
wherein, N is the number of antennas, θ is the channel AOA or AOD, and the transmission angle and the arrival angle in the space of the ith path are assumed to be
Figure BDA0002155394170000035
And
Figure BDA0002155394170000036
then
Figure BDA0002155394170000037
To obtain
Figure BDA0002155394170000038
Further, in step (3), the method for designing the hierarchical codebook of the user end for estimating the arrival angle of the signal path in step (2) is as follows:
(3.1) setting VUE(s, m) represents the mth codeword of the s-th layer of the hierarchical codebook, and m is 1, 2, …, 2s；
(3.2) setting the number of antennas at the user end to be NUEWhen N is presentUEThe codebook has the following characteristics when the power of exponent is 2: (3.2.1) the codebook at the transmitting end has T +1 layers, T is determined by the number of antennas, and T is log2NUE；
(3.2.2) the s-th layer of the codebook has 2 in totalsA codeword, s ═ 0, 1, 2, … T; and, the bottom layer of the codebook has N in commonUEEach code word is a channel steering vector, and the ith code word is represented as wi＝α(NUE，-1+(2i-1)/NUE)，i＝1，2，…，NUE；
(3.2.3) layer s each codeword covers a width of 2/2sThe width covered by the bottom code word is 2/NUE；
(3.2.4) the width covered by each upper layer codeword can be represented as a set of widths covered by a plurality of bottom layer codewords;
(3.3) the hierarchical codebook described in step (3.1) and step (3.2) is designed by the following steps:
(3.3.1) the number s of layers of the currently designed hierarchical codebook is 1;
(3.3.2) mixing VUE(s, 1) into
Figure BDA0002155394170000039
Subsets, each subset being assigned Ns＝NUE/tsElement, tth subset zt，t＝1，2，…，tsThe design is as follows:
Figure BDA00021553941700000310
wherein, if T-s is an odd number, NA＝N s2; if T-s is an even number, NA＝Ns；
(3.3.3) mixing tsThe sub-sets are spliced to obtain
Figure BDA00021553941700000311
(3.3.4) passing through VUE(s，1)/||VUE(s，1)||2Normalized VUE(s, 1), wherein | · | | calvities 22 norm representing the vector;
(3.3.5) calculation of VUE(s，m)＝VUE(s，1)。
Figure BDA0002155394170000041
m＝1，2，…，2sWherein o represents a kronecker product;
(3.3.6) s ← s +1, repeating steps (3.3.2) to (3.3.5) until s ═ T.
Further, the base station side codebook in step (4) is designed by adopting the following steps:
(4.1) define the base station end codebook as C, the mth codeword used in the S-th beam training as C (S, m), where S is 1, 2, … S-1, and m is 1, 2, where S is log2NBSRepresenting the number of beam trainings;
(4.2) the beam coverage of codeword C (1, m) designed for the first beam training is:
Figure BDA0002155394170000042
wherein the beam coverage refers to the transformed cos angular domain range according to
Figure BDA0002155394170000043
Construction of Ψ1，mComprises the following steps:
Ψ1，m＝{{i|16m-15≤i≤16m，i＝1，2，…，N}}
according to Ψ1，mDesign C (1, m) is:
Figure BDA0002155394170000044
wherein the content of the first and second substances,
Figure BDA0002155394170000045
(4.3) designing codewords for S-th sub-beam training
Figure BDA0002155394170000046
Wherein the content of the first and second substances,
Figure BDA0002155394170000047
Figure BDA0002155394170000048
and (4.4) performing the S-th beam training by using the code word C (S, m), and designing the code word C (S +1, m) for the (S +1) -th beam training according to the beam training result, wherein S is 1, 2, … S-1.
Further, the step (4.4) specifically includes:
(4.4.1) during the first beam training, the base station sends codewords C (1, 1) and C (1, 2) to all K users in turn, and each user uses VUE(1, 1) and VUE(1, 2) receiving, then each user independently compares the received signal power corresponding to the code words C (1, 1) and C (1, 2), and feeds back the code word index with larger power to the base station, and defines the K-dimensional vector formed by the code word indexes fed back by all K users after the first beam training is finished as a vector gamma1Wherein [ gamma ] is1]kRepresenting a vector r1Represents feedback information of the kth user, [ Γ [ ], and1]k∈{1，2}；
(4.4.2) the coverage of codewords C (s, 1) and C (s, 2) designed for the s-th beam training is:
Figure BDA0002155394170000051
wherein, S is 2, 3, …, S-1,
Figure BDA0002155394170000052
vector Γ of dimension Ks-1Represents the set of codeword indexes, Γ, calculated by all K users after the s-1 st beam training has endeds-1Calculating according to the result of the s-1 th beam training;
according to beam coverage
Figure BDA0002155394170000053
Designing a code word C (S, m), when the S-th beam training is carried out, S is 2, 3, … and S-1, the base station sequentially sends the code words C (S, 1) and C (S, 2) to all K users, and each user uses VUE(s, 1) and VUE(s, 2) receiving, then each user independently compares the received signal power corresponding to the code words C (s, 1) and C (s, 2), and feeds the code word index with larger power back to the base station, and defines the K-dimensional vector formed by the code word indexes fed back by all K users after the beam training is finished as a vector phisThe following can be calculated:
[Γs]k＝2([Γs-1]k-1)+[Φs]k，k＝1，2，…，K
(4.4.3) repeating the step (4.4.2) until S-1 times of beam training is completed;
(4.4.4) when the S-th wave beam training is carried out, K users carry out ascending wave beam training in sequence, and when the K-th user and the base station carry out wave beam training, the base station end respectively uses the code words
Figure BDA0002155394170000054
And
Figure BDA0002155394170000055
receiving, and determining the best received code word for the k-th user by comparing the power of the received signal, defining a set phiSStoring the index of the best code word received by the base station after the S-th beam training of all K users, [ phi ]S]kE {1, 2}, if it is the code word of the kth user
Figure BDA0002155394170000056
Is greater than
Figure BDA0002155394170000057
Received power of [ phi ]S]k1, or vice versa [ phi ]S]kCalculate [ Γ ] 2S]kThe following were used:
[ΓS]k＝2([ΓS-1]k-1)+[ΦS]k，k＝1，2，…，K
calculating an analog precoding matrix of a transmitting end
Figure BDA0002155394170000058
Define its k column as
Figure BDA0002155394170000059
Calculating out
Figure BDA00021553941700000510
The following were used:
Figure BDA00021553941700000511
and the best base station side receiving code word of the k user obtained by finishing the beam training is shown.
Further, step (4.4.2), said coverage according to beam
Figure BDA00021553941700000512
Designing a codeword C (s, m), specifically including:
(4.2.2.1) connecting the continuous space angle theta epsilon-1, 1]Discretizing, wherein the number of discrete bits is Q which is more than or equal to NBSQuantized Angle written as θq-1+ (2Q-1)/Q, Q-1, 2, …, Q; defining the beam gain to be designed as g (theta) and the phase as ejf(theta), the vector obtained after sampling at equal intervals is defined as g, wherein,
Figure BDA00021553941700000610
the qth element representing vector g, g (θ) is given by:
Figure BDA0002155394170000061
wherein f (theta) is a variable to be designed, and M is the sum of the widths of the coverage areas of the wave beams;
(4.2.2.2) designing a codeword from the vector g
Figure BDA0002155394170000062
The method specifically comprises the following steps:
defining a matrix
Figure BDA0002155394170000063
The qth column of the matrix A indicates the pointing angle θ in step (2)qIs (N) ofBs，θq)，q＝1，2，…，Q；
The design problem of the code word v is converted into the following optimization problem:
Figure BDA0002155394170000064
where Ω represents the phase of the vector g, [ Ω ]]q＝f(θq) The qth element of the vector Ω, Q1, 2, …, Q, for a given Ω or g, the least squares solution for v is calculated as:
Figure BDA0002155394170000065
the second equal sign of the above formula is according to
Figure BDA0002155394170000066
Wherein the content of the first and second substances,
Figure BDA0002155394170000067
with a representation dimension of NBS×NBSThe identity matrix of (a);
the optimization objective translates into:
Figure BDA0002155394170000068
solving the optimization problem specifically includes:
(1-1) randomly generating an initial value omega of omega0Setting r to be 1;
(1-2), calculating a current optimization variable Q ═ mod (r-1, Q) +1, wherein mod (·) represents a modular operation, and r is accumulated by 1;
(1-3), update [ omega ]]qComprises the following steps:
Figure BDA0002155394170000069
in the above formula:
Figure BDA0002155394170000071
Figure BDA0002155394170000072
wherein the content of the first and second substances,
Figure BDA0002155394170000073
re {. and Im {. respectively represent the real and imaginary parts of the complex phasor (matrix), and "\" represents the operation of set exclusion, [. cndot.]q，iThe i-th element, representing the q-th row of the matrix, [. ]]i，：Represents the ith row of the matrix;
(1-4) repeatedly executing (1-2) and (1-3) until R is equal to the preset maximum number of times Rmax；
(1-5) omega obtained according to (1-4), using the omega obtained in step (4.2.2.1)
Figure BDA0002155394170000074
Calculating g, calculating code word
Figure BDA0002155394170000075
And to
Figure BDA0002155394170000076
Is normalized to obtain
Figure BDA0002155394170000077
Further, the designing of the digital precoding matrix in step (1) specifically includes: the base station side optimal transmission code word according to the step (4.4.4)
Figure BDA0002155394170000078
The equivalent channel matrix is designed as:
Figure BDA0002155394170000079
wherein the content of the first and second substances,
Figure BDA00021553941700000710
representing the optimal receiving code word of the kth user after the completion of the S-th beam training, designing a digital precoding matrix as follows:
Figure BDA00021553941700000711
has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
(1) compared with the existing serial layered beam training method, the method can greatly reduce the training overhead;
(2) the method can obtain equivalent sum rate performance and approach the sum rate performance of beam scanning on the premise of high signal-to-noise ratio.
Drawings
FIG. 1 is a schematic diagram of a millimeter wave communication system model used by embodiments of the present invention;
FIG. 2 is a diagram of codewords in a user hierarchical codebook according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating codewords in a base station-side codebook according to an embodiment of the present invention;
FIG. 4 is a simulation diagram of codewords used for base station beam training according to an embodiment of the present invention;
FIG. 5 is a comparison of the accuracy of channel information obtained by the method of the present invention and the methods of documents [1] and [2 ];
FIG. 6 is a comparison of user average and rate for the methods of the present invention and documents [1] and [2 ].
Detailed Description
The technical solution of the present invention is further described in detail with reference to the accompanying drawings and embodiments.
(1) As shown in fig. 1, the millimeter wave communication system contemplated by the present invention is as follows:
the present invention considers the communication between one base station and K users. The base station adopts a mixed pre-coding structure comprising digital pre-coding and analog pre-coding; each user only adopts analog precoding; the number of radio frequency links of the base station and the user is N respectivelyRFAnd 1, the antenna arrays of the sending end and the receiving end are uniform linear arrays with the interval of half-wavelength and respectively have NBSAnd NUEA root antenna.
The millimeter wave communication system model between the base station and the kth user is described as follows:
after digital pre-coding, radio frequency link and analog pre-coding, the signal is sent out through an antenna array at a sending end. After the signals are transmitted in a wireless channel, the signals reach the kth user, and the signals received by the antenna array of the kth user are subjected to analog combination and a radio frequency link to obtain final received signals. The received signal may be expressed as:
Figure BDA0002155394170000081
wherein K is 1, 2BB、FRF、HkAnd wkIndicating digital numbersCoding matrix, analog precoding matrix, channel matrix between base station and kth user, analog combining vector, ykS and nkRespectively representing the received signal, the transmitted signal and the additive white Gaussian noise vector of the kth user-HThe representation is subjected to conjugate transposition.
(2) The channel model in the millimeter wave communication system model of the invention is described as follows:
l is set to be shared between the base station and the k userkA transmission path, information of each transmission path being represented by a transmission angle, a reception angle, and a channel gain, the channel of this millimeter wave communication system is modeled as follows according to the widely used Saleh-valeazulia (S-V) model:
Figure BDA0002155394170000082
wherein N isBS、NUE、Lk、λl、
Figure BDA0002155394170000083
And
Figure BDA0002155394170000084
respectively indicate the number of base station antennas, the number of user antennas, the number of paths, the channel gain of the ith path, the angle of arrival (AOA) of the channel, and the angle of transmission (AOD) of the channel, where α (N, θ) indicates a channel steering vector, and is defined as:
Figure BDA0002155394170000085
where N is the number of antennas, θ is the channel AOA or AOD, and in fact, it is assumed that the transmission angle and the arrival angle of the space of the l-th path are respectively
Figure BDA0002155394170000086
And
Figure BDA0002155394170000087
then
Figure BDA0002155394170000088
Thus, we can obtain
Figure BDA0002155394170000091
(3.1) setting VUE(s, m) represents the mth codeword of the s-th layer of the hierarchical codebook, and m is 1, 2, …, 2s；
(3.2) setting the number of antennas at the user end to be NUEWhen N is presentUEThe codebook has the following characteristics when the power of exponent is 2: (3.2.1) the codebook at the transmitting end has T +1 layers, T is determined by the number of antennas, and T is log2NUE；
(3.2.2) the s-th layer of the codebook has 2 in totalsA codeword, s ═ 0, 1, 2, … T; and, the bottom layer of the codebook has N in commonUEEach code word is a channel steering vector, and the ith code word is represented as wi＝α(NUE，-1+(2i-1)/NUE)，i＝1，2，…，NUE；
(3.2.3) layer s each codeword covers a width 2/2sThe width covered by the bottom code word is 2/NUE；
(3.2.4) the width covered by each upper layer codeword can be represented as a set of widths covered by a plurality of bottom layer codewords;
(3.3) the hierarchical codebook described in step (3.1) and step (3.2) is designed by the following steps:
(3.3.1) the number s of layers of the currently designed hierarchical codebook is 1;
(3.3.2) mixing VUE(s, 1) into
Figure BDA0002155394170000095
Subsets, each subset being assigned Ns＝NUE/tsElement, tth subset zt，t＝1，2，…，tsThe design is as follows:
Figure BDA0002155394170000092
wherein, if T-s is an odd number, NA＝N s2; if T-s is an even number, NA＝Ns；
(3.3.3) mixing tsThe sub-sets are spliced to obtain
Figure BDA0002155394170000093
(3.3.4) passing through VUE(s，1)/||VUE(s，1)||2Normalized VUE(s, 1), wherein | · |. non-woven phosphor 22 norm representing the vector;
(3.3.5) calculation of VUE(s，m)＝VUE(s，1)。
Figure BDA0002155394170000094
m＝1，2，…，2sWherein o represents a kronecker product;
(3.3.6) s ← s +1, repeating steps (3.3.2) to (3.3.5) until s ═ T.
(4) As shown in fig. 3, the base station-side codebook for estimating the signal transmission angle AOD of the present invention is designed by the following steps:
(4.1) define the base station end codebook as C, and the mth codeword used in the S-th beam training as C (S, m), where S is 1, 2, … S-1 and m is 1, 2, where S is log2NBSRepresenting the number of beam trains.
(4.2) the beam coverage of codeword C (1, m) designed for the first beam training is:
Figure BDA0002155394170000101
wherein, the beam coverage refers to the transformed cos angular domain. According to
Figure BDA0002155394170000102
Construction of Ψ1，mComprises the following steps:
Ψ1，m＝{{i|16m-15≤i≤16m，i＝1，2，…，N}}
according to Ψ1，mDesign C (1, m) is:
Figure BDA0002155394170000103
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002155394170000104
(4.3) designing codewords for training of S-th beam
Figure BDA0002155394170000105
Wherein the content of the first and second substances,
Figure BDA0002155394170000106
Figure BDA0002155394170000107
and (4.4) implementing the S-th beam training by using the code word C (S, m), and designing the code word C (S +1, m) for the (S +1) -th beam training according to the beam training result, wherein S is 1, 2, … S-1.
(4.4.1) when the first beam training is carried out, the base station sends code words C (1, 1) and C (1, 2) to all K users in sequence, and each user uses VUE(1, 1) and VUE(1, 2) receiving, then each user independently compares the received signal power corresponding to the codewords C (1, 1) and C (1, 2), and feeds back the codeword index with larger power to the base station. Defining a K-dimensional vector formed by code word indexes fed back by all K users after the first beam training is finished as a vector gamma1Wherein [ gamma ] is1]kRepresenting a vector r1Represents feedback information of the kth user, [ Γ [ ], and1]k∈{1，2}；
(4.4.2) the coverage of codewords C (s, 1) and C (s, 2) designed for the s-th beam training is:
Figure BDA0002155394170000108
wherein S is 2, 3, …, S-1,
Figure BDA0002155394170000109
a K-dimensional vector Γs-1The set of codeword indexes calculated by all K users after the s-1 th beam training is finished can be obtained by calculation according to the result of the s-1 th beam training. In particular, Γ1As shown in step (4.4.1).
When the S-th beam training is carried out, S is 2, 3, … and S-1, the base station sequentially transmits code words C (S, 1) and C (S, 2) to all K users, and each user uses VUE(s, 1) and VUE(s, 2) and then each user independently compares the received signal power corresponding to codewords C (s, 1) and C (s, 2) and feeds back the codeword index with the larger power to the base station. Defining a K-dimensional vector formed by code word indexes fed back by all K users after the beam training is finished as a vector phisFurther, it can be calculated that:
[Γs]k＝2([Γs-1]k-1)+[Φs]k，k＝1，2，…，K
a beam width of
Figure BDA0002155394170000111
The codeword C (s, m) of (a) is designed by:
(4.2.2.1) connecting the continuous space angle theta epsilon-1, 1]Discretizing, wherein the number of discrete bits is Q which is more than or equal to NBSThe angle of quantization being written as thetaq-1+ (2Q-1)/Q, Q-1, 2, …, Q; defining the beam gain to be designed as g (theta) and the phase as ejf(θ)And the vector obtained after sampling at equal intervals is defined as g, wherein,
Figure BDA0002155394170000112
the qth element representing vector g, g (θ) is given by:
Figure BDA0002155394170000113
wherein f (theta) is a variable to be designed, and M is the sum of the widths of the coverage areas of the wave beams;
(4.2.2.2) designing a codeword from the vector g
Figure BDA0002155394170000114
The method specifically comprises the following steps:
defining a matrix
Figure BDA0002155394170000115
The qth column of the matrix A indicates the pointing angle θ in step (2)qIs (N) ofBS，θq)，q＝1，2，…，Q；
The design problem of the codeword v is converted into the following optimization problem:
Figure BDA0002155394170000116
where Ω represents the phase of the vector g, [ Ω ]]q＝f(θq) Represents the qth element of the vector Ω, Q1, 2, …, Q. For a given Ω or g, calculate the least squares solution for v as:
Figure BDA0002155394170000117
second equal sign of the above formula according to
Figure BDA0002155394170000118
Wherein the content of the first and second substances,
Figure BDA0002155394170000119
with a representation dimension of NBS×NBSThe identity matrix of (2).
The optimization objective translates into:
Figure BDA00021553941700001110
solving the optimization problem specifically includes:
first, an initial value Ω of Ω is randomly generated0Setting r to be 1;
and secondly, calculating a current optimization variable Q ═ mod (r-1, Q) +1, wherein mod (·) represents a modulus operation, and r accumulates 1 and is used for r ← r + 1.
③ updating omega]qComprises the following steps:
Figure BDA0002155394170000121
in the above formula:
Figure BDA0002155394170000122
Figure BDA0002155394170000123
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002155394170000124
re {. and Im {. respectively represent the real and imaginary parts of the complex phasor (matrix), and "\" represents the operation of set exclusion, [. cndot.]q，iThe i-th element, representing the q-th row of the matrix, [. ]]i，：Represents the ith row of the matrix;
fourthly, repeatedly executing the third step and the fourth step until the R is equal to the preset maximum times Rmax；
Utilizing the omega obtained in the step (4.2.2.1)
Figure BDA0002155394170000125
And g is calculated. Calculating code words
Figure BDA0002155394170000126
And to
Figure BDA0002155394170000127
Is normalized to obtain
Figure BDA0002155394170000128
(4.4.3) repeating the step (4.4.2) until the S-1 beam training is completed;
(4.4.4) when the S-th wave beam training is carried out, the K users carry out ascending wave beam training in sequence, and when the K-th user and the base station carry out wave beam training, the base station end respectively passes through
Figure BDA0002155394170000129
And
Figure BDA00021553941700001210
receiving, judging the power of the received signal to determine the best received code word of the k-th user, and defining a set phiSStoring the S-th beam training information of K users, [ phi ]S]kE {1, 2}, if it is the code word of the kth user
Figure BDA00021553941700001211
Is greater than
Figure BDA00021553941700001212
Received power of [ phi ]S]k1, otherwise [ phi ]S]k2, from this it is possible to obtain:
[ΓS]k＝2([ΓS-1]k-1)+[ΦS]k，k＝1，2，…，K
finally, the simulation pre-matrix of the sending end can be obtained
Figure BDA00021553941700001213
The k column thereof
Figure BDA00021553941700001214
k is represented as:
Figure BDA00021553941700001215
representing the optimal transmitting code word of the kth user base station end obtained by beam training;
(5) the design of the digital precoding matrix in step (1) is as follows:
the base station side optimally sends the code word according to the step (4.4.4)
Figure BDA00021553941700001216
The equivalent channel matrix is designed as:
Figure BDA0002155394170000131
wherein
Figure BDA0002155394170000132
Indicating the k-th user best receives the codeword after the S-th beam training is completed. Designing a digital precoding matrix design as follows:
Figure BDA0002155394170000133
the invention is further described below with reference to simulation conditions and results:
consider a multi-user millimeter wave massive MIMO system, where NBS128. Each user is equipped with N UE16 antenna. The millimeter wave MIMO channel consists of 1 line-of-sight path and 2 non-line-of-sight paths, Lk3. The path gain beam gain conforms to complex Gaussian distribution
Figure BDA0002155394170000134
Of the l-th path of the channel
Figure BDA0002155394170000135
And
Figure BDA0002155394170000136
Figure BDA0002155394170000137
all conform to [ -1, 1 [)]Uniformly distributed therein.
(1) Fig. 4 is a simulation diagram of code words in a codebook at a base station end of millimeter wave communication designed by the invention. Number of base station antennas NBSThe number of users K is 4, 128. During the first beam training, the codewords C (1, 1) and C (1, 2) are designed by the method in step (4.4.2), and the designed codeword beam shape is as shown in the first subgraph of fig. 4. After the first beam training is finished, the pointer set Γ 1 fed back from the user end is assumed to be {1, 1, 2, 2 }. Gamma-shaped1The values of (a) mean that the AoD of the first and second users are within the beam coverage of C (1, 1), and the AoD of the third and fourth users are within the beam coverage of C (1, 2). Based on gamma1From step (4.4.2), it can be determined
Figure BDA0002155394170000138
And
Figure BDA0002155394170000139
the beam shapes of C (2, 1) and C (2, 2) are designed by the codeword design method in step (4.4.2) as shown in the second diagram of fig. 4. Suppose that after the second beam training is finished, the set of pointers fed back from the four users is phi 21, 2, 2, 2. Then, according to the method of step (4.4.2), Γ can be calculated21, 2, 4, 4. Based on gamma2From step (4.4.2), it can be determined
Figure BDA00021553941700001310
And
Figure BDA00021553941700001311
then, according to the codeword design method of step (4.4.2), the beam shapes of C (3, 1) and C (3, 2) are designed as shown in the third diagram of fig. 4.
(2) As shown in fig. 5, we compared the search success rates of the different schemes. The beam search success rate is defined as follows: if the line-of-sight path of the kth user is successfully detected, the beam training of the kth user is said to be successful; otherwise, we say that the beam training of the kth user fails. The successful beam training times compared to the total training times is defined as the search success rate. Since the base station serves K users at the same time, the search success rate of fig. 5 is an average of the search success rates of the K users. As can be seen from fig. 5, our scheme is superior to the results in document [2] and can approach the performance of TDMA hierarchical search. At low signal-to-noise ratio, our scheme is slightly worse than the performance of TDMA hierarchical search. This is because, our scheme performs parallel multi-user training for multiple users, and the transmit power is averaged over all users. However, the number of training times of our scheme is much smaller than that of the TDMA hierarchical codebook.
(3) Figure 6 compares the average sum rates of the different schemes. As can be seen from the figure, our scheme and the hierarchical search scheme of TDMA almost coincide. In addition, with the increase of success rate, the difference between the scheme of our invention and the scheme in the document [1] is smaller and smaller. For example, at a signal-to-noise ratio of 15dB, the gap does not exceed 0.5 bps/Hz.
(4) As shown in table 1, we compared the number of training sessions for different protocols. For example, if NBS＝128，N UE16, K8, scheme of the present invention [1]]The scheme and TDMA layered beam training requires 36, 2048 and 176 time slots, respectively. Compared with the latter two schemes, our scheme can reduce the beam training overhead by 98.2% and 79.2%.
TABLE 1
Figure BDA0002155394170000141
The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only examples of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. A millimeter wave communication multi-user parallel beam training method based on a codebook is characterized by comprising the following steps:
(1) establishing a signal transmission model of millimeter wave multi-user communication;
(2) establishing a millimeter wave communication channel model of a base station and multiple users;
(3) designing a user terminal hierarchical codebook for estimating the channel model channel path arrival angle;
(4) designing a base station end codebook for estimating the channel path transmitting angle of the channel model, implementing multi-user parallel beam training by utilizing the user side hierarchical codebook and the base station end codebook, and designing a new base station end codebook according to a beam training result for next multi-user parallel beam training until the beam training is finished;
(5) designing digital precoding of a transmitting end on the basis of the steps (1) to (4);
in step (3), the method for designing the user-side hierarchical codebook for estimating the arrival angle of the signal path in step (2) is as follows:
(3.1) setting VUE(s, m) represents the mth codeword of the s-th layer of the hierarchical codebook, and m is 1, 2, …, 2s；
(3.2) setting the number of antennas at the user end to be NUEWhen N is presentUEThe codebook has the following characteristics when the power of exponent is 2: (3.2.1) the codebook at the transmitting end has T +1 layers, T is determined by the number of antennas, and T is log2NUE；
(3.2.2) the s-th layer of the codebook has 2s codewords, s is 0, 1, 2, … T; and, the bottom layer of the codebook has N in commonUEEach code word is a channel steering vector, and the ith code word is represented as wi＝α(NUE，-1+(2i-1)/NUE)，i＝1，2，…，NUE；
(3.2.3) layer s each codeword covers a width 2/2sThe width covered by the bottom code word is 2/NUE；
(3.2.4) the width covered by each upper layer codeword can be represented as a set of widths covered by a plurality of bottom layer codewords;
(3.3) the hierarchical codebook described in step (3.1) and step (3.2) is designed by the following steps:
(3.3.1) the number s of layers of the currently designed hierarchical codebook is 1;
(3.3.2) mixing VUE(s, 1) into
Figure FDA0003651531320000011
Subsets, each subset being assigned Ns＝NUE/tsElement, tth subset zt，t＝1，2，…，tsThe design is as follows:
Figure FDA0003651531320000012
wherein, if T-s is an odd number, NA＝Ns2; if T-s is an even number, NA＝Ns；
(3.3.3) mixing tsThe sub-sets are spliced to obtain
Figure FDA0003651531320000013
(3.3.4) passing through VUE(s，1)/||VUE(s，1)||2Normalized VUE(s, 1), wherein | · |. non-woven phosphor22 norm representing the vector;
(3.3.5) calculation
Figure FDA0003651531320000021
Wherein the content of the first and second substances,
Figure FDA0003651531320000022
represents a kronecker product;
(3.3.6) s ← s +1, repeating steps (3.3.2) to (3.3.5) until s ═ T;
the base station terminal codebook in the step (4) is designed by adopting the following steps:
(4.1) define the base station end codebook as C, and the mth codeword used in the S-th beam training as C (S, m), where S is 1, 2, … S-1 and m is 1, 2, where S is log2NBSRepresenting the number of beam trainings;
(4.2) the beam coverage of codeword C (1, m) designed for the first beam training is:
Figure FDA0003651531320000023
wherein the beam coverage refers to the transformed cos angular domain range according to
Figure FDA0003651531320000024
Construction of Ψ1，mComprises the following steps:
Ψ1，m＝{{i|16m-15≤i≤16m，i＝1，2，…，N}}
according to Ψ1，mDesign C (1, m) is:
Figure FDA0003651531320000025
wherein the content of the first and second substances,
Figure FDA0003651531320000026
(4.3) designing codewords for S-th sub-beam training
Figure FDA0003651531320000027
Wherein the content of the first and second substances,
Figure FDA0003651531320000028
Figure FDA0003651531320000029
and (4.4) performing the S-th beam training by using the code word C (S, m), and designing the code word C (S +1, m) for the (S +1) -th beam training according to the beam training result, wherein S is 1, 2, … S-1.
2. The method according to claim 1, wherein in step (1), the millimeter wave multi-user parallel beam training method based on codebook comprises the following steps:
setting a base station for communication with K users, wherein the base station adopts a mixed pre-coding structure comprising digital pre-coding and analog pre-coding; each user only adopts analog pre-coding; the number of radio frequency links of the base station and the user is N respectivelyRFAnd 1, the antenna arrays of the sending end and the receiving end are uniform linear arrays with the interval of half-wavelength and respectively have NBSAnd NUEThe signal is sent out through the antenna array after being subjected to digital pre-coding, radio frequency link and analog pre-coding at a sending end, the signal reaches the kth user after being transmitted in a wireless channel, the signal received by the antenna array of the kth user is subjected to analog combination and radio frequency link to obtain a final received signal, and the received signal can be expressed as:
Figure FDA0003651531320000031
wherein K is 1, 2.. K, FBB、FRF、HkAnd wkRespectively representing a digital precoding matrix, an analog precoding matrix, a channel matrix between the base station and the kth user, an analog combining vector, ykS and nkRespectively representing the received signal, the transmitted signal and the additive white Gaussian noise vector of the kth user, (. cndot.)HThe representation is subjected to conjugate transposition.
3. The method according to claim 1 or 2, wherein in step (2), the millimeter wave multi-user communication channel model is established as follows:
l is set to be shared between the base station and the k userkInformation of each transmission path is expressed by a transmission angle, a reception angle and a channel gain, and a channel of the millimeter wave communication system is modeled as follows:
Figure FDA0003651531320000032
wherein N isBS、NUE、Lk、λl、
Figure FDA0003651531320000033
And
Figure FDA0003651531320000034
respectively representing the number of base station antennas, the number of user antennas, the number of paths, the channel gain of the ith path, the arrival angle of a channel and the transmission angle of the channel, wherein alpha (N, theta) represents a channel steering vector and is defined as:
Figure FDA0003651531320000035
wherein, N is the number of antennas, θ is the channel AOA or AOD, and the transmission angle and the arrival angle in the space of the ith path are assumed to be
Figure FDA0003651531320000036
And
Figure FDA0003651531320000037
then
Figure FDA0003651531320000038
To obtain
Figure FDA0003651531320000039
Figure FDA00036515313200000310
4. The codebook-based millimeter wave communication multi-user parallel beam training method as claimed in claim 1, wherein the step (4.4) specifically comprises:
(4.4.1) during the first beam training, the base station sends codewords C (1, 1) and C (1, 2) to all K users in turn, and each user uses VUE(1, 1) and VUE(1, 2) receiving, then each user independently compares the received signal power corresponding to the code words C (1, 1) and C (1, 2), and feeds back the code word index with larger power to the base station, and defines the K-dimensional vector formed by the code word indexes fed back by all K users after the first beam training is finished as a vector gamma1Wherein [ gamma ] is1]kRepresenting vector r1Represents feedback information of the kth user, [ Γ [ ], and1]k∈{1，2}；
(4.4.2) the coverage of codewords C (s, 1) and C (s, 2) designed for the s-th beam training are:
Figure FDA00036515313200000311
wherein S is 2, 3, …, S-1,
Figure FDA00036515313200000312
a K-dimensional vector Γs-1Denotes the set of codeword indices, Γ, computed by all K users after the s-1 th beam training has endeds-1Calculating according to the result of the s-1 th beam training;
according to beam coverage
Figure FDA0003651531320000041
Designing a code word C (S, m), when carrying out the S-th beam training, S is 2, 3, … and S-1, the base station sequentially sends the code words C (S, 1) and C (S, 2) to all K users,v for each userUE(s, 1) and VUE(s, 2) receiving, then each user independently compares the received signal power corresponding to the code words C (s, 1) and C (s, 2), and feeds the code word index with larger power back to the base station, and defines the K-dimensional vector formed by the code word indexes fed back by all K users after the beam training is finished as a vector phisThe following can be calculated:
[Γs]k＝2([Γs-1]k-1)+[Φs]k，k＝1，2，…，K
(4.4.3) repeating the step (4.4.2) until the S-1 beam training is completed;
(4.4.4) when the S-th wave beam training is carried out, K users carry out ascending wave beam training in sequence, and when the K-th user and the base station carry out wave beam training, the base station end respectively uses the code words
Figure FDA0003651531320000042
And
Figure FDA0003651531320000043
receiving, and determining the best received code word for the k-th user by comparing the power of the received signal, defining a set phiSStoring the index of the best code word received by the base station after the S-th beam training of all K users, [ phi ]S]kE {1, 2}, if it is the code word of the kth user
Figure FDA0003651531320000044
Is greater than
Figure FDA0003651531320000045
Received power of [ phi ] thenS]k1, otherwise [ phi ]S]kCalculate [ Γ ] 2S]kThe following were used:
[ΓS]k＝2([ΓS-1]k-1)+[ΦS]k，k＝1，2，…，K
calculating an analog precoding matrix of a transmitting end
Figure FDA0003651531320000046
Define its k column as
Figure FDA0003651531320000047
Computing
Figure FDA0003651531320000048
The following were used:
Figure FDA0003651531320000049
and the best base station side receiving code word of the k user obtained by finishing the beam training is shown.
5. The method as claimed in claim 4, wherein in step (4.4.2), the millimeter wave communication multi-user parallel beam training method based on the codebook is characterized in that the method is based on the coverage of the beam
Figure FDA00036515313200000410
Designing a codeword C (s, m), specifically including:
(4.2.2.1) connecting the continuous space angle theta epsilon-1, 1]Discretizing, wherein the number of discrete bits is Q which is more than or equal to NBSThe angle of quantization being written as thetaq-1+ (2Q-1)/Q, Q-1, 2, …, Q; defining the beam gain to be designed as g (theta) and the phase as ejf(θ)And the vector obtained after sampling at equal intervals is defined as g, wherein,
Figure FDA00036515313200000411
the qth element representing vector g, g (θ) is given by:
Figure FDA00036515313200000412
wherein f (theta) is a variable to be designed, and M is the sum of the widths of the coverage areas of the wave beams;
(4.2.2.2) designing a codeword from the vector g
Figure FDA0003651531320000051
The method specifically comprises the following steps:
defining a matrix
Figure FDA0003651531320000052
The qth column of the matrix A indicates the pointing angle θ in step (2)qIs (N) ofBS，θq)，q＝1，2，…，Q；
The design problem of the codeword v is converted into the following optimization problem:
Figure FDA0003651531320000053
where Ω represents the phase of the vector g, [ Ω ]]q＝f(θq) The qth element of the vector Ω, Q1, 2, …, Q, for a given Ω or g, the least squares solution for v is calculated as:
Figure FDA0003651531320000054
the second equal sign of the above formula is according to
Figure FDA0003651531320000055
Wherein the content of the first and second substances,
Figure FDA0003651531320000056
with a representation dimension of NBS×NBSThe identity matrix of (1);
the optimization objective translates into:
Figure FDA0003651531320000057
solving the optimization problem specifically includes:
(1-1) randomly generating an initial value omega of omega0Setting r to be 1;
(1-2), calculating a current optimization variable Q ═ mod (r-1, Q) +1, wherein mod (·) represents a modular operation, and r is accumulated by 1;
(1-3), update [ omega ]]qComprises the following steps:
Figure FDA0003651531320000058
in the above formula:
Figure FDA0003651531320000059
Figure FDA00036515313200000510
Ψ＝{1，2，…，2Q}\{q，q+Q}
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00036515313200000511
re {. and Im {. respectively represent the real and imaginary parts of the complex phasor (matrix), and "\" represents the operation of set exclusion, [. cndot.]q，iThe i-th element, representing the q-th row of the matrix, [. ]]i，：Represents the ith row of the matrix;
(1-4) repeatedly executing (1-2) and (1-3) until R is equal to the preset maximum number of times Rmax；
(1-5) omega obtained according to (1-4), using the omega obtained in step (4.2.2.1)
Figure FDA0003651531320000061
Calculating g, calculating code word
Figure FDA0003651531320000062
And to
Figure FDA0003651531320000063
Is normalized to obtain
Figure FDA0003651531320000064
6. The method for millimeter wave communication multi-user parallel beam training based on the codebook according to claim 5, wherein the designing of the digital precoding matrix in step (1) specifically comprises: the base station side optimally sends the code word according to the step (4.4.4)
Figure FDA0003651531320000065
The equivalent channel matrix is designed as:
Figure FDA0003651531320000066
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003651531320000067
representing the optimal receiving code word of the kth user after the completion of the S-th beam training, designing a digital precoding matrix as follows:
Figure FDA0003651531320000068
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