CN109861731B - Hybrid precoder and design method thereof - Google Patents

Hybrid precoder and design method thereof Download PDF

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CN109861731B
CN109861731B CN201910065149.0A CN201910065149A CN109861731B CN 109861731 B CN109861731 B CN 109861731B CN 201910065149 A CN201910065149 A CN 201910065149A CN 109861731 B CN109861731 B CN 109861731B
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radio frequency
synthesizer
precoder
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antenna
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高镇
孙艺玮
肖振宇
王�华
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Beijing Institute of Technology BIT
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Abstract

The invention provides a hybrid precoder and a design method thereof, which can realize low computation complexity, higher frequency spectrum effectiveness and error code performance and can fully explore the advantages of partial connection structure in energy effectiveness. The pre-coding method of the invention performs mixed pre-coding based on principal component analysis, and improves the spectrum effectiveness and the error code performance. The invention relates to a mixed precoding design method based on principal component analysis, which can be realized under the conditions of full connection and partial connection, wherein the full connection is used for processing all radio frequency links of all antennas, and the partial connection subarrays are used for independently processing the subarrays corresponding to each radio frequency link. Before the principal component analysis of a part of connected subarrays, the invention utilizes a shared aggregation level analysis method to carry out dynamic subarray antenna grouping, thereby not only paying attention to the correlation among the antennas, but also paying attention to the antennas, and achieving better effect.

Description

Hybrid precoder and design method thereof
Technical Field
The invention belongs to the technical field of precoding of mobile communication, and relates to a hybrid precoder under a millimeter wave large-scale (generally tens to hundreds of antenna arrays) MIMO (Multiple-Input Multiple-Output) system and a design method thereof.
Background
In recent years, with the development of aircraft technologies such as unmanned aerial vehicles and satellites, applications based on the two technologies are also rapidly developing. In future Smart Cities (Smart Cities), unmanned aerial vehicles and satellites will play an important role in logistics, emergency communication, fire fighting, aerial photography, remote sensing, rescue and other affairs. To take full advantage of both, the construction of an efficient and reliable communication system is essential. The new development trend can integrate the global coverage and local enhancement capability of a spatial information network, and improve the mobility and timeliness of applications such as high-frequency observation, public safety emergency response, disaster relief real-time observation and the like in key areas. However, the unmanned aerial vehicle/satellite system has some technical problems to be solved in reliable transmission of the communication system. Therefore, the application of MIMO technology to drone/satellite communication is considered as one of the key technologies to achieve the ambitious goal described above. In MIMO, the precoding technique is a very important technique because it can ensure that the system obtains enough array gain to solve the path loss problem and at the same time, significantly reduce the interference between users, thereby increasing the system capacity by several times.
In the prior art, an analog precoder is selected from a steering vector of a channel by adopting an orthogonal matching tracking method in compressed sensing on the basis of a single carrier MIMO system. However, since most of engineering applications are multi-carrier scenarios, the single carrier technology is not practical, and some design methods cannot be extended to the multi-carrier environment. Therefore, a precoding design method for a multi-carrier system, especially for a MIMO-OFDM system, becomes a hot topic. For example, MIMO-OFDM systems based on finite feedback in "a.akhateeb, and r.w.heat jr", "Frequency selective hybrid precoding for limited feedback combiner wave systems", "IEEE trans.commun., vol.64, No.5, May 2016, pp.1801-1818", propose a codebook design method for radio Frequency precoding, and propose a general solution for baseband precoding (adopt water-filling algorithm to realize digital domain coding design). In the codebook design method, the structure design is carried out based on the precoding of the full connection, but the full connection has the characteristics of high energy consumption and high complexity, so the method is not suitable for being applied to a mobile scene with large limitation on the power consumption, and the frequency spectrum effectiveness and the error code performance of the MIMO-OFDM system are low.
Based on the above research, documents "s.park, a.akhateeb, and r.w.heath jr", "Dynamic ancillary for hybrid precoding in wireless band mm wave MIMO system", "IEEE trans.wireless commun., vol.16, No.5, May 2017, pp 2907 + 2920" propose a precoder design method based on channel statistical information for radio frequency precoding, and apply this method to the scenario of fixed subarray connection; inspired by fixed subarray connection design, the document also provides a dynamic subarray connection mode based on a greedy algorithm, and although a subarray design method is provided, the calculation complexity of the greedy algorithm is higher, and the advantage of a part of connected structures in energy effectiveness is not fully developed.
It can be seen that the precoding technology is concentrated in a single carrier environment at present, and in a millimeter wave communication scene in which a multi-carrier environment (for example, OFDM) is mostly adopted in practical application, the fully-connected hybrid precoding technology is mostly based on a fully-connected array structure, and the array structure has high hardware complexity and high energy consumption; the existing dynamic connection-based method can solve the problem of energy consumption to a certain extent, but the existing dynamic subarray has high calculation complexity and does not fully explore the advantages of partial connection structures in energy efficiency.
Disclosure of Invention
In view of this, the present invention provides a hybrid precoder and a design method thereof, which can achieve low computational complexity, high spectrum effectiveness and high error performance, and can fully exploit the advantage of partial connection structure in energy effectiveness.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the invention provides a hybrid precoder, which is suitable for a large-scale MIMO-OFDM system under a millimeter wave scene, and comprises a transmitting end radio frequency precoder, a transmitting end baseband precoder, a receiving end radio frequency synthesizer and a receiving end baseband synthesizer, wherein the phase of the transmitting end radio frequency precoder is the main component of an optimal all-digital precoder under all subcarriers of the radio frequency precoder, and the main component of the optimal all-digital precoder is a front component obtained by singular value decomposition of the precoder
Figure BDA00019554418500000313
Left singular vectors corresponding to the singular values, wherein
Figure BDA00019554418500000314
The number of the radio frequency links of the transmitting terminal is; the phase of the radio frequency synthesizer at the receiving end is the main component of the optimal all-digital MMSE synthesizer, and the main component of the optimal all-digital MMSE synthesizer is that the optimal all-digital MMSE synthesizer is connected withThe front end obtained by singular value decomposition after weighting of the autocorrelation matrix of the signals at the receiving antenna end
Figure BDA00019554418500000315
Left singular vectors corresponding to the singular values, wherein
Figure BDA00019554418500000316
The number of the radio frequency links at the receiving end.
Wherein, when the RF pre-coding is full connection, the RF pre-coder at the transmitting end is
Figure BDA0001955441850000031
Wherein N istFor receiving the number of antennas, UfAnd obtaining a left singular vector for the singular value decomposition of the optimal all-digital precoder.
Wherein, when the RF pre-coding is partial connection, the RF pre-coder at the transmitting end is
Figure BDA0001955441850000032
Wherein
Figure BDA00019554418500000318
Presentation fetch set
Figure BDA00019554418500000319
A cardinality of (a);
Figure BDA00019554418500000320
the antenna number set of the corresponding subarray for the r-th radio frequency link,
Figure BDA0001955441850000033
Figure BDA00019554418500000317
for the r-th radio link containing the set
Figure BDA00019554418500000323
Middle correspondence
Figure BDA0001955441850000034
And (4) obtaining a left singular vector by singular value decomposition of the optimal all-digital precoder of the row number.
Wherein, when the RF pre-coding is full connection, the RF synthesizer at the receiving end is
Figure BDA0001955441850000035
Wherein the content of the first and second substances,
Figure BDA0001955441850000036
is the number of RF links, U, at the receiving endfThe left singular vector is obtained by singular value decomposition after the optimal all-digital MMSE synthesizer is weighted by a receiving antenna end signal autocorrelation matrix.
Wherein, when the RF pre-coding is partial connection, the RF synthesizer at the receiving end is
Figure BDA0001955441850000037
Wherein
Figure BDA0001955441850000038
Presentation fetch set
Figure BDA0001955441850000039
The base number of (c) is,
Figure BDA00019554418500000310
the antenna number set of the corresponding subarray for the r-th radio frequency link,
Figure BDA00019554418500000311
Figure BDA00019554418500000321
for the r-th radio link containing the set
Figure BDA00019554418500000312
Middle correspondence
Figure BDA00019554418500000322
The optimal all-digital MMSE synthesizer of the number of lines is via the receiving antennaAnd obtaining a left singular vector by singular value decomposition after the weighting of the end signal autocorrelation matrix.
Wherein, when the RF pre-coding is full connection, the receiving end baseband synthesizer is WBB[k]＝WBB[k]Λeq；
Wherein K is 1,2 … … K, K is the number of antenna carriers,
Figure BDA0001955441850000041
wherein WRFFor a receiving end radio frequency synthesizer, an upper corner mark H represents that the matrix is subjected to conjugate transposition;
Figure BDA0001955441850000042
w is an autocorrelation matrix of the received signal; woptAn optimal all-digital MMSE synthesizer;
Figure BDA0001955441850000043
wherein FRFIs a radio frequency pre-coder at the transmitting end,
Figure BDA0001955441850000044
a transmit end baseband precoder.
The invention relates to a design method of a hybrid precoder, which comprises the following steps of designing a transmitter radio frequency precoder when radio frequency precoding is full connection:
step 1.1, defining optimal full-digital precoder
Figure BDA00019554418500000412
Performing singular value decomposition on the frequency domain matrix on each subcarrier and taking the maximum N of the frequency domain matrixsRight singular vectors corresponding to singular values, wherein the singular value decomposition of the channel corresponding to the k-th subcarrier is defined as H [ k ]]＝U[k]Σ[k]VH[k]Wherein K is 1,2 … … K, and K is the number of antenna carriers;
step 1.2, the optimal full-digital precoder under all subcarriers
Figure BDA0001955441850000045
Arranged in a word as a data set matrix
Figure BDA0001955441850000046
Step 1.3, singular value decomposition is carried out on the data set matrix obtained in the step 1.2
Figure BDA0001955441850000047
Wherein U isfIn the form of the left singular vector,fΣfv is a diagonal matrix and the diagonal matrix is,
Figure BDA0001955441850000048
a conjugate transpose matrix of the right singular vector;
step 1.4, make the transmitting end radio frequency precoder
Figure BDA0001955441850000049
Wherein N istIn order to receive the number of antennas,
Figure BDA00019554418500000410
is the number of radio frequency links at the transmitting end.
When the radio frequency precoding is full connection, the design of the radio frequency synthesizer at the receiving end comprises the following steps:
step 2.1, obtaining an autocorrelation matrix of a received signal on a subcarrier and an optimal all-digital MMSE synthesizer; wherein the autocorrelation matrix of the received signal on the kth subcarrier is:
Figure BDA00019554418500000411
wherein FRFIs a radio frequency pre-coder at the transmitting end,
Figure BDA0001955441850000051
for the transmitting end band precoder, hk]For the frequency domain channel on the K-th subcarrier, K is 1,2 … … K, K is the number of antenna carriers, the upper corner mark H represents the conjugate transpose of the matrix, NsFor sequences transmitted on the k sub-carrierThe number of the streams is such that,
Figure BDA0001955441850000052
representing the variance of the noise, INrIs of size Nr*NrThe identity matrix of (1), wherein NrThe number of transmitting antennas;
the conjugate matrix of the optimal all-digital MMSE synthesizer on the kth subcarrier is:
Figure BDA0001955441850000053
step 2.2, multiplying the optimal all-digital MMSE synthesizer under all subcarriers by the autocorrelation matrix under the corresponding subcarrier and then arranging the product in a word as a data set matrix:
Figure BDA0001955441850000054
step 2.3, singular value decomposition is carried out on the data set matrix obtained in the step 2.2
Figure BDA0001955441850000055
Step 2.4, the receiving end radio frequency synthesizer is:
Figure BDA0001955441850000056
wherein
Figure BDA0001955441850000057
For the number of rf links at the receiving end, the number of matrix columns is the number of rf links, and each element in the number of matrix columns can be implemented in a transverse mode constraint form by a phase shifter.
When the radio frequency precoding is full connection, the design of the baseband synthesizer at the receiving end comprises the following steps:
firstly, a receiving end baseband synthesizer
Figure BDA00019554418500000511
And (3) minimum mean square error estimation is carried out:
Figure BDA0001955441850000058
wherein WRFA receiving end radio frequency synthesizer, wherein K is 1,2 … … K, and K is the number of antenna carriers;
then, in conjunction with equalization on the stream and the carrier, the coefficients on the k sub-carrier are calculated as follows:
Figure BDA0001955441850000059
wherein FRFIs a radio frequency pre-coder at the transmitting end,
Figure BDA00019554418500000510
a precoder for a transmitting end band;
finally, the baseband synthesizer W after the equalization process is obtainedBB[k]＝WBB[k]Λeq。
Under the condition of the fully-connected phase shifter network and antenna combination, the number of radio frequency links of a transmitting end and the number of radio frequency links of a corresponding receiving end are the total number of all antennas;
under the combination of the partially connected phase shifter network and the partially connected antennas, the number of the radio frequency links at the transmitting end and the number of the radio frequency links at the corresponding receiving end are the total number of the antennas of the sub-array corresponding to each radio frequency link;
and before the subarrays corresponding to each radio frequency link are independently processed, dynamic subarray antenna grouping is carried out by utilizing a shared aggregation level analysis method.
Has the advantages that:
the pre-coding method of the invention performs mixed pre-coding based on principal component analysis, and improves the spectrum effectiveness and the error code performance. The invention relates to a mixed precoding design method based on principal component analysis, which can be realized under the conditions of full connection and partial connection, wherein the full connection is used for processing all radio frequency links of all antennas, and the partial connection subarrays are used for independently processing the subarrays corresponding to each radio frequency link.
According to the invention, before the principal component analysis of the partial connection subarrays, the dynamic subarray antenna grouping is carried out by using a shared aggregation level analysis method, not only the correlation among the antennas can be concerned, but also the antennas can be concerned, so that a better effect can be achieved, the advantages of the partial connection structure in energy effectiveness can be fully excavated, and the method has good performance under the evaluation standard of the energy effectiveness.
Drawings
FIG. 1 is a diagram of a system model of the present invention;
FIG. 2 is a schematic diagram of an antenna structure according to the present invention;
wherein the abbreviations in the figures correspond to the Chinese: DPX/S (duplexer or switch), LNA (low noise amplifier), PA (power amplifier), AD/DA (analog/digital converter), LO (local oscillator), Mixer (Mixer).
FIG. 3 illustrates three connection modes according to the present invention;
among them PS (phase shifter), Ant (antenna).
FIG. 4 is a schematic diagram of four exemplary partially connected immobilization subarrays according to the present invention: respectively a horizontal array, a vertical array, a block array and a parallel array.
Fig. 5 is a schematic diagram of evaluation of precoding spectrum effectiveness performance of a receiver of the fully-connected array according to the present invention.
Fig. 6 is a schematic diagram of evaluation of precoding spectrum effectiveness performance of a receiver of a partial connection array according to the present invention.
FIG. 7 is a diagram illustrating the evaluation of the spectrum effectiveness of the fully-connected and partially-connected arrays of the present invention.
FIG. 8 is a schematic diagram of the error performance evaluation of fully-connected and partially-connected arrays according to the present invention.
Fig. 9 is a schematic diagram of the energy efficiency performance evaluation of fully-connected and partially-connected arrays of the present invention in a passive antenna structure.
Fig. 10 is a schematic diagram of the energy efficiency performance evaluation of fully-connected and partially-connected arrays of the present invention in an active antenna configuration.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The system modeling and evaluation standard based on the invention is as follows:
firstly, a system model:
the invention relates to a large-scale MIMO-OFDM system using a hybrid precoding scheme under the millimeter wave scene, which is shown in the attached figure 1. Considering the carrier number as K, the transmitting antenna and the receiving antenna are both area arrays, and the number of the receiving antennas is NtWherein the number of antennas in the horizontal direction is
Figure BDA0001955441850000071
Number of antennas in vertical direction is
Figure BDA0001955441850000072
The number of radio frequency links of the transmitting end is
Figure BDA0001955441850000073
The number of transmitting antennas is NrWherein the number of antennas in the horizontal direction is
Figure BDA0001955441850000074
Number of antennas in vertical direction is
Figure BDA0001955441850000075
The number of RF links at the receiving end is
Figure BDA0001955441850000076
The hybrid precoding architecture divides the traditional precoding system into two parts of a baseband and a radio frequency, and comprises the following steps: transmitting end radio frequency precoder FRFTransmitting end baseband precoder
Figure BDA0001955441850000077
Receiving end baseband synthesizer
Figure BDA0001955441850000078
And a receiving end radio frequency synthesizer WRF. In the OFDM system, the baseband precoders of different subcarriers may be different, but a set of rf precoders must be shared by multiple subcarriers. Suppose basebandN transmitted in the k sub-carriersThe stream sequence is x [ k ]]，NsNsFor the number of sequence streams transmitted on the k sub-carrier, x k]Satisfying a power normalization condition for transmitting a bitstream
Figure BDA0001955441850000081
Wherein
Figure BDA0001955441850000082
Expressing mathematical expectation, I expressing identity matrix, and upper corner mark H expressing conjugate transpose to matrix, and the final received signal is r [ k ]]The transmission of a signal in a system, i.e. the reception of a bitstream, is represented as:
r[k]＝(WRFWBB[k])H(H[k]FRFFBB[k]x[k]+n[k])
h [ K ] is a frequency domain channel on the kth subcarrier, K is 1,2 … … K, and K is the number of antenna carriers; n [ k ] is noise. Specifically, the signal received by the receiving-end antenna is represented as:
y[k]＝H[k]FRFFBB[k]x[k]+n[k]，
the invention relates to a transmitting end radio frequency precoder F under a mixed precoding frameworkRFTransmitting end baseband precoder
Figure BDA0001955441850000083
Receiving end baseband synthesizer
Figure BDA0001955441850000084
And a receiving end radio frequency synthesizer WRFAnd (5) designing.
II, channel model:
the invention takes the inherent sparsity of the massive MIMO original channel as the basic premise. Time delay domain matrix H of millimeter wave MIMO-OFDM systemd[d]Can be expressed as:
Figure BDA0001955441850000085
wherein A isrFor receiving end guideLead matrix, Pt[d]Is a gain matrix in the time domain, AtThe matrix is steered for the transmitting end. Wherein, Pt[d]The concrete expression is as follows:
Figure BDA0001955441850000086
wherein N istFor receiving the number of antennas, NrFor transmitting the number of antennas, taui,lIs a time delay (i ═ 1, …, N)ray，l＝1,…,Ncl)，αi,lIs a complex gain (i ═ 1, …, Nray，l＝1,…,Ncl) And p (-) is a pulse waveform. For AtAnd ArTwo steering matrices, consider the clustered channel model. Suppose there is N in the channelclClustered multipath with N in each clusterrayStrip multipath. At the transmitting end, the horizontal angle and the pitch angle of the ith multipath of the ith cluster are respectively
Figure BDA0001955441850000087
And
Figure BDA0001955441850000088
then the receiving end vertical and horizontal steering vectors are as follows:
Figure BDA0001955441850000091
Figure BDA0001955441850000092
wherein the content of the first and second substances,
Figure BDA0001955441850000093
Figure BDA0001955441850000094
λ is the carrier frequency, dvAnd dhAntenna spacing in the vertical and horizontal directions, respectively. The steering vector of this multipath is
Figure BDA0001955441850000095
(wherein,
Figure BDA0001955441850000096
representing the Kronecker product). Thus the steering matrix of the receiver is
Figure BDA0001955441850000097
The same way can obtain the receiving end guide matrix Ar。
Thirdly, evaluation criteria:
the invention considers evaluation criteria of three dimensions: spectrum effectiveness, error performance, and energy effectiveness.
For the spectrum effectiveness, the calculation method is as follows:
Figure BDA0001955441850000098
wherein
Figure BDA0001955441850000099
Figure BDA00019554418500000910
Representing the noise variance, det represents the determinant for computing the correspondence matrix.
For error performance, the error rate of the received bit stream r k relative to the transmitted bit stream x k is considered.
For energy efficiency, the present invention contemplates two different antenna configurations as shown in fig. 2: a passive antenna pattern 2(a) and an active antenna pattern 2 (b). A comparative all-digital pre-coded antenna structure is also shown in fig. 2.
The invention provides a hybrid precoder, which is suitable for a large-scale MIMO-OFDM system under a millimeter wave scene, and comprises a transmitting end radio frequency precoder, a transmitting end baseband precoder, a receiving end radio frequency synthesizer and a receiving end baseband synthesizer, wherein the phase of the transmitting end radio frequency precoder is the optimal all-digital precoding of all subcarriers of the radio frequency precoderThe main component of the optimal all-digital precoder is the one obtained by singular value decomposition of the precoder
Figure BDA00019554418500000911
Left singular vectors corresponding to the singular values, wherein
Figure BDA00019554418500000912
The number of the radio frequency links of the transmitting terminal is; the phase of the receiving end radio frequency synthesizer is the main component of the optimal all-digital MMSE synthesizer, and the main component of the optimal all-digital MMSE synthesizer is the front component obtained by singular value decomposition after the optimal all-digital MMSE synthesizer is weighted by a receiving antenna end signal autocorrelation matrix
Figure BDA0001955441850000101
Left singular vectors corresponding to the singular values, wherein
Figure BDA0001955441850000102
The number of the radio frequency links at the receiving end.
In the radio frequency precoding part, different connection modes can be generated according to different combinations of the phase shifter network and the antenna. The radio frequency precoding connection mode considered by the invention is shown in figure 3 and comprises three conditions of full connection, partial connection of a fixed subarray and partial connection of a dynamic subarray, wherein the full connection condition is a base stone of the latter two connection schemes, the partial connection of the fixed subarray is the expansion of full connection, and the partial connection of the dynamic subarray is the optimization of the partial connection of the fixed subarray.
Example 1: and designing a precoding system under the full connection condition.
For the design of the rf precoder at the transmitting end, in the OFDM system, the baseband precoders of different subcarriers may be different, but a set of rf precoders must be shared by multiple subcarriers, so the rf precoder can be regarded as the main component of the optimal all-digital precoder under all subcarriers. Therefore, the design of the transmitting-end radio frequency precoder can be obtained by adopting a principal component analysis method. The method specifically comprises the following steps:
step 1.1, defining optimal full-digital precoder
Figure BDA0001955441850000103
Performing singular value decomposition on the frequency domain matrix on each subcarrier and taking the maximum N of the frequency domain matrixsRight singular vectors corresponding to individual singular values, i.e.
Figure BDA0001955441850000105
Wherein the singular value decomposition of the channel corresponding to the k sub-carrier is defined as H [ k ]]＝U[k]Σ[k]VH[k]；
Step 1.2, the optimal all-digital precoder under all subcarriers is arranged in a word as a data set matrix F ═ Fopt[1]Fopt[2]…Fopt[K]]；
Step 1.3, singular value decomposition is carried out on the data set matrix obtained in the step 12
Figure BDA0001955441850000104
Step 1.4, in order to meet the hardware requirement of the radio frequency precoder, that is, to meet the transverse mode constraint form that the number of matrix columns is the number of radio frequency links and each element can be realized by a phase shifter, the radio frequency precoder at the transmitting end is made
Figure BDA0001955441850000111
And secondly, for the design of the transmitting end sideband precoder, a water filling algorithm design mode is adopted. The radio precoding has been designed to take into account the transmitting end, i.e.
Figure BDA00019554418500001111
Wherein the content of the first and second substances,
Figure BDA0001955441850000113
is composed of
Figure BDA0001955441850000114
Singular value decomposition of Λ k]Is dimension Ns×NsSatisfies the following equation:
Figure BDA0001955441850000115
wherein mu is the power distributed on each channel after the water algorithm is carried out, and satisfies the following conditions:
Figure BDA0001955441850000116
function (·)+Means that if a > 0, (a)+A, otherwise (a)+＝0。
And thirdly, for the design of the radio frequency synthesizer at the receiving end, the method is obtained by performing principal component analysis on the optimal all-digital MMSE synthesizer after the signal autocorrelation matrix at the receiving antenna end is weighted. The method comprises the following steps:
step 2.1, obtaining an autocorrelation matrix of a received signal on a subcarrier and an optimal all-digital MMSE synthesizer; wherein the received signal autocorrelation matrix on the k sub-carrier is
Figure BDA0001955441850000117
The conjugate matrix of the optimal all-digital MMSE synthesizer is as follows:
Figure BDA0001955441850000118
step 2.2, multiplying the optimal all-digital MMSE synthesizer under all subcarriers by the autocorrelation matrix under the corresponding subcarrier and then arranging the result in a word as a data set matrix
Figure BDA0001955441850000119
Step 2.3, singular value decomposition is carried out on the data set matrix obtained in the step 2.2
Figure BDA00019554418500001110
Step 2.4, in order to meet the hardware requirements of the radio frequency synthesizer, that is, to meet the transverse mode constraint form that the number of matrix columns is the number of radio frequency links and each element can be realized by a phase shifter, the receiving end radio frequency synthesizer is:
Figure BDA0001955441850000121
and fourthly, for the design of a baseband synthesizer at the receiving end, a method combining minimum mean square estimation and equalization is adopted. The method specifically comprises the following steps: considering the design completion of the mixed pre-coding of the transmitting end and the radio frequency pre-coding of the receiving end, firstly, the minimum mean square error estimation is carried out
Figure BDA0001955441850000122
Then, in combination with equalization on the stream and the carrier, the coefficients are calculated as follows
Figure BDA0001955441850000123
Finally, the baseband synthesizer added with the equalization process is obtained as WBB[k]＝WBB[k]Λeq(1≤k≤K)。
Example 2: and designing a precoding system under the condition of partially connecting the fixed subarrays.
The difference between the partial connection fixed subarray and the full connection situation is that the full connection is performed on all radio frequency links of all antennas, and the partial connection fixed subarray is performed on a subarray corresponding to each radio frequency link independently.
For the transmitting end radio frequency precoder, the following is specifically: suppose the antenna number set of the sub-array corresponding to the r-th radio frequency link is
Figure BDA0001955441850000124
For the r-th radio link, the order contains the set
Figure BDA00019554418500001216
Middle correspondence
Figure BDA0001955441850000125
The optimal all-digital precoder of the number of rows is
Figure BDA0001955441850000126
The data set corresponding to the subarray is set as
Figure BDA00019554418500001214
Taking the left singular vector corresponding to the maximum singular value of the matrix
Figure BDA00019554418500001217
The corresponding RF pre-coding for the RF link is designed as
Figure BDA0001955441850000127
(wherein
Figure BDA0001955441850000128
Presentation fetch set
Figure BDA00019554418500001215
Cardinality of).
For the receiving end radio frequency synthesizer, the method specifically comprises the following steps: suppose the antenna number set of the sub-array corresponding to the r-th radio frequency link is
Figure BDA0001955441850000129
For the r-th radio link, the order contains the set
Figure BDA00019554418500001210
Middle correspondence
Figure BDA00019554418500001211
The optimal all-digital MMSE synthesizer of the number of lines of
Figure BDA00019554418500001212
Let Heff[k]＝H[k]FRFFBB[k]Then the autocorrelation matrix of the signal at the receiving antenna end is
Figure BDA00019554418500001213
The weighted data set corresponding to the subarray is:
Figure BDA0001955441850000131
taking the left singular vector corresponding to the maximum singular value of the matrix
Figure BDA00019554418500001310
The corresponding RF pre-coding for the RF link is designed as
Figure BDA0001955441850000132
Example 3: a dynamic subarray antenna grouping scheme based on shared agglomerative hierarchy analysis.
In the above embodiments 1 and 2, it is known from the precoding analysis under the condition of partially connecting the fixed subarrays that the performance of the system can be improved by reasonably combining the subarrays. In view of this, the present embodiment uses a shared aggregation level analysis method to perform dynamic subarray grouping on the antennas, so as to achieve an optimal antenna allocation scheme — dynamic subarray. In the past, a greedy algorithm is adopted to perform dynamic subarray allocation, but the greedy algorithm only focuses on the correlation degree between antennas and does not focus on the antennas, so the effect is not ideal. The shared aggregation level analysis method adopted by the embodiment can not only pay attention to the association between the antennas, but also pay attention to the antennas, and can achieve better effects.
The core idea of the shared coacervation hierarchical analysis algorithm is as follows: initially, each antenna is set to be a group, and each iteration combines two groups of antennas with the maximum correlation degree into one group until the number of antenna groups is the number of radio frequency links. The design standard basis of the algorithm is as follows: the maximum emission spectral efficiency that can be achieved by the system is the sum of the squares of the maximum singular values of the corresponding data sets of the relevant subarrays, i.e. the sum of the squares of the maximum singular values of the corresponding data sets of the relevant subarrays
Figure BDA0001955441850000133
Generally adopted in engineering
Figure BDA0001955441850000134
Norm to approximate singular values, i.e.:
Figure BDA0001955441850000135
wherein the content of the first and second substances,
Figure BDA0001955441850000136
RF＝FFH. Thus, the dynamic subarray partitioning problem may be expressed as
Figure BDA0001955441850000137
Figure BDA0001955441850000138
Figure BDA0001955441850000139
Thus, define
Figure BDA00019554418500001311
Correlation between two groups of antennas:
Figure BDA0001955441850000141
dividing the antenna subarray according to the following specific steps:
step 3.1, divide each antenna into a group
Figure BDA00019554418500001414
Number of antenna groups Nsub＝Nt。
Step 3.2, number of antenna groups
Figure BDA0001955441850000142
And then iteration is performed. When each iteration starts, the iteration result of the previous step is stored
Figure BDA0001955441850000143
Each iteration traverses all groups, for the current group
Figure BDA00019554418500001415
Finding the group with the greatest relevance
Figure BDA00019554418500001416
Wherein
Figure BDA0001955441850000144
For group
Figure BDA00019554418500001419
Also find the group with the maximum association degree in the existing groups
Figure BDA0001955441850000145
Wherein
Figure BDA0001955441850000146
If i ═ i0Then will be grouped
Figure BDA00019554418500001417
And
Figure BDA00019554418500001418
are combined into one group, otherwise they are not combined together and go to the processing of the next group. The number of antenna groups obtained in this iteration
Figure BDA0001955441850000147
Stopping iteration and using the iteration result of the previous step
Figure BDA0001955441850000148
To output the result, i.e.
Figure BDA0001955441850000149
Figure BDA00019554418500001410
If the total number is the same
Figure BDA00019554418500001411
Arranging all groups in the order of radix from small to large, and arranging the radix with the smallest radix
Figure BDA00019554418500001412
Group merging with the largest base number with the largest degree of association
Figure BDA00019554418500001413
In a group.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (5)

1. A hybrid precoder suitable for large-scale MIMO-OFDM system in millimeter wave scene comprises a transmitting end radio frequency precoder, a transmitting end baseband precoder, a receiving end radio frequency synthesizer and a receiving end baseband synthesizer, and is characterized in that the phase of the transmitting end radio frequency precoder is a front end radio frequency precoder obtained by singular value decomposition of the precoder
Figure FDA0003431324090000011
Left singular vectors corresponding to the singular values, wherein
Figure FDA0003431324090000012
The number of the radio frequency links of the transmitting terminal is; the phase of the receiving end radio frequency synthesizer is obtained by the optimal all-digital MMSE synthesizer through singular value decomposition after the autocorrelation matrix weighting of the receiving antenna end signal
Figure FDA0003431324090000013
Left singular vectors corresponding to the singular values, wherein
Figure FDA0003431324090000014
The number of the radio frequency links of the receiving end is;
when the radio frequency pre-coding is full connection, the radio frequency pre-coder at the transmitting end is
Figure FDA0003431324090000015
Wherein N istFor receiving the number of antennas, UfA left singular vector is obtained by singular value decomposition of the optimal all-digital precoder;
when the RF pre-coding is partial connection, the RF pre-coder at the transmitting end is
Figure FDA0003431324090000016
Wherein
Figure FDA0003431324090000017
Presentation fetch set
Figure FDA0003431324090000018
A cardinality of (a);
Figure FDA00034313240900000122
the antenna number set of the corresponding subarray for the r-th radio frequency link,
Figure FDA0003431324090000019
Figure FDA00034313240900000110
for the r-th radio link containing the set
Figure FDA00034313240900000123
Middle correspondence
Figure FDA00034313240900000111
Row number of optimal all-digital precoder singular valuesDecomposing the obtained left singular vector;
when the RF pre-coding is full connection, the RF synthesizer at the receiving end is
Figure FDA00034313240900000112
Wherein the content of the first and second substances,
Figure FDA00034313240900000113
is the number of RF links, U, at the receiving endfThe left singular vector is obtained by singular value decomposition after the optimal all-digital MMSE synthesizer is weighted by a receiving antenna end signal autocorrelation matrix.
2. The hybrid precoder of claim 1, wherein the receiving side radio frequency synthesizer is a partial concatenation when radio frequency precoding
Figure FDA00034313240900000114
Wherein
Figure FDA00034313240900000115
Presentation fetch set
Figure FDA00034313240900000116
The base number of (c) is,
Figure FDA00034313240900000117
the antenna number set of the corresponding subarray for the r-th radio frequency link,
Figure FDA00034313240900000118
Figure FDA00034313240900000119
for the r-th radio link containing the set
Figure FDA00034313240900000120
Middle correspondence
Figure FDA00034313240900000121
The optimal all-digital MMSE synthesizer of the line number obtains a left singular vector through singular value decomposition after the signal autocorrelation matrix weighting of the receiving antenna end.
3. The hybrid precoder of claim 1, wherein the receive-side baseband synthesizer is W when radio frequency precoding is full-concatenatedBB[k]＝WBB[k]Λeq；
Wherein K is 1,2 … … K, K is the number of antenna carriers,
Figure FDA0003431324090000021
wherein WRFFor a receiving end radio frequency synthesizer, an upper corner mark H represents that the matrix is subjected to conjugate transposition;
Figure FDA0003431324090000022
an autocorrelation matrix for the received signal; woptAn optimal all-digital MMSE synthesizer;
equalizer
Figure FDA0003431324090000023
Wherein FRFIs a radio frequency pre-coder at the transmitting end,
Figure FDA0003431324090000024
a transmit end baseband precoder.
4. A method for designing a hybrid precoder according to claim 1, wherein the method for designing a receiving-side rf synthesizer when rf precoding is full-concatenated comprises the following steps:
step 2.1, obtaining an autocorrelation matrix of a received signal on a subcarrier and an optimal all-digital MMSE synthesizer; wherein the autocorrelation matrix of the received signal on the kth subcarrier is:
Figure FDA0003431324090000025
wherein FRFIs a radio frequency pre-coder at the transmitting end,
Figure FDA0003431324090000026
for the transmitting end band precoder, hk]For the frequency domain channel on the K-th subcarrier, K is 1,2 … … K, K is the number of antenna carriers, the upper corner mark H represents the conjugate transpose of the matrix, NsFor the number of sequence streams transmitted on the k-th subcarrier,
Figure FDA0003431324090000027
representing the variance of the noise, INrIs of size Nr*NrThe identity matrix of (1), wherein NrThe number of transmitting antennas;
the conjugate matrix of the optimal all-digital MMSE synthesizer on the kth subcarrier is:
Figure FDA0003431324090000028
step 2.2, multiplying the optimal all-digital MMSE synthesizer under all subcarriers by the autocorrelation matrix under the corresponding subcarrier and then arranging the product in a word as a data set matrix:
Figure FDA0003431324090000031
step 2.3, singular value decomposition is carried out on the data set matrix obtained in the step 2.2
Figure FDA0003431324090000032
Step 2.4, the receiving end radio frequency synthesizer is:
Figure FDA0003431324090000033
wherein
Figure FDA0003431324090000034
For the number of rf links at the receiving end, the number of matrix columns is the number of rf links, and each element in the number of matrix columns can be implemented in a transverse mode constraint form by a phase shifter.
5. The method of claim 4, wherein under a fully connected phase shifter network and antenna combination, the number of transmit end RF links and the corresponding number of receive end RF links are the total number of all antennas;
under the combination of the partially connected phase shifter network and the partially connected antennas, the number of the radio frequency links at the transmitting end and the number of the radio frequency links at the corresponding receiving end are the total number of the antennas of the sub-array corresponding to each radio frequency link;
before independently processing the subarrays corresponding to each radio frequency link, dynamically grouping the subarray antennas by using a shared aggregation level analysis method, which comprises the following specific steps:
step 3.1, divide each antenna into a group
Figure FDA00034313240900000316
Number of antenna groups Nsub＝Nt；
Step 3.2, number of antenna groups
Figure FDA0003431324090000035
Then, iteration is carried out; when each iteration starts, the iteration result of the previous step is stored
Figure FDA0003431324090000036
Each iteration traverses all groups, for the current group
Figure FDA00034313240900000321
Finding the group with the greatest relevance
Figure FDA00034313240900000317
Wherein
Figure FDA0003431324090000037
For group
Figure FDA00034313240900000318
Also find the group with the maximum association degree in the existing groups
Figure FDA0003431324090000038
Wherein
Figure FDA0003431324090000039
If i ═ i0Then will be grouped
Figure FDA00034313240900000319
And
Figure FDA00034313240900000320
combining into one group, otherwise not combining them together and going to the next group's processing; the number of antenna groups obtained in this iteration
Figure FDA00034313240900000310
Stopping iteration and using the iteration result of the previous step
Figure FDA00034313240900000311
To output the result, i.e.
Figure FDA00034313240900000312
(i＝1,…,Nt) (ii) a If the total number is the same
Figure FDA00034313240900000313
Arranging all groups in the order of radix from small to large, and arranging the radix with the smallest radix
Figure FDA00034313240900000314
Group merging with the largest base number with the largest degree of association
Figure FDA00034313240900000315
In a group.
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