CN114759959A - Phased array beam forming method for inhibiting interference between beams - Google Patents

Phased array beam forming method for inhibiting interference between beams Download PDF

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CN114759959A
CN114759959A CN202210381030.6A CN202210381030A CN114759959A CN 114759959 A CN114759959 A CN 114759959A CN 202210381030 A CN202210381030 A CN 202210381030A CN 114759959 A CN114759959 A CN 114759959A
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CN114759959B (en
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戚晨皓
胡金林
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Southeast University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • 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
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    • H04B7/043—Power distribution using best eigenmode, e.g. beam forming or beam steering
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract

The invention discloses a phased array beam forming method for inhibiting interference between beams, which optimally designs a single or a plurality of beams by introducing a weight factor under the condition of meeting the constant modulus constraint of a phased array to minimize the linear combination of the power of the beams in the interference direction and the power of the beams in the central area of a main lobe as an optimization target and by means of a manifold optimization tool box. In a millimeter wave multi-user communication system, the invention can achieve the average and rate performance similar to hybrid beam forming under the condition of only using analog beam forming but not using digital beam forming, and has effective inhibition effect on the interference among users. In a radar system, the phased array beam forming method provided by the invention has better interference suppression performance than the existing method.

Description

Phased array beam forming method for inhibiting interference between beams
Technical Field
The invention relates to the technical field of phased array beam forming for inhibiting interference between beams, in particular to a phased array beam forming method for inhibiting interference between beams.
Background
In recent years, with the development of wireless communication, wireless telephone services are continuously upgraded, and mobile communication systems face explosive data traffic growth and mass device connection, which stimulates people to research related to the application of millimeter waves to wireless communication. The length of the millimeter wave is only several millimeters, so that millimeter wave communication can be performed under the condition of a smaller antenna size, a receiving and transmitting end can be provided with a large-scale antenna array in a limited area, and the millimeter wave system mainly utilizes the large-scale antenna array to form a beam to realize high-speed transmission. However, due to the existence of a large number of antennas, the allocation of a dedicated rf link to each antenna is not only difficult to implement in terms of hardware, but also causes high power consumption and high rf link cost, so that a hybrid architecture that uses a small number of rf links to drive all antenna elements through a certain number of phase shifters is widely used in the existing millimeter wave system.
In a millimeter wave multi-user wireless communication system, different data streams can occupy the same time-frequency resource, and different data are transmitted by forming a beam through space division multiplexing. In practical engineering, mutual interference between different data streams occurs. Due to the constraint of the number of radio frequency chains, a phased array network formed by phase shifters is required to design a beam for transmitting data, so as to achieve the purpose of suppressing interference between data streams. However, since the phase shifter has only adjustable phase, and each element in the phased array has a constraint of a constant modulus value, how to design the beam forming for suppressing the interference between beams on the phased array is a difficult point of the millimeter wave multi-user wireless communication system.
Furthermore, in radar systems, it is often desirable to suppress clutter and interference from other signals by minimizing the power of signals transmitted to and received from noise sources, and therefore, interference suppression designs for beams are of great importance to improve the performance of radar systems. The formation of the null in the specific direction of the beam pattern is an effective anti-interference technology in the radar system, the pure phased array network is paid much attention in a large phased array system due to the economy and simplicity of a feed network of the pure phased array network, and the difficulty of designing the beam to form the null in the specific direction so as to achieve the purpose of interference suppression is also the difficulty of the radar system with constant mode value constraint.
Disclosure of Invention
In view of the above, the present invention provides a phased array beamforming method for suppressing inter-beam interference, which optimally designs a single or multiple beams by means of a manifold optimization toolbox by introducing a weight factor under a constant modulus constraint of a phased array to minimize a linear combination of the power of the beam in the interference direction and the power of the beam in the central region of the main lobe as an optimization target.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method of phased array beamforming with suppression of inter-beam interference, the method comprising the steps of:
step S1, aiming at a wireless system, constructing an optimization problem taking the linear combination of the power of the minimum wave beam in the interference direction and the power of the wave beam in the central area of the main lobe as an optimization target; the wireless system comprises a millimeter wave multi-user wireless communication system and a radar system, and the optimization problem meets the constant modulus constraint of all phase shifters in the phased array;
step S2, designing single or multiple beams for the wireless system by solving the optimization problem constructed in step S1.
Further, in step S1, when the wireless system is a millimeter wave multi-user wireless communication system, a downlink signal transmission model is first constructed to minimize a linear combination of the power of the beam of the current user in the central area of the main lobe and the power of the beam in the central areas of the main lobes of the beams of the other users to construct an optimization problem as an optimization target.
Further, in step S1, if the base station can obtain the precise departure angle of each user, the central area of the main lobe is simplified to a central point.
Further, the downlink signal transmission model is specifically represented as:
Figure BDA0003591797470000021
wherein, yqRepresenting a signal received by a user;
Figure BDA0003591797470000022
represents a downlink channel vector between the base station and the qth user,
Figure BDA0003591797470000023
representing a complex field (·)HRepresenting a conjugate transpose operation;
Figure BDA0003591797470000024
of the K column vectors
Figure BDA0003591797470000025
A beamforming vector representing the transmission of K users by the base station;
Figure BDA0003591797470000026
represents the data stream sent by the base station to K users, which satisfies
Figure BDA0003591797470000027
Power constraint of PsQ-th element s representing the transmission power of the base station, s]qData representing the data transmitted by the base station to the qth user; etaqRepresents the additive white noise received by the qth user, obeys the mean value of 0 and the variance of sigma2Complex gaussian distribution of (a).
Further, in the downlink signal transmission model, the channel modeling is as follows:
Figure BDA0003591797470000028
wherein N istIndicates the number of base station antennas, LqRepresenting the total number of multipaths, alpha, of the channel between the base station and the q-th userq,lAnd phiq,lRespectively representing the complex gain and the departure angle of the ith path of the qth user; a (phi)q,l) An array steering vector representing the ith path of the qth user is specifically expressed as:
Figure BDA0003591797470000029
wherein λ iscFor carrier wavelength, d represents the antenna element spacing, (.)TRepresenting a transpose operation.
Further, the optimization problem is specifically expressed as:
Figure BDA0003591797470000031
wherein λ is a positive real number weight factor, θk,jJ-th sampling point, K being 1,2, …, K, J being 1,2, …, J, representing the central region of the main lobe at the K-th beam; w is aqIs represented by FRFThe q-th column of (1);
Figure BDA0003591797470000032
representing the power sum of the sampling points of the qth beam in the central area of the mainlobe of other beams, and defining the power sum of the interference of the qth beam to the rest beams; m represents the number of sampling points in the central region of the main lobe of the qth beam,
Figure BDA0003591797470000033
representing the power sum of M sampling points of the q wave beam in the central area of the main lobe; | represents the modulus value, [ w ]q]nRepresenting a beamforming vector wqAccording to the constant modulus constraint of all phase shifters of the phased array, wqEach of the elements of (1) satisfies
Figure BDA0003591797470000034
Further, when the base station can obtain the accurate departure angle of each user and the center area of the main lobe is simplified to a central point, the optimization problem corresponding to the center area is specifically expressed as:
Figure BDA0003591797470000035
wherein, thetakRepresenting the main lobe center point of the k-th beam.
Further, when the wireless system is a radar system, an optimization problem is established by taking the linear combination of the power of the minimum beam in the central area of the main lobe of the beam and the power of the minimum beam in the interference area as an optimization target.
Further, when the wireless system is a radar system, the optimization problem is specifically expressed as:
Figure BDA0003591797470000036
where λ is a positive real weight factor, w represents the beamforming vector, θi,jRepresents the j-th sampling point in the i-th interference region,
Figure BDA0003591797470000037
represents the sum of the powers of the sampling points of the wave beams in the interference area; m represents the number of sample points in the central region of the main lobe of the beam,
Figure BDA0003591797470000038
representing the sum of the powers of the M sampling points of the beam in the central area of the main lobe of the beam; [ w ]]nRepresenting the nth element of a beamforming vector w, each element of w satisfying a constant modulus constraint of all phase shifters of a phased array
Figure BDA0003591797470000039
Further, in step S2, the optimization problem is solved by a manifold optimization toolbox.
The invention has the beneficial effects that:
1. for the millimeter wave multi-user beam forming problem under the full connection framework, the invention establishes an optimization problem model by considering interference suppression between beams emitted by a base station to different users, and provides a beam forming method based on the problem, wherein the method can achieve the average and rate performance of approximate hybrid beam forming under the condition of only using analog beam forming but not using digital beam forming;
2. for the problem of phase-only beam design for suppressing interference in radar systems, the invention provides an effective beam design scheme, and the method has better performance compared with the existing phase-only beam null design scheme.
Drawings
Fig. 1 and 2 are schematic diagrams of a millimeter wave multi-user wireless communication system model used in embodiment 1 of the present invention;
fig. 3 is a diagram of comparison between the user average sum rate and the user average sum rate of hybrid beam forming and all-digital beam forming by using the beam forming method provided in embodiment 1 of the present invention when the base station is equipped with 64 array elements at the base station end, the array element interval is a half-wavelength, the number of radio frequency links is 4, the total number of transmission paths between the user and the base station is equal to 1, and the accurate departure angle is acquired by the base station;
fig. 4 is a diagram comparing the user average sum rate of the beamforming method designed under the inaccurate starting angle condition by using embodiment 1 of the present invention with the user average sum rate of the hybrid beamforming and the all-digital beamforming designed under the accurate starting angle condition when the base station is equipped with 64 array elements, the array element interval is a half-wavelength, the number of radio frequency links is 4, and the total number of transmission paths between the user and the base station is equal to 1;
fig. 5 is a diagram comparing the user average sum rate of the beamforming method designed under the inaccurate starting angle condition by using embodiment 1 of the present invention with the user average sum rate of the hybrid beamforming and the all-digital beamforming designed under the accurate starting angle condition when the base station is equipped with 64 array elements, the array element interval is half-wavelength, the number of radio frequency links is 4, and the total number of transmission paths between the user and the base station is equal to 3;
fig. 6 is a comparison between a beam designed in embodiment 2 of the present invention and a beam designed using the semi-fixed relaxation algorithm in document [1] and the kronecker decomposition algorithm in document [2] when a radar antenna array is provided with 32 array elements and the interval between the array elements is half wavelength.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
Referring to fig. 1 to 5, the present embodiment provides a phased array beam method for suppressing inter-beam interference in a millimeter wave multi-user wireless communication system, where the method specifically includes the following steps:
step S1, constructing a millimeter wave-based multi-user wireless communication system model, where the structure of the model is shown in fig. 1, specifically:
aiming at a downlink communication scene that one base station serves K users, the users are all single-antenna users, the base station adopts a fully-connected hybrid beam forming framework, the number of radio frequency links is equal to the number of the users, namely NRFWhen K, the array is NtThe antennas are spaced apart by a uniform linear array of half wavelengths.
Specifically, taking the qth user as an example, the downlink signal transmission model can be established as follows:
Figure BDA0003591797470000051
wherein, yqRepresenting a signal received by a user;
Figure BDA0003591797470000052
represents a downlink channel vector between the base station and the qth user,
Figure BDA0003591797470000053
representing a complex field;
Figure BDA0003591797470000054
represents the data stream sent by the base station to K users, which satisfies
Figure BDA0003591797470000055
Power constraint of PsIndicating a base stationOf the q-th element of s]qData representing the data transmitted by the base station to the qth user; etaqRepresents the additive white noise received by the qth user, obeys a mean of 0 and a variance of σ2A complex Gaussian distribution of (i.e.
Figure BDA0003591797470000056
An analog beamforming matrix representing the base station, the analog beamforming being performed on a phased array network of phase shifters, constrained by the constant mode values of the phase shifters, i.e. FRFEach element of (1) satisfies
Figure BDA0003591797470000057
Figure BDA0003591797470000058
Representing a digital beamforming matrix of a base station.
Specifically, in the present embodiment, the beamforming method employed is phased array beamforming without using digital beamforming, and therefore, the digital beamforming matrix is set to be an identity matrix, i.e., FBB＝IKThen, the hybrid beamforming architecture in fig. 1 is simplified to the analog beamforming architecture in fig. 2, and the downlink signal transmission model is simplified to:
Figure BDA0003591797470000059
wherein, FRFOf the K column vectors
Figure BDA00035917974700000510
Respectively representing the beamforming vectors sent by the base station to the K users.
Specifically, in this embodiment, in the downlink signal transmission model, the channel modeling is as follows:
Figure BDA00035917974700000511
wherein L isqIndicates the total number of multipaths, alpha, of the channel between the base station and the q-th userq,lAnd phiq,lRespectively, the complex gain and Departure Angle (AOD) of the ith path of the qth user. a (phi)q,l) An array steering vector representing the ith path of the qth user is specifically expressed as:
Figure BDA00035917974700000512
wherein λcFor carrier wavelength, d represents the antenna element spacing, (.)TRepresenting a transpose operation.
Step S2, aiming at the millimeter wave multi-user wireless communication system model constructed in the step S1, a beam forming model with constant modulus constraint and capable of suppressing the interference between beams is established;
specifically, since the users are all single-antenna single-radio-frequency-chain users, to maximize the signal power received by the users, the analog beamforming matrix F is usedRFThe centers of the main lobes of the formed K beams need to be respectively aligned with the AOD of the path (generally, the line-of-sight path) with the maximum complex gain of the K users, and are recorded as
Figure BDA0003591797470000061
But due to the existence of the sidelobe, interference inevitably exists between beams, and communication between a base station and a user is influenced.
Step S201, according to whether the base station can obtain each user' S accuracy
Figure BDA0003591797470000062
To construct different optimization problems if the base station cannot obtain the accuracy of each user
Figure BDA0003591797470000063
Then the optimization problem is constructed with the linear combination of minimizing the power of the current user beam in the center area of the main lobe thereof and the power of the beam in the center areas of the main lobes of the rest user beams as the optimization target.
Specifically, in this embodiment, the step S201 includes:
to reduce the influence of the inter-beam interference on the communication quality, the inter-beam interference needs to be suppressed. In addition, it is considered that the base station may not be accurately acquired by each user due to the influence of the beam resolution in the beam scanning phase
Figure BDA0003591797470000064
But can only obtain
Figure BDA0003591797470000065
An angular domain range omega with the width of beam resolutionkExist and are paired
Figure BDA0003591797470000066
The error of positioning is the error of beam scanning, so that the beam center is aligned with the angular domain range omega when the base station actually transmits the beamkNot precisely
Figure BDA0003591797470000067
Is accurate
Figure BDA0003591797470000068
May be distributed at omegakAny position of (a). Therefore, in order to suppress interference between beams transmitted to different users while ensuring the communication quality of each user, it is necessary to make the individual beams omega of the remaining beams with the main lobe offset as small as possiblekThe regions form nulls. The design problem of the beams of multiple users is K sub-problems independent of each other.
More specifically, in the present embodiment, the beamforming vector w is designed as an example of the design of the beam for transmitting to the q-th userq＝FRFThe design problem of q can be established as an optimization problem of the beam region null:
Figure BDA0003591797470000069
wherein λ is a positive real number weight factorSub, thetak,jJ-th sample point, K being 1,2, …, K, J being 1,2, …, J, which represents the central region of the main lobe at the K-th beam; w is aqIs shown as FRFThe q-th column of (1);
Figure BDA00035917974700000610
the beam distribution of the q user is in the central area omega of the main lobe of the beams of other userskThe power sum of the sampling points of (1), that is, the interference power sum of the beam of the qth user to the beams of the other users; m represents the number of sampling points in the central region of the main lobe of the current beam to be designed, i.e. the qth beam,
Figure BDA00035917974700000611
representing the power sum of M sampling points of the q wave beam in the central area of the main lobe; | represents the modulus value, [ w ]q]nRepresenting a beamforming vector wqAccording to the constant modulus constraint of all phase shifters of the phased array, wqEach of the elements of (1) satisfies
Figure BDA00035917974700000612
Step S202, if the base station can obtain the accuracy of each user
Figure BDA00035917974700000613
Then there is no need for the mainlobe central region omega for each beamkSampling is performed, and the central region of the main lobe in the optimization problem is simplified to be a central point, so that the optimization problem of the null in the beam region constructed in step S201 can be simplified to be an optimization problem of the multi-point null, which is specifically expressed as:
Figure BDA0003591797470000071
wherein, thetakRepresenting the main lobe center point of the k-th beam.
Step S203, aiming at the above-constructed optimization problem of the null in the beam region or the optimization problem of the multi-point nullSolving, which comprises: setting a weight factor lambda, and solving an optimization problem through a manifold optimization tool box to obtain a beam forming vector wq. By analogy, w can be solved in turnk(K is more than or equal to 1 and less than or equal to K) and obtaining an analog beam forming matrix FRFIn which F isRF(:,k)＝wk。
Example 2
Referring to fig. 6, this embodiment provides a method for designing a phased array beam for suppressing inter-beam interference in a radar system, where the method is based on a radar antenna array with an array element interval of half-wavelength, and the number of array elements is NtThe array is arranged as a uniform linear array. The method specifically comprises the following steps:
step S1, determining the radar system, and constructing a beam pattern expression thereof, specifically including:
step S101, for the uniform linear array, the array steering vector in the θ direction is expressed as:
Figure BDA0003591797470000072
step S102, if the beamforming vector is w, the corresponding beam pattern may be represented as:
f(θ)＝|wHa(θ)|2
wherein, | · | represents a modulus value.
Step S2, designing the beam pattern constructed in step S1, the designing including: and constructing an optimization problem by taking the linear combination of the power of the minimized beam in the central area of the main lobe of the minimized beam and the power of the minimized beam in the interference area as an optimization target, and solving the optimization problem to obtain a beam forming vector.
Specifically, in this embodiment, the step S2 specifically includes:
in step S201, in order to suppress interference in a specific direction, a beam needs to be designed, so that a beam pattern forms a null in the specific direction, and this problem can be translated into minimizing the power allocated to the beam in the specific direction. Meanwhile, in order to reduce the offset of the main lobe as much as possible, it is also necessary to ensure that the power of the beam is maximum in the central region of the main lobe. The design problem of the beamforming vector w can be established as an optimization problem as follows:
Figure BDA0003591797470000081
wherein λ is a positive real number weight factor, θi,jThe j-th sampling point, I-1, 2, …, I,
Figure BDA0003591797470000082
representing the sum of the powers of the beams at the sample points in the interference region. M represents the number of sample points in the central region of the main lobe of the beam,
Figure BDA0003591797470000083
representing the sum of the powers of the M sample points of the beam in the central region of its main lobe. | represents the modulus value, [ w ]]nRepresenting the nth element of a beamforming vector w, each element of w satisfying a constant modulus constraint of all phase shifters of a phased array
Figure BDA0003591797470000084
And S202, setting a weight factor lambda, and solving an optimization problem through a manifold optimization tool box to obtain a beam forming vector w.
In order to verify the correctness and the advancement of the methods in the above embodiments 1 and 2, a simulation experiment was performed, which specifically includes:
the simulation parameters of FIG. 3 are: number of base station antennas NtNumber of RF links N of 64RFFor 4, the base station serves a total of 4 users. Total number of transmission paths L between user and base stationkEqual to 1, containing only 1 main path, the gain of the main path obeying a complex Gaussian distribution, i.e.
Figure BDA0003591797470000088
The channel state information of the base station end is the accurate path AOD, the weight factorSub λ 1000. In fig. 3, an optimization problem model is first established in step S202 in embodiment 1, and then a beamforming vector of each user is obtained through a beamforming optimization toolbox, so as to form a simulated beamforming matrix. Combining with the actual channel, changing the transmission signal-to-noise ratio, carrying out 2000 monte carlo simulations, and drawing the relation curve of the user average sum rate and the SNR, as shown by the solid circular line in fig. 3. Also, the average sum rate of the users versus SNR for the hybrid beamforming condition is plotted as shown by the solid star in fig. 3, and the average sum rate of the users versus SNR for the all-digital beamforming condition is plotted as shown by the dashed line in fig. 3. The expression of the user average sum rate is
Figure BDA0003591797470000085
Wherein R iskThe reachable rate of the kth user is represented by the specific expression
Figure BDA0003591797470000086
Wherein F ═ FRFFBBIt is noted that F of hybrid beamforming, all-digital beamforming and phased array beamforming proposed by the present invention is F respectively2、F3And F1. Phased array beamformed F1＝FRF(ii) a Hybrid beamforming, i.e. solid asterisk
Figure BDA0003591797470000087
By an equivalent channel matrix Heq＝HFRFPerforming zero-forcing precoding to obtain, i.e. FBB＝(Heq)-1＝(HFRF)-1Wherein H ═ H1,h2,…,hK]HPreliminary hybrid beamforming matrix FHB＝FRFFBBSince hybrid beamforming does not have power gain, it is also necessary to perform FHBEach column is processed by energy normalization to obtain final F2I.e. by
Figure BDA0003591797470000091
Figure BDA0003591797470000092
All digital beam forming
Figure BDA0003591797470000093
As zero-forcing precoder, F3＝HH(HHH)-1. Comparing the three curves, the beam forming method provided by the invention can achieve the same performance as the hybrid beam forming, and compared with the full digital beam forming, the user average sum rate of the two is only 0.0457bps/Hz when the SNR is 15 dB. This is because the phased array beamforming method proposed by the present invention, when designing the beam of the user, makes the energy of the beam of the current user distributed at the center position of the beams of other users as close to zero as possible, and the equivalent channel matrix Heq＝HFRFThe off-diagonal elements have a modulus value close to 0, and the task of inter-user interference suppression is completed, so that the same performance as hybrid beam forming can be achieved.
The simulation parameters of FIG. 4 are: number of base station antennas NtNumber of RF links N of 64RFFor 4, the base station serves K ═ 4 users in common. Total number of transmission paths L between user and base stationkEqual to 1, the path gain of the main path obeys a complex Gaussian distribution, i.e.
Figure BDA0003591797470000094
The channel state information at the base station end is an inaccurate path starting angle, and the weighting factor lambda is 1000. In fig. 4, an optimization problem model is first established in step S201 in embodiment 1, and then a beamforming vector of each user is obtained through a beamforming optimization toolbox, so as to form a phased array beamforming matrix. Combining with the actual channel, changing the transmission signal-to-noise ratio, carrying out 2000 monte carlo simulations, and drawing the relation curve of the user average sum rate and the SNR, as shown by the solid circular line in fig. 4. Also, the average sum rate of the users under mixed beamforming conditions is plotted against the SNR, e.g., using a two-dimensional matrixThe solid star in fig. 4, and the average sum rate versus SNR for all digital beamforming, as shown by the dashed line in fig. 4. In order to indicate the upper performance bound, H used in calculating the hybrid beamforming matrix and the all-digital beamforming matrix is accurate channel state information, i.e., an accurate path departure angle. Comparing the three curves, it can be found that the beamforming method provided by the invention can be used in SNR<The same performance as hybrid beamforming is achieved at 20dB and the user average sum rate differs by only 1.13bps/Hz at a SNR of 15dB compared to all-digital beamforming. This is because the phased array beamforming method proposed by the present invention, when designing the beam of the user, makes the energy of the beam of the current user distributed in the central area of the beams of other users as small as possible, and the equivalent channel matrix Heq＝HFRFClose to the diagonal matrix, it acts as interference suppression and thus can achieve the same performance as hybrid beamforming when the SNR is small, i.e., noise is the main factor for the impact and rate.
The simulation parameters of FIG. 5 are: number of base station antennas NtNumber of RF links N of 64RFFor 4, the base station serves K ═ 4 users in common. Total number of transmission paths L between user and base stationkEqual to 3, comprising 1 main path, 2 slave paths, wherein the path gain of the main path follows a complex Gaussian distribution, i.e.
Figure BDA0003591797470000095
The path gain of the slave path also follows a complex Gaussian distribution and the energy is 1/100 of the master path, i.e.
Figure BDA0003591797470000096
The channel state information at the base station end is an inaccurate path starting angle, and the weighting factor lambda is 1000. In fig. 5, first, an optimization problem model is established in step S201 in embodiment 1, and a beamforming vector for each user is obtained through a manifold optimization toolbox, so as to form a simulated beamforming matrix. Combining with the actual channel, changing the transmission signal-to-noise ratio, performing 2000 monte carlo simulations, and drawing the relation curve of the user average sum rate and the SNR, as shown by the circular solid line in fig. 5. All in oneThe average sum rate of the users versus SNR for the hybrid beamforming condition is plotted as shown by the solid star in fig. 5, and the average sum rate of the users versus SNR for the all-digital beamforming condition is plotted as shown by the dashed line in fig. 5. In order to indicate the upper performance bound, H used in calculating the hybrid beamforming matrix and the all-digital beamforming matrix is accurate channel state information, i.e., an accurate path departure angle. Comparing the three curves, it can be seen that the performance of the phased array beamforming proposed by the present invention is lower than the performance of the hybrid beamforming combined with zero-forcing precoding due to the interference of 2 slave paths, but still at SNR<The same performance as hybrid beamforming is achieved at 10 dB. The phased array beam forming method provided by the invention enables the energy of the beam of the current user distributed in the central area of the beams of other users to be as small as possible when the beam of the user is designed, and plays a role in interference suppression.
The simulation parameters of FIG. 6 are: number of antennas N of a uniform linear array of radartThe array element spacing is half wavelength, 32. Beam center angle θ0The range corresponding to the central region of the main lobe is [ -1.7 °,1.7 ° ] when the angle is 0 °, the angle is equal to the angle]The number of sampling points M is 5. The interference region, i.e. the null interval, is [ -10.8 °, -14.45 ° ]]∪[14.9°,18.2°]I.e., I is 2, the number of sampling points per interference region is J10, and the weighting factor λ is 5000. In fig. 6, an optimization problem model is first established in step S201 in embodiment 2, and a beamforming vector w is solved by a manifold optimization toolbox, and a beam corresponding to w is plotted, as shown by a solid line in fig. 6. At the same time, a document [1] is drawn]Beam and document designed by semi-definite relaxation algorithm [2]]The beams designed by the kronecker decomposition algorithm in (1) and the quasi-static beams without beam null design are shown by chain lines, dotted lines and broken lines in fig. 6. Comparing the 4 curves, it can be found that in the null region, the array gain of the beam designed by the invention reaches below-60 dB, which is lower than that of the document [1]]And document [2]]The array gain of the quasi-static beam is reduced by about 40dB compared with the array gain peak value of the quasi-static beam in the interval; in the central position of the wave beam, compared with the quasi-static wave beam, the wave beam designed by the invention has the advantage that the array gain is reduced by only 1.16dB, which is compared with the document [1]]Compared with the designed wave beam, the array gain only differs by 0.26dB, and compared with the document [2]]Compared with the designed beam, the array gain is 10.06dB higher. Therefore, the wave beam designed by the invention can obtain the optimal performance of interference suppression on the premise of ensuring the array gain of the central area of the main lobe.
The above-mentioned document [1] is: P.J.Kajenski.phase Only Antenna patterning attenuation [ J ] IEEE Transactions on Antennas and amplification, 2012,60(5): 2562-.
The above-mentioned document [2] is: gu T, Zhang X, He Z, et al, phase-Only lubrication for Uniform Linear Array via Kronecker decompensation [ A ]. In 2021XXXIVth General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS) [ C ].2021, pp.1-4.
In summary, the phased array beamforming method for suppressing inter-beam interference provided by the present invention can achieve the average and rate performance similar to hybrid beamforming under the condition of only using analog beamforming instead of digital beamforming, and has an effective suppression effect on the inter-user beam interference. Meanwhile, when a single wave beam is designed in the radar system, the wave beam null design scheme provided by the invention has better performance compared with the existing method.
The invention is not described in detail, but is well known to those skilled in the art.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (10)

1. A method of phased array beamforming with interference between beams, the method comprising the steps of:
step S1, aiming at a wireless system, constructing an optimization problem taking the linear combination of the power of the minimum wave beam in the interference direction and the power of the wave beam in the central area of the main lobe as an optimization target; the wireless system comprises a millimeter wave multi-user wireless communication system and a radar system, and the optimization problem meets the constant modulus constraint of all phase shifters in the phased array;
step S2, designing single or multiple beams for the wireless system by solving the optimization problem constructed in step S1.
2. The method according to claim 1, wherein in step S1, when the wireless system is a mm-wave multi-user wireless communication system, a downlink signal transmission model is first constructed to minimize a linear combination of the power of the current user beam in the central region of its main lobe and the power of the beam in the central regions of the main lobes of the other user beams as an optimization target to construct an optimization problem.
3. The method for phased array beamforming with interference suppression between beams according to claim 2, wherein in step S1, if the base station can obtain the precise departure angle of each user, the central area of the main lobe is simplified to a central point.
4. The phased array beamforming method for suppressing inter-beam interference according to claim 3, wherein the downlink signal transmission model is specifically represented as:
Figure FDA0003591797460000011
wherein, yqRepresenting a signal received by a user;
Figure FDA0003591797460000012
represents a downlink channel vector between the base station and the qth user,
Figure FDA0003591797460000013
representing a complex field (·)HRepresents a conjugate transpose operation;
Figure FDA0003591797460000014
of the K column vectors
Figure FDA0003591797460000015
A beamforming vector representing the beamforming vector sent by the base station to K users;
Figure FDA0003591797460000016
represents the data stream sent by the base station to K users, which satisfies
Figure FDA0003591797460000017
Power constraint of PsQ-th element s representing the transmission power of the base station, s]qData representing the data transmitted by the base station to the qth user; etaqRepresents the additive white noise received by the qth user, obeys the mean value of 0 and the variance of sigma2Complex gaussian distribution.
5. The method of claim 4, wherein in the downlink signal transmission model, the channel is modeled as:
Figure FDA0003591797460000018
wherein, NtIndicates the number of base station antennas, LqRepresenting the total number of multipaths, alpha, of the channel between the base station and the q-th userq,lAnd phiq,lRespectively representing the complex gain and the departure angle of the ith path of the qth user; a (phi)q,l) An array steering vector representing the ith path of the qth user is specifically expressed as:
Figure FDA0003591797460000021
wherein λ iscFor carrier wavelength, d represents the antenna element spacing, (.)TRepresenting a transpose operation.
6. The method of claim 5, wherein the optimization problem is specifically expressed as:
Figure FDA0003591797460000022
Figure FDA0003591797460000023
wherein λ is a positive real weight factor, θk,jJ-th sampling point, K being 1,2, …, K, J being 1,2, …, J, representing the central region of the main lobe at the K-th beam; w is aqIs represented by FRFThe q-th column of (1);
Figure FDA0003591797460000024
representing the power sum of the sampling points of the qth beam in the center area of the mainlobe of other beams, and defining the power sum of the interference of the qth beam to the rest beams; m represents the number of sampling points in the central region of the main lobe of the qth beam,
Figure FDA0003591797460000025
representing the power sum of M sampling points of the qth beam in the central area of the main lobe; | represents the modulus value, [ w ]q]nRepresenting a beamforming vector wqAccording to the constant modulus constraint of all phase shifters of the phased array, wqEach of the elements of (1) satisfies
Figure FDA0003591797460000026
7. The phased array beamforming method for suppressing inter-beam interference according to claim 6, wherein when the base station can obtain an accurate departure angle of each user, and the central region of the main lobe is simplified to a central point, the optimization problem corresponding thereto is specifically expressed as:
Figure FDA0003591797460000027
Figure FDA0003591797460000028
wherein, thetakRepresenting the main lobe center point of the k-th beam.
8. The method of claim 1, wherein the wireless system is a radar system, and wherein the optimization problem is constructed with a linear combination of the power of the beam in the central region of its main lobe and the power of the beam in the interference region as an optimization objective.
9. The method of claim 8, wherein when the wireless system is a radar system, the optimization problem is specifically expressed as:
Figure FDA0003591797460000031
Figure FDA0003591797460000032
where λ is a positive real weight factor, w represents the beamforming vector, θi,jJ, I1, 2, …, I, J1, 2, …, J, which represents the J sample point in the I interference region;
Figure FDA0003591797460000033
represents the sum of the powers of the sampling points of the wave beams in the interference area; m represents the number of sample points in the central region of the main lobe of the beam,
Figure FDA0003591797460000034
representing the sum of the powers of the M sampling points of the beam in the central area of the main lobe of the beam; [ w ]]nRepresenting the nth element of a beamforming vector w, each element of w satisfying a constant modulus constraint of all phase shifters of a phased array
Figure FDA0003591797460000035
10. The method for phased array beamforming with interference suppression between beams according to any of claims 1-9, wherein in step S2, the optimization problem is solved through a manifold optimization toolbox.
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