CN110391830B - Robust multi-group multicast beam forming method - Google Patents

Robust multi-group multicast beam forming method Download PDF

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CN110391830B
CN110391830B CN201910625511.5A CN201910625511A CN110391830B CN 110391830 B CN110391830 B CN 110391830B CN 201910625511 A CN201910625511 A CN 201910625511A CN 110391830 B CN110391830 B CN 110391830B
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beam forming
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CN110391830A (en
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杨峰
丁良辉
钱良
易笃裕
刘威
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Shanghai Jiaotong University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters
    • H04B17/336—Signal-to-interference ratio [SIR] or carrier-to-interference ratio [CIR]
    • 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
    • H04B7/0408—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas using two or more beams, i.e. beam diversity
    • 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

Abstract

The invention relates to a robust multi-group multicast beam forming method, which firstly obtains two basic scenes of a multi-group multicast field: the method comprises the steps of ensuring that the minimum SNR in users meets a given condition and the robust beam forming problem under the minimum SNR in the maximized users is relaxed to be a convex problem to be solved; and then, using a continuous convex approximation method to relax the non-convex problem in the next iteration and carrying out iterative solution, and obtaining the optimal solution which finally approximates the original problem through continuous iterative steps. Compared with the prior art, the method has the advantages of better robustness, lower complexity, suitability for the requirements of actual engineering and the like.

Description

Robust multi-group multicast beam forming method
Technical Field
The invention relates to the technical field of multiple antennas, in particular to a robust multi-group multicast beam forming method.
Background
The multi-antenna technology is widely applied to practical communication systems such as Long Term Evolution Advanced (LTE-a) and 5G. A system using the multi-antenna technology can greatly improve the communication rate and the communication quality without increasing the bandwidth, and thus is subjected to a great deal of research by researchers. In some practical application scenarios, data received by different users are the same, such as group chat, webcast, video conference, and the like, and the transmission in such a scenario is called multicast transmission. In a multicast propagation scenario, if the conventional point-to-point unicast technology is still used, a large amount of system resources are wasted, so that the overall throughput of the system is reduced, and the communication quality is also reduced. Therefore, research on high-efficiency transmission schemes in multicast scenarios is one of the current research hotspots. Multicasting may be implemented separately at the physical layer, link layer, and network layer in a communication system. The signal transmission in the wireless transmission scheme of the physical layer naturally has the broadcasting characteristic, and the multicast technology based on the physical layer fully utilizes the characteristic, thereby greatly saving the time-frequency resource of the base station. The multicast technology of the physical layer is an important means for improving communication quality and improving system performance.
The existing classical robust multi-group multicast beam forming method needs a large number of Gaussian randomization steps and subsequent scaling factor solving steps, so that the problem of high computational complexity is caused.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a robust multi-group multicast beam forming method which has better robust performance and lower complexity and is suitable for the requirements of actual engineering.
The purpose of the invention can be realized by the following technical scheme:
a robust multi-group multicast beam forming method includes the following steps: the method comprises the steps of ensuring that the minimum SNR in users meets a given condition and the robust beam forming problem under the minimum SNR in the maximized users is relaxed to be a convex problem to be solved;
and then, using a continuous convex approximation method to relax the non-convex problem in the next iteration and carrying out iterative solution, and obtaining the optimal solution which finally approximates the original problem through continuous iterative steps.
Preferably, the method comprises the following steps:
the method comprises the following steps that (1) under a robust beam forming scene that the minimum SNR in users meets given conditions is guaranteed, additive channel errors are considered, the SINR of the users can be solved, the SINR lower bound influenced by the errors is obtained by numerator scaling to the minimum and denominator scaling to the maximum, and the robust beam forming problem under the scene is relaxed by utilizing the SINR lower bound to obtain a new problem model; under the robust beamforming scene of maximizing the minimum SNR in users, the robust beamforming problem is relaxed to obtain a new problem model by utilizing the property that the module value of a complex number on a complex plane is certainly larger than the real part of the complex number.
And (2) solving a new problem model obtained by relaxation under two multi-group multicast robust beam forming scenes by using a continuous convex approximation method to obtain a required beam forming weight vector.
Preferably, the step (1) is specifically:
consider being provided with NtThe base station of the root antenna communicates with the users in G groups, and each user end device only has a single antennaThe line, i.e. the communication system, is a MISO system; if additive channel error is considered, then the true channel for user i is
Figure BDA0002126967150000021
Wherein
Figure BDA0002126967150000022
Channel information estimated for the base station side, ei∈CNIs a corresponding error and has
Figure BDA0002126967150000023
Then it is located in the kth packet GkThe ith user of (1), its SINR can be expressed as
Figure BDA0002126967150000024
Wherein wkAssigning a weight coefficient, h, to the kth packetiFor the channel of the user i,
Figure BDA0002126967150000025
channel information estimated for the base station side, eiFor corresponding error, σiIs the norm square of error corresponding to the channel information of the ith user base station, where l is the ith packet, [ 2 ]]HWhich represents the transpose of the conjugate,
Figure BDA0002126967150000026
IMis a unit array;
by minimizing the numerator scaling and maximizing the denominator scaling, the lower bound of the SINR after being affected by the error can be obtained
Figure BDA0002126967150000027
Wherein wkFor the kth group, wlFor the l-th groupεThe norm square of the error corresponding to the channel information of the base station end is obtained;
by combining the property that the modulus value of the complex number on the SINR lower bound and the complex plane is certainly larger than the real part, the two robust beam forming problems under two scenes of ensuring that the minimum SNR in the users meets the given condition and maximizing the minimum SNR in the users after relaxation are respectively as follows:
Figure BDA0002126967150000031
wherein, PnIs the maximum power constraint value of the nth antenna, r is an optimization parameter variable,
Figure BDA0002126967150000032
Given a complex weight coefficient, gammaiSINR index, G, for the ith userkGrouping for the kth user, NtThe number of the antennas is;
Figure BDA0002126967150000033
wherein t epsilon R is an optimized parameter variable, R is a real domain, and Re [ ] is a complex real part.
Preferably, for the robust beamforming problem that the minimum SNR in the users satisfies the given condition, the procedure of using the successive convex approximation method in step (2) is as follows:
1) given a randomly generated initial feasible solution
Figure BDA0002126967150000034
Giving a convergence condition delta, wherein the iteration number i is 0;
2) solving the problem to obtain an optimal solution
Figure BDA0002126967150000035
And an optimum value εi+1；
3) Order to
Figure BDA0002126967150000036
The iteration number i is i + 1;
4) repetition of 2) and 3) Up to epsiloni+1-εi＜Δ。
Preferably, for the robust beamforming problem of the robust beamforming scenario that maximizes the minimum SNR in the user, the procedure of using the successive convex approximation method is as follows:
1) given a randomly generated initial feasible solution
Figure BDA0002126967150000037
Given an iterative convergence condition Δ1Convergence to dichotomy condition Delta2The number of iterations i is 0, and L is tmin，U＝tmax；
2) Fixing
Figure BDA0002126967150000038
Solving a problem model;
3) if the problem in step 2 is not solved, let
Figure BDA0002126967150000039
If the problem in step 2 has a solution, order
Figure BDA00021269671500000310
Repeating the step 2 until the U-L is less than or equal to delta2Obtaining an optimal solution
Figure BDA00021269671500000311
And an optimum value εi+1Let us order
Figure BDA00021269671500000312
Let iteration number i equal to i +1, reset L equal to tmin，U＝tmax；
4) Repeating steps 2 and 3 until epsiloni+1-εi＜Δ1。
Preferably, the optimized value for each iteration is continuously reduced and thus gradually converges.
Compared with the prior art, the method has the advantages that a large number of Gaussian randomization steps and scaling factor solving steps are not needed by utilizing the continuous convex approximation algorithm, so that the method has the advantage of high calculation speed, and is more suitable for actual engineering requirements compared with a classical robust multi-group multicast beam forming algorithm.
Drawings
FIG. 1 is a graph of the effect of error on the transmit power required by a base station;
FIG. 2 is a graph of the effect of the number of users in a packet on the transmit power required by a base station;
fig. 3 is a graph of the effect of SINR on the transmit power required by a base station;
FIG. 4 is a graph comparing simulation time as a function of user within a packet;
FIG. 5 is a graph comparing simulation time with the number of antennas;
FIG. 6 is a graph of the effect of channel error magnitude on user communication rate;
FIG. 7 is a graph of the effect of the number of users in a packet on the communication rate of the users;
FIG. 8 is a graph of the effect of antenna power on user communication rate;
FIG. 9 is a graph comparing simulation time with the number of users in a packet;
fig. 10 is a graph comparing simulation time with the number of antennas.
Detailed Description
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, not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
The following is a detailed description of the implementation for ensuring that the minimum SNR among users satisfies given conditional questions:
considering that the base station side is equipped with 8 antennas, two groups exist in the communication scene, and each group has four users. The channel satisfies the independent Gaussian distribution with the mean value of 0 and the variance of 1, the Gaussian white noise received by the base station end is 0dB, and the threshold of SINR is set to be 1. FIG. 1 shows the channel error magnitude
Figure BDA0002126967150000041
As can be seen from fig. 1, in order to maintain the preset SINR limit in the case of an error, the influence of the change on the base station power increases to a certain extent, and the power increases as the error increases. However, compared to the RB-QoS-SDP algorithm, whether it is 20 gaussian randomization times or 100 gaussian randomization times, the algorithm proposed herein corresponds to lower power, which means that the algorithm proposed herein can maintain the predetermined threshold value with lower power.
Considering that the base station side is equipped with 8 antennas, two groups exist in the communication scene. The channel satisfies the independent Gaussian distribution with the mean value of 0 and the variance of 1, the white Gaussian noise received by the base station end is 0dBw, the threshold of SINR is set to be 1, and the square of the error norm is set to be
Figure BDA0002126967150000051
Figure 2 shows the effect of varying number of users in a packet on the power of a base station. As can be seen from fig. 2, as the number of users in a packet increases, the base station needs to increase the transmission power to meet the communication requirements of more users, but the power required by the algorithm proposed herein is lower than that of the RB-QoS-SDP algorithm with 100 gaussian randomization or 20 gaussian randomization. It should be noted that if the number of users in a group is too large (6 or more) in the simulation process, the probability of no solution to the problem will be greatly increased due to too serious interference.
Considering that the base station side is equipped with 8 antennas, two groups exist in the communication scene, and each group has four users. The channel satisfies the independent Gaussian distribution with the mean value of 0 and the variance of 1, the white Gaussian noise received by the base station end is 0dB, and the square of the error norm is
Figure BDA0002126967150000052
Fig. 3 shows the variation of the required power at the base station side for setting different SINRs. As can be seen from the figure, to meet the higher SINR requirement, the base station needs to increase the transmission power, but the power required by the algorithm proposed herein is lower than the RB-QoS-SDP algorithm with 20 Gaussian randomisation and 100 Gaussian randomisationThe organizing effect is similar.
The RB-QoS-SCA algorithm has the advantage of low complexity because the algorithm provided by the chapter only needs iteration steps and does not need a large number of Gaussian randomization steps. Fig. 4 and 5 show the comparison of simulation times for RB-QoS-SDP versus the algorithm presented herein for different numbers of users in a packet versus different numbers of antennas. Two groups exist in the communication scene, the power of Gaussian white noise is set to be 0dB, the channel satisfies the independent Gaussian distribution with the mean value of 0 and the variance of 1, and the error of the channel at the base station end is set to be 0
Figure BDA0002126967150000053
The SINR threshold is set to 1. In the simulation scenario of fig. 4, 8 antennas are equipped at the base station, and it can be seen from the figure that the simulation time of the algorithm proposed herein is similar to that of the RB-QoS-SDP algorithm with 20 randomization times and is much lower than that of the RB-QoS-SDP algorithm with 100 gaussian randomization times. The simulation scenario of fig. 5 has 4 users in each packet, and it can also be seen that the simulation time of the algorithm proposed herein is much lower than that of RB-QoS-SDP algorithm with 100 gaussian randomization, similar to that of 20 gaussian randomization. Therefore, the algorithm provided by the invention not only has excellent performance, but also has the advantage of low complexity, and is more suitable for practical communication systems.
The following is a detailed description of the robust beamforming problem to maximize the minimum SNR among users:
the condition for stopping iteration of the algorithm is epsiloni+1-εiLess than 0.001, with the condition that the two-step process is stopped being U-L<0.001。
Considering that the base station side is equipped with 4 antennas, two groups exist in the communication scene, and each group has two users. The channel satisfies an independent Gaussian distribution with a mean value of 0 and a variance of 1, the white Gaussian noise received by the base station end is 0dBw, and the maximum power capable of being provided by each antenna is 0 dBw. Fig. 6 shows the effect of channel error magnitude variation on the minimum user communication rate. It can be seen from the figure that as the error increases, the communication rate of the minimum user will decrease somewhat as the power is given, and the decrease in communication rate will be more pronounced the larger the error, but the algorithm proposed herein, which takes the channel error into account, is higher than the 20 and 100 times gaussian randomized RB-MMF-SDP algorithms.
Considering that the base station side is equipped with 4 antennas, two groups exist in the communication scene, and each group has a plurality of users. The channel is set to satisfy the independent Gaussian distribution with the mean value of 0 and the variance of 1, the Gaussian white noise received by the base station end is 0dBw, the maximum power capable of being provided by each antenna is 0dBw, and the channel of the base station end exists
Figure BDA0002126967150000061
The error of (2). Fig. 7 shows the influence of the change of the number of users in the packet on the minimum user communication rate, and it can be seen from the figure that when the number of users in the packet increases, the base station can meet the requirement that the minimum user communication rate is continuously reduced under the same transmission power, but the minimum user communication rate provided by the algorithm provided by the present invention is higher than that of the RB-MMF-SDP algorithm of 20 and 100 gaussian randomization steps, which shows that the performance of the algorithm provided by the present invention is better than that of the RB-MMF-SDP algorithm.
Considering that the base station side is equipped with 4 antennas, two groups exist in the communication scene, and each group has two users. The channel is set to satisfy the independent Gaussian distribution with the mean value of 0 and the variance of 1, the Gaussian white noise received by the base station end is 0dBw, and the channel of the base station end exists
Figure BDA0002126967150000063
The error of (2). Fig. 8 shows the effect of the change of the power limit of a single antenna on the communication rate of the minimum user, and it can be seen from the figure that the communication rate of the minimum user is continuously increased when the power provided by the antenna is increased, but the minimum user communication rate provided by the algorithm disclosed herein is higher than the RB-MMF-SDP algorithm with 20 and 100 gaussian randomization steps, i.e. the effect of the algorithm disclosed herein is better under different antenna power limits.
The algorithm provided by the invention has low algorithm complexity because a large number of Gaussian randomization steps are not carried out. FIGS. 9 and 10 show the simulation time versus number of users or antennas in a packet for the algorithm and RB-MMF-SDP algorithm presented hereinAnd (4) the ratio. In a simulation scene, each group has 2 users, channels satisfy independent Gaussian distribution with mean value of 0 and variance of 1, Gaussian white noise received by a base station end is 0dBw, the maximum power capable of being provided by each antenna is 0dBw, and the channels of the base station end exist
Figure BDA0002126967150000062
The error of (2). The number of Gaussian randomization times in RB-MMF-SDP is 20 times and 100 times respectively, and the algorithm proposed herein stops the iteration condition. As can be seen from fig. 9, as the number of users in a packet increases, the computation time of both algorithms increases, but the computation time of the algorithm proposed herein is lower than that of the RB-MMF-SDP algorithm with 100 gaussian randomizations, which is similar to that of the RB-MMF-SDP algorithm with 20 gaussian randomizations. It can also be seen from fig. 10 that the increased number of antennas increases the size of the optimization variables, and thus the computation time of different algorithms increases, but the computation time of the algorithm proposed herein is lower than that of the RB-MMF-SDP algorithm with 100 gaussian randomizations, which is similar to the simulation time of the algorithm with 20 gaussian randomizations. The simulation shows that the algorithm provided by the invention has better effect than the RB-MMF-SDP algorithm under the condition of lower calculation time.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications and substitutions can be easily made by those skilled in the art within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (3)

1. A robust multi-group multicast beam forming method is characterized in that the method firstly obtains two basic scenes of a multi-group multicast field: the method comprises the steps of ensuring that the minimum SNR in users meets a given condition and the robust beam forming problem under the minimum SNR in the maximized users is relaxed to be a convex problem to be solved;
then, using a continuous convex approximation method to relax the non-convex problem in the next iteration and carrying out iterative solution, and obtaining the optimal solution which finally approximates the original problem through continuous iterative steps;
the method specifically comprises the following steps:
the method comprises the following steps that (1) under a robust beam forming scene that the minimum SNR in users meets given conditions is guaranteed, additive channel errors are considered, the SINR of the users can be solved, the SINR lower bound influenced by the errors is obtained by numerator scaling to the minimum and denominator scaling to the maximum, and the robust beam forming problem under the scene is relaxed by utilizing the SINR lower bound to obtain a new problem model; under the robust beam forming scene of the minimum SNR in the maximized user, utilizing the property that the module value of a complex number on a complex plane is certainly larger than the real part of the complex number, relaxing the robust beam forming problem to obtain a new problem model;
aiming at a new problem model obtained by relaxation under two multi-group multicast robust beam forming scenes, solving by using a continuous convex approximation method to obtain a required beam forming weight vector;
the step (1) is specifically as follows:
consider being provided with NtThe base station of the root antenna communicates with users in G groups, each user side device only has a single antenna, namely the communication system is a MISO system; if additive channel error is considered, then the true channel for user i is
Figure FDA0003212136560000011
Wherein
Figure FDA0003212136560000012
Channel information estimated for the base station side, ei∈CNIs a corresponding error and has
Figure FDA0003212136560000013
Then it is located in the kth packet GkThe ith user of (1), its SINR can be expressed as
Figure FDA0003212136560000014
Wherein wkAssigning a weight coefficient, h, to the kth packetiFor the channel of the user i,
Figure FDA0003212136560000015
channel information estimated for the base station side, eiFor corresponding error, σiIs the norm square of error corresponding to the channel information of the ith user base station, where l is the ith packet, [ 2 ]]HWhich represents the transpose of the conjugate,
Figure FDA0003212136560000016
IMis a unit array;
by minimizing the numerator scaling and maximizing the denominator scaling, the lower bound of the SINR after being affected by the error can be obtained
Figure FDA0003212136560000021
Wherein wkFor the kth group, wlFor the assigned weight coefficient of the ith packet, σεThe norm square of the error corresponding to the channel information of the base station end is obtained;
by combining the property that the modulus value of the complex number on the SINR lower bound and the complex plane is certainly larger than the real part, the two robust beam forming problems under two scenes of ensuring that the minimum SNR in the users meets the given condition and maximizing the minimum SNR in the users after relaxation are respectively as follows:
Figure FDA0003212136560000022
Figure FDA0003212136560000023
Figure FDA0003212136560000024
Figure FDA0003212136560000025
wherein, PnIs the maximum power constraint value of the nth antenna, r is an optimization parameter variable,
Figure FDA0003212136560000026
Given a complex weight coefficient, gammaiSINR index, G, for the ith userkGrouping for the kth user, NtThe number of the antennas is;
Figure FDA0003212136560000027
Figure FDA0003212136560000028
Figure FDA0003212136560000029
Figure FDA00032121365600000210
t≥0
wherein t epsilon R is an optimized parameter variable, R is a real domain, and Re [ ] is a complex real part;
aiming at the robust beam forming problem that the minimum SNR in the users meets the given conditions, the step (2) utilizes the continuous convex approximation method to have the following flow:
1) given a randomly generated initial feasible solution
Figure FDA00032121365600000211
Given a convergence condition Δ, the number of iterations i ═0；
2) Solving the problem to obtain an optimal solution
Figure FDA00032121365600000212
And an optimum value εi+1；
3) Order to
Figure FDA00032121365600000213
The iteration number i is i + 1;
4) repeating 2) and 3) until εi+1-εi＜Δ。
2. The robust multi-group multicast beamforming method according to claim 1, wherein the step (2) utilizes the sequential convex approximation method for the robust beamforming problem of the robust beamforming scenario that maximizes the minimum SNR among users as follows:
1) given a randomly generated initial feasible solution
Figure FDA0003212136560000031
Given an iterative convergence condition Δ1Convergence to dichotomy condition Delta2The number of iterations i is 0, and L is tmin，U＝tmax；
2) Fixing
Figure FDA0003212136560000032
Solving a problem model;
3) if the problem in step 2 is not solved, let
Figure FDA0003212136560000033
If the problem in step 2 has a solution, order
Figure FDA0003212136560000034
Repeating the step 2 until the U-L is less than or equal to delta2Obtaining an optimal solution
Figure FDA0003212136560000035
And an optimum value εi+1Let us order
Figure FDA0003212136560000036
Let iteration number i equal to i +1, reset L equal to tmin，U＝tmax；
4) Repeating steps 2 and 3 until epsiloni+1-εi＜Δ1。
3. A robust multi-group multicast beamforming method according to claim 1 or 2, wherein the optimized value for each iteration is decreasing and thus gradually converging.
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