CN114513268A - Joint sensing communication waveform obtaining method based on double thresholds - Google Patents

Joint sensing communication waveform obtaining method based on double thresholds Download PDF

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CN114513268A
CN114513268A CN202210019552.1A CN202210019552A CN114513268A CN 114513268 A CN114513268 A CN 114513268A CN 202210019552 A CN202210019552 A CN 202210019552A CN 114513268 A CN114513268 A CN 114513268A
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CN114513268B (en
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杨凯
倪志同
高晓铮
远航
石珉巍
周荣花
杨杰
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Beijing Institute of Technology BIT
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • 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]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses a joint sensing communication waveform obtaining method based on double thresholds, and belongs to the field of wireless communication. The implementation method of the invention comprises the following steps: under the premise of limited transmitting energy, a joint sensing communication optimization problem which restrains a radar MI performance threshold and a multi-user communication SINR performance threshold is established, radar performance and communication performance are controlled by adopting two thresholds simultaneously, an objective function of the joint sensing communication optimization problem is simplified, and optimization solving efficiency of the joint sensing communication optimization problem is improved. In addition, the communication SINR relaxation lower bound is not less than 0 to equivalently replace that the communication SINR is not less than the SINR threshold value, so that the joint perception communication optimization problem is similar to the joint perception communication convex optimization problem. By solving the convex optimization problem of the joint sensing communication, the efficiency of obtaining the joint sensing communication waveform is improved, and the complexity of obtaining the communication waveform is reduced. The invention can realize the optimal radar MI performance and multi-user SINR performance of the joint perception communication system.

Description

Joint sensing communication waveform obtaining method based on double thresholds
Technical Field
The invention belongs to the field of wireless communication, and particularly relates to a joint sensing communication waveform acquisition method based on double thresholds, which is used for a multi-user communication sensing integrated system or a multi-antenna communication system.
Background
Independent communication and radar sensing systems will soon merge into a unified system and this trend is inevitable. There is much uniformity in both hardware modules and signal processing means. Moreover, the integrated system is beneficial to improving the overall performance and the frequency spectrum sharing of the system. Li et al, in ("optimal co-design for spectral mapping between MIMO radars and a MIMO communication system," IEEE Trans. Signal Process, vol.64, pp.4562-4575, Sep.2016 ") used a convex optimization technique to design optimal joint communication and radar waveforms. However, in the multi-user communication system, the multi-user interference makes the communication performance index not convex, so that the joint design becomes more difficult.
At present, some schemes can solve the problem that the multi-user system realizes the function of integrating the joint communication and the radar. Liu et al, "MIMO radar and cellular assisted by interference" in IEEE Trans.Signal Process, vol.66, pp.3681-3695, Jul.2018, minimizes transmission power while ensuring a certain communication signal-to-interference-and-noise ratio, and achieves an improvement in energy utilization rate. However, this scheme requires setting a specific threshold for the sir, which cannot be obtained without knowing the channel information. Y.l.site et al ("On multiple interference cancellation in a MIMO OFDM multi-user radar-communication network," IEEE trans. veh.technol., vol.67, pp.3339-3348, apr.2018.) use a wideband multi-carrier system to allocate multiple users to mutually orthogonal subcarriers, thereby avoiding interference of multiple users and presenting a convex signal-to-interference-plus-noise ratio. However, this scheme erases the multiuser interference causing a decrease in spectrum utilization. The work of really introducing multi-user interference into a joint communication perception system is not much, and the problem caused by the multi-user interference can be effectively solved by weighting and summing independent Optimal communication waveforms and Optimal radar waveforms in a 'powered dual-functional radio-communication systems,' IEEE Trans. Signal Process, vol.66, pp.4264-4279, and Aug.2018. However, the above scheme employs at most one performance control threshold (which controls either the communication performance or the radar performance), making the optimization process very complicated and difficult to grasp the performance index of the other side.
Disclosure of Invention
The invention discloses a joint perception communication waveform obtaining method based on double thresholds, which aims to solve the technical problems that: the method comprises the steps of taking a weighted sum of a constraint radar mutual information MI performance threshold and a signal-to-interference-and-noise ratio SINR performance threshold of multi-user communication as an optimization target, taking the actual MI of a radar not smaller than the MI performance threshold and the multi-user communication SINR not smaller than the SINR performance threshold as constraint conditions, establishing a joint sensing communication optimization problem of the constraint radar MI performance threshold and the multi-user communication SINR performance threshold under the premise of limited transmission energy, adopting two thresholds to simultaneously control radar performance and communication performance so as to simplify an objective function of the joint sensing communication optimization problem, increasing the constraint conditions and simultaneously reducing the size of an optimization problem solution space, and improving the optimization solving efficiency of the joint sensing communication optimization problem. In addition, the constraint condition that the radar actual MI is not less than the MI threshold value meets the convex optimization constraint condition, the communication actual SINR is not less than the SINR threshold value and does not meet the convex optimization constraint condition, and the communication SINR relaxation lower bound is not less than 0 to equivalently replace the communication SINR to be not less than the SINR threshold value, so that the joint perception communication optimization problem is approximate to the joint perception communication convex optimization problem. By solving the joint sensing communication convex optimization problem, the joint sensing communication waveform acquisition efficiency is further improved, and the complexity of communication waveform acquisition can be reduced. And performing joint communication and radar perception by using the joint perception communication waveform obtained by the joint perception communication convex optimization problem, so as to realize the optimal radar MI performance and multi-user SINR performance of the joint perception communication system.
The object of the present invention is achieved by the following method.
The invention discloses a joint sensing communication waveform obtaining method based on double thresholds, which comprises the following steps:
the method comprises the following steps: and respectively constructing a communication and radar precoding framework. At the transmitting end of the base station, the plurality of data information streams are parallelly sent to a baseband pre-coder for digital baseband pre-coding processing. The processed signals can realize the combined communication and perception functions. At a user receiving end, each user receives information sent by a base station by adopting a single antenna. At the base station end, the base station is simultaneously provided with a multi-antenna receiving end, and the multi-antenna receiving end is adjacent to the transmitting end. The receiving end is used for radar sensing.
The information flow of the sending end is s, and s is N on the baseband digital domainSAnd a vector of x 1 dimension, and precoding by a baseband precoder P. The baseband precoder is NT×NSThe digital device of (1). The precoded signal is transmitted to an antenna, NTFor the number of antennas at the transmitting end, the expression for transmitting signals is
x＝Ps (1)
The transmitted signal passes through a communication channel denoted huThe received signal arriving at each ue is expressed as
Figure BDA0003461879670000031
Wherein n isuIs Gaussian complex noise with mean of 0 and variance of σ2. Since the transmitting terminal has NSX 1-dimensional data stream, so the total number of users is NS. At the receiving end of the base station, the base station receives the transmitted signals using multiple antennas. The radar channel, denoted G, is experienced during this period. Ignoring noise, the base station receives a perceptual signal of
r＝GHPs (3)
The equations (1), (2) and (3) are the constructed communication and radar precoding structure.
Step two: and establishing an optimized performance target of communication as an SINR performance threshold of the multi-user communication, and giving a communication constraint condition that the SINR of the multi-user communication is not less than the SINR threshold.
Establishing an optimized performance target for communications as an SINR performance threshold for multi-user communications, expressed as
Figure BDA0003461879670000032
Wherein p isuIs the u-th column vector of P.
In order to guarantee the communication performance, the communication constraint condition is that the multi-user communication SINR is not less than the SINR threshold value gamma.
Step three: and establishing an optimized performance target of the radar as a constraint radar mutual information MI performance threshold, and giving out a constraint condition of radar sensing performance that the actual MI of the radar is not less than the MI performance threshold, wherein the constraint condition that the actual MI of the radar is not less than the mutual information threshold meets a convex optimization constraint condition.
For a receiving end of a radar base station, a plurality of indexes for measuring sensing performance are provided, an optimal performance target of the radar is determined as a constraint radar mutual information MI performance threshold, and the expression is
MI＝log|I+PHGGHP| (5)
The mutual information optimization problem has an optimal solution, namely that the coding matrix P is equal to a left singular matrix obtained after singular value decomposition of G.
In order to guarantee the radar performance, the constraint condition of the radar sensing performance is that the actual MI of the radar is not less than the MI performance threshold eta, and the constraint condition that the actual mutual information MI of the radar is not less than the mutual information threshold eta meets the convex optimization constraint condition.
Step four: and establishing a joint perception communication optimization problem which restricts the radar MI performance threshold and the communication SINR performance threshold on the premise of limited transmission energy P by taking the weighted sum of the restricted radar MI performance threshold and the SINR performance threshold of multi-user communication as an optimization target and taking the actual radar MI not less than eta and the multi-user communication SINR not less than gamma as constraint conditions. And simultaneously controlling the radar performance and the communication performance by adopting two thresholds to simplify the objective function of the joint sensing communication optimization problem, and increasing the limiting conditions while reducing the size of the solution space of the optimization problem to improve the optimization solution efficiency of the joint sensing communication optimization problem.
The method comprises the steps of taking the weighted sum of a constraint radar MI performance threshold and a multi-user communication SINR performance threshold as an optimization target, taking the actual radar MI not less than eta and the multi-user communication SINR not less than gamma as constraint conditions, and on the premise of limited transmission energy P, establishing a joint perception communication optimization problem of the constraint radar MI performance threshold and the communication SINR performance threshold as
Figure BDA0003461879670000041
μ is the bias for radar communication.
Step five: in the constraint conditions, the communication signal to interference plus noise ratio is not less than the SINR threshold value and does not satisfy the convex optimization constraint conditions, and the communication signal to interference plus noise ratio is equivalently replaced by the constraint conditions that the communication SINR relaxation lower bound is not less than 0 and is not less than gamma, so that the joint perception communication optimization problem is approximately the joint perception communication convex optimization problem. By solving the joint sensing communication convex optimization problem, the joint sensing communication waveform acquisition efficiency is further improved, and the complexity of communication waveform acquisition can be reduced.
Because the SINR expression has no convexity, the combined optimization with radar perception is difficult. The SINR approximation is thus made to be a convex function using a SINR relaxation lower bound expressed as
Figure BDA0003461879670000042
Wherein
Figure BDA0003461879670000043
Using the additive commutative property, equation (7) is equivalently expressed as
Figure BDA0003461879670000044
The equation (7) of 0 or more is equivalent to the SINR of γ or more. Equation (9) is quadratic and appears as a function of saddle surface type.
Substituting SINR relaxation lower bound of not less than 0 for SINR of not less than γ into equation (6).
The optimization problem (6) becomes
Figure BDA0003461879670000045
By pair waveform vector puDecomposition is carried out, the expression of which is as follows
Figure BDA0003461879670000051
Wherein b isu,iIs a scalar quantity, q, to be solved unknowniThe expression is as follows
Figure BDA0003461879670000052
Figure BDA0003461879670000053
Wherein U isGIs an N X X matrix, represents the left singular matrix of G, and X is the number of non-0 in the singular values of G, so that the optimization problem (10) is approximately a convex optimization problem.
The decomposition of equation (11) is substituted into the three constraints in the optimization problem (10). Wherein the first constraint becomes
Figure BDA0003461879670000054
Wherein
Figure BDA0003461879670000055
Is the x-th non-0 singular value of G.
The second limitation becoming
Figure BDA0003461879670000056
The third constraint is approximately changed to
Figure BDA0003461879670000057
Order to
Figure BDA0003461879670000058
The transformed optimization problem (10) becomes a convex optimization problem, i.e.
arg max(1-μ)γ+μη
s.t.
Figure BDA0003461879670000059
To obtain
Figure BDA0003461879670000061
Namely obtain
Figure BDA0003461879670000062
Thereby obtaining an optimal precoder P.
By solving the joint perception communication convex optimization problem (16), the joint perception communication waveform obtaining efficiency is further improved, and the complexity of communication waveform obtaining can be reduced.
The method also comprises the following six steps: and performing joint communication and radar sensing by using the joint sensing communication waveform obtained by optimization in the step five, so as to realize the optimal radar MI performance and multi-user SINR performance of the joint sensing communication system.
Has the advantages that:
1. the invention discloses a joint sensing communication waveform obtaining method based on double thresholds, which takes the weighted sum of a constraint radar mutual information MI performance threshold and a signal-to-interference-plus-noise ratio SINR performance threshold of multi-user communication as an optimization target, takes the actual MI of a radar not less than the MI performance threshold and the multi-user communication SINR not less than the SINR threshold as constraint conditions, and establishes a joint sensing communication optimization problem of the constraint radar MI performance threshold and the multi-user communication SINR performance threshold on the premise of limited transmitting energy; the double thresholds are adopted to replace a single threshold, so that the number of constraint conditions is increased, and the size of a solution interval is reduced, and therefore, the optimization efficiency can be improved.
2. According to the method for acquiring the joint sensing communication waveform based on the double thresholds, the non-convex communication SINR is approximately set to be a loose lower bound, so that the optimization problem is close to the convex optimization problem. By approximation, the problem can be solved by a convex optimization means, and the optimization acquisition difficulty of the joint sensing communication waveform is obviously reduced.
3. The invention discloses a joint sensing communication waveform obtaining method based on double thresholds, which optimizes the weighted sum of radar MI and communication SINR by continuously raising the thresholds, and realizes the optimal radar MI performance and multi-user SINR performance of a joint sensing communication system.
Drawings
Fig. 1 is a general flowchart of a "dual-threshold-based joint sensing communication waveform acquisition method" according to the present invention.
Fig. 2 is a schematic diagram of a communication-aware unified system.
Fig. 3 is a growth curve of a communication threshold in an optimization process of the novel dual-threshold-based joint sensing communication waveform design method of the invention.
FIG. 4 is a graph showing the variation of the total performance with respect to the signal-to-noise ratio achieved by the novel waveform design method based on the lower bound of the signal-to-interference-and-noise ratio of the present invention.
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1:
as shown in fig. 1, the method for acquiring a joint sensing communication waveform based on dual thresholds disclosed in this embodiment includes the following specific steps:
the method comprises the following steps: and respectively constructing a communication and radar precoding framework. At the transmitting end (base station), 4 data information streams are parallelly sent to a baseband precoder for digital baseband precoder P processing, and the number of transmitting end antennas is 16. The processed signals can realize the combined communication and perception functions. At a user receiving end, each user receives information sent by a base station by adopting a single antenna, and the channel matrix of all the users is recorded as H ═ H1,…,hU]As shown in fig. 2. At the base station side, the base station is simultaneously provided with a multi-antenna receiving side, which is adjacent to the transmitting side. The receiving end is used for radar sensing as shown in fig. 2.
The information flow of the sending end is s, the s is a 4-dimensional vector on a baseband digital domain, and precoding processing is carried out through a baseband precoder P. The baseband precoder is a 16 x 4 digital device. The precoded signal is transmitted by a digital-to-analog converter (DAC) to a 16-dimensional antenna.
The transmitted signal travels through the communication channel to each subscriber station. Since the transmitting end has 4 × 1-dimensional data streams, the total number of users can be considered as 4. At the receiving end of the base station, the base station receives the transmitted signals by using 16 receiving antennas. During which radar channels are experienced. Variance of noise σ2Given as the minus 6 th power of 10. The total emission energy P was 1 (Watt). The joint performance of multi-user communication and radar sensing will be optimized by designing the coding matrix P.
Step two: the SINR of the communication is established. The communication channel is assumed to be known as a random gaussian distribution vector.
Step three: an optimal performance target for the radar is established. At the base station receiving end, the radar channel is a known parameter.
Step four: but not shown.
Step five: determining a vector q based on known communication and radar channelsiThe expression is shown in (12). Vector q is divided intoiSubstituting equation (13) to equation (15). Fixing double thresholds, solving the problem (16) by using MATLAB and other convex optimization tools, and obtaining a solution after solving
Figure BDA0003461879670000071
The threshold is raised and the solution to the problem (16) is continued. And continuously increasing the double threshold until the solution space of (16) does not exist. Thus, the dual threshold is maximized.
Through the implementation of the above steps one to five, the communication threshold obtained by the "dual-threshold joint sensing communication waveform acquisition method" in this embodiment is as shown in fig. 3, and it can be seen that the higher the communication threshold is, the lower the corresponding radar threshold is. The total value stabilizes on a performance bound. The overall performance obtained by the method for acquiring a dual-threshold joint sensing communication waveform of the embodiment varies with the signal-to-noise ratio as shown in fig. 4, and it can be seen that the joint scheme is very close to the individual performance boundary. The individual capabilities can only enable a single party functionality, while the combined capabilities can enable simultaneous communication and radar functionality.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (7)

1. A joint perception communication waveform obtaining method based on double thresholds is characterized in that: the method comprises the following steps:
the method comprises the following steps: respectively constructing a communication and radar precoding framework; at a transmitting end of a base station, a plurality of data information streams are parallelly transmitted to a baseband precoder for digital baseband precoding processing; the processed signals can realize the functions of joint communication and perception; at a user receiving end, each user receives information sent by a base station by adopting a single antenna; at a base station end, the base station is simultaneously provided with a multi-antenna receiving end which is adjacent to a transmitting end; the receiving end is used for radar sensing;
step two: establishing an optimized performance target of communication as an SINR performance threshold of multi-user communication, and giving a communication constraint condition that the SINR of the multi-user communication is not less than the SINR threshold;
step three: the method comprises the steps of establishing an optimized performance target of the radar as a constraint radar mutual information MI performance threshold, giving out a constraint condition of radar sensing performance that the actual MI of the radar is not less than the MI performance threshold, and meeting a convex optimization constraint condition that the actual MI of the radar is not less than the mutual information threshold;
step four: the method comprises the steps of establishing a joint perception communication optimization problem which restrains a radar MI performance threshold and a communication SINR performance threshold on the premise of limited transmitting energy P by taking the weighted sum of the constraint radar MI performance threshold and the SINR performance threshold of multi-user communication as an optimization target and taking the actual radar MI not less than eta and the multi-user communication SINR not less than gamma as constraint conditions; the method comprises the steps that two thresholds are adopted to simultaneously control radar performance and communication performance to simplify a target function of the joint sensing communication optimization problem, and the size of an optimization problem solution space is reduced by increasing limiting conditions, so that the optimization solving efficiency of the joint sensing communication optimization problem is improved;
step five: in the constraint conditions, the communication signal to interference plus noise ratio is not less than the SINR threshold value and does not satisfy the convex optimization constraint conditions, and the communication signal to interference plus noise ratio is equivalently replaced by the constraint conditions that the communication SINR relaxation lower bound is not less than 0 and is not less than gamma, so that the joint perception communication optimization problem is approximately the joint perception communication convex optimization problem; by solving the joint sensing communication convex optimization problem, the joint sensing communication waveform acquisition efficiency is further improved, and the complexity of communication waveform acquisition can be reduced.
2. The method for acquiring a joint sensing communication waveform based on dual thresholds according to claim 1, characterized in that: further comprises the following steps: and performing joint communication and radar sensing by using the joint sensing communication waveform obtained by optimization in the step five, so as to realize the optimal radar MI performance and multi-user SINR performance of the joint sensing communication system.
3. A method as claimed in claim 1 or 2, wherein the method comprises: the first implementation method comprises the following steps of,
the information flow of the sending end is s, and s is N on the baseband digital domainSA vector of x 1 dimension, which is precoded by a baseband precoder P; the baseband precoder is NT×NSThe digital type device of (1); the precoded signal is transmitted to an antenna, NTFor the number of antennas at the transmitting end, the expression for transmitting signals is
x＝Ps (1)
The transmitted signal passes through a communication channel denoted huThe received signal arriving at each ue is expressed as
Figure FDA0003461879660000021
Wherein n isuIs Gaussian complex noise with mean of 0 and variance of σ2(ii) a Since the transmitting terminal has NSX 1-dimensional data stream, so the total number of users is NS(ii) a At a receiving end of a base station, the base station receives a transmitted signal by adopting multiple antennas; the radar channel is experienced during the period, and is marked as G; ignoring noise, the base station receives a perceptual signal of
r＝GHPs (3)
The formulas (1), (2) and (3) are the constructed communication and radar precoding architectures.
4. The method of claim 3, wherein the method for obtaining the joint sensing communication waveform based on the dual threshold comprises: the second step is realized by the method that,
establishing an optimized performance target for communications as an SINR performance threshold for multi-user communications, expressed as
Figure FDA0003461879660000022
Wherein p isuIs the u-th column vector of P;
in order to guarantee the communication performance, the communication constraint condition is that the multi-user communication SINR is not less than the SINR threshold value gamma.
5. The method of claim 4, wherein the method for obtaining the joint sensing communication waveform based on the dual threshold comprises: the third step is to realize the method as follows,
for a receiving end of a radar base station, a plurality of indexes for measuring sensing performance are provided, an optimal performance target of the radar is determined as a constraint radar mutual information MI performance threshold, and the expression is
MI＝log|I+PHGGHP| (5)
The mutual information optimization problem has an optimal solution, namely a coding matrix P is equal to a left singular matrix after singular value decomposition of G;
in order to guarantee the radar performance, the constraint condition of the radar sensing performance is that the actual MI of the radar is not less than the MI performance threshold eta, and the constraint condition that the actual mutual information MI of the radar is not less than the mutual information threshold eta meets the convex optimization constraint condition.
6. The method of claim 5, wherein the method for obtaining the joint sensing communication waveform based on the dual threshold comprises: the implementation method of the fourth step is that,
the method comprises the steps of taking the weighted sum of a constraint radar MI performance threshold and a multi-user communication SINR performance threshold as an optimization target, taking the actual radar MI not less than eta and the multi-user communication SINR not less than gamma as constraint conditions, and on the premise of limited transmission energy P, establishing a joint perception communication optimization problem of the constraint radar MI performance threshold and the communication SINR performance threshold as
Figure FDA0003461879660000031
μ is the bias for radar communication.
7. The method of claim 6, wherein the method for obtaining a joint sensing communication waveform based on dual thresholds is characterized by: the fifth step is to realize that the method is that,
because the SINR expression has no convexity, the combined optimization with radar perception is difficult; the SINR approximation is thus made to become a convex function with a lower bound on the SINR relaxation, expressed as
Figure FDA0003461879660000032
Wherein
Figure FDA0003461879660000033
Using the additive commutative property, equation (7) is equivalently expressed as
Figure FDA0003461879660000034
Equation (7) 0 or more is equivalent to SINR γ or more; equation (9) is quadratic and appears as a function of saddle surface type;
substituting the SINR relaxation lower bound of not less than 0 for the SINR of not less than gamma into formula (6);
the optimization problem (6) becomes
Figure FDA0003461879660000035
By applying a waveform vector puDecomposition is carried out, the expression of which is as follows
Figure FDA0003461879660000036
Wherein b isu,iIs a scalar quantity, q, to be solved unknowniThe expression is as follows
Figure FDA0003461879660000041
Figure FDA0003461879660000042
Wherein U isGIs an NxX matrix which represents a left singular matrix of G, and X is the number of non-0 in singular values of G, so that the optimization problem (10) is approximately a convex optimization problem;
substituting the decomposition formula of the formula (11) into three limiting conditions in the optimization problem (10); wherein the first constraint becomes
Figure FDA0003461879660000043
Wherein
Figure FDA00034618796600000410
Is the x-th non-0 singular value of G;
the second limitation becoming
Figure FDA0003461879660000044
The third constraint is approximately changed to
Figure FDA0003461879660000045
Order to
Figure FDA0003461879660000046
The transformed optimization problem (10) becomes a convex optimization problem, i.e.
arg max(1-μ)γ+μη
s.t.
Figure FDA0003461879660000047
To obtain
Figure FDA0003461879660000048
Namely obtain
Figure FDA0003461879660000049
Thereby obtaining an optimal precoder P;
by solving the joint perception communication convex optimization problem (16), the joint perception communication waveform obtaining efficiency is further improved, and the complexity of communication waveform obtaining can be reduced.
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