CN113364494B - IRS (inter-Range instrumentation System) assisted MISO (multiple input single output) system performance optimization method for hardware distortion - Google Patents
IRS (inter-Range instrumentation System) assisted MISO (multiple input single output) system performance optimization method for hardware distortion Download PDFInfo
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Abstract
The invention discloses an IRS (inter-range interference rejection) assisted MISO (multiple input single output) system performance optimization method aiming at hardware distortion.A multi-antenna base station performs wide linear precoding on messages of M information users to generate a baseband transmission signal, processes the baseband transmission signal into an asymmetric Gaussian signal and generates an output signal through a high-power amplifier; under the assistance of the intelligent reflecting surface, the multi-antenna base station transmits an output signal generated by the high-power amplifier in a broadcasting mode, and controls the phase shift of the reflecting element in real time through a controller on the intelligent reflecting surface; decoding to obtain the rates of M information users; and taking the speed of M information users as performance evaluation, optimizing a beam forming vector of the base station and a phase shift vector at the intelligent reflection surface under the condition of meeting the total power constraint of the base station, maximizing the minimum reachable speed of the information users, and finishing performance optimization. The invention adopts IGS to transmit, further improving the reachable rate of the information user.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to an IRS (inter-range instrumentation system) auxiliary MISO (multiple input single output) system performance optimization method aiming at hardware distortion.
Background
In a wireless communication system, in order to simultaneously co-frequency serve multiple users, a multi-antenna technique needs to be employed at a base station. The multi-antenna technology obviously improves the spatial freedom degree, and is beneficial to eliminating the interference among users, thereby improving the reachable rate of information users. Meanwhile, an Intelligent Reflection Surface (IRS) is arranged near the user, and radio frequency signals from a base station are gathered at the information user receiver by adjusting the phase shift at the IRS, so that the signal strength at the information user receiver can be obviously improved, and the reachable rate of the information user is further improved.
In a communication system, hardware distortion is always present. Hardware distortion includes amplitude error and phase error (I/Q imbalance) due to mismatch of phase shifters and local oscillators, and additive distortion noise due to nonlinearity of digital-to-analog conversion, band-pass filter, and high-power amplifier. This results in a mismatch between the desired and actual transmitted signals, thereby reducing the achievable rate for the information user. In existing studies, additive noise caused by hardware distortion at the base station is modeled as circularly symmetric complex gaussian noise, and the power of the distortion noise at the base station is proportional to the signal power at the base station antenna. However, this model does not accurately model the asymmetric nature of base station hardware distortion (I/Q imbalance).
Disclosure of Invention
The technical problem to be solved by the present invention is to provide an IRS-assisted MISO system performance optimization method for hardware distortion, which improves the reachable rate of information users by jointly optimizing a base station beamforming vector and an IRS-located phase shift vector by using an asymmetric gaussian signal transmission scheme.
The invention adopts the following technical scheme:
an IRS-assisted MISO system performance optimization method for hardware distortion, comprising the steps of:
s1, the multi-antenna base station performs wide linear precoding on the messages of the M information users to generate baseband transmission signals, the baseband transmission signals are asymmetric Gaussian signals, the asymmetric Gaussian signals are converted into analog signals through a digital-to-analog converter, then the analog signals are up-converted to carrier frequencies through a mixer, and finally output signals are generated through a high-power amplifier; under the assistance of the intelligent reflecting surface, the multi-antenna base station transmits an output signal generated by the high-power amplifier in a broadcasting mode, and controls the phase shift of the reflecting element in real time through a controller on the intelligent reflecting surface;
s2, M information users receive the signals transmitted by the multi-antenna base station in the step S1, and the speed of the M information users is obtained through decoding;
and S3, taking the speed of the M information users obtained in the step S2 as performance evaluation, optimizing a beam forming vector of the base station and a phase shift vector at the intelligent reflection surface under the condition of meeting the total power constraint of the base station, maximizing the minimum reachable speed of the information users, and finishing performance optimization.
Specifically, in step S1, let
Is an information user d l Message, multi-antenna base station pair
Asymmetric Gaussian signal generated after wide linear precoding
The following were used:
wherein,
forming a vector for the information beam;
after wide linear precoding, the base station transmits signal x BS Comprises the following steps:
wherein d is l For the information user, k I Is a collection containing all information users.
Specifically, in step S1, the multi-antenna base station is equipped with N T An antenna at the transmitter of the base station, mixer I/Q imbalance causes the transmission signal to generate self-interference, and nonlinearity of the analog-to-digital converter, high-power amplifier, band-pass filter generates additive distortion noise d T ～CN(0,C T )，C T For the variance of the additive distortion noise,
for the variance of the additive distortion noise at each antenna,
is N T ×N T The identity matrix of (1); the actual transmission signal of the multi-antenna base station is x' BS +d T 。
Further, after I/Q imbalance, equivalent baseband transmission signal x' BS Expressed as:
wherein,
is a diagonal matrix containing amplitude distortion and rotation error caused by mixer mismatch; lambda 1 ,Λ 2 Respectively expressed as:
wherein,
the diagonal matrix contains the amplitude error generated by each radio frequency link of the base station;
the diagonal matrix contains the phase error generated by each radio frequency link of the base station.
Specifically, in step S2, the rate of the M information users obtained by decoding is specifically:
in each channel coherence time, the multi-antenna base station knows the channel state information of all channels, considers the signals reflected once by the intelligent reflection surface, and all the channels are quasi-static flat fading channel models;
indicating base station to information user d j The base-band equivalent channel of (a),
for intelligently reflecting surfaces to information users d j The baseband equivalent channel of (a); considering the signal reflected once by the intelligent reflecting surface, ignoring the signals reflected twice and many times
Representing the base band equivalent channel from the base station to the intelligent reflecting surface, the matrix of the reflection coefficient at the intelligent reflecting surface is
β n ∈(0,1]Is the reflection amplitude of the nth reflection element, theta n E [0,2 pi) is the phase shift of the nth reflection element; set up beta n ＝1,n∈1…N L Maximizing signal reflection at IRS, and obtaining information user d by wireless channel propagation j A received signal of
Using interference as noise, determining information user d j Achievable rate of
Further, information user d j Achievable rate of
Expressed as:
wherein,
for all information users, the set of beamforming vectors, θ is the phase shift vector at the intelligent reflecting surface, I 2 Is a 2 x 2 unit matrix and is,
an augmented representation of the received useful signal for the jth information user,
a wide linear transformation of the beamforming vector for the jth information user,
for the jth information user to receive an augmented representation of the signals sent by the multi-antenna base station to other users,
for the variance of additive hardware distortion noise at each transmit antenna of the base station,
for the combined channel from the base station to the jth information user,
is composed of
Of conjugated transpose form, σ 2 For variance of thermal noise of information user receiver, d l Is the information user of the I < th >.
Specifically, in step S3,obtaining beamforming vectors at a multi-antenna base station by an alternating optimization algorithm within each channel coherence time
And the phase shift vector theta at the intelligent reflecting surface maximizes the minimum reachable rate of the M information users, and then the multi-antenna base station sends the phase shift vector theta to the intelligent reflecting surface controller through a control link to control each reflecting element at the intelligent reflecting surface;
the minimum achievable rate optimization problem of the maximized information user is expressed as:
wherein,
a set of beamforming vectors for all information users, theta is the phase shift vector at IRS,
d j ∈κ I and gamma denotes the achievable rate of all information users
Minimum value of (d);
unit mode constraint of phase shift matrix at intelligent reflective surface
Is represented as follows:
where N ∈ {1, … N L N is the index value of the reflection element of the intelligent reflection surface, N L The number of the reflection elements is shown.
Further, optimizing multi-antenna base station beamforming vectors
The method specifically comprises the following steps:
wherein,
for the k-th iteration
Approximation of concave lower bound of d j For the jth information user, [ kappa ] I P is the total transmit power of the base station for the set containing all information users.
Further, optimizing the reflection phase shift vector θ at the intelligent reflection surface specifically includes:
wherein, theta (n) Is the initial value of theta of the nth iteration, eta is a penalty factor, eta | | | theta (n) || 2 +2η<θ (n) ,θ-θ (n) >In the form of a negative mean square penalty term,
for the nth iteration
Is approximated by a concave lower bound.
Another technical solution of the present invention is an IRS-assisted MISO system performance optimization system for hardware distortion, including:
the multi-antenna base station performs wide linear precoding on the information of the information user to generate a baseband transmission signal, processes the baseband transmission signal into an asymmetric Gaussian signal, converts the asymmetric Gaussian signal into an analog signal through a digital-to-analog converter, obtains a carrier frequency through frequency conversion of a mixer, and generates an output signal through a high-power amplifier; under the assistance of the intelligent reflecting surface, the multi-antenna base station transmits output signals generated by the high-power amplifier in a broadcasting mode, and the phase shift of the reflecting element is controlled in real time through a controller on the intelligent reflecting surface;
the decoding module is used for receiving the signals transmitted by the multi-antenna base station of the processing module by the M information users and decoding the signals to obtain the rates of the M information users;
and the optimization module is used for optimizing a beam forming vector of the base station and a phase shift vector at the intelligent reflection surface under the condition of meeting the total power constraint of the base station by taking the speed of the M information users obtained by the decoding module as performance evaluation, maximizing the minimum reachable speed of the information users and finishing performance optimization.
Compared with the prior art, the invention has at least the following beneficial effects:
in the IRS-assisted MISO system, I/Q imbalance is generated due to distortion of a base station mixer, so that the amplitudes of a same-direction component and an orthogonal component of a transmission signal are different, and the phase difference is not accurate pi/2. Assuming that the base station transmits a circularly symmetric complex Gaussian signal, the signal actually transmitted by the base station is an asymmetric Gaussian signal after I/Q imbalance. As can be seen from the information theory, the information entropy of the circularly symmetric complex gaussian signal is the largest. Therefore, I/Q imbalance will reduce the achievable rate for information users. In the invention, a precompensation scheme, namely an asymmetric Gaussian signal is introduced for transmission, the statistical characteristic of the asymmetric Gaussian signal is optimized, and after I/Q is unbalanced, the signal actually transmitted by the base station is a circularly symmetric complex Gaussian signal, thereby improving the reachable rate of a user.
Further, the message sent by the base station is a circularly symmetric complex gaussian signal, and an asymmetric gaussian signal is generated after wide linear precoding. By optimizing the wide linear precoding vector, the statistical properties of the asymmetric gaussian signal can be adjusted. The asymmetric Gaussian signal generated after the wide linear precoding is used for compensating the I/Q imbalance at the base station, and is beneficial to offsetting the influence of an interference signal at the receiver of the information user. By increasing the dimensionality of the precoding vector, the complex signal processing of the asymmetric Gaussian signal is avoided, and the traditional signal processing method of the circularly symmetric complex Gaussian signal is converted.
Further, the base station is equipped with N T The antennas use the space diversity technology to make the base station can simultaneously serve multiple users with the same frequency. The intelligent reflective surface IRS has N L And the reflection element focuses the radio frequency signal from the base station to the information receiver by adjusting the phase shift at the IRS, so that the received signal strength of the information user is improved. The mismatch of the local oscillator and the phase shifter introduces phase error and amplitude error, and the distortion generated by the local oscillator and the phase shifter is accurately modeled by adopting an I/Q mismatch model. At the base station transmitter, the nonlinearity of the high power amplifier, band pass filter produces additive distortion noise d T ～CN(0,C T )，
And (3) modeling by adopting circularly symmetric complex Gaussian noise verified by experiments, so that the actual hardware distortion wireless communication system is accurately described.
Furthermore, for I/Q imbalance, an equivalent baseband distortion model is adopted, so that analysis and calculation are facilitated. Furthermore, according to the fading characteristics of the wireless channel, the channel is basically kept unchanged in each channel coherence time, so that a quasi-static flat fading channel model is adopted for modeling. For signal reflections at IRS, the twice and multiple reflected signals are negligible due to large scale fading. Meanwhile, the amplitude and phase shift of the reflection coefficient at the IRS are independently controlled to have a complicated circuit structure, which is not beneficial to actual design and implementation, so that the phase shift of the reflection element at the IRS is only adjusted by considering that the reflection amplitude is always 1.
Furthermore, the information user receiver regards the interference as noise, and through coherent detection, the reachable rate of the user can be obtained. Meanwhile, in order to ensure fairness among users, it is necessary to optimize a beamforming vector of a base station and a phase shift vector at an IRS, so as to maximize a minimum achievable rate among all users as much as possible.
Further, the optimization problem is decomposed into a base station beam forming optimization sub-problem and an IRS phase shift optimization sub-problem by adopting an alternating optimization algorithm, a path tracking algorithm is proposed to solve each optimization sub-problem, and the maximum and minimum achievable rate of the information user is solved when the total power constraint of the base station is met.
Furthermore, in each channel coherence time, the beam vector of the base station (i.e. the power distribution coefficient between different antennas) is optimized, and the transmission power is distributed to the antenna with better instantaneous channel condition, so as to improve the reachable rate of the information user.
Furthermore, by adjusting the phase shift vector at the IRS, the radio frequency signal from the base station is reflected to the user receiver as much as possible, and coherent interference is generated, thereby improving the signal strength of the received signal.
In summary, the present invention considers that an IRS is deployed near an information user, and by adjusting the phase shift at the IRS, the radio frequency signal from the base station is reflected to the receiver of the information user, thereby increasing the signal strength at the information user, and thus increasing the reachable rate of the information user.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a diagram of an IRS assisted MISO system model of the present invention;
FIG. 2 is a diagram of the distortion of the base station transmitter hardware of the present invention;
FIG. 3 is a diagram of a simulation setup of the present invention;
FIG. 4 is a graph illustrating the effect of hardware distortion on the maximum achievable minimum rate for a user according to the present invention.
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 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.
It will be understood that the terms "comprises" and/or "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the specification of the present invention and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.
Various structural schematics according to the disclosed embodiments of the invention are shown in the drawings. The figures are not drawn to scale, wherein certain details are exaggerated and possibly omitted for clarity of presentation. The shapes of various regions, layers and their relative sizes and positional relationships shown in the drawings are merely exemplary, and deviations may occur in practice due to manufacturing tolerances or technical limitations, and a person skilled in the art may additionally design regions/layers having different shapes, sizes, relative positions, according to actual needs.
The invention provides an IRS (inter-range interference rejection) auxiliary MISO (single input single output) system optimization design method aiming at hardware distortion, aims to accurately model asymmetric hardware distortion at a base station, and proposes to adopt an asymmetric Gaussian signal transmission scheme to eliminate the influence of asymmetric hardware distortion in an IRS auxiliary MISO system, considers that the phase shift of a reflection element at the IRS is continuously adjustable, but is also suitable for the condition that the phase shift of the reflection element at the IRS is a discrete value.
The definition is as follows:
the lower case letters in bold (e.g., X) represent vectors, the upper case letters in bold (e.g., X) represent matrices, and the lower case letters (e.g., X) represent scalars.
The mean is 0 and the circularly symmetric complex Gaussian random variable with variance of 1 is represented as x-CN (0, 1).
For the scalar x, the number of bits in the vector x,
representing the real part of x.
For the vector x, x * Denotes the conjugate of x, x T Denotes the transposition of x, x H Representing the conjugate transpose of x. Xi (x) denotes the expected value of x, diag (x) denotes the diagonal matrix, and the nth element of x is the nth diagonal element of the matrix.
For a square matrix X, tr (X) represents the trace of matrix X, X -1 Denotes the inverse of matrix X, | X | denotes the determinant of matrix X, [ X [ ]] 2 Denotes XX H ,||X|| F Is the F-norm of the matrix X,<X>＝tr(X),<X,Y>＝tr(X H Y)。
for an Hermite symmetric matrix X, X > 0(X ≧ 0) indicates that X is a positive definite matrix (positive semi-definite matrix), X S (set S as subscript) represents the set { x } s ,s∈S}。
The invention relates to an IRS (intelligent resilient framework) assisted MISO (multiple input single output) system optimization design method for hardware distortion, which comprises the following steps of:
s1, under the assistance of IRS, the base station transmits asymmetric Gaussian signals to information users in a broadcasting mode, meanwhile, the mismatch of a mixer and a phase shifter at a transmitter of the base station and the nonlinearity of a digital-to-analog converter, a band-pass filter and a high-power amplifier cause the distortion of the signals transmitted by the base station;
referring to fig. 1, a multi-antenna base station transmits information to M information users with the assistance of IRS, assuming that the base station is equipped with N T An antenna, a set
Representing a single antenna information user group, facilitating communication by deploying an IRS in the vicinity of the information user, assuming that the IRS has N L And the phase shift of the reflection element is controlled in real time by a controller on the IRS.
S101, a base station performs wide linear precoding on information of an information user to generate a baseband transmission signal;
suppose that
Is an information user d l Message, base station pair
After wide linear precoding, the following asymmetric Gaussian signals are generated for transmission.
In the formula (1), the acid-base catalyst,
for the information beam forming vector, the baseband transmission signal after wide linear precoding of the base station is:
and S102, converting the digital signal into an analog signal by the baseband transmission signal through a digital-to-analog converter, up-converting the analog signal to a carrier frequency through a mixer, and finally generating an output signal through a band-pass filter and a high-power amplifier.
Referring to fig. 2, self-interference is caused by phase error and amplitude error (i.e., I/Q imbalance) introduced by the mismatch of the local oscillator and the phase shifter. According to the I/Q mismatch model, the equivalent quadrature unbalanced baseband transmission signal is represented as:
wherein,
the diagonal matrix contains amplitude errors and rotation errors caused by mixer mismatch.
Λ 1 ,Λ 2 Respectively expressed as:
wherein,
the diagonal matrix contains the amplitude error generated by each radio frequency link of the base station;
the diagonal matrix contains the phase error generated by each radio frequency link of the base station.
Meanwhile, at the base station transmitter, additive distortion noise d is generated due to the nonlinearity of the high power amplifier, the band pass filter T ～CN(0,C T )，C T For the variance of the additive distortion noise,
a variance of distortion noise at each antenna of the base station; the signal actually transmitted by the base station is x' BS +d T 。
S2, decoding the signal transmitted by the base station by the information user to obtain the corresponding message;
in each channel coherence time, assuming that the channel state information of all channels is perfectly known by the base station, considering only the signal reflected once by the IRS due to significant path loss, ignoring the signal reflected twice or more; in addition to this, a quasi-static flat fading channel model is assumed for all channels.
Suppose that
Indicating base station to information user d j The base-band equivalent channel of (a),
for IRS to information user d j Is received in the base band equivalent channel.
Baseband equivalent trust for base station to IRSRoad, use
Make an expression, assume
Representing a reflection coefficient matrix at the IRS; wherein: beta is a n ∈(0,1]Is the reflection amplitude of the nth reflection element, theta n E 0,2 pi) is the phase shift of the nth reflection element.
In the present invention, to maximize signal reflection at the IRS, β is set n ＝1,n∈1…N L (ii) a Thus, information user d j The received signal at (a) is represented as:
in the case of the formula (6),
is the phase shift vector at the smart reflective surface;
additive white gaussian noise at the information user receiver.
Suppose that
Then
Definition of
The expansion equation of equation (6) is expressed as:
in the formula (7), the reaction mixture is,
represents from
To
The linear mapping of (a) to (b),
information user d j For decoding the desired information, the interference is regarded as noise, and the information user d j The achievable rate of (d) is expressed as:
wherein,
the achievable rate for the jth information user,
is represented by a symbol, has no practical meaning,
set of beamforming vectors for all information users, θ is the phase shift vector at IRS, I 2 Is a 2 x 2 unit matrix and is,
for augmented representation of the useful signal received at the jth information userIn the form of a sheet of paper,
a wide linear transformation of the beamforming vector for the jth information user,
for an augmented representation of the interference signal received at the jth information user,
for the variance of additive hardware distortion noise at each antenna of the base station,
for the combined channel from the base station to the jth information user,
is composed of
Of conjugated transpose form, σ 2 For variance of thermal noise of information user receiver, d l Is the information user of the I < th >.
And S3, under the condition of meeting the total power constraint of the base station, optimizing the beam forming vector of the base station and the phase shift vector at the IRS, and maximizing the minimum achievable rate of the information user.
The minimum achievable rate optimization problem of the maximized information user is expressed as:
in the optimization problem (P1), P is the total transmission power of the base station.
As can be seen from the equation (11), γ in the equation (10) represents the reachable rate of all information users
Minimum value of (i), i.e.
Constraint (12) represents the unity mode constraint of the phase shift matrix at the IRS.
The constraint (13) represents a total power constraint of the base station.
The constraint (14) represents a transmit power constraint for each user.
In constraint (11), the vector is beamformed due to the base station
And the reflected phase shift vector θ at IRS, and the optimization problem (P1) is non-convex and difficult to solve because the constraint (12) is a non-convex set.
The invention utilizes an alternative optimization algorithm to alternately optimize the beam forming loss of the base station
And a reflected phase shift vector θ at IRS.
S301, optimizing base station beam forming vector
Phase shift vector θ at fixed IRS, with respect toBase station beamforming vectors
Is expressed as
s.t.(13)(14) (16)
In the optimization problem (P1.1), the rate constraint (17) is non-convex. Therefore, the optimization problem (P1.1) is a non-convex optimization problem, and a path tracking algorithm is adopted to solve. In each iteration, the objective function value is raised. For the non-convex constraint (17), an inner convex approximation is performed on it, assuming
The feasible point found for the k-1 st time.
For a matrix of dimensions 2 × 2, according to inequality (18):
the concave upper bound of the non-convex constraint (17) is approximately:
at the k-th iteration, a feasible point is given
By solving the optimization problem (P1.2), the next feasible point of the problem (P1.1) is generated
Until the problem converges
S302, optimizing phase shift vector theta at IRS
Fixed base station beamforming vectors
The optimization of the IRS phase shift vector θ is represented as:
in the optimization problem (P1.3), the rate constraint (25) is non-convex, and the IRS phase shift constraint (26) is a non-convex constraint set, so that the optimization problem (P1.3) is a non-convex optimization problem and is difficult to solve. For the non-convex constraint set (26), the optimization problem (P1.3) is first transformed into a more tractable form using a negative mean square penalty.
Where η is the penalty coefficient, the problem (P1.4) is a tight scaling of the problem (P1.3) by adding a sufficiently large penalty term to the objective function. Also, in the optimization problem (P1.4), a constraint set
n∈1,…,N L Is a convex set.
The objective function is still non-concave because | | θ | | luminance 2 ≥||θ (n) || 2 +2<θ (n) ,θ-θ (n) >The objective function (27) is approximated as:
for the non-convex constraint (28) type, will
Substituting into the formula (7) to obtain:
equation (31) is a linear mapping with respect to IRS phase shift vector θ, similar to the base station beamforming vector
Is optimized assuming (theta) n ,γ (n) ) For the feasible point found at (n-1), the concave upper bound of the rate constraint (25) is approximated by the inequality (18):
at the nth iteration, a feasible point theta is given (n) Generating the next feasible point theta of the optimization problem (P1.4) by solving the optimization problem (P1.5) (n+1) Until the problem (P1.5) converges.
Obtaining a beam forming vector at the base station by an alternative optimization algorithm in each channel coherence time
The phase shift vector θ at the IRS, and the base station then sends the phase shift vector θ to the IRS controller via the control link, thereby controlling each reflection element at the IRS.
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. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be obtained by a person skilled in the art without inventive step based on the embodiments of the present invention, are within the scope of protection of the present invention.
Simulation verification
To evaluate the impact of asymmetric hardware distortion at the base station on the performance of the IRS assisted MISO system, we used the following simulation setup. Assuming that the system operates at a carrier frequency of 750MHz, the system bandwidth is 1MHz and the noise power spectral density is-150 dBm/Hz.
Referring to the simulation setup in FIG. 3, the base station is located on the x-axis with the coordinate (d) x 0, 0); the IRS is positioned on a y-z plane so as to establish a local hot spot cluster; cluster center is (d) x ,d y 0), cluster radius r 2.5 m. The reference element coordinate of IRS is (0, d) y ,0). The distance between adjacent reflecting elements being half a wavelength, i.e.
Setting N L ＝N y N z ，N y ,N z The numbers of the y-axis reflection elements and the z-axis reflection elements are respectively.
In this experiment, N y ＝5,N z 10; the path loss model is
Is a reference distance D 0 Where d denotes a link distance and α is a path loss exponent, 1 m. For the BS-IRS and BS-user links, a plane wave model is employed. Due to IRS small signalAnd (4) covering range, wherein a spherical wave model is adopted for the IRS-user link. This means that the distance between each reflection element of the IRS and the user is calculated separately from the three-dimensional coordinates.
The path loss index of the BS-IRS and IRS-user links is 2.2. the path loss index of the BS-user links is 3.8. for small scale fading, it is assumed that the BS-IRS, IRS-user, BS-user links obey the rayleigh fading channel model. The initial value of the phase shift vector theta at IRS is randomly selected from-180 DEG to 180 DEG, d x ＝3.5m,d y ＝8m，
It is assumed that information users are randomly distributed within an information cluster.
Referring to fig. 4, the maximum minimum achievable rates of four information users are increased according to the increase of the transmission power, and the maximum minimum achievable rates of the information users under the asymmetric gaussian signal transmission scheme (IGS) and the symmetric gaussian signal transmission scheme (PGS) are increased. Under the influence of asymmetric hardware distortion, compared with a PGS transmission scheme, the rate improvement of 0.5 bit is brought by adopting IGS for transmission without the assistance of IRS, because the IGS transmission scheme can eliminate the influence of asymmetric hardware distortion on the system performance, thereby improving the reachable rate of information users. Under the assistance of the IRS, the maximum and minimum achievable rates of the information users under the PGS transmission scheme are increased by about 1 bit, and meanwhile, the IRS-assisted IGS transmission scheme is significantly better than the IRS-assisted PGS transmission scheme, and the maximum and minimum achievable rates of the information users are significantly increased.
In summary, the IRS-assisted MISO system optimization design method for hardware distortion of the present invention considers that hardware distortion seriously degrades system performance in an actual wireless communication system. Hardware distortion at the base station includes amplitude errors and phase errors (I/Q imbalance) due to local oscillator and phase shifter mismatch in the mixer, additive hardware distortion noise due to non-linearities of the digital-to-analog converter, band-pass filter, high power amplifier. I/Q imbalance and additive hardware distortion noise are respectively modeled through an I/Q mismatch model and circularly symmetric complex Gaussian noise verified through experiments. Assuming that the base station transmits a circularly symmetric complex gaussian signal, under the influence of the above-mentioned hardware distortion, the signal actually transmitted by the base station is an asymmetric gaussian signal. As can be seen from the information theory, the information entropy is the maximum (corresponding to the information rate) only when the base station transmits a signal that is a circularly symmetric complex gaussian signal. The invention creatively uses a precompensation scheme, namely asymmetric Gaussian signals, to transmit, optimizes the statistical characteristics of the asymmetric Gaussian signals, and enables the signals actually sent by the base station to be circularly symmetric complex Gaussian signals after hardware distortion, thereby improving the reachable rate of information users. By deploying the IRS near the information user, the radio frequency signal from the base station is focused at the receiver of the information user, so that the strength of the received signal is improved, and the reachable rate of the information user is further improved. Meanwhile, fairness among users is considered, in each channel coherence time, a base station beam forming vector and an IRS phase shift vector are optimized alternately according to channel state information, and information transmission rate of poor users is improved as far as possible. The optimization framework proposed by the present invention is also applicable to the case where the phase shift of the reflection element at the IRS is a finite phase shift level.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (3)
1. An IRS-assisted MISO system performance optimization method for hardware distortion, comprising the steps of:
s1, the multi-antenna base station performs wide linear precoding on the messages of the M information users to generate baseband transmission signals, the baseband transmission signals are asymmetric Gaussian signals, the asymmetric Gaussian signals are converted into analog signals through a digital-to-analog converter, then the analog signals are up-converted to carrier frequencies through a mixer, and finally output signals are generated through a high-power amplifier; high-power amplifier is transmitted in broadcasting mode to multi-antenna base station with assistance of intelligent reflecting surfaceGenerating an output signal and controlling the phase shift of the reflecting element in real time by a controller on the intelligent reflecting surface, and providing the multi-antenna base station with N T An antenna at the transmitter of the base station, mixer I/Q imbalance causes the transmission signal to generate self-interference, and nonlinearity of the analog-to-digital converter, high-power amplifier, band-pass filter generates additive distortion noise d T ～CN(0,C T )，C T For the variance of the additive distortion noise,
for the variance of the additive distortion noise at each antenna,
is N T ×N T The identity matrix of (1); the actual transmission signal of the multi-antenna base station is x' BS +d T Equivalent baseband transmit signal x 'after I/Q imbalance' BS Expressed as:
wherein x is BS For the base-band transmission of signals by the base station,
for information beam forming vectors, d l As the information user of the l-th party,
is an information user d l The message of (a) is received,
is a diagonal matrix, containing amplitude distortion and rotation caused by mixer mismatchError, N T The number of the antennas is; lambda 1 ,Λ 2 Respectively expressed as:
wherein,
the diagonal matrix comprises amplitude errors generated by each radio frequency link of the base station;
the diagonal matrix contains the phase error generated by each radio frequency link of the base station;
s2, M information users receive the signals transmitted by the multi-antenna base station in the step S1, and the speed of the M information users is obtained through decoding;
s3, taking the speed of M information users obtained in the step S2 as performance evaluation, optimizing the beam forming vector of the base station and the phase shift vector at the intelligent reflection surface under the condition of meeting the total power constraint of the base station, maximizing the minimum reachable speed of the information users, completing performance optimization, and obtaining the beam forming vector at the multi-antenna base station through an alternating optimization algorithm in each channel coherence time
And a phase shift vector theta at the intelligent reflection surface, so that the minimum reachable rate of the M information users is maximized, and then the multi-antenna base station sends the phase shift vector theta to the intelligent reflection surface controller through a control link to control each reflection element at the intelligent reflection surface;
the minimum achievable rate optimization problem of the maximized information user is expressed as:
wherein,
a set of beamforming vectors for all information users, theta is the phase shift vector at IRS,
gamma denotes all information user achievable rate
Minimum value of (d);
unit mode constraint of phase shift matrix at intelligent reflective surface
Is represented as follows:
where N ∈ {1, … N L N is the index value of the reflection element of the intelligent reflection surface, N L The number of the reflection elements is;
optimizing multi-antenna base station beamforming vectors
The method comprises the following specific steps:
wherein,
for the k-th iteration
Approximation of concave lower bound of d j For the jth information user, k I For the set containing all information users, P is the total transmission power of the base station, information user d j Achievable rate of
Expressed as:
wherein,
for all information users, the set of beamforming vectors, θ is the phase shift vector at the intelligent reflecting surface, I 2 Is a 2 x 2 unit matrix and is,
an augmented representation of the received useful signal for the jth information user,
a wide linear transformation of the beamforming vector for the jth information user,
for the jth information user to receive an augmented representation of the signals transmitted by the multi-antenna base station to other users,
for the variance of additive hardware distortion noise at each transmit antenna of the base station,
for the combined channel from the base station to the jth information user,
is composed of
Conjugate transpose of (a) 2 For variance of thermal noise of information user receiver, d l The first information user;
the optimization of the reflection phase shift vector theta at the intelligent reflection surface is specifically as follows:
wherein, theta (n) Is the initial value of theta of the nth iteration, eta is a penalty factor, eta | | | theta (n) || 2 +2η<θ (n) ,θ-θ (n) >In the form of a negative mean square penalty term,
for the nth iteration
Is approximated by a concave lower bound.
2. The method according to claim 1, wherein in step S1, let
Is an information user d l Message, multi-antenna base station pair
Asymmetric Gaussian signal generated after wide linear precoding
The following were used:
wherein,
forming a vector for the information beam;
after wide linear precoding, the base station transmits signal x BS Comprises the following steps:
wherein d is l For the information user, k I Is a collection containing all information users.
3. The method according to claim 1, wherein in step S2, the rate of M information users obtained by decoding is specifically:
in each channel coherence time, the multi-antenna base station knows the channel state information of all channels, considers the signals reflected once by the intelligent reflection surface, and all the channels are quasi-static flat fading channel models;
indicating base station to information user d j The base-band equivalent channel of (a),
for intelligently reflecting surfaces to information users d j The baseband equivalent channel of (a); considering the signal reflected once by the intelligent reflecting surface, ignoring the signals reflected twice and many times
Representing the base band equivalent channel from the base station to the intelligent reflecting surface, the matrix of the reflection coefficient at the intelligent reflecting surface is
Is the reflection amplitude of the nth reflection element, theta n E [0,2 pi) is the phase shift of the nth reflection element; set up beta n ＝1,n∈1…N L Maximizing signal reflection at IRS, and spreading through wireless channel to obtain information user d j A received signal of
Using interference as noise, determining information user d j Achievable rate of
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