Disclosure of Invention
In view of this, the present invention provides a beamforming method for a MIMO heterogeneous wireless network considering hardware damage, which establishes a network model and optimizes the network model under the condition that the MIMO heterogeneous wireless network has hardware damage, improves robustness and adaptability of the heterogeneous wireless network, and reduces interruption probability of a user.
In order to achieve the purpose, the invention provides the following technical scheme:
a MIMO heterogeneous wireless network beam forming method considering hardware damage specifically comprises the following steps:
s1: using an imperfect hardware transmitter and a receiver in a downlink of a two-layer MIMO heterogeneous wireless network, analyzing hardware damage sources in a macro cellular network and a femtocell network, and establishing a downlink signal transmission model of a macro cellular user and a femtocell user with hardware damage;
s2: respectively modeling hardware damage of a macro cell base station transmitter, a macro cell user receiver, a femtocell base station transmitter and a femtocell user receiver;
s3: considering hardware damage at a base station transmitter and a user receiver, the maximum transmitting power constraint of each base station and the minimum signal-to-interference-and-noise ratio constraint of each user, and establishing a beam forming design problem of minimizing the total energy consumption of the system;
s4: and based on an equivalent transformation method and a semi-definite relaxation method, converting the problem established in the step S3 into a convex optimization problem and solving the convex optimization problem.
Further, in step S1, analyzing the sources of hardware damage in the macro cellular network and the femto cellular network includes: hardware impairments at the base station transmitter and the user receiver can be modeled as additive hardware impairment noise and amplified thermal noise;
establishing a downlink signal transmission model of the macro cell user with hardware damage, namely, a signal received by the mth macro cell user
Expressed as:
wherein the content of the first and second substances,
and
respectively representing a channel vector of the macrocell base station to the mth macrocell user and a channel vector of the nth femtocell base station to the mth macrocell user;
and s
mRespectively representing beamforming vectors and information of the macrocell base station to the mth macrocell user;
and s
n,kRespectively representing beamforming vectors and information of an nth femtocell base station to a kth femtocell user; wherein the content of the first and second substances,
N
Mindicating the total number of antennas, N, provided in the macrocell base station
FRepresenting the total number of antennas equipped by the femtocell base station,
respectively represent N
MX 1 dimension, N
FA complex column vector of
x 1 dimension;
and
additive hardware impairment noise for the macrocell base station transmitter, the nth femtocell base station transmitter and the mth macrocell user receiver,
means zero variance of mean at the mth macrocell user receiver
Amplified thermal noise.
Further, in step S1, a femtocell user downlink signal transmission model with hardware impairments is established, that is, in the nth femtocell network, the signal from the base station to the kth femtocell user receiver can be represented as:
wherein the content of the first and second substances,
and
respectively representing a channel vector of the nth femtocell base station to the kth femtocell user in the network and a channel vector of the macrocell base station to the kth femtocell user in the nth femtocell;
representing additive hardware impairment noise at a kth femtocell user receiver in an nth femtocell;
means that the mean value at the k-th femtocell user receiver in the n-th femtocell is zero variance
Amplified thermal noise.
Further, in step S2, additive hardware impairment noise at the macrocell base station transmitter, the femtocell base station transmitter, the macrocell user receiver, and the femtocell user receiver can be modeled as:
where ψ represents the covariance matrix of additive hardware impairment noise at the macrocell base station transmitter, Φ
nA covariance matrix representing additive hardware impairment noise at the nth femtocell transmitter,
represents the variance of additive hardware impairment noise at the mth macrocell user receiver,
representing the variance of additive hardware impairment noise at the kth femtocell user receiver in the nth femtocell.
Further, in step S3, the beamforming design problem that minimizes the total energy consumption of the system is constructed by:
wherein, C
1And C
2Representing maximum transmit power constraints, P, for the macrocell base station and the nth femtocell base station, respectively
maxAnd
representing maximum transmit power thresholds for the macrocell base station and the nth femtocell base station, respectively; c
3Represents a minimum signal-to-interference-and-noise ratio constraint for each femtocell user,
representing a minimum signal-to-interference-and-noise ratio threshold for a kth femtocell user in the nth femtocell; c
4Represents the minimum signal-to-interference-and-noise ratio constraint for the mth macrocell user,
a minimum signal-to-interference-and-noise ratio threshold representing an mth macrocell user; p
CRepresents the circuit power consumption of the macro cell and all femtocells, and ζ ≧ 1 represents the power amplification factor.
Further, in step S4, P1 is a non-convex optimization problem, and P1 is converted into a convex optimization problem by using an equivalent transformation method and a semi-definite relaxation method to solve, where the specific conversion step includes:
s41: definition of
Transforming the optimization problem P1 into an easily processable form;
s42: introducing an auxiliary matrix StAnd SlCovariance matrices psi and phi to process hardware impairment vectorsnIn which S istAnd SlRespectively representing the t-th diagonal element and the l-th diagonal element as 1, and the rest elements as 0;
s43: processing the constraint with the coupling variable by using an equivalent transformation method, and converting the non-convex optimization problem P1 into a convex optimization problem to solve; based on the interior point method, the optimal solution of the convex optimization problem can be obtained
And
by using eigenvalue decomposition method, the optimal beam forming vector can be obtained
And
the invention has the beneficial effects that: the invention considers the maximum transmitting power constraint of the macro cellular base station, the maximum transmitting power constraint of each femtocell base station, the minimum signal to interference and noise ratio constraint of the macro cellular user and the femtocell user, takes the total energy consumption of the system as an optimization target, and establishes a network model and optimizes the problem under the condition that the MIMO heterogeneous wireless network has hardware damage. And converting the original non-convex optimization problem into a convex optimization problem by using an equivalent transformation method and a semi-positive definite relaxation method, and solving an optimal solution by using an interior point method. Compared with the traditional ideal hardware algorithm, the method has the characteristics of low calculation complexity, low user interruption probability, high robustness and high adaptability.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Referring to fig. 1 to 4, the MIMO heterogeneous wireless network beamforming method considering hardware impairments, as shown in fig. 2, specifically includes the following steps:
s1: and under an ideal transceiver hardware state, establishing a downlink signal transmission model of a macro cellular user and a femtocell user of the two-layer MIMO heterogeneous wireless network.
The present invention considers a downlink transmission scenario of a multi-cellular multi-user MIMO heterogeneous wireless network, as shown in fig. 1. The network comprises a network provided with N
MRoot antenna macrocell base station and N devices equipped with N
FFemtocell base station with root antenna, where there are M single-antenna macrocell users in a macrocell network and K in each femtocell network
nA single antenna femtocell user. Wherein the macrocell base station and the femtocell base station transmit information to the macrocell user and the femtocell user, respectively, via a downlink. Definition of
And
respectively, a set of macro cell users, femto cell users, and femto cell numbers. The femtocell user is assumed to use the spectrum resource of the macrocell user in a underlay-type spectrum sharing mode, so that the total cross-layer interference of the femtocell user to any one macrocell user receiver is not more than a certain specific interference temperature threshold value, and the spectrum utilization rate and the throughput of the whole network are improved. The channel is assumed to be a block fading channel, i.e., the channel gain is a constant in the same time slot and varies in different time slots. According to the 3GPP context of heterogeneous wireless networks, since femtocells generally have lower transmit power than macrocells, indoor femtocells generally suffer strong wall penetration loss. Thus, as with most work, we assume that the mutual interference between different femtocells is negligible.
As can be seen from fig. 1, the reception of the signal from the macrocell base station by the mth macrocell user can be represented as:
wherein the content of the first and second substances,
and s
mRespectively, the beamforming vectors and information for the macrocell base station to the mth macrocell user.
And s
n,kRespectively, a beamforming vector and information for an nth femtocell base station to a kth femtocell user, wherein,
respectively represent N
MX 1 dimension, N
FComplex column vector of
x 1 dimension.
And
respectively representing the channel vectors of the macrocell base station to the mth macrocell user and the channel vectors of the nth femtocell base station to the mth macrocell user.
Means that the mean value at the mth macrocell user is zero and the variance is
White additive gaussian noise.
In the nth femtocell network, the signal from the base station to the kth femtocell user receiver can be expressed as:
wherein the content of the first and second substances,
and
respectively representing the channel vector from the nth femtocell base station to the kth femtocell user in the network and the channel vector from the macrocell base station to the kth femtocell user in the nth femtocellA track vector.
Means that the mean value at the k-th femtocell user in the n-th femtocell is zero and the variance is
White additive gaussian noise.
S2: and using an imperfect hardware transmitter and a receiver in the two-layer MIMO heterogeneous wireless network, analyzing hardware damage sources in the macro cellular network and the femtocell network, and establishing downlink signal transmission models of the macro cellular user and the femtocell user again.
In practical systems, both the base station and the user equipment may be affected by hardware impairments of different degrees, causing distortion of the desired signal. Residual hardware impairment errors distort the desired signal, resulting in a large gap between the theoretical received signal and the actual received signal. To more truly describe the physical signal, the sources of hardware impairments in the macrocellular and femtocellular networks are analyzed, and the hardware impairments at the base station transmitter and the user receiver can be modeled as additive hardware impairment noise and amplified thermal noise. The reception of a signal from a macrocell base station by an mth macrocell user can be represented as:
wherein the content of the first and second substances,
and r
mAdditive hardware impairment noise for the macrocell base station transmitter, the nth femtocell base station transmitter and the mth macrocell user receiver,
means zero variance of mean at the mth macrocell user receiver
Amplified thermal noise. According to equation (3), the mth macrocell user receives a signal-to-interference-and-noise ratio of
Wherein the content of the first and second substances,
analyzing the source of hardware impairments in a femtocell network, in an nth femtocell network, the signal from the base station to a kth femtocell user receiver can be represented as:
wherein the content of the first and second substances,
representing additive hardware impairment noise at the kth femtocell user receiver in the nth femtocell.
Means that the mean value at the k-th femtocell user receiver in the n-th femtocell is zero and the variance is
Amplified thermal noise. According to equation (5), in the n femtocell networks, the signal-to-interference-and-noise ratio received by the kth femtocell user is:
wherein the content of the first and second substances,
s3: hardware impairments of the macrocell base station transmitter, the macrocell user receiver, the femtocell base station transmitter and the femtocell user receiver are modeled separately.
In general, the impact of hardware impairments can be partially mitigated by transmitter correction schemes or receiver compensation algorithms, but there can still be some residual hardware impairments at the transmitter and receiver. We model this portion of residual hardware impairments as additive hardware impairment noise, which describes the combined effect of various residual hardware impairments. In addition, additive hardware impairment noise can be modeled as a gaussian distributed random process. Thus, additive hardware impairment noise at a macrocell base station transmitter, a femtocell base station transmitter, a macrocell user receiver, and a femtocell user receiver can be modeled as
Where ψ represents the covariance matrix of additive hardware impairment noise at the macrocell base station transmitter, Φ
nA covariance matrix representing additive hardware impairment noise at the nth femtocell transmitter,
represents the variance of additive hardware impairment noise at the mth macrocell user receiver,
representing the variance of additive hardware impairment noise at the kth femtocell user receiver in the nth femtocell. Definition of
Is provided with
Wherein the content of the first and second substances,
and
the degree of transmitter and receiver hardware impairment is described separately and is numerically expressed as the ratio of the variance of additive hardware impairment noise to the signal power. In practice, these parameters can be obtained by error vector magnitude measurements. In addition to this, the present invention is,
and
covariance matrix P of signal vector transmitted by macrocell base station and covariance matrix Q of signal vector transmitted by nth femtocell base station
nThe main diagonal element of (1). Comprises the following steps:
s4: and (3) considering hardware damage at a base station transmitter and a user receiver, the maximum transmission power constraint of each base station and the minimum signal-to-interference-and-noise ratio constraint of each user, and establishing a beam forming design problem of minimizing the total energy consumption of the system.
Considering the constraints of the maximum transmission power of the macrocell base station and each femtocell base station, the constraint of the quality of service of each macrocell user and the constraint of the minimum signal-to-interference-and-noise ratio of each femtocell user, the beamforming design problem of minimizing the total energy consumption of the constructed system can be expressed as
Wherein, C
1And C
2Representing maximum transmit power constraints, P, for the macrocell base station and the nth femtocell base station, respectively
maxAnd
representing maximum transmit power thresholds for the macrocell base station and the nth femtocell base station, respectively; c
3Represents a minimum signal-to-interference-and-noise ratio constraint for each femtocell user,
representing a minimum signal-to-interference-and-noise ratio threshold for a kth femtocell user in the nth femtocell; c
4Represents the minimum signal-to-interference-and-noise ratio constraint for the mth macrocell user,
representing the minimum signal to interference plus noise ratio threshold for the mth macrocell user. P
CRepresents the circuit power consumption of the macro cell and all femtocells, and ζ ≧ 1 represents the power amplification factor.
S5: and based on an equivalent transformation method and a semi-definite relaxation method, converting the original non-convex optimization problem established in the step S4 into a convex optimization problem and solving the convex optimization problem.
P1 is a non-convex optimization problem, and the P1 is converted into a convex optimization problem by an equivalent transformation method and a semi-definite relaxation method for solving. The specific conversion steps include:
s51: definition of
Is provided with
According to equations (14) and (15), the optimization problem P1 can be transformed into:
s52: introducing an auxiliary matrix StAnd SlCovariance matrices psi and phi to process hardware impairment vectorsnIn which S istAnd SlRespectively, the t-th diagonal element and the l-th diagonal element are 1, and the rest elements are all 0. The optimization problem P2 can be converted into:
wherein the content of the first and second substances,
s53: processing constraints with coupling variables by using equivalent transformation method
And
in addition, rank-one constraint C is discarded based on a semi-positive definite relaxation method
6The original non-convex optimization problem can be transformed into a convex optimization problem. The optimization problem P3 can be converted into:
based on the interior point method, the optimal solution of the convex optimization problem can be obtained
And
by using eigenvalue decomposition method, the optimal beam forming vector can be obtained
And
otherwise, an approximate solution can be obtained using gaussian randomness.
The application effect of the present invention will be described in detail with reference to the simulation.
1) Simulation conditions
Suppose there is one macro-cellular network, two femto-cellular networks, two macro-cellular users in the macro-cellular network, and two femto-cellular users in each femto-cellular network. The coverage radii of the macro network and each femtocell network are 500 m and 20 m respectively, with a minimum distance of 40 m between different femtocells. Assume that the number of femtocells and macrocells antennas is 4. The channel fading model is assumed to contain large-scale fading and small-scale fading. Large scale fading is modeled as D ═ A
0(d/d
0)
-αWherein A is
01, d denotes the distance between the transmitter and the receiver, reference distance d
020 m, and α -3 denotes the path loss exponent.The small scale fading coefficients follow a gaussian distribution with a mean of 0 and a variance of 1. Without loss of generality, it is assumed that the noise variance at all transceivers is equal, i.e.,
in addition, suppose
Different hardware damage levels are in the interval [0,0.3 ]]An internal variation. Assume that the conventional algorithm is an ideal transceiver, i.e., κ
t=κ
rOther parameters are given in table 1, 0.
TABLE 1 simulation parameters Table
2) Simulation result
In the present embodiment, fig. 3 shows the relationship between the total energy consumption of the system and the minimum sir threshold of the user. Figure 4 shows the average outage probability of a macrocell user versus a minimum signal to interference plus noise ratio threshold. As can be seen from fig. 3, the total energy consumption of the system increases as the user signal to interference plus noise ratio threshold increases. As the sir threshold of the user increases, the base station needs to allocate higher power for information transmission to meet the user minimum sir requirement, resulting in an increase in the total energy consumption of the system. On the other hand, under the same signal-to-interference-and-noise ratio threshold condition, the total energy consumption of the system of the algorithm is higher than that of the traditional algorithm. Since the conventional algorithm does not take into account the impact of hardware impairments on the transceiver. In order to reduce the occurrence of communication interruption events, the base station allocates higher power to overcome the influence of hardware damage parameters on the signal-to-interference-and-noise ratio of the user, and prevents the user from generating harmful interruption. Fig. 4 shows that as the minimum signal to interference plus noise ratio threshold of a macrocell user increases, the average outage probability for the macrocell user gradually increases. The reason for this is that the larger the minimum signal to interference plus noise ratio threshold is, the more difficult it is to satisfy the signal to interference plus noise ratio constraint of the macro cell user, so that the outage probability of the macro cell user increases. On the other hand, the average outage probability is reduced by about 8.1% for the inventive algorithm compared to the conventional algorithm. This is because the algorithm herein greatly reduces the probability of interruption by allocating higher power to the user in order to overcome the adverse effects of hardware damage, but the total system power consumption increases. In addition, in the algorithm, when the hardware damage parameter is increased, the system considers larger hardware damage and has stronger hardware damage resistance. When the transceiver has more serious hardware damage, the system can still ensure the communication quality of the user without communication interruption.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.