CN112566159B - Enhanced small cell downlink communication method based on MIMO-NOMA - Google Patents
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Abstract
The invention discloses an enhanced small cell downlink communication method based on MIMO-NOMA, which comprises the following steps: firstly, acquiring relevant initialization parameters such as a base station, an NOMA user and an NOMA pairing strategy and statistical state information of a channel; then, designing a receiving linear filter of a NOMA near-far user by utilizing an interference alignment technology; then determining a precoding matrix of the base station end; finally, the transmission rates of all NOMA users are optimally designed by maximizing the long-term average throughput given a maximum tolerable outage probability. Compared with the existing methods such as pre-coding MIMO-OMA, non-pre-coding MIMO-OMA and non-pre-coding MIMO-NOMA, the method provided by the invention can effectively improve the throughput, and particularly has better performance when the channel difference of NOMA user pairs is more remarkable.
Description
Technical Field
The invention relates to the technical field of wireless communication, in particular to an enhanced small cell downlink communication method based on MIMO-NOMA.
Background
With the proliferation of wireless data traffic and the number of mobile devices, 5G cellular networks are increasingly required to provide higher spectral efficiency and more connection volume. By the time of 2023, 5G speed is expected to increase by about 13 times over the average mobile connection speed of 2018, as predicted by the cisco Visual Network Index (VNI), while the number of mobile devices is expected to grow from 88 to 131 billions. To address these unprecedented challenges, small cell communication technology is considered one of the most promising solutions in 5G, which can provide greater network capacity to meet the traffic demands of a large number of users. However, excessive frequency reuse is caused by ultra-dense small cell communication, thereby causing severe co-channel interference. To solve this problem, applying non-orthogonal multiple access (NOMA) technology to small cell communication is a very promising solution. Specifically, the small cell communication is enhanced by using a multiple-input multiple-output (MIMO) assisted NOMA technology, the spectrum efficiency is obviously improved through reasonable beam forming, a receiving filter and power distribution optimization design, and meanwhile, the communication reliability requirement is ensured.
To support access to more users, the small cell communication technology in the 5G system significantly increases the system capacity by a more frequent frequency reuse technology. However, excessive frequency reuse also introduces strong co-channel interference, which poses a great challenge to large-scale communication system design. In order to further improve the capacity of the small cell system, a mode of combining MIMO with NOMA is urgently needed to further enhance the communication performance of the small cell. However, in an actual communication system, the channel state information is difficult to be perfectly estimated, and estimation errors inevitably exist. Therefore, in an actual communication system, a communication system design problem under an imperfect channel state information condition should be considered.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides an enhanced small cell downlink communication method based on MIMO-NOMA, which remarkably improves the spectrum efficiency through reasonable beam forming, a receiving filter and a power distribution optimization design scheme and simultaneously ensures the communication reliability requirement.
The purpose of the invention can be achieved by adopting the following technical scheme:
an enhanced small cell downlink communication method based on MIMO-NOMA comprises the following implementation steps:
s1, initializing system parameters, determining the number M of base station antennas and the number N of user antennas, wherein the transmitting power of each transmitting antenna is P, K user pairs of non-orthogonal multiple access (NOMA), and a channel statistical state information set obtained through measurement
Wherein,
is the known channel state, R, from base station z to near end user k rk Receiving covariance matrix, R, representing channel estimation error tk A transmit covariance matrix representing the channel estimation error,
is base station z to remote user
Is known to be in the channel state of the channel,
a receive covariance matrix representing channel estimation errors,
transmit covariance matrix representing channel estimation error, d k Being the distance from base station z to user k,
for base station z to user
A denotes a path loss exponent, σ 2 Is the variance, σ, of additive white Gaussian noise h 2 To measure the variance of the error, p I Representing the average power of the interference, λ b For the deployment density of the base station, k is equal to [1, K ]]；
S2, through the following equation
Determining the reception filters u of the users k separately k And the user
Of the receiving filter
Wherein the vector
And satisfy | z k | 2 ＝1，
By a matrix
The (2N-K) right singular vectors corresponding to the zero singular value of the matrix
Selecting a matrix for the antenna and satisfying L H L＝I K Wherein (·) H Representing a matrix conjugate operation, I K Is a K-order identity matrix;
s3, determining a precoding matrix V = LG of a base station end -H D, where the matrix G = (G) 1 ,…,g K ) And the column vector composed in the matrix G consists of
Given, diagonal matrix
Symbol (·) -H Representing the matrix conjugate inversion operation, sign
For root operation, symbol (·) m,n Is the element corresponding to the mth row and the nth column of the matrix;
s4, solving the optimal transmission rate of all NOMA users through the following optimization problem
Wherein R is k And with
A near end user k and a far end user respectively
The rate of transmission of the information of (c),
and
a near end user k and a far end user respectively
Given statistical channel state information conditions
Probability of interruption of k 2 Epsilon represents the maximum allowable outage probability for the power allocation factor for the information transmitted to the near-end user k.
Further, the vector z in step S2 k The antenna selection matrix L is determined by the following procedure:
s201, structure z k Wherein each candidate vector in the set has only one element of 1 and the other elements are 0; similarly, a candidate value set of the antenna selection matrix L is constructed, wherein each column of each candidate matrix only contains exactly one 1 element, each row contains at most one 1 element, and all other places are 0;
s202, according to the vector z k Determining the effective channel for each pair of users in combination with the candidate values of the antenna selection matrix LGain gamma k ＝1/(G -1 G -H ) k,k ；
S203, finding out the minimum effective channel gain, namely gamma min,i ＝min{γ 1 ,…,γ K I is antenna z k A sequence number combined with the L candidate value;
s204, finding out the combination serial number i which maximizes the minimum effective channel gain, namely
Thereby determining z k And L in reasonable combination.
Further, the non-convex optimization problem in step S4 is solved by an optimization tool including continuous convex optimization or an interior point method.
Further, the step S4 selects to obtain the correlation between successive NOMA decoding
The upper bound of (2) not only simplifies the solution of the optimization problem, but also can carry out robust design on the communication system.
Compared with the prior art, the invention has the following advantages and effects:
1. the invention fully considers the influence of the uncertainty of the channel and the randomness of the position of the same-frequency interference source on the optimization design of the system;
2. substituting the approximate expression of the interruption probability into the optimization problem can greatly simplify the design of the optimization scheme;
3. compared with the precoding MIMO-orthogonal multiple access technology (OMA), the non-precoding MIMO-OMA and the non-precoding MIMO-NOMA scheme, the optimization scheme provided by the invention can bring remarkable throughput improvement.
Drawings
Fig. 1 is a flowchart of an implementation of a MIMO-NOMA enhanced small cell downlink communication method disclosed in the present invention;
FIG. 2 is a graph of conditional outage probability versus channel K factor;
fig. 3 is a graph comparing throughput performance of the proposed technique with other reference techniques.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
Examples
The embodiment specifically introduces an implementation process of an enhanced small cell downlink communication method based on MIMO-NOMA from four aspects of a system model, interruption probability analysis, interruption probability and optimal system design.
1. System model
Considering an enhanced small cell network based on multiple-input multiple-output (MIMO) -non-orthogonal multiple access (NOMA) techniques under imperfect channel state information conditions, it is first assumed that the location of the small cell base station obeys the poisson point process and the distribution density is λ b . Each user is associated with its closest base station, and the base station and the users are equipped with M and N antennas, respectively. Further, assume that there are at least 2K users in a typical Voronoi cell and that K ≦ min { M, N }. In general, NOMA users are evenly distributed within a Voronoi cell, the distance between a user and an associated base station is approximately subject to a rayleigh distribution, and its probability density function is
Wherein the parameter c =5/4.
A. Signal transmission model
According to the MIMO-NOMA transmission scheme, the signal vector transmitted by the base station z can be expressed as
Wherein s is k 、
Signals representing the near end user and far end user of the k-th pair, and assuming that they have unity average power, i.e. power
β k 、
Represents the power distribution coefficient of the corresponding user and
user k (or)
) The received signal at (A) can be expressed as
Wherein o is k Representing the position of user k, P represents the transmit power of one data stream,
a matrix representing the channel response from base station x to user k, V = (V) 1 ,…,v K ) Is a normalized M × K precoding matrix, i.e., K =1, \8230, K, and satisfies | | v k | | =1. Because the interference source x belongs to phi b The channel state information with user k is usually unknown, so the co-channel interference is modeled by a classical shot noise model. Further, l (x) = x -α Denotes the path loss, alpha denotes the path loss exponent, w x Indicating the normalized signal, p, transmitted by the interferer I Representing the average power of the interference, n k Representing the variance σ 2 I M Is prepared fromAdditive white gaussian noise.
B. Imperfect channel state information model
It is assumed that only partial channel state information is available at the transmitter and receiver, thus H zk Can be constructed as
Wherein,
is the known channel state of base station z to user k, and E zk Is the channel estimation error. In addition, the error E is estimated zk A common error model, kronecker correlation model, is used, so the channel uncertainty matrix E zk Is given by
E zk ＝R rk 1/2 E w R tk 1/2 (5)
Wherein, vec (E) w )～CN(0,σ h 2 I) .1. The It is worth noting that there is a correlation between the elements of the error matrix due to the structure of the transmit and receive antennas. Thus, E zk Is a circularly symmetric complex Gaussian random matrix, i.e.
It is assumed that base station z and user k know partial channel state information
R tk And R rk . In order to characterize the quality of the channel state information, a channel K factor is introduced
Wherein,
representing the power ratio of the known channel portion to the unknown channel portion, by which the quality of the channel state information can be quantified. In addition, similar definitions apply equally to imperfect channel state information associated with user k.
C. Received signal-to-noise ratio
At the receiving end, the superimposed signal is continuously decoded according to the descending order of the link distance. In particular, for near users k, by applying the receiver filter u k To detect a desired data stream k, which may be expressed in mathematical form as
Wherein, | | z-o k ||＝d k . Based on NOMA decoding principle, successive Interference Cancellation (SIC) technique is used to cancel users
Is given by the following equation
Wherein,
I k is the co-channel interference power received by user k and may be expressed specifically as
By subtracting messages
Decoding self-message s by near-end user k Can be expressed as
In a similar manner, the remote user
SINR to decode the self information can be written as
Wherein,
and is provided with
Finger application to a user
The detection filter of (1) is set,
interference term
Is shown as
2. Outage probability analysis
Since the outage probability is a key performance index, the outage probability analysis needs to be performed for the MIMO-NOMA enhanced small cell communication technology under the imperfect channel condition. The users can be deduced respectively by the following steps
And the outage probability of k.
A. Remote user
Probability of interruption of
1) Conditional outage probability: when the channel capacity is less than the preset transmission rate
Then the remote user
An interrupt event occurs. Given a set of statistical channel state information
Wherein,
indicating channel state information at a given statistic
The probability of success under the conditions of (a). Therefore, there is a need to continue the derivation
Can be obtained by using (11)
Wherein,
then, by using the equation
Can be simplified into
Wherein,
as is clear from the equation (15), to ensure
The transmission rate should satisfy the condition
It is clear that,
is a circularly symmetric Gaussian random vector with a mean of zero and a covariance matrix of
Namely that
Applying the inverse Laplace transform to (15) can result in
Wherein the last step derives an inverse Laplace transform using a step function, i.e.
u (x) represents a unit step function,
represent
The joint probability density function of (a). Due to the fact that
Is a joint probability density function of
Therefore (16) can be further rewritten as
By using quadratic form and formula, the internal integral in (17) can be calculated as
In addition, by using
The expectation term in (17) can be derived as
Wherein,
therefore, by substituting (18) and (19) into (17), it is possible to obtain
Decomposition with eigenvalues
(20) Simplified to
Wherein,
to calculate expression (21), a numerical calculation method of inverse laplace transform may be applied. More specifically, by using the Abate-Whitt method, (21) can be approximated with any small discrete error
Wherein M represents the quantity of Euler summation terms, Q represents truncation sequence, and discretization error is within e -A /(1-e -A ) And the truncation error can be controlled by appropriate selection of M and Q. For example, if the dispersion error is limited to a maximum of 10 -10 A may be set to a ≈ 23. Further, M =11 and Q =15 are typically selected. By substituting (22) into (13), the conditional interruption probability can be derived
The final expression of (2).
2) Average outage probability: in addition, by finding the distance
Expected value of, user
Can be expressed as
Wherein,
and is provided with
Also, by calling the Abate-Whitt method, obtained
Is composed of
It is noted that the user pairing strategy directly determines
Distribution of (2). Under the condition of different grouping strategies, the grouping strategy is different,
there are different forms. In view of this, the average outage probability is next analyzed by looking at two different grouping strategies, specifically a random grouping strategy and a distance-based grouping strategy.
Theorem 1: regarding the random NOMA grouping strategy, 2K users are randomly grouped into K pairs. Under the strategy of such a grouping, it is,
can be obtained by some algebraic operations
Wherein,
representing the Fox-H function. Furthermore, in case of interference limitation, i.e. σ 2 The result of the process is simplified to
And (3) proving that: since the distance between a user and its associated base station follows a Rayleigh distribution, as shown in (1), it can be obtained by using the following order statistics
Probability density function of
Wherein,
is the cumulative distribution function corresponding to d. Based on the result of (28),
can be obtained by some algebraic operations
By using the Barcela property of the Mellin transform, (29) can be expressed using the Fox-H function.
Theorem 2: for the distance-based NOMA grouping strategy, it is assumed that the 2K users are sorted in ascending order according to their distance from the associated base station. Order to
Representing a user
The order of (a). Under such a grouping strategy, it is possible to deduce
Is specifically expressed as
In the case of interference limitation, i.e. σ 2 /P → 0, can be derived
And (3) proving that: by using the order statistics, it is possible to,
can be expressed as
Then, substituting (32) into the desired expression can be deduced (30).
According to the two theories, since
And λ b Uncorrelated, so average outage probability
Independent of the base station strength in the interference limited regime. This is due to λ b The effect of (c) is a twofold fact. In one aspect, λ b This increase in (c) results in severe co-channel interference and ultimately a high outage probability. On the other hand, the size of a Voronoi cell varies with λ b Is reduced, thus resulting in attenuation of path loss.
According to the two theorems, because
And λ b Uncorrelated, and therefore average outage probability under interference limited conditions
Independent of the base station distribution density. This is due to λ b The effect of (2) is twofold. In one aspect, λ b This increase in the number of bits results in severe co-channel interference and ultimately in a high outage probability. On the other hand, the size of a Voronoi cell varies with λ b And thus a reduction in path loss.
B. Probability of outage near user k
1) Conditional outage probability: by successive interference cancellation techniques, at a given point
Is given by the following equation
It is clear that, due to the co-channel interference and channel uncertainty involved,
and SINR k Has strong correlation. The presence of such spatial correlation presents a significant challenge to the analysis of incoming interrupts. By using (8) and (10), the compound (I) can be prepared
Is rewritten as
Wherein,
χ i ＝u k H E zk v i ,
and is
Also, χ = (χ) is easily demonstrated 1 ,…,χ K ) T ＝(u k H E zk V) T Is a circularly symmetric Gaussian random vector with zero mean and covariance matrix
Namely χ -CN (0, Σ). With the definition of a step-wise unit function,
can be expressed as
Wherein f is χ (x) Represents x and f χ (x)＝exp(-x H Σ -1 x)/(π K det (Σ)). Similar to the derivation of equation (16), by using the inverse laplace transform of a step unit function,
can be further written as follows
Wherein,
regarding the desired term in the formula (36), the following can be derived similarly to the formula (19)
Wherein,
in addition, to obtain
A specific expression of (d), defined as the following vector μ = (μ) 1 ,…,μ K ) T ，
Therefore, the temperature of the molten metal is controlled,
can be rewritten as
Can be obtained by using quadratic sum
(x+μ) H A(x+μ)+x H (B+Σ -1 )x＝(x+ν) H Ξ(x+ν)+φ(s,t) (42)
Wherein xi = A + B + Σ -1 ＝(s+t)I+Σ -1 ，ν＝Ξ -1 A mu and
φ(s,t)＝μ H Aμ-μ H AΞ -1 Aμ＝μ H AΞ -1 (B+Σ -1 )μ (43)
substitution of (42) into (41) can give
By substituting (38) and (44) into (36), it can be deduced that
Further, by decomposing Σ = Ψ Δ Ψ using eigenvalues H And defines Ψ = (Ψ) 1 ,…,ψ K ) And Δ = diag (δ) 1 ,…,δ K ) Phi (s, t) can be simplified in (45) to
Therefore, the temperature of the molten metal is controlled,
can be written as a double complex integral
The two-dimensional inverse laplace transform can be numerically calculated by means of the Moorthy (Moorthy) algorithm. More specifically, the present invention is described in detail,
by using the trapezoidal integration rule to approximate:
wherein the parameter T determines the sampling period, L is the truncation order,
discretization error E r By setting c appropriately i To control, i.e. c 2 ＝-1/(2T)ln((E r -a)/(1-ξ)),
According to Moorthy's algorithm, (48) can be approximated by truncating an infinite series, such as l i ∈[0,L]. The experiment shows that the content of the active carbon,
furthermore, applying the Epsilon algorithm can infer residuals in order to speed up convergence and improve accuracy. Specifically, portion 2P +1 is used for the Epsilon algorithm, and experiments show that setting parameter P =2 is appropriate.
Thereafter, by substituting (47) into (33), we can get the conditional outage probability
2)
Approximate expression of (c): the two-dimensional value inversion of the laplace transform requires a considerable computational cost, which imposes a large burden on the real-time optimization system design. Next, the present invention provides a method
To solve this computational difficulty. By ignoring
And SINR k The correlation between (33) can be approximately written as
Similar to the previous analysis, it can be deduced
And
the expression (c). Specifically, by introducing two vectors:
ν 1 ＝(μ 1 ,…,μ k-1 ,β k 2 μ k ,μ k+1 ,…,μ K ) T v and v 2 ＝(μ 1 ,…,μ k-1 ,0,μ k+1 ,…,μ K ) T ，
And
can be respectively simplified into
Wherein the derivation process of (52) is similar to (15). Obviously, (52) and (53) can be calculated similarly to (22), and will be (22)
Respectively replaced by
And (theta) k ,ν 2 ,Σ,ω k ,d k ). Furthermore, it is worth emphasizing that the approximate expression provided (51) underestimates the interruption performance, since the approximation process ignores the positive correlation between successful events of decoding the far-end user message and its own message. FIG. 2 confirms thisAn assertion. Thus, (51) effectively acts as p k|H The upper limit of (2). Thus with (51) a robust optimized design of the system can be achieved.
3) Average outage probability: furthermore, the average probability of interruption is determined by the distance d k If desired, is given by
Wherein,
can be given by the following equation
Wherein,
and
by using Moorthy algorithm, p k Can be deduced as
Wherein,
similar to theorems 1 and 2,
the specific expressions can also be derived separately by considering two different grouping strategies, random and distance-based.
Theorem 3: under the random NOMA grouping strategy,
is given by
In the interference-limited range, i.e. sigma 2 /P→ 0,
Can be simplified as follows:
and (3) proving that: similar to (28), d k Is given by
By using (59), the (57) can be obtained accordingly.
Theorem 4: under the distance-based NOMA grouping strategy, similar to (30), by using k respectively,
r k and (s + t) direct substitution
And s, can obtain
The expression (c). Under interference limited conditions, i.e. sigma 2 /P→ 0，
Can be further simplified into
Wherein r is k Represents the rank of user k and
obviously, due to
And λ b Independent, therefore average outage probability p k Is not influenced by the distribution density of the base stations.
And (3) proving that: the attestation process is similar to the attestation method of theorem 2.
3. Probability of interruption
The precise expression of the probability of interruption is too complex to reach valuable conclusions. Special cases are considered here, i.e. when the channel state information quality is investigated to improve, i.e. when
Or
Time, asymptotic behavior of the outage probability. For ease of analysis, the following analysis assumes the case of no inter-cell interference, i.e. λ b =0. Next, an upper bound on the probability of interruption is provided by the chernoff bound.
1) Remote user
Asymptotic outage probability of
If λ b =0, user
Is a conditional interruption probability of
By using the Cherenov community, the method can be used,
has an upper bound of
Wherein,
by using
And (18) formula (62) can be rewritten as
Wherein,
in order to avoid
To pair
Is defined herein
Wherein
Is that
The characteristic value of (2). Also, in the same manner as above,
is that
The characteristic value of (2). Therefore, (63) can be expressed as
Wherein,
from (64), it can be found
Asymptotic nature.
can guarantee the interrupt probability
The attenuation is zero.
Prove that when
When, the right side of the inequality (64) is only at
It approaches zero. By using
Definition of, setting up
Generating
The upper bound of (c).
2) Asymptotic outage probability for near-end user k
As can be seen from (32), in this example,
the upper limit of (A) can be obtained by the inclusion-exclusion principle
By setting lambda b =0 and defines v 1 ＝(μ 1 ,…,μ k-1 ,β k 2 μ k ,μ k+1 ,…,μ K ) T ,ν 2 ＝(μ 1 ,…,μ k-1 ,0,μ k+1 ,…,μ K ) T Can rewrite (66) to
Wherein the first term on the right side of the inequality is derived by analogy with equation (15). Further, applying the Cherenov boundary to (67) would result in (62) and (63) being similar
Wherein s ∈ (0,min coarse 1/δ i ,i∈[1,K]})。
Similarly to (64), define { upsilon 1 ,…,υ K Is a matrix u k H R rk u k (V H R tk V) T The characteristic value of (2). Therefore, we have
Wherein delta i Is the characteristic value of Σ. (67) Can be rewritten as
Wherein,
obtaining based on the formula (69)
The asymptotic nature of (a).
Theorem 6: when the channel uncertainty disappears, i.e.
Or
Only if the target transmission rate satisfies the following two conditions,
probability of interruption p k|H Can follow
The increase in (c) converges to zero.
And (3) proving that: when in use
The right expression of inequality (69) is only in
And is
It will approach zero. By using
And theta k By setting
Can obtain
And R k The upper bound of (c).
4. Optimal system design
By reasonably configuring parameters of the MIMO-NOMA enhanced small cell communication system to adapt to imperfect fading channels and ensure service quality, the designed system parameter configuration comprises a precoding matrix (namely V), a receiving filter (namely u) k ,
k∈[1,K]) Power distribution coefficient (i.e. beta) k ，
k∈[1,K]) Transmission rate (i.e. R) k ，
k∈[1,K]). For example, the goal is to maximize long-term throughput, i.e., average the number of information bits transmitted per successful transmission.
Indicating the known channel state information, the conditional throughput of a MIMO-NOMA system can be expressed as
Based on this, here maximizing the long-term average throughput and guaranteeing low outage probability, the optimization problem can be constructed
Where ε represents the maximum allowable outage probability. Furthermore, it is worth noting that, in order not to violate the intent of the NOMA principle, there is no joint optimization of the power allocation coefficient β in the above equation k And transmission rate (R) k And with
) This is because if user fairness is ignored, β k And R k &
The joint optimization of (a) will behave like a water-filling algorithm, i.e. all power will be allocated to users with good channel conditions, while no information bits will be transmitted to users with poor channel conditions. For this reason, in the subsequent optimization design, the power distribution coefficient will be fixed to ensure user fairness.
Unfortunately, due to the complex outage probability expressions, it is virtually impossible to get a globally optimal solution of (73). To solve this problem, the concept of interference alignment is used to select a suitable low implementation complexity V, u k And
in particular, in order to sufficiently suppress mutual interference between pairs of NOMA users, it is necessary to impose constraints
Where i ≠ k. Based on this, can obtain
To apply interference alignment, the following decomposition V = LP is applied here, where
L H L＝I K And is
In a sense, L serves to select K out of M transmit antennas. Therefore, the optimum L is obtained by an exhaustive method. In addition, by definition
And
can obtain
Wherein P = (P) 1 ,…,p K ). To ensure p i Is that interference alignment is performed
This ensures u k And
both are present. u. of k And
can be rewritten as
Wherein,
by a matrix
The zero singular value of (2N-K) right singular vectors,
and | z k | 2 =1.P is represented by P = G -H D is given, where G = (G) 1 ,…,g K ) And
ensure | | | v k ||＝||p k | | =1. Thus, V can be expressed as
V＝LG -H D (76)
At the moment of deciding V, u k And
(73) Can be written as
Obviously, (77) can be further decoupled into K independent sub-problems, i.e.
As shown in fig. 3, it can be verified that the optimization scheme proposed by the present invention is significantly superior to other existing small cell communication schemes, wherein existing reference schemes include precoded MIMO-orthogonal multiple access technology (OMA), non-precoded MIMO-OMA, and non-precoded MIMO-NOMA schemes. By contrast, the optimization scheme provided by the invention can bring about remarkable throughput improvement, especially under the condition that the channel gains are remarkably different.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (4)
1. An enhanced small cell downlink communication method based on MIMO-NOMA is characterized in that the method comprises the following implementation steps:
s1, initializing system parameters, determining the number M of base station antennas and the number N of user antennas, wherein the transmitting power of each transmitting antenna is P, K user pairs accessed by non-orthogonal multiple access, and a channel statistical state information set obtained through measurement
Wherein,
is the known channel state, R, from base station z to near end user k rk Receive covariance matrix, R, representing near-end user k channel estimation error tk A transmit covariance matrix representing the near-end user k channel estimation error,
is base station z to remote user
Is known to be in the channel state of the channel,
representing remote users
A received covariance matrix of the channel estimation error,
representing remote users
Transmit covariance matrix of channel estimation errors, d k Being the distance from base station z to user k,
for base station z to user
A denotes a path loss exponent, σ 2 Is the variance, σ, of additive white Gaussian noise h 2 For measuring the variance of the error, p I Representing the average power of the interference, λ b For the deployment density of the base station, k is equal to [1, K ]]；
S2, through the following equation
Determining the reception filter u for each user k k And the user
Of the receiving filter
Wherein the vector
And satisfy | z k | 2 ＝1，
From a matrix
The (2N-K) right singular vectors corresponding to the zero singular value of (a), and a matrix
Selecting a matrix for the antenna and satisfying L H L＝I K Wherein (·) H Representing a matrix conjugate operation, I K Is a K-order identity matrix;
s3, determining a precoding matrix V = LG of a base station end -H D, where the matrix G = (G) 1 ,…,g K ) And the column vector composed in the matrix G consists of
Given, diagonal matrix
Symbol (·) -H Representing the matrix conjugate inversion operation, sign
For root operation, symbol (·) m,n Is the element corresponding to the mth row and the nth column of the matrix;
s4, solving the optimal transmission rate of all NOMA users by the following optimization problem
Wherein R is k And
a near end user k and a far end user respectively
The rate of transmission of the information of (c),
and with
Respectively, near end user k andremote user
Given statistical channel state information conditions
Probability of interruption, β k 2 Epsilon represents the maximum allowable outage probability for the power allocation factor for the information transmitted to the near-end user k.
2. The method as claimed in claim 1, wherein the vector z in step S2 is z k And the antenna selection matrix L is determined by the following procedure:
s201, structure z k And wherein each candidate vector in the set has only one element of 1 and the other elements are 0; similarly, a candidate value set of the antenna selection matrix L is constructed, wherein each column of each candidate matrix comprises exactly only one 1 element, each row comprises at most one 1 element, and all other places are 0;
s202, according to the vector z k Determining the effective channel gain gamma for each pair of users in combination with the antenna selection matrix L candidate values k ＝1/(G -1 G -H ) k,k ；
S203, finding out the minimum effective channel gain, namely gamma min,i ＝min{γ 1 ,…,γ K I is antenna z k A sequence number combined with the L candidate value;
s204, finding the combination serial number i for maximizing the minimum effective channel gain, namely
Thereby determining z k And L in reasonable combination.
3. The method as claimed in claim 1, wherein the non-convex optimization problem in step S4 is solved by using an optimization tool including continuous convex optimization or interior point method.
4. The method as claimed in claim 1, wherein the step S4 of selecting the enhanced small cell downlink communication method based on MIMO-NOMA includes ignoring correlation between successive decoding of NOMA
The upper bound of (c).
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