CN108777588B - MMSE precoding-based downlink two-user MISO system power allocation method - Google Patents

MMSE precoding-based downlink two-user MISO system power allocation method Download PDF

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CN108777588B
CN108777588B CN201810428990.7A CN201810428990A CN108777588B CN 108777588 B CN108777588 B CN 108777588B CN 201810428990 A CN201810428990 A CN 201810428990A CN 108777588 B CN108777588 B CN 108777588B
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rate
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CN108777588A (en
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赵志信
江晓林
谢玉鹏
孙辉
刘鑫
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Heilongjiang University of Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention provides a power distribution method of a downlink two-user MISO system based on MMSE precoding. Firstly, deriving a rate pair expression on a boundary of an achievable rate domain of a downlink two-user multiple-input single-output (MISO) system based on Minimum Mean Square Error (MMSE) precoding according to duality of an uplink and a downlink; aiming at the power distribution problem of maximizing the user 2 rate under the constraint conditions of the user 1 target rate and the system total power, establishing a mathematical model; then, obtaining an analytic solution of the optimal power distribution of the users by using pareto optimality of rate pairs on the reachable rate domain boundary of a downlink two-user MISO system based on MMSE precoding; and finally, obtaining a user transmitting signal according to the MMSE precoding vector and the optimal power distribution of the user. By combining the invention with the existing user pairing algorithm, the invention can be applied to the actual multi-user downlink MISO system.

Description

MMSE precoding-based downlink two-user MISO system power allocation method
Technical Field
The invention discloses a power distribution method of a downlink two-user MISO system based on MMSE precoding, and relates to the field of wireless communication.
Background
The main technical challenge faced by the current cellular mobile communication system is how to provide high-speed downlink data service on a limited frequency spectrum, and the downlink transmission performance is crucial to the cellular mobile system; minimum Mean Square Error (MMSE) precoding can realize the optimal compromise between interference and noise between users, so the MMSE precoding is an optimal linear precoding scheme and can maximize the signal-to-interference-and-noise ratio of users of a downlink MISO system.
For a large-scale downlink MIMO system scenario, documents s.zarei, w.gerstackers, r.r.muller, and r.schober, "Low-complexity linear precoding for downlink large-scale MIMO systems," in proc.ieee int.symp.pimrc, 2013, pp.1119-1124, propose a Low-complexity MMSE precoding scheme based on a matrix polynomial, which greatly reduces the computational complexity compared with the conventional MMSE precoding scheme, and can almost achieve the same performance in terms of system and rate (sum rate). The documents s.zarei, w.gerstacker and r.schober, "Low-Complexity wide-Linear Precoding for Downlink Large-Scale MU-MISO Systems," IEEE COMMUNICATIONS Linear Precoding Systems, vol.19, No.4, APRIL 2015, pp.665-668, propose a generalized Linear-Linear (MMSE) MMSE Precoding scheme for real transmitted signals, which greatly improves the system and rate compared to the conventional MMSE Precoding scheme. In addition, based on the random matrix theory, a generalized MMSE precoding scheme based on polynomial expansion is provided, and the computational complexity is reduced. Documents x.yi and d.gesbert, "Precoding Methods for the MISO Broadcast Channel with Delayed CSIT," IEEE transport ON WIRELESS COMMUNICATIONS, vol.12, No.5, my 2013, pp.2344-2354, a Virtual minimum mean square error (Virtual MMSE) Precoding scheme is proposed, i.e., GMAT-MMSE, which can obtain an optimal solution by a gradient-based iterative algorithm, and compared with the MAT algorithm, a better compromise between signal enhancement and interference alignment can be achieved, and the system and rate are greatly improved. S.zarei et al avoid a large number of matrix inversion operations in the conventional MMSE precoding scheme by using a matrix polynomial, x.yi et al can obtain an optimal solution by a gradient-based iterative algorithm, but the complexity of the above algorithm is still high.
Disclosure of Invention
Therefore, the existing MMSE precoding scheme has high calculation complexity and cannot be directly applied to an actual downlink MISO system.
Therefore, in order to overcome the defects in the prior art, the technical problem to be solved by the present invention is to provide a power allocation method for a downlink two-user MISO system based on MMSE precoding.
In order to solve the technical problem, from the perspective of the user reachable rate domain, the invention designs a power allocation method of a downlink dual-user MISO system based on MMSE precoding, which is realized by the following steps:
a power distribution method of a downlink two-user MISO system based on MMSE precoding comprises the following steps:
step one, according to the duality of an uplink and a downlink, the rate pair (r) on the boundary of the reachable rate domain of a downlink two-user MISO system based on MMSE precoding1，r2) The expression can be equivalently given by the rate on the boundary of the reachable rate domain of an uplink two-user single-input multiple-output (SIMO) system of which the base station end adopts an MMSE receiver; obtaining rate pair (r) on reachable rate domain boundary of downlink two-user MISO system based on MMSE precoding1，r2) Expression formula
Figure BSA0000163426430000021
Wherein the content of the first and second substances,
Figure BSA0000163426430000022
hiis a complex channel vector (a column vector containing M elements) from the base station to the user i, M is the number of antennas configured by the base station, | | hi| is hiThe norm of (a) of (b),
Figure BSA0000163426430000023
σ2is the noise power of the user, qiAnd j is 3-i, i is 1,2, of the transmission power of the user i in an uplink two-user SIMO system adopting the MMSE receiver at the base station end. Alpha is an element of [ O, pi/2 ]]Is h1And h2The included angle between the two parts is smaller than the included angle,
Figure BSA0000163426430000024
step two, aiming at the power distribution problem of the maximized user 2 speed rate under the condition that the total power constraint and the user 1 target speed rate are met in a downlink two-user MISO system based on MMSE precoding, establishing a mathematical model:
Figure BSA0000163426430000025
Figure BSA0000163426430000026
p1+p2≤P
p1≥0，p2≥0
wherein p isiFor the power allocated to user i, RiFor the rate of user i, a rate pair (R) over the reachable rate domain1，R2) Satisfy R1≤r1，R2≤r2When the rate is paired with (R)1，R2) The equal sign holds when located on the reachable rate domain boundary.
Figure BSA0000163426430000027
Is the target rate for the user 1 and,
Figure BSA0000163426430000028
the maximum rate that user 1 can achieve when allocating the base station full transmit power P to user 1.
Step three, according to the step two, rate pair (r) on the boundary of the reachable rate domain of the downlink two-user MISO system based on MMSE precoding is considered1，r2) Is pareto optimal, order
Figure BSA0000163426430000029
Wherein q is2＝P-q1. Obtaining equation (a) for q13 root of
Figure BSA00001634264300000210
Wherein the content of the first and second substances,
Figure BSA00001634264300000211
a＝||h1||2||h2||4sin4α，
b＝-2||h1||2||h2||2sin2α(σ2+||h2||2P sin2α)-η0||h2||4σ2 sin2α
c＝||h2||2Pσ2 sin2α(2||h1||2+||h2||2sin2α+2η0||h2||2)+||h1||2σ4+η0||h2||2(1+sin2α)σ4
Figure BSA0000163426430000031
step four, according to the step three, in the interval [0, P]Upper, q1，1，q1，2And q is1，3In which there is only one root, use
Figure BSA0000163426430000032
Representing the root, obtaining the optimal power allocated to user 1 in the "step two" optimization problem
Figure BSA0000163426430000033
The corresponding transmitting power of user 1 in the SIMO system of two uplink users
Figure BSA0000163426430000034
Step five, considering that the base station adopts the rate pair (r) on the boundary of the reachable rate domain of an uplink dual-user SIMO system (a downlink dual-user MISO system based on MMSE precoding) of an MMSE receiver1，r2) The corresponding power allocation is full, i.e. q1+q2＝P(p1+P2P), the optimal power allocated to user 2 in the "step two" optimization problem is obtained
Figure BSA0000163426430000035
Corresponding SIMO system of two uplink usersTransmission power of user 2 in the system
Figure BSA0000163426430000036
Step six, aiming at the power distribution problem of maximizing the user 2 rate under the condition of meeting the user 1 target rate and the system total power constraint in the step two, the optimal power distributed to the user i in the MMSE precoding-based downlink two-user MISO system is obtained
Figure BSA0000163426430000037
Wherein the content of the first and second substances,
Figure BSA0000163426430000038
Figure BSA0000163426430000039
j＝3-i，i＝1，2.
step seven, obtaining the user emission signal according to the step six
Figure BSA00001634264300000310
Wherein the content of the first and second substances,
Figure BSA00001634264300000311
sifor a signal to be transmitted for user i, j-3-i, i-1, 2.
The invention has the beneficial effects that: from the perspective of an achievable rate domain, the method for distributing the power of the MISO system of the two downlink users based on MMSE precoding is provided, the method can maximize the rate of the user 2 under the condition that the constraint conditions of the target rate of the user 1 and the total power of the system are met, compared with the traditional MMSE precoding scheme, the method has the advantages that the system frequency spectrum efficiency is greatly improved, the analytic solution of the optimal power distribution of the user is obtained, iteration and complex matrix inversion operation are not needed, and the algorithm complexity is low. By combining the invention with the existing user pairing algorithm, the invention can be applied to the actual downlink multi-user MISO system.
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FIG. 1 is a model of a MMSE precoding based downlink two-user MISO system;
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.
The invention provides a power distribution method of a two-point downlink user MISO system based on MMSE precoding, which is applied to a point-to-two-point downlink user MISO system model shown in figure 1. The system has 2 single-antenna users, one base station configured with M antennas; in each subframe, the base station in the model feeds back CSI (channel vector h) according to usersi) Calculating a user channel vector hiNorm h ofi1, 2; the base station according to the channel vector hiAnd performing optimal user power distribution and MMSE precoding, performing overlapping coding on signals of two users to obtain a transmitting signal, and transmitting the transmitting signal to the users through an MISO wireless channel.
A power distribution method of a downlink two-user MISO system based on MMSE precoding comprises the following steps:
step one, according to the duality of an uplink and a downlink, the rate pair (r) on the boundary of the reachable rate domain of a downlink two-user MISO system based on MMSE precoding1，r2) The expression can be equivalently given by the rate on the boundary of the reachable rate domain of an uplink two-user single-input multiple-output (SIMO) system of which the base station end adopts an MMSE receiver; obtaining rate pair (r) on reachable rate domain boundary of downlink two-user MISO system based on MMSE precoding1，r2) Expression formula
Figure BSA0000163426430000041
Wherein the content of the first and second substances,
Figure BSA0000163426430000042
hiis a complex channel vector (a column vector containing M elements) from the base station to the user i, M is the number of antennas configured by the base station, | | hi| is hiThe norm of (a) of (b),
Figure BSA0000163426430000043
σ2is the noise power of the user, qiAnd j is 3-i, i is 1,2, of the transmission power of the user i in an uplink two-user SIMO system adopting the MMSE receiver at the base station end. Alpha is an element of [ O, pi/2 ]]Is h1And h2The included angle between the two parts is smaller than the included angle,
Figure BSA0000163426430000044
step two, aiming at the power distribution problem of the maximized user 2 speed rate under the condition that the total power constraint and the user 1 target speed rate are met in a downlink two-user MISO system based on MMSE precoding, establishing a mathematical model:
Figure BSA0000163426430000045
Figure BSA0000163426430000046
p1+p2≤P
p1≥0，p2≥0
wherein p isiFor the power allocated to user i, RiFor the rate of user i, a rate pair (R) over the reachable rate domain1，R2) Satisfy R1≤r1，R2≤r2When the rate is paired with (R)1，R2) The equal sign holds when located on the reachable rate domain boundary.
Figure BSA0000163426430000047
Is the target rate for the user 1 and,
Figure BSA0000163426430000048
the maximum rate that user 1 can achieve when allocating the base station full transmit power P to user 1.
Step three, according to the step two, rate pair (r) on the boundary of the reachable rate domain of the downlink two-user MISO system based on MMSE precoding is considered1，r2) Is pareto optimal, order
Figure BSA0000163426430000051
Wherein q is2＝P-q1. Obtaining equation (3) for q13 root of
Figure BSA0000163426430000052
Wherein the content of the first and second substances,
Figure BSA0000163426430000053
a＝||h1||2||h2||4sin4α，
b＝-2||h1||2||h2||2sin2α(σ2+||h2||2P sin2α)-η0||h2||4σ2 sin2α，
c＝||h2||2Pσ2 sin2α(2||h1||2+||h2||2sin2α+2η0||h2||2)+||h1||2σ4+η0||h2||2(1+sin2α)σ4，
Figure BSA0000163426430000054
step four, according to the step three, in the interval [0, P]Upper, q1，1，q1，2And q is1，3In which there is only one root, use
Figure BSA0000163426430000055
Representing the root, obtaining the optimal power allocated to user 1 in the "step two" optimization problem
Figure BSA0000163426430000056
The corresponding transmitting power of user 1 in the SIMO system of two uplink users
Figure BSA0000163426430000057
Step five, considering that the base station adopts the rate pair (r) on the boundary of the reachable rate domain of an uplink dual-user SIMO system (a downlink dual-user MISO system based on MMSE precoding) of an MMSE receiver1，r2) The corresponding power allocation is full, i.e. q1+q2＝P(p1+p2P), the optimal power allocated to user 2 in the "step two" optimization problem is obtained
Figure BSA0000163426430000058
The corresponding transmitting power of user 2 in the SIMO system of two uplink users
Figure BSA0000163426430000059
Step six, aiming at the power distribution problem of maximizing the user 2 rate under the condition of meeting the user 1 target rate and the system total power constraint in the step two, obtaining the optimal power distribution distributed to the user i in the MMSE precoding-based downlink two-user MISO system
Figure BSA00001634264300000510
Wherein the content of the first and second substances,
Figure BSA0000163426430000061
j＝3-i，i＝1，2.
step seven, obtaining the user emission signal according to the step six
Figure BSA0000163426430000062
Wherein the content of the first and second substances,
Figure BSA0000163426430000063
sifor a signal to be transmitted for user i, j-3-i, i-1, 2.
Further, the specific step of obtaining the expression of the rate on the boundary of the reachable rate domain of the downlink two-user MISO system based on MMSE precoding in the step one is as follows:
step A1, according to the uplink and downlink dual principle, the MMSE precoding vector in the downlink user MISO system and the MMSE receiving filter vector in the uplink user SIMO system are the same vector, and the MMSE precoding (receiving filter) vector of user i is obtained
Figure BSA0000163426430000064
Wherein, I is an M multiplied by M unit array.
Step A2, obtaining the expression of signal-to-interference-and-noise ratio of user i at the receiver in the uplink two-user SIMO system using MMSE receiver at the base station end
Figure BSA0000163426430000065
Step A3, substituting formula (6) into formula (7) to obtain the signal-to-interference-and-noise ratio of user i at the receiver in the uplink dual-user SIMO system with MMSE receiver at the base station end
Figure BSA0000163426430000066
Wherein the content of the first and second substances,
Figure BSA0000163426430000067
step A4, considering the definition of the inner product of the vectors, equation (9) can be expressed as
Figure BSA0000163426430000068
Step A5, according to equation (10), taking into account [ < h ]i，hj〉hj/||hj||2Is hiTo hjOrthogonal projection of (a) to obtain siNorm of
Figure BSA0000163426430000071
Step A6, formula (11) is substituted into formula (8) to obtain formula (2), and rate pair (r) on the boundary of reachable rate domain of downlink two-user MISO system based on MMSE precoding is obtained1，r2) Expression (1).
Further, the specific step of obtaining the optimal power allocated to the user i in the step six is as follows:
step S1, obtaining the expression of the SINR of the user i in the MMSE precoding based downlink two-user MISO system
Figure BSA0000163426430000072
Step S2, according to the duality of the uplink and downlink, considering that the SINR of the user on the boundary of the reachable rate domain of the downlink dual-user MISO system based on MMSE precoding is equal, the SINR of the user on the boundary of the reachable rate domain of the uplink dual-user SIMO system of the MMSE receiver is adopted by the base station end to obtain
Figure BSA0000163426430000073
Step S3, formula (6) is substituted into formula (12), then formula (12) and formula (2) are respectively substituted into formula (13), and power distributed to user i on reachable rate domain boundary of downlink dual-user MISO system based on MMSE precoding is obtained
Figure BSA0000163426430000074
Wherein e isi＝||hi||4(qi)2 sin2α/σ2+2||hi||2qisin2α+σ2，
ej＝||hj||4(qj)2sin2α/σ2+2||hj||2qjsin2α+σ2，j＝3-i，i＝1，2.
Step S4, using the formulas (4) and (5)
Figure BSA0000163426430000075
Instead of q in the formula (14)iAnd (i is 1 and 2), obtaining the optimal power distributed to the user i in the MMSE precoding based downlink two-user MISO system.

Claims (3)

1. A power distribution method of a downlink two-user MISO system based on MMSE precoding is characterized by comprising the following steps:
step one, according to the duality of an uplink and a downlink, the rate pair (r) on the boundary of the reachable rate domain of a downlink two-user MISO system based on MMSE precoding1,r2) The expression can be equivalently given by the rate on the boundary of the reachable rate domain of the SIMO system through single input of uplink two users of the MMSE receiver at the base station end; obtaining two downlinks based on MMSE precodingRate pair (r) on the boundary of reachable rate domain of user MISO system1,r2) Expression formula
Figure FDA0002721991270000011
Wherein the content of the first and second substances,
Figure FDA0002721991270000012
hiis a complex channel vector from the base station to the user i, and comprises a column vector of M elements, wherein M is the number of antennas configured by the base station, | | hi| is hiThe norm of (a) of (b),
Figure FDA0002721991270000013
σ2is the noise power of the user, qiThe method comprises the steps that the transmitting power of a user i in an uplink two-user SIMO system of an MMSE receiver is adopted at a base station end, j is 3-i, and i is 1 and 2; alpha is an element of [0, pi/2 ]]Is h1And h2The included angle between the two parts is smaller than the included angle,
Figure FDA0002721991270000014
step two, aiming at the power distribution problem of the maximized user 2 speed rate under the condition that the total power constraint and the user 1 target speed rate are met in a downlink two-user MISO system based on MMSE precoding, establishing a mathematical model:
Figure FDA0002721991270000015
Figure FDA0002721991270000016
p1+p2≤P
p1≥0,p2≥0
wherein p isiFor the power allocated to user i, RiFor the rate of user i, a rate pair (R) over the reachable rate domain1,R2) Satisfy R1≤r1,R2≤r2When the rate is paired with (R)1,R2) When the position is located on the reachable rate domain boundary, the equal sign is established;
Figure FDA0002721991270000017
is the target rate for the user 1 and,
Figure FDA0002721991270000018
the maximum rate that user 1 can achieve when the base station full transmitting power P is allocated to user 1;
step three, according to the step two, rate pair (r) on the boundary of the reachable rate domain of the downlink two-user MISO system based on MMSE precoding is considered1,r2) Is pareto optimal, order
Figure FDA0002721991270000019
Wherein q is2＝P-q1(ii) a Obtaining equation (3) for q13 root of
Figure FDA0002721991270000021
Wherein the content of the first and second substances,
Figure FDA0002721991270000022
a＝||h1||2||h2||4sin4α,b＝-2||h1||2||h2||2sin2α(σ2+||h2||2Psin2α)-η0|h2|4σ2sin2αc＝||h2||2Pσ2sin2α(2||h1||2+||h2||2sin2α+2η0||h2||2)+||h1||2σ4+η0||h2||2(1+sin2α)σ4
Figure FDA0002721991270000023
step four, according to the step three, in the interval [0, P]Upper, q1,1，q1,2And q is1,3In which there is only one root, use
Figure FDA0002721991270000029
Representing the root, obtaining the optimal power allocated to user 1 in the "step two" optimization problem
Figure FDA00027219912700000210
The corresponding transmitting power of user 1 in the SIMO system of two uplink users
Figure FDA0002721991270000024
Step five, considering that the base station adopts the rate pair (r) on the boundary of the reachable rate domain of the uplink dual-user SIMO system of the MMSE receiver or the downlink dual-user MISO system based on MMSE precoding1,r2) The corresponding power allocation is full, i.e. q1+q2＝P，p1+p2Obtaining the optimal power allocated to user 2 in the "step two" optimization problem, P
Figure FDA00027219912700000211
The corresponding transmitting power of user 2 in the SIMO system of two uplink users
Figure FDA0002721991270000025
Step six, aiming at the power distribution problem of maximizing the user 2 rate under the condition of meeting the user 1 target rate and the system total power constraint in the step two, the optimal power distributed to the user i in the MMSE precoding-based downlink two-user MISO system is obtained
Figure FDA0002721991270000026
Wherein the content of the first and second substances,
Figure FDA0002721991270000027
Figure FDA0002721991270000028
j＝3-i,i＝1,2；
step seven, obtaining the user emission signal according to the step six
Figure FDA0002721991270000031
Wherein the content of the first and second substances,
Figure FDA0002721991270000032
i is an M multiplied by M unit array; siFor a signal to be transmitted for user i, j-3-i, i-1, 2.
2. The method for allocating power to a downlink dual-user MISO system based on MMSE precoding according to claim 1, wherein in the step one, the specific step of obtaining the rate-to-expression at the boundary of the reachable rate domain of the downlink dual-user MISO system based on MMSE precoding is:
step A1, according to the uplink and downlink dual principle, MMSE precoding vector in the downlink user MISO system and MMSE receiving filter vector in the uplink user SIMO system are the same vector, and MMSE receiving filter vector of user i is obtained
Figure FDA0002721991270000033
Wherein I is an M × M unit array;
step A2, obtaining the expression of signal-to-interference-and-noise ratio of user i at the receiver in the uplink two-user SIMO system using MMSE receiver at the base station end
Figure FDA0002721991270000034
Step A3, substituting formula (6) into formula (7) to obtain the signal-to-interference-and-noise ratio of user i at the receiver in the uplink dual-user SIMO system with MMSE receiver at the base station end
Figure FDA0002721991270000035
Wherein the content of the first and second substances,
Figure FDA0002721991270000036
step A4, obtaining an equivalent expression of formula (9)
Figure FDA0002721991270000037
Step A5, obtaining s according to formula (10)iNorm of
Figure FDA0002721991270000041
Step A6, formula (11) is substituted into formula (8) to obtain formula (2), and rate pair (r) on the boundary of reachable rate domain of downlink two-user MISO system based on MMSE precoding is obtained1,r2) Expression ofFormula (1).
3. The MMSE precoding-based downlink two-user MISO system power allocation method according to claim 1, wherein in the sixth step, the specific step of obtaining the optimal power allocated to user i is:
step S1, obtaining the expression of the SINR of the user i in the MMSE precoding based downlink two-user MISO system
Figure FDA0002721991270000042
Step S2, according to the duality of the uplink and downlink, considering that the SINR of the user on the boundary of the reachable rate domain of the downlink dual-user MISO system based on MMSE precoding is equal, the SINR of the user on the boundary of the reachable rate domain of the uplink dual-user SIMO system of the MMSE receiver is adopted by the base station end to obtain
Figure FDA0002721991270000043
Step S3, formula (6) is substituted into formula (12), then formula (12) and formula (2) are respectively substituted into formula (13), and power distributed to user i on reachable rate domain boundary of downlink dual-user MISO system based on MMSE precoding is obtained
Figure FDA0002721991270000044
Wherein e isi＝||hi||4(qi)2sin2α/σ2+2||hi||2qisin2α+σ2,ej＝||hj||4(qj)2sin2α/σ2+2||hj||2qjsin2α+σ2,j＝3-i,i＝1,2；
Step S4, using the formulas (4) and (5)
Figure FDA0002721991270000045
Instead of q in the formula (14)iAnd (i is 1 and 2), obtaining the optimal power distributed to the user i in the MMSE precoding based downlink two-user MISO system.
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