CN112600642A - Two-sending multi-receiving X channel message transmission method based on propagation delay interference alignment - Google Patents

Two-sending multi-receiving X channel message transmission method based on propagation delay interference alignment Download PDF

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CN112600642A
CN112600642A CN202011478746.5A CN202011478746A CN112600642A CN 112600642 A CN112600642 A CN 112600642A CN 202011478746 A CN202011478746 A CN 202011478746A CN 112600642 A CN112600642 A CN 112600642A
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message
propagation delay
channel
interference
interference alignment
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李从改
刘锋
王淑萍
甘茜
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Shanghai Maritime University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J11/00—Orthogonal multiplex systems, e.g. using WALSH codes
    • H04J11/0023—Interference mitigation or co-ordination
    • H04J11/0026—Interference mitigation or co-ordination of multi-user interference
    • H04J11/003—Interference mitigation or co-ordination of multi-user interference at the transmitter
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J11/00—Orthogonal multiplex systems, e.g. using WALSH codes
    • H04J11/0023—Interference mitigation or co-ordination
    • H04J11/0026—Interference mitigation or co-ordination of multi-user interference
    • H04J11/0036—Interference mitigation or co-ordination of multi-user interference at the receiver
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/0446—Resources in time domain, e.g. slots or frames
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/12—Wireless traffic scheduling
    • H04W72/1263—Mapping of traffic onto schedule, e.g. scheduled allocation or multiplexing of flows
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/50—Allocation or scheduling criteria for wireless resources
    • H04W72/54—Allocation or scheduling criteria for wireless resources based on quality criteria
    • H04W72/541—Allocation or scheduling criteria for wireless resources based on quality criteria using the level of interference

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Abstract

The invention provides a two-sending multi-receiving X channel message transmission method based on propagation delay interference alignment, which utilizes propagation delay difference between links to select a proper propagation delay matrix to reasonably schedule the sending time slot of a message, a receiving end uses cyclic decoding to ensure that the expected message is received without interference, and the interference messages are aligned in pairs to maximally compress the occupied time slot resources. The scheme can reach the upper bound of theoretical freedom degree, and realizes optimal transmission. In addition, the invention analyzes the feasibility condition of the general conclusion in a two-dimensional or three-dimensional Euclidean space and is suitable for scenes with the same propagation speed of each link.

Description

Two-sending multi-receiving X channel message transmission method based on propagation delay interference alignment
Technical Field
The invention relates to an interference alignment method based on propagation delay, in particular to a method for reasonably scheduling the sending time slot of a message by selecting a proper propagation delay matrix, wherein a receiving end uses cyclic decoding to ensure that the expected message is received without interference, and interference messages are aligned to the minimum number of time slots pairwise.
Background
The interference alignment technique can be designed by a propagation delay matrix in time, and aligns interference in a desired smaller dimension at a signal receiving end, leaving more signal dimensions to an expected message of each receiving end. The interference alignment technology based on propagation delay is applied to simple networks, and the technology is not applied to 2 xKX networks at present.
Aiming at the problems, the invention utilizes the characteristic of large time delay in propagation to realize the interference alignment of the 2 XKX network on the time domain.
Disclosure of Invention
The invention provides a two-sending multi-receiving X channel message transmission method based on propagation delay interference alignment, which comprises the steps of firstly selecting a proper propagation delay matrix by utilizing propagation delay difference between links, secondly reasonably scheduling sending time slots of messages, and then ensuring that the expected messages are received without interference by a receiving end by using cyclic decoding, wherein the interference messages are aligned to the minimum number of time slots pairwise. Finally, the general conclusion is analyzed for feasibility conditions in two-dimensional or three-dimensional euclidean space.
Specifically, the invention realizes the method by the following steps:
s1, constructing a two-sending multi-receiving X network;
s2, selecting a proper propagation delay matrix;
s3, reasonably scheduling the sending time slot of the message;
s4, circularly decoding by a receiving end;
s5, verifying that K ═ 3 and K ═ 4 are suitable for the method;
the step S1 includes the steps of:
s1.1, the two-sending multi-receiving X network has two source nodes and K destination nodes, respectively using SjAnd DiIndicating that i belongs to {1, 2.,. K }, and j belongs to {1,2 }; using WijRepresenting a source node SjSent to the destination node DiIs uniquely expected, τijRepresenting a source node SjTo destination node DiThe time delay therebetween; v. ofjAnd riRespectively representing source nodes SjTransmitting and destination node DiA received message polynomial.
The step S2 includes the steps of:
s2.1, each Source node SjAnd destination node DiThe channel between the two is divided into n time slots, and only one message can be sent in each time slot; assuming that the propagation delay is a static and non-negative integer multiple of one time slot; similar to the conventional orthogonal multiple access scheme, the message is circularly right-shifted according to the channel characteristics of the propagation delay after n time slots; the process can establish a model by circularly right-shifting a polynomial, and the period is n;
s2.2, the message to be sent sets an offset at the source node to
Figure BDA0002836698520000021
Transmitting and the channel delay matrix is delayed by tauijA time slot; after n time slots of a cycle, the resulting delay message is sent
Figure BDA0002836698520000022
Represents; for convenience, we set the elements of the propagation delay matrix to
Figure BDA0002836698520000023
Assuming that all nodes know the propagation delay matrix of the channel, the propagation delay is defined as:
Figure BDA0002836698520000024
the step S3 includes the steps of:
s3.1, coding: slave source node S1The message sent is encoded by an encoding function e1Encoding into polynomials v1(x) In the function with K message W11，W21，W31，...，WK1(ii) a Likewise, S2Message polynomial v2(x) By e2Code therein comprisingW12，W22，W32，...，WK2(ii) a The method comprises the following steps:
e1:(W11,W21,…,WK1)→v1(x)
e2:(W12,W22,…,W2K)→v2(x)
s3.2, circulation propagation function through vector v ═ v (v)1(x),v2(x) A superposition of the input polynomials in):
v1(x)＝x0W11+x1W21+…+xK-1WK1mod(xn-1)
v2(x)＝x0WK2+…+xK-2W22+xK-1W12mod(xn-1)
the step S4 includes the steps of:
s4.1, decoding: each destination node decodes the message polynomial received by the destination node to obtain the estimation of the expected message; received polynomial ri(x) From fiDecoding, the method comprises:
f1:v1(x)→(W11,W12),
f2:v2(x)→(W21,W22),
…
fK:vK(x)→(WK1,WK2).
s4.2. the vector of the receive polynomial is defined by r ═ r (r)1(x),r2(x),…,rK(x) ) represents:
Figure BDA0002836698520000031
s4.3, for the interference alignment channel model based on the propagation delay, when the signal-to-noise ratio in the channel tends to be infinite, the reachable degree of freedom (DoF) is defined as: the ratio of the total number of messages M transmitted in a cycle to the total number of slots n in a cycle is:
Figure BDA0002836698520000032
s4.4 at receiver DiIn the received message polynomial, DiDesired message Wi1And Wi2Received in (n-i +1) th and nth slots without interference; and destination node DiThe (2K-2) interference messages of (a) are perfectly aligned in the remaining (n-2) time slots; in this scheme, the 2 × KX channel can achieve perfect cyclic interference alignment, i.e., its freedom can be achieved
Figure BDA0002836698520000033
The step S5 includes the steps of:
s5.1, K ═ 3, for destination node D1，D2And D3By this scheme it is possible to receive their respective expected messages without interference and align the corresponding interference messages all in the remaining time slots. Therefore, the perfect cyclic interference alignment of the 2X 3X channel can be realized by the scheme, and the upper bound of the DoF is reached
Figure BDA0002836698520000041
S5.2, K4, for destination node D1，D2，D3And D4By this scheme it is possible to receive their respective expected messages without interference and align the corresponding interference messages all in the remaining time slots. Therefore, the perfect cyclic interference alignment of the 2X 4X channel can be realized by the scheme, and the upper bound of the DoF is reached
Figure BDA0002836698520000042
The invention has the beneficial effects that: the perfect cyclic interference alignment scheme based on the propagation delay is popularized to a 2 × K X channel model, which is not involved in the existing research and is very friendly to the channel with the large propagation delay, and the defect of the large propagation delay can be converted into the IA scheme based on the time dimension by using the IA technology on the time dimension to improve the channel capacity.
Drawings
Fig. 1 is a flowchart of a two-transmitter multiple-receiver X channel message transmission method based on propagation delay interference alignment according to the present invention.
Fig. 2 is a 2 × 3X channel network model of the two-transmitter multiple-receiver X channel message transmission method based on propagation delay interference alignment according to the present invention.
Fig. 3 is a 2 × 4X channel network model of the two-transmitter multiple-receiver X channel message transmission method based on propagation delay interference alignment according to the present invention.
Fig. 4 is a 2 × K X channel network model of the two-transmitter multiple-receiver X channel message transmission method based on propagation delay interference alignment according to the present invention.
Fig. 5 is a node layout diagram of 2 × K X channels centered on a source node in euclidean space according to the two-transmitter multiple-receiver X channel message transmission method based on propagation delay interference alignment of the present invention.
Detailed Description
S1, constructing a two-sending multi-receiving X network;
s2, selecting a proper propagation delay matrix;
s3, reasonably scheduling the sending time slot of the message;
s4, circularly decoding by a receiving end;
s5, verifying that K ═ 3 and K ═ 4 are suitable for the method;
s6, carrying out European style spatial feasibility analysis;
s2.1, establishing a propagation delay matrix as follows:
Figure BDA0002836698520000051
s3.1, the method for establishing the cyclic coding comprises the following steps:
v1(x)＝x0W11+x1W21+…+xK-1WK1 mod(xn-1)
v2(x)＝x0WK2+…+xK-2W22+xK-1W12 mod(xn-1)
s4.1, the method for establishing the cyclic decoding comprises the following steps:
Figure BDA0002836698520000052
s4.2, for the interference alignment channel model based on the propagation delay, when the signal-to-noise ratio in the channel tends to be infinite, the reachable degree of freedom (DoF) is defined as: the ratio of the total number of messages M transmitted in a cycle to the total number of slots n in a cycle is:
Figure BDA0002836698520000053
s4.3, at receiver DiIn the received message polynomial, DiDesired message Wi1And Wi2Received in (n-i +1) th and nth slots without interference; and destination node DiThe (2K-2) interference messages of (a) are perfectly aligned in the remaining (n-2) time slots; in this scheme, the 2 × KX channel can achieve perfect cyclic interference alignment, i.e., its freedom can be achieved
Figure BDA0002836698520000061
S5.1, K ═ 3, for destination node D1，D2And D3By this scheme it is possible to receive their respective expected messages without interference and align the corresponding interference messages all in the remaining time slots. Therefore, the perfect cyclic interference alignment of the 2X 3X channel can be realized by the scheme, and the upper bound of the DoF is reached
Figure BDA0002836698520000062
S5.2, K4, for destination node D1，D2，D3And D4By which all can be inTheir respective expected messages are received without interference and the corresponding interference messages are all aligned in the remaining time slots. Therefore, the perfect cyclic interference alignment of the 2X 4X channel can be realized by the scheme, and the upper bound of the DoF is reached
Figure BDA0002836698520000063
S6.1: euclidean space model
The propagation velocity v is assumed to be constant in all links, where SjAnd DiThe distance between can be used
Figure BDA0002836698520000064
Where k is a scaling factor, τ0Is the reference starting point of the propagation delay matrix. In our model, an increase in the propagation delay matrix with a step size Δ τ ═ 1 indicates an increase in the distance between the respective transceiving ends, the step size Δ p ═ vk ═ Δ τ ═ vk, and the reference distance is denoted p0＝vτ0。SjAnd DiThe conditions are as follows:
Figure BDA0002836698520000065
with Oj(Di) Is represented by SjA circle/sphere with a center, wherein DiAt the source node SjAt the center circle/sphere intersection, a feasibility condition can be established by ensuring that the associated circle/sphere has an intersection of all node arrangements of 2 source nodes, which can be expressed as:
Figure BDA0002836698520000066
s6.2: analysis of the Euclidean space feasibility
When the nodes are arranged in Euclidean space, the source node S is used1，S2When being the center, K destination nodes D1，D2,…DkAre respectively positioned by the source nodeAt the intersection of the circles/spheres representing the respective distances at the center, we denote the distance between the two source nodes by a, i.e.
Figure BDA0002836698520000071
Since each destination node DiA triangle may be formed with two source nodes. For the source node S1And S2The triangle inequality is:
Figure BDA0002836698520000072
by calculation, we can deduce the range of a:
(K-1)△p≤a≤2p0+△p
wherein
Figure BDA0002836698520000073
The feasibility range of the method in the Euclidean space is analyzed, and the feasibility of the scheme is proved to be suitable for the scenes with the same propagation speed of each link.

Claims (3)

1. A two-transmission multi-reception X channel message transmission method based on propagation delay interference alignment is characterized by comprising the following steps:
s1, constructing a two-sending multi-receiving X network;
s2, selecting a proper propagation delay matrix;
s3, reasonably scheduling the sending time slot of the message;
s4, circularly decoding by a receiving end;
the step S1 includes the steps of:
s1.1, the two-sending multi-receiving X network has two source nodes and K destination nodes, respectively using SjAnd DiIndicating that i belongs to {1, 2.,. K }, and j belongs to {1,2 }; using WijRepresenting a source node SjSent to the destination node DiIs uniquely expected, τijRepresenting a source node SjTo destination node DiThe time delay therebetween; v. ofjAnd riRespectively representing source nodes SjTransmitting and destination node DiA received message polynomial;
the step S2 includes the steps of:
s2.1, each Source node SjAnd destination node DiThe channel between the two is divided into n time slots, and only one message can be sent in each time slot; assuming that the propagation delay is a static and non-negative integer multiple of one time slot; similar to the conventional orthogonal multiple access scheme, the message is circularly right-shifted according to the channel characteristics of the propagation delay after n time slots; the process can establish a model by circularly right-shifting a polynomial, and the period is n;
s2.2, the message to be sent sets an offset x at the source nodepijTransmitting and the channel delay matrix is delayed by tauijA time slot; after n time slots of a cycle, the resulting delay message is sent
Figure FDA0002836698510000011
Represents; for convenience, the elements of the propagation delay matrix are set to
Figure FDA0002836698510000012
Assuming that all nodes know the propagation delay matrix of the channel, the propagation delay is defined as:
Figure FDA0002836698510000013
the step S3 includes the steps of:
s3.1, coding: slave source node S1The message sent is encoded by an encoding function e1Encoding into polynomials v1(x) In the function with K message W11，W21，W31，...，WK1(ii) a Likewise, S2Message polynomial v2(x) By e2Code of which W is contained12，W22，W32，...，WK2(ii) a The method comprises the following steps:
e1:(W11,W21,…,WK1)→v1(x)
e2:(W12,W22,…,W2K)→v2(x)
s3.2, circulation propagation function through vector v ═ v (v)1(x),v2(x) A superposition of the input polynomials in):
v1(x)＝x0W11+x1W21+…+xK-1WK1mod(xn-1)
v2(x)＝x0WK2+…+xK-2W22+xK-1W12mod(xn-1)
the step S4 includes the steps of:
s4.1, decoding: each destination node decodes the message polynomial received by the destination node to obtain the estimation of the expected message; received polynomial ri(x) From fiDecoding, the method is as follows:
Figure FDA0002836698510000021
s4.2. the vector of the receive polynomial is defined by r ═ r (r)1(x),r2(x),…,rK(x) ) represents:
Figure FDA0002836698510000022
s4.3, for the interference alignment channel model based on the propagation delay, when the signal-to-noise ratio in the channel tends to be infinite, the reachable degree of freedom (DoF) is defined as: the ratio of the total number of messages M transmitted in a cycle to the total number of slots n in a cycle is as follows:
Figure FDA0002836698510000031
s4.4 at receiver DiIn the received message polynomial, DiDesired message Wi1And Wi2Received in (n-i +1) th and nth slots without interference; and destination node DiThe (2K-2) interference messages of (a) are perfectly aligned in the remaining (n-2) time slots; in this scheme, the 2 × KX channel can achieve perfect cyclic interference alignment, i.e., its freedom can be achieved
Figure FDA0002836698510000032
2. The method for transmitting two-transmitter-multiple-receiver X channel messages based on propagation delay interference alignment of claim 1, wherein K is 3.
3. The method for transmitting two-transmitter-multiple-receiver X channel messages based on propagation delay interference alignment of claim 1, wherein K is 4.
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