CN109510653B - Array division multiple access method using two-dimensional precoding in orthogonal frequency division multiplexing - Google Patents

Array division multiple access method using two-dimensional precoding in orthogonal frequency division multiplexing Download PDF

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CN109510653B
CN109510653B CN201811648534.XA CN201811648534A CN109510653B CN 109510653 B CN109510653 B CN 109510653B CN 201811648534 A CN201811648534 A CN 201811648534A CN 109510653 B CN109510653 B CN 109510653B
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matrix
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multiple access
mark
orthogonal frequency
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CN109510653A (en
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徐任晖
邓海
彭来献
耿哲
赵文栋
张磊
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Army Engineering University of PLA
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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

Abstract

The invention discloses an array division multiple access method using two-dimensional precoding in orthogonal frequency division multiplexing, which meets the requirements of small-scale central wireless network real-time and low interception probability transmission. The multiple access method is characterized in that signals of each user are subjected to two-dimensional pre-coding before orthogonal frequency division multiplexing modulation, and the signals of the users are dispersed on all subcarriers to obtain frequency diversity. By designing the marking matrix and detecting signals at a receiving end according to the marking matrix and the characteristics of the received signals, the signals to be transmitted by different users can be perfectly recovered.

Description

Array division multiple access method using two-dimensional precoding in orthogonal frequency division multiplexing
Technical Field
The invention belongs to the technical field of wireless local area networks, in particular to a multi-user multi-access method for distinguishing different user signals by using two-dimensional precoding, and provides a data link layer solution for a network formed by a plurality of wireless nodes adopting an Orthogonal Frequency Division Multiplexing (OFDM) modulation mode.
Background
Orthogonal Frequency Division Multiplexing (OFDM) is a communication technology with high spectrum utilization efficiency, and is easy to implement in engineering by Fast Fourier Transform (FFT) algorithm, and thus becomes a candidate technology for many wireless communication systems at present. Even some dedicated wireless communication systems consider using OFDM as a transmission technology.
Precoding is performed before a data symbol modulation mapping module in an OFDM communication system, and data symbols are coded in advance, so that the correlation and statistical characteristics among the data symbols are changed, and the purposes of reducing OFDM signal frequency spectrum sidelobes, reducing OFDM signal peak-to-average power ratio, compensating wireless channel fading and the like are achieved.
The wireless local area network refers to a network formed by a plurality of wireless nodes in a local area by using radio waves as communication transmission media. Since a plurality of wireless nodes transmit and receive wireless signals in the same time period using the same frequency band, the wireless signals may interfere with each other in the air, and therefore, a method for distinguishing signals of different users, i.e., a multiple access method, needs to be designed at a data link layer.
The method of multi-user communication is considered in this scenario, assuming that there are multiple wireless nodes in a local area and there are bursts of data that need to be aggregated from multiple nodes to a central node in real time. First, a large amount of collisions and backoffs caused by random access cause network throughput to decrease, and data timeliness to decrease, so that a wireless resource allocation method based on slot synchronization is an inevitable choice for ensuring multi-user real-time communication. Next, among the multiple access schemes for various resource allocation classes, time division multiple access, frequency division multiple access, and code division multiple access are common multiple access schemes. Under the condition that the time slot is longer or some nodes have no data transmission, the efficiency of time division multiple access is lower; frequency Division Multiple Access (OFDMA) or orthogonal frequency division multiple access (orthogonal frequency division multiple access) is also low in spectrum utilization rate under the condition that part of nodes do not have data transmission; the performance of a direct sequence spread spectrum code division multiple access (DS-CDMA) system is susceptible to inter-symbol interference (ISI) caused by multipath propagation and multi-user interference (MUI) caused by incomplete spreading code orthogonality.
Disclosure of Invention
The invention aims to provide an array division multiple access method using two-dimensional precoding in orthogonal frequency division multiplexing.
The technical solution for realizing the purpose of the invention is as follows: a method for array division multiple access using two-dimensional precoding in orthogonal frequency division multiplexing, the transmitting end of each user uses orthogonal frequency division multiplexing modulation, before modulation, two-dimensional precoding is used to process the data symbol to be modulated, the precoding mark matrix of each user is different, at the receiving end, the signal of the corresponding user is recovered by using the symbol detection estimation method using the user mark matrix as parameter.
Compared with the prior art, the invention has the following remarkable advantages: (1) the invention designs a multiple access mode, which realizes the simultaneous communication of a plurality of users at the same frequency and ensures certain communication performance; (2) the marking matrix is multiplied before the data modulation of the transmitting terminal, the receiving terminal recovers the data of different users by using a detection method, and the multi-access system only depends on the marking matrix and the receiving detection method, so that the realization is simple; (3) the design of the mark matrix has a complete calculation rule, and the realization is convenient.
Drawings
Fig. 1 is a schematic diagram of baseband signal processing in an array division multiple access communication system.
Detailed Description
The invention aims to design a multi-access mode based on OFDM, namely matrix division multiple access (matrix division multiple access), which is suitable for a multi-user broadband communication scene that a plurality of nodes simultaneously have data transmission. Multiple users with data transmission use the same set of subcarriers, but each user uses a different precoding matrix. Through matrix multiplication, the precoding matrix disperses the data of the users to all subcarriers in the subcarrier set, so that all users can obtain frequency diversity gain. At a receiving end, signals of a plurality of users are overlapped together in a frequency domain and a time domain, and data of each user is recovered by multiplying pseudo-inverse matrixes of different precoding matrixes. Orthogonality among the precoding matrixes of all users ensures that multi-user interference is reduced as much as possible; meanwhile, the existence of Cyclic Prefix (CP) can not only reduce inter-code crosstalk caused by multipath transmission, but also alleviate the problem of time slot asynchronism caused by the difference of arrival time of multi-user signals.
The invention is established on the basis of two-step system modeling, firstly, a signal model of a point-to-point pre-coding OFDM system is established, and a system model of multi-user communication is established on the basis.
1. Point-to-point signal model
The multipath channel propagated by the OFDM baseband signal is modeled as a finite impulse response filter with (L +1) taps. The tap gain is represented by a function h (·). Because the cyclic prefix is added to the head of the OFDM baseband signal at the transmitting end, and the CP is removed at the receiving end, the intersymbol interference caused by multipath propagation is eliminated, and simultaneously, the channel transfer matrix is in a cyclic matrix form. Assuming that the operating band of the OFDM system is divided into N subcarriers, the channel transfer matrix can be represented as an N × N circulant matrix
Figure BDA0001932500550000031
The (i, m) th element is [ H ]]i,mH ((i-m) modN) and the rank of the matrix is N. Let F denote a Fourier transform matrix of size P N, with the (P, N) -th element being [ F]p,n＝e-j2πpn/N. The channel transfer matrix is right-multiplied by the inverse Fourier transform matrix of the transmitting end, then is left-multiplied by the Fourier transform matrix of the receiving end, and is changed from a cyclic matrix into a diagonal matrix, namely
D＝FHFH (2)
Wherein (·)HRepresenting the conjugate transpose of the matrix.
After the above processing of the channel model, the OFDM baseband signal vector received by the receiving end can be represented as
y＝F HFHs+n＝Ds+n (3)
Where s is a data vector of size P x 1 to be transmitted, assuming here that the data of different users are uncorrelated, chosen from the same signal mapping constellation, subject to uniform distribution, and with a covariance E { ss }H}；nIs a complex white Gaussian noise vector with size of Nx 1, which is independently and identically distributed, has a mean value of 0 and a covariance matrix of Enn H}；yIs an FFT-processed data vector of size N × 1.
2. Multiple access signal model
Assume that there are K sending nodes and 1 receiving node in the network. Suppose that each transmitting node will first send a vector s to be transmitted(k)Preprocessing, i.e. left-multiplying by a marking matrix theta(k)Size N × P, where user index K is 1, …, K. The multiple access OFDM baseband signal received by the receiving node can be expressed as
Figure BDA0001932500550000032
Where y and N are each N x 1 vectors, representing the block of OFDM received symbols and noise, respectively. The flow of the baseband signal processing is shown in fig. 1.
Assuming that the kth sending node is the destination node, the above equation can also be written as
Figure BDA0001932500550000041
The first part to the right of the equation is the desired data and the second part is the interference from other transmitting nodes. On the basis of the model, a marking matrix theta is designed(k)And multiple access interference is suppressed.
3. Design principles of a marking matrix
According to the established matrix division multiple access system model, an ideal user mark matrix has the following characteristics:
(i) each column of the marker matrix has a high autocorrelation peak;
(ii) low cross-correlation between columns of each marker matrix;
(iii) the elements of the rows of each marking matrix have the same modulus;
(iv) the design of the marking matrix is independent of the data modulated on the subcarriers;
(v) orthogonal or with low cross-correlation between different user signature matrices.
The (i) (ii) th characteristic ensures a sufficiently high signal-to-noise ratio of the received signal on each subcarrier; the (ii) property ensures that inter-subcarrier interference (ICI) is avoided; item (iii) guarantees that the tag matrix operation has no impact on power-loading and bit-loading of each subcarrier; bar (iv) indicates that the user mark matrix is fixed; the (v) th bar ensures that no interference occurs between user signals operated by different tag matrices.
Assume the labeling matrix Θ of the kth user(k)Size and breadthIs NxP, defined as
Figure BDA0001932500550000042
P column thereof
Figure BDA0001932500550000043
Is shown as
Figure BDA0001932500550000044
Wherein (·)TRepresenting a matrix transposition.
In an ideal case, the two characteristics (i) and (ii) can be expressed as
Figure BDA0001932500550000045
Wherein
Figure BDA0001932500550000046
Indicating the power allocated by the symbol matrix on the nth subcarrier. When some of the sub-carriers are not in use,
Figure BDA0001932500550000047
all being other than 0
Figure BDA0001932500550000048
Should be equal so as to satisfy the property (iii). And orthogonal between any two columns of the marking matrix, i.e.
Figure BDA0001932500550000051
That is, the marking matrix is of full column rank, and the columns of the marking matrix are the basis of the subspace spanned by the user transmit signal.
The invention is further described below with reference to the accompanying drawings.
When the method is implemented specifically, firstly, the mark matrix is designed according to the mark matrix design principle, and secondly, the signal recovery method of the receiving end is designed according to the characteristics of the received signals. After the mark matrix and the receiving end recovery method are realized, the whole system can complete multiple access communication, namely, a plurality of users transmit signals simultaneously and user data is perfectly recovered at the receiving end.
1. Mark matrix design
According to the design principle of the mark matrix, there are the following 3 simple design methods.
(1) A convenient matrix design method is from the IDFT matrix
Figure BDA0001932500550000052
Respectively extracting P columns as the mark matrix of each user to obtain the mark matrix of the k-th user
Figure BDA0001932500550000053
(2) N-order complex Hadamard matrix W constructed by using Kronecker productN. First, 2-order complex Hadamard matrix is defined
Figure BDA0001932500550000054
The order of the matrix is the same as the number of subcarriers, and is a power of 2, then the complex Hadamard matrix of order N is given by a recursive form,
Figure BDA0001932500550000055
wherein the content of the first and second substances,
Figure BDA0001932500550000056
representing the Kronecker product.
From Hadamard matrix WNRespectively extracting P columns as the mark matrix of each user to obtain the mark matrix of the k-th user
Figure BDA0001932500550000057
(3) An arbitrary unitary orthogonal matrix can be used to construct the marker matrix. For example, construct an N matrix AN×NThe (p, N) th element is [ (p-1) N + N [ ]]+j[(N-p+1)N-n]Through a matrix AN×NThe Schur decomposition of (A) to obtain,
T＝UHAN×NU (12)
where T is an N × N upper triangular matrix and U is an N × N unitary matrix.
Taking the example of extracting the mark matrix from the U, the mark matrix of the k-th user is obtained
Figure BDA0001932500550000061
Suppose U[p]Mark matrix for p column, k user of U
Figure BDA0001932500550000062
2. Receiver side signal detection
In order to recover the data transmitted by the kth user, the receiving end needs to know the mark matrix of the target user. Suppose the data symbols of the users are uncorrelated and obey a uniform distribution, with a mean of 0 and a covariance matrix of E { s }(k)(s(k))H}; the noise vector also has a zero mean and the covariance matrix is E { nnH}＝σ2IN×N。
1) Zero forcing estimation (zero-forcing estimation)
The zero forcing estimation method is used for carrying out the symbol vector s of the kth user(k)Recovered from the received block y of symbols. Assume that the received symbol vector is represented as
y＝D(k)Θ(k)s(k)+z(k) (13)
Wherein an interference plus noise vector is defined as
Figure BDA0001932500550000063
The zero forcing estimation method will receiveLeft-multiplying a block of symbols by a decoding matrix phi(k)The estimated symbol vector can be expressed as
Figure BDA0001932500550000064
Figure BDA0001932500550000065
Figure BDA0001932500550000066
Ideally, the set of decoding matrices Ψ ═ Φ(1),Φ(2),…,Φ(K)The following conditions are satisfied,
Figure BDA0001932500550000067
wherein 0N×NRepresenting a zero matrix of size N x N. When the 3 rd equation condition is satisfied, the subspace spanned by the columns of one user marking matrix is the null space of the subspaces spanned by the columns of the other user marking matrix, then the 2 nd other user interference term in the formula (17) is 0, and the detector facing the single user can recover the original data of the user.
Assuming an interference noise term z(k)Obey a complex Gaussian distribution, so that the received symbol vector has a mean value of D(k)Θ(k)s(k)Covariance of Qz＝E[z(k)(z(k))H]Can be described by an N-dimensional conditional complex Gaussian distribution
Figure BDA0001932500550000071
Then s(k)Is that the best linear estimate of (a) is the likelihood function
Figure BDA0001932500550000072
Minimized s(k)Value, which minimized results in
Figure BDA0001932500550000076
Wherein the content of the first and second substances,
Figure BDA0001932500550000073
represents the Moore-Penrose inverse of the matrix. Namely, it is
Φ(k)＝[D(k)Θ(k)(D(k)Θ(k))H]-1(D(k)Θ(k))H (22)
Wherein [. ]]-1The inverse of a square matrix is shown.
2) Minimum mean square error estimation (minimum mean square error estimation)
Minimum Mean Square Error (MMSE) estimation is another less complex MDMA system symbol estimation method. It is equivalent to solving the following optimization problem by estimating the user's data symbol vector from the received signal vector y,
Figure BDA0001932500550000074
wherein, CP×NRepresenting a P × N-dimensional complex space, | | | |, represents the modulus of the vector, where E [ ·]For a user data symbol vector s(k)And the noise vector n is taken as desired.
To solve the above minimization problem, a covariance matrix of estimation errors is first given
cov(s(k)-Φ(k)y) (24)
Figure BDA0001932500550000075
Using matrix derivation method, equation (24) is applied to Φ: (k) DerivationAnd let the result equal to 0, get the following equation
Φ(k)E[yyH]-E[s(k)yH]＝0 (26)
Wherein the covariance matrix of the received symbol vector is expressed as
Figure BDA0001932500550000081
＝D(k)Θ(k)E[s(k)(s(k))H](D(k)Θ(k))H+E[z(k)(z(k))H] (28)
From this, an MMSE estimation matrix is obtained, denoted as
Figure BDA0001932500550000082
Therefore, for a multi-user MDMA system, at a transmitting end, a precoding mark matrix with a full rank needs to be designed for each user respectively for distinguishing different users; at the receiving end, the symbol vector is received and multiplied by zero forcing estimation matrix phi(k)Or MMSE estimation matrix
Figure BDA0001932500550000083
And recovering the data of each user.

Claims (3)

1. An array division multiple access method using two-dimensional precoding in orthogonal frequency division multiplexing, characterized in that: the transmitting end of each user uses orthogonal frequency division multiplexing modulation, a two-dimensional precoding is used for processing a data symbol to be modulated before modulation, the precoding mark matrix of each user is different, and a symbol detection estimation method taking the user mark matrix as a parameter is used for recovering the signal of the corresponding user at the receiving end; the number of rows of the mark matrix is equal to the number of symbols to be modulated, and the number of columns of the mark matrix is equal to the number of subcarriers modulated by orthogonal frequency division multiplexing.
2. The method of claim 1, wherein the mark matrix design rule comprises: each column of the marker matrix has a high autocorrelation peak; low cross-correlation between columns of each marker matrix; the elements of the rows of each marking matrix have the same modulus; the design of the mark matrix is independent of the data modulated on the subcarrier; the different user signature matrices are orthogonal or have low cross-correlation.
3. The method of claim 1, wherein the method comprises the following steps:
first from the IDFT matrix
Figure FDA0003063299150000011
Or Hadamard matrix WNOr extracting P columns from any orthogonal unitary matrix U as a mark matrix of each user;
then each user uses the mark matrix to process the input symbol of the sending end and transmit the signal, and the signal received at the receiving end is
Figure FDA0003063299150000012
Where y and N are each a vector of N x 1, representing the block of OFDM received symbols and the noise, s, respectively(k)For user data symbol vectors, theta(k)Is a mark matrix;
zero forcing estimation method used by receiving end
Φ(k)＝[D(k)Θ(k)(D(k)Θ(k))H]-1(D(k)Θ(k))H
Or minimum mean square error estimation method
Figure FDA0003063299150000013
Multiplying the received signal to recover the information data sent by the kth user; and the received data of all the users are processed in the same way one by one, so that the information data sent by all the users can be recovered.
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