CN105049154A - Precoding optimization method for multi-user cognition network based on MIMO-VFDM - Google Patents

Abstract

The present invention provides a multi-user cognitive network precoding optimization method based on MIMO-VFDM. On the basis of CTP suppressing interlayer interference, ITP is used to control the mutual interference between users in the SC. By selecting the null space and Rotating and constructing the optimized ITP coding matrix can maximize the channel capacity of the SC, thereby increasing the capacity of the cognitive network while suppressing the interference between multiple users in the two-layer network.

Description

A precoding optimization method for multi-user cognitive network based on MIMO-VFDM

technical field

The present invention relates to an optimized design scheme for multi-user two-layer cognitive network precoding using Multiple-Input Multiple-Output (MIMO) and Vandermonde-subspace Frequency Division Multiplexing (Vandermonde-subspace Frequency Division Multiplexing, VFDM) transmission, It is used to suppress the interference between users in the two-layer cognitive network and maximize the channel capacity of the two-layer network.

Background technique

The continuous growth of wireless services has led to increasingly scarce frequency domain resources, so wireless transmission with high spectrum efficiency has become a research hotspot in modern communications. The deployment of two-layer networks such as cognitive networks is a feasible solution to solve spectrum resources. In a two-layer network communication system based on cognitive radio technology, small cells (small-cells, SCs) are deployed around macro cells (macro-cell, MC) as a second-layer network and share spectrum transmission with them. The MC has the priority to use the shared spectrum, and the Layer 2 network accesses the spectrum opportunistically and must ensure that there is no interference to the MC or the interference is within a tolerable range. Therefore, how to control the interference of SCs to MC has become the main problem in the implementation of the two-layer cognitive network.

As an emerging method to solve the problem of interference control in cognitive networks, VFDM technology utilizes the frequency band redundancy provided by the cyclic prefix in block transmission systems (such as OFDM systems) to establish new transmission links for SCs without disturbing the normal operation of MCs. communication. After VFDM is adopted, the signal sent by the Layer 2 transmitter is constrained to the zero space of the interference channel from the Layer 2 network to the Layer 1 network through the Cross-Tier Precoder (CTP). Afterwards, intra-tier precoding (Intra-Tier Precoder, ITP) is used to control mutual interference between users within the SC.

Document 1 "Channel estimation impact for lte small cells basedon mu-vfdm [Wireless Communications and Networking Conference (WCNC), IEEE, 2012: 2560-2565]" introduced the concept of multi-user VFDM in the process of designing CTP, in which the first layer of communication links constitutes MC, and the second layer of communication links constitutes SCs.

Document 2 "Spatial-Frequency Signal Alignment for Opportunistic Transmission [IEEE Transaction on Signal Processing, 2014, 62: 1561-1575]." extends the research of multi-user VFDM to MIMO system.

Document 3 "Zero-forcing methods for downlinkspatial multiplexing in multiple user MIMO channels. [Signal Processing, IEEE Transactionson, 2004, 52 (2): 461-471] proposes a block-diagonal zero-forcing (Block-Diagonal Zero-Forcing, BD-ZF) precoding algorithm to solve multiple Inter-user interference in user MIMO downlink. BD-ZF precoding algorithm has the advantages of convenient design and simple structure, and is very suitable for the design of ITP precoding matrix among multiple users.

Contents of the invention

In order to overcome the deficiencies of the prior art, the present invention proposes a BD-ZF-based two-layer network precoding optimization method on the basis of the existing precoding algorithm. By selecting and rotating the null space to construct the optimized ITP coding matrix, the channel capacity of the SC can be maximized, thereby suppressing the interference between multiple users in the two-layer network and improving the capacity of the cognitive network.

The technical solution adopted by the present invention to solve its technical problems comprises the following steps:

Step 1, perform singular value decomposition on the overall interlayer channel matrix H _SM from the SC base station SBS to the MC user MU to obtain $h_{\mathrm{SM}}=u_{\mathrm{ctp}}{\mathrm{\Λ}}_{\mathrm{ctp}}{V}_{\mathrm{ctp}}^h,$ where U _ctp ∈ C ^K×K and are unitary matrices, is a diagonal matrix, ${\mathrm{\Λ}}_{\mathrm{ctp}}=({\mathrm{\Σ}}_{\mathrm{ctp}},o_{K\×[(N_T-1)K+N_{T}L]}),$ Among them, ∑ _ctp ∈ C ^K×K is a diagonal matrix, and the diagonal elements are the singular values of _HSM ;

Step 2, partition matrix V _ctp = (V ₁ , V ₂ ), where V ₂ is a group of orthonormal basis of _HSM null space, design CTP matrix C=V ₂ , get J=(N _T -1)K+N _T L, where N _T is the number of SBS antennas, K is MC effective symbol length, L is the MC cyclic prefix length;

Step 3, the equivalent channel matrix after the channel matrix in the SC layer is precoded by CTP Split into N _SU K×[(N _T -1)K+N _T L]-dimensional sub-matrices by row n=1,..., N _SU , N _SU represents the number of SC users, namely ${\stackrel{\‾}{h}}_{\mathrm{SS}}={({\stackrel{\‾}{h}}_{\mathrm{SS}}{\left[1\right]}^h,{\stackrel{\‾}{h}}_{\mathrm{SS}}{\left[2\right]}^h,...,{\stackrel{\‾}{h}}_{\mathrm{SS}}{\left[N_{\mathrm{SU}}\right]}^h)}^h,$ in Depend on The elements from the (n-1)K+1th row to the nKth row of , represent the equivalent channel matrix from the SBS to the nth SU in the SC;

Step 4. Divide the interference item w _S into N _SU K×1-dimensional sub-matrices w _S [i], i=1, ..., N _SU , that is, w _S =(w _S [1] ^H , w _S [ 2] ^H ,..., w _S [N _SU ] ^H ) ^H , where w _s [i] consists of elements from row (i-1)K+1 to row iK of w _S , indicating that the i-th SU received interference items;

Step 5, initialize m=0;

Step 6, calculating a set of orthonormal basis V _null [m] of the matrix null space corresponding to the mth SU user ITP, including the following steps:

i. Construct the equivalent interference channel matrix within the mth SU layer

in, It is a [(N _SU -1)K]×[( _{NT -1)K+N T L} ]-dimensional matrix, at least one N _null [m]=N _T L+( _NT -N _SU )K dimension the null space of

ii. yes Perform singular value decomposition obtain The null-space orthonormal basis V _null [m], where, and are unitary matrices, is a diagonal matrix whose diagonal elements are (N _SU -1)K singular values of ; then A set of orthonormal basis V _null [m]=V _SS [m](:,(N _SU -1)K+1:(N _T -1)K+N _T L);

Step 7, calculate the postprocessing matrix $Q\left[m\right]=R_w^{-1/2}\left[m\right],$ in, $R_w\left[m\right]=\mathrm{E.}\left(w_S\right[m\left]w_S^h\right[m\left]\right)$ is the autocorrelation matrix of w _S [m];

Step 8, solve the selection and rotation operation matrix T[m], so that the channel capacity of the mth SU reaches the maximum, including the following steps:

i. Calculation matrix Do eigenvalue decomposition of X ^H [m]X[m]:

${\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; \&Lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ;</span>$

in, $Q_{\mathrm{xxx}}\left[m\right]\&Element;C^{N_{\mathrm{null}}\left[m\right]\&times;N_{\mathrm{null}}\left[m\right]}$ is a unitary matrix, ${\mathrm{\&Lambda;}}_{\mathrm{xx}}\left[m\right]\&Element;C^{N_{\mathrm{null}}\left[m\right]\&times;N_{\mathrm{null}}\left[m\right]}$ is a diagonal matrix, and its diagonal elements are the eigenvalues of the matrix X ^H [m]X[m];

ii. The matrix T[m] is composed of the first D[m] columns of Q _xx [m], that is, T[m]=Q _xx [m](:, 1:D[m]), where D[m] is the sending dimension corresponding to SU, when , D[m]=N _null [m], when $N_T>\frac{(N_{\mathrm{SU}}+1)K}{K+L}$ When D[m]=K;

Step 9, find the optimized ITP matrix of the mth SU

Step 10, calculate the channel capacity of the mth SU

$\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; SS</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; null</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; null</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; SS</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span>$

Among them, I _K represents the identity matrix of K×K dimension, Indicates the signal power allocation matrix sent to the mth SU, and P[m] is obtained by the water injection power algorithm;

Step 11, add 1 to m, repeat steps 6-10 until m=N _SU optimization design is completed.

The beneficial effect of the invention is that the transmission capacity of the two-layer network can be maximized while effectively suppressing interference among users.

Description of drawings

Fig. 1 is a schematic diagram of an OFDMA-based MC and a MIMO-VFDM-based multi-user SC system model;

Figure 2 is a schematic diagram of the corresponding relationship between the BD-ZF-based ITP available dimension area and _NT when the N _SU is fixed;

Fig. 3 is a schematic diagram of the relationship between the channel capacity of SC and the number of users N _SU ;

Fig. 4 is a schematic diagram of the relationship between the channel capacity of SC and the number of users _NT ;

Fig. 5 is a schematic diagram of channel capacity of SC under different SNRs.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and embodiments, and the present invention includes but not limited to the following embodiments.

The system model of the two-layer cognitive network is shown in Figure 1. The cognitive network is composed of MCs on the first floor and SCs on the second floor. MCs use LTE-OFDMA to communicate, and SCs use MIMO-VFDM to communicate. MC and SC share spectrum bandwidth, but MC has priority to use the shared spectrum. The MC of the layer-1 network consists of an MC base station (MCBaseStation, MBS) and an MC user (MCUser, MU), and the SC of the layer-2 network consists of an SC base station (SCBaseStation, SBS) and N _SU SC users (SCUser, SU) composition. Assume that all nodes can perfectly obtain the required channel state information, and set the system model as follows: MBS and all MUs in the first-layer network MC use single antennas, SBS in the second-layer network SC uses multi-antenna communication, and SBS The number of antennas is N _T , and all SUs use a single antenna. MC adopts the OFDM transmission mode with an effective symbol length of K and a cyclic prefix length of L.

Combined with the system model, define x _M ∈ C ^K×1 as the symbol vector sent by MBS, y _M ∈ C ^K×1 as the signal vector received by MU, x _S [n]∈C ^(K+L)×1 , n =1, 2,..., N _T is the signal vector sent by the nth antenna of the SBS, y _S [m]∈CK ^×1 , m=1, 2,..., N _SU is the signal vector received by the mth SU signal vector, is the overall noise signal received by all SUs. The intra-layer channel matrix of MC is H _MM ∈ C ^K×K , which represents the channel frequency domain response matrix from MBS to MU. The intra-layer channel matrix of SC is Indicates the overall channel matrix from SBS to each SU in SC. The inter-layer channel matrix includes: and denote the overall interlayer channel matrix from SBS to MU and MBS to all SUs, respectively.

On the basis of CTP suppressing interlayer interference, ITP controls mutual interference between users within SC. The present invention will be described in two parts, namely CTP design and ITP optimization design.

I. Design of CTP

Let s _S ∈ C ^J×1 be the transmitted signal vector of SBS before CTP coding, is the CTP coding matrix, where J represents the maximum transmission dimension of the SBS. The design of the CTP matrix must ensure that the signal sent by the SC does not interfere with the communication of the MC, satisfying Right now

H _SM C = 0(1)

The CTP matrix that satisfies formula (1) _falls on the null space of matrix HSM, then the specific design scheme of CTP is as follows:

1) Perform singular value decomposition on the channel matrix _HSM to get $h_{\mathrm{SM}}=u_{\mathrm{ctp}}{\mathrm{\&Lambda;}}_{\mathrm{ctp}}{V}_{\mathrm{ctp}}^h,$ where U _ctp ∈ C ^K×K and are unitary matrices, is a diagonal matrix, its expression is ${\mathrm{\&Lambda;}}_{\mathrm{ctp}}=({\mathrm{\&Sigma;}}_{\mathrm{ctp}},o_{K\&times;[(N_T-1)K+N_{T}L]}),$ Among them, ∑ _ctp ∈ C ^K×K is a diagonal matrix, and the diagonal elements are the singular values of _HSM .

2) The matrix V _ctp is divided as follows:

V _ctp = (V ₁ , V ₂ )(2)

in It is easy to prove that V ₂ satisfies H _SM V ₂ =0, so V ₂ is a set of orthonormal basis of H _SM null space. Design the CTP matrix C=V ₂ , it can be obtained that J=(N _T -1)K+N _T L .

II. OPTIMIZED DESIGN OF ITP

The design principle of ITP is similar to that of CTP, and its main purpose is to eliminate the mutual interference of signals in the SC while maximizing the channel capacity of the SC. The equivalent channel matrix after the channel matrix in the SC layer is precoded by CTP can be expressed as SU receives external interference term and noise as The optimization design steps of ITP are as follows:

1) the matrix Split into N _SU K×[(N _T -1)K+N _T L]-dimensional sub-matrices by row n=1, ..., N _SU , namely ${\stackrel{\&OverBar;}{h}}_{\mathrm{SS}}={({\stackrel{\&OverBar;}{h}}_{\mathrm{SS}}{\left[1\right]}^h,{\stackrel{\&OverBar;}{h}}_{\mathrm{SS}}{\left[2\right]}^h,...,{\stackrel{\&OverBar;}{h}}_{\mathrm{SS}}{\left[N_{\mathrm{SU}}\right]}^h)}^h,$ in Depend on Elements from the (n-1)K+1th row to the nKth row of , represent the equivalent channel matrix from the SBS to the nth SU in the SC.

2) Divide the interference item w _S into N _SU K×1-dimensional sub-matrices w _S [i], i=1, ..., N _SU , that is, w _S =(w _S [1] ^H , w _S [2 ] ^H ,..., w _S [N _SU ] ^H ) ^H , where w _s [i] consists of elements from row (i-1)K+1 to row ik of w _S , which means the i-th SU received Interfering items.

3) Initialize m=0.

4) Calculate a set of orthonormal basis V _null [m] of the matrix null space corresponding to the mth SU user ITP.

iii. Construct the equivalent interference channel matrix in the mth SU layer as follows:

in, It is a [(N _SU -1)K]×[( _{NT -1)K+N T L} ]-dimensional matrix, at least one N _null [m]=N _T L+( _NT -N _SU )K dimension the null space of

iv. yes Perform singular value decomposition to get The null-space orthonormal basis V _null [m]. The singular value decomposition of is:

in, and are unitary matrices, is a diagonal matrix whose diagonal elements are (N _SU -1)K singular values of .

but A set of orthonormal basis for the null space can be expressed as follows:

V _null [m] = V _SS [m] (:, (N _SU -1) K + 1: (N _T -1) K + N _T L) (5)

5) Calculate the post-processing matrix Q[m]. In order to maximize the SC channel capacity, a post-processing matrix is used at each SU receiver to whiten the signal vector y _S [m] ∈ C ^{K × 1} received by the m-th SU to eliminate interference from MC and noise signals. The calculation formula of Q[m] is:

$\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

in, $R_w\left[m\right]=\mathrm{E.}\left(w_S\right[m\left]w_S^h\right[m\left]\right)$ is the autocorrelation matrix of w _S [m].

6) Solve the selection and rotation operation matrix T[m], so that the channel capacity of the mth SU reaches the maximum. Then the solution process of T[m] is as follows:

ii. Calculation matrix Do eigenvalue decomposition of X ^H [m]X[m]:

${\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; \&Lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

in, is a unitary matrix, is a diagonal matrix whose diagonal elements are the eigenvalues of the matrix X ^H [m]X[m].

iii. The matrix T[m] is composed of the first D[m] columns of Q _xx [m], that is, T[m]=Q _xx [m](:, 1:D[m]), wherein, D[m] is the sending dimension corresponding to SU, and its selection rules are given in Figure 2: when , D[m]=N _null [m], when When D[m]=K.

7) Find the optimized ITP matrix of the mth SU Calculated as follows:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; BD</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; ZF</span>}}_{\mathrm{<span\; class="notranslate">\; opt</span>}}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; null</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

8) Calculate the channel capacity C[m] of the mth SU, the calculation formula is as follows:

$C\left[m\right]=\frac{1}{K+L}{\log }_2|I_K+Q[m\left]{\stackrel{\&OverBar;}{h}}_{\mathrm{SS}}\right[m\left]V_{\mathrm{null}}\right[m\left]T\right[m\left]P\right[m\left]T^h\right[m\left]V_{\mathrm{null}}^h\right[m\left]{\stackrel{\&OverBar;}{h}}_{\mathrm{SS}}^h\right[m\left]{Q\left[m\right]}^h\right|$ (9) Among them, I _K represents the identity matrix of K×K dimension, Represents the signal power allocation matrix sent to the mth SU, and P[m] is obtained by the water injection power algorithm.

9) Add 1 to m, repeat 4) to 9) until m=N _SU optimization design is completed.

The one-layer network of the embodiment adopts OFDM transmission with K=64, L=16, and a bandwidth of 1.92 MHz; the channel impulse response does not change during OFDM symbol transmission, and all obey complex Gaussian random distribution.

Figure 2 shows the relationship between BD-ZF-based ITP available dimension area and _NT when N _SU is a constant value. The shaded part in the figure indicates the available transmission dimension area of the link from the SBS to the mth SU when CTP is adopted. It was observed that: i) when When , the dimension of the null space is equal to the upper bound of the available dimension of SU; ii) when When , the null space dimension is larger than the desired dimension. Case i) It needs to be rotated to V _null [m] to construct matrix to maximize the channel capacity of SC; case ii) needs to select and rotate V _null [m] to construct matrix. Maximize the SC channel capacity. Both operations on V _null [m] can be achieved by selecting and rotating the matrix T[m].

Figure 3 shows the corresponding relationship between SC channel capacity and N _SU when using optimized and unoptimized BD-ZFITP matrices under the conditions of N _T =8, SNR = SNR = 10dB and SNR = 10dB. It can be seen from the figure that when N _SU <9, the performance of the optimized ITP algorithm proposed by the present invention is significantly better than that of the unoptimized ITP algorithm, and when N _SU =9, the performance of the two algorithms is the same. It can also be observed that with the increase of _NSU , the SC channel capacity of the optimized ITP algorithm proposed by the present invention does not increase monotonically, but first increases and then decreases. This shows that the number of users in the cell is not as many as possible, but there is a number of users that makes the channel capacity of the cell optimal.

Figure 4 shows the corresponding relationship between SC channel capacity and NT when using optimized and unoptimized BD- _ZFITP matrices under the conditions of N _SU =2, SNR = SNR = 10dB and SNR = 30dB. It can be seen from Fig. 4 that with the increase of the number _NT of transmitting antennas, the performance of the optimized ITP design algorithm is significantly better than that of the unoptimized ITP design algorithm.

Figure 5 shows the SC transmission capacity comparison results of the optimized ITP algorithm and the unoptimized ITP algorithm under different SNRs. In Fig. 5, the number of transmitting antennas of the SBS is set as N _T =8, and two cases of the number of SC users N _SU =4 and N _SU =9 are given. It can be seen from Fig. 5 that when N _SU = 4, the channel capacity performance of the optimized ITP algorithm is significantly better than that of the unoptimized ITP algorithm. When N _SU = 9, the performance of the optimized ITP design algorithm is consistent with that of the unoptimized algorithm, which is consistent with Fig. The results shown in 3 are consistent.

Claims (1)

1. A multi-user cognitive network precoding optimization method based on MIMO-VFDM, is characterized in that comprising the steps: Step 1, perform singular value decomposition on the overall interlayer channel matrix H _SM from the SC base station SBS to the MC user MU to obtain $h_{\mathrm{SM}}=u_{\mathrm{ctp}}{\mathrm{\&Lambda;}}_{\mathrm{ctp}}{V}_{\mathrm{ctp}}^h,$ in, and are unitary matrices, is a diagonal matrix, ${\mathrm{\&Lambda;}}_{\mathrm{ctp}}=({\mathrm{\&Sigma;}}_{\mathrm{ctp}},0_{K\&times;[(N_T-1)K+N_{T}L]}),$ in, is a diagonal matrix, and the diagonal elements are the singular values of _HSM ; Step 2, partition matrix V _ctp = (V ₁ , V ₂ ), where V ₂ is a group of orthonormal basis of _HSM null space, design CTP matrix C=V ₂ , get J=(N _T -1)K+N _T L, where N _T is the number of SBS antennas, K is MC effective symbol length, L is the MC cyclic prefix length; Step 3, the equivalent channel matrix after the channel matrix in the SC layer is precoded by CTP Split into N _SU K×[(N _T -1)K+N _T L]-dimensional sub-matrices by row n=1,..., N _SU , N _SU represents the number of SC users, namely ${\stackrel{\&OverBar;}{h}}_{\mathrm{SS}}={({\stackrel{\&OverBar;}{h}}_{\mathrm{SS}}{\left[1\right]}^h,{\stackrel{\&OverBar;}{h}}_{\mathrm{SS}}{\left[2\right]}^h,...,{\stackrel{\&OverBar;}{h}}_{\mathrm{SS}}{\left[N_{\mathrm{SU}}\right]}^h)}^h,$ in Depend on The elements from the (n-1)K+1th row to the nKth row of , represent the equivalent channel matrix from the SBS to the nth SU in the SC; Step 4. Divide the interference item w _S into N _SU K×1-dimensional sub-matrices w _S [i], i=1, ..., N _SU , that is, w _S =(w _S [1] ^H , w _S [ 2] ^H ,..., w _S [N _SU ] ^H ) ^H , where w _s [i] consists of elements from row (i-1)K+1 to row iK of w _S , indicating that the i-th SU received interference items; Step 5, initialize m=0; Step 6, calculating a set of orthonormal basis V _null [m] of the matrix null space corresponding to the mth SU user ITP, including the following steps: i. Construct the equivalent interference channel matrix within the mth SU layer in, It is a [(N _SU -1)K]×[( _{NT -1)K+N T L} ]-dimensional matrix, at least one N _null [m]=N _T L+( _NT -N _SU )K dimension the null space of ii. yes Perform singular value decomposition obtain The null-space orthonormal basis V _null [m], where, and U _SS [m]∈ are unitary matrices, is a diagonal matrix whose diagonal elements are (N _SU -1)K singular values of ; then A set of orthonormal basis V _null [m]=V _SS [m](:,N _SU -1)K+1:(N _T -1)K+N _T L); Step 7, calculate the postprocessing matrix $Q\left[m\right]=R_w^{-1/2}\left[m\right],$ in, $R_w\left[m\right]=\mathrm{E.}\left(w_S\right[m\left]w_S^h\right[m\left]\right)$ is the autocorrelation matrix of w _S [m]; Step 8, solve the selection and rotation operation matrix T[m], so that the channel capacity of the mth SU reaches the maximum, including the following steps: i. Calculation matrix Do eigenvalue decomposition of X ^H [m]X[m]: ${\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; \&Lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ;</span>$ in, is a unitary matrix, is a diagonal matrix, and its diagonal elements are the eigenvalues of the matrix X ^H [m]X[m]; ii. The matrix T[m] is composed of the first D[m] columns of Q _xx [m], that is, T[m]=Q _xx [m](:, 1:D[m]), where D[m] is the sending dimension corresponding to SU, when , D[m]=N _null [m], when $N_T>\frac{(N_{\mathrm{SU}}+1)K}{K+L}$ When D[m]=K; Step 9, find the optimized ITP matrix of the mth SU Step 10, calculate the channel capacity of the mth SU $\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; SS</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; null</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; null</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}}_{\mathrm{<span\; class="notranslate">\; SS</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; Q</span>}{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; ,</span>$ Among them, I _K represents the identity matrix of K×K dimension, Indicates the signal power allocation matrix sent to the mth SU, and P[m] is obtained by the water injection power algorithm; Step 11, add 1 to m, repeat steps 6-10 until m=N _SU optimization design is completed.