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

Abstract

The invention provides a precoding optimization method for a multi-user cognition network based on MIMO-VFDM. On the basis that a CTP inhibits interlayer interference, an ITP controls the mutual interference among users in an SC. Through the selection and rotation of a null space, an optimized ITP code matrix is built. The method can enable the channel capacity of the SC to be maximized, thereby enlarging the capacity of a cognition network while the interference among a plurality of two-layer network users.

Description

Multi-user cognitive network precoding optimization method based on MIMO-VFDM

Technical Field

The invention relates to an optimization design scheme of multi-user two-layer cognitive network precoding transmitted by adopting multi-input multi-Output (MIMO) and Vandermonde-subspace frequency division multiplexing (VFDM), which is used for inhibiting interference among users in a two-layer cognitive network and maximizing the channel capacity of the two-layer network.

Background

The continuous increase of wireless services leads to the increasing scarcity of frequency domain resources, so that wireless transmission with high spectrum utilization becomes a research hotspot of modern communication. Deployment of two-layer networks such as a cognitive network is a feasible scheme for solving spectrum resources. In a two-layer network communication system based on cognitive radio technology, small-cells (SCs) are arranged as a second-layer network around and sharing spectrum transmission with a macro-cell (MC). The MC has priority over the shared spectrum, and the two-tier network has opportunistic access to the spectrum and must ensure that no or within a tolerable range interference is generated for the MC. Therefore, how to control the interference of SCs on MC becomes a main problem for research in the implementation of two-layer cognitive network.

The VFDM technology, as an emerging method for solving the problem of interference control in the cognitive network, utilizes the frequency band redundancy provided by the cyclic prefix in the block transmission system (e.g., OFDM system) to establish a new transmission link for the SCs without interfering with the normal communication of the MC. After adopting VFDM, signals transmitted by the two-layer transmitter are constrained to the null space from the two-layer network to the one-layer network interference channel by means of Cross-tiorpecoder (CTP). Intra-layer precoding (ITP) is then used to control the inter-user interference within the SC.

Document 1, "channel signaling information and signaling cells base done-vddm [ wireless communication and network connectivity (wcnc), IEEE 2012: 2560-.

Document 2, "Spatial-frequency signaling alignment for opportunistic transmission [ ieee transaction in signaling processing,2014,62: 1561-.

Document 3 "Zero-while method for downlink signaling MIMO channels, [ signaling processing, ieee transactions son,2004,52(2):461-471] proposes a Block-DiagonalZero-Forcing (BD-ZF) precoding algorithm to solve the inter-user interference problem in the multi-user MIMO downlink. The BD-ZF precoding algorithm has the advantages of convenience in design, simple structure and the like, and is very suitable for designing an ITP precoding matrix among multiple users.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a two-layer network precoding optimization method based on BD-ZF on the basis of the prior precoding algorithm. The optimized ITP coding matrix is constructed through selection and rotation of the null space, the channel capacity of the SC can be maximized, and therefore interference among two-layer networks and multiple users is suppressed, and the capacity of a cognitive network is improved.

The technical scheme adopted by the invention for solving the technical problem comprises the following steps:

step 1, carrying out overall interlayer channel matrix H from SC base station SBS to MC user MU_SMPerforming singular value decomposition to obtain <math> <mrow> <msub> <mi>H</mi> <mi>SM</mi> </msub> <mo>=</mo> <msub> <mi>U</mi> <mi>ctp</mi> </msub> <msub> <mi>&Lambda;</mi> <mi>ctp</mi> </msub> <msubsup> <mi>V</mi> <mi>ctp</mi> <mi>H</mi> </msubsup> <mo>,</mo> </mrow> </math> Wherein, U_ctp∈C^K×KAndare all unitary matrices that are used for the transmission of the signal,in the form of a diagonal matrix, <math> <mrow> <msub> <mi>&Lambda;</mi> <mi>ctp</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>&Sigma;</mi> <mi>ctp</mi> </msub> <mo>,</mo> <msub> <mi>O</mi> <mrow> <mi>K</mi> <mo>&times;</mo> <mo>[</mo> <mrow> <mo>(</mo> <msub> <mi>N</mi> <mi>T</mi> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>K</mi> <mo>+</mo> <msub> <mi>N</mi> <mi>T</mi> </msub> <mi>L</mi> <mo>]</mo> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> therein, sigma_ctp∈C^K×KIs a diagonal matrix with diagonal elements of H_SMThe singular value of (a);

step 2, partitioning the matrix V_ctp＝(V₁，V₂) Wherein V₂Is H_SMDesigning a CTP matrix C as V based on a set of standard orthogonal bases in null space₂To obtain J ═ N_T-1)K+N_TL, wherein, N_TThe number of SBS antennas is, K is the effective symbol length of MC, L is the cyclic prefix length of MC;

step 3, carrying out CTP precoding on the channel matrix in the SC layer to obtain an equivalent channel matrixSplitting into N by row_SUK x [ (N)_T-1)K+N_TL]Sub-matrix of dimensionn＝1，…，N_SU，N_SUIndicating the number of SC users, i.e. <math> <mrow> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <msup> <mrow> <mo>[</mo> <mn>1</mn> <mo>]</mo> </mrow> <mi>H</mi> </msup> <mo>,</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <msup> <mrow> <mo>[</mo> <mn>2</mn> <mo>]</mo> </mrow> <mi>H</mi> </msup> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <msup> <mrow> <mo>[</mo> <msub> <mi>N</mi> <mi>SU</mi> </msub> <mo>]</mo> </mrow> <mi>H</mi> </msup> <mo>)</mo> </mrow> <mi>H</mi> </msup> <mo>,</mo> </mrow> </math> WhereinByThe (n-1) th K +1 row to the nK row of (a) represents an equivalent channel matrix from SBS to nth SU within SC;

step 4, interference item w_SIs divided into N_SUA K x 1 dimensional sub-matrix w_S[i]，i＝1，…，N_SUI.e. w_S＝(w_S[1]^H，w_S[2]^H，…，w_S[N_SU]^H)^HWherein w is_s[i]From w_SThe (i-1) K +1 line to the iK line of (A) of (B) of (C of) of;

step 5, initializing m to be 0;

step 6, calculating a group of standard orthogonal bases V of the matrix null space corresponding to the m-th SU user ITP_null[m]The method comprises the following steps:

i. constructing an in-layer equivalent interference channel matrix of the mth SU

Wherein,is a [ (N)_SU-1)K]×[(N_T-1)K+N_TL]Matrix of dimensions of at least one N_null[m]＝N_TL+(N_T-N_SU) A null space of dimension K;

ii, toPerforming singular value decompositionTo obtainZero space orthonormal basis V of_null[m]Whereinand are all unitary matrices and are used as a matrix,is a diagonal matrix whose diagonal elements areIs (N)_SU-1) K singular values; thenSet of orthonormal bases V of null space_null[m]＝V_SS[m](：，(N_SU-1)K+1：(N_T-1)K+N_TL)；

Step 7, calculating a post-processing matrix $Q\left[m\right]=R_w^{-1/2}\left[m\right],$ Wherein, $R_w\left[m\right]=E\left(w_S\right[m\left]w_S^H\right[m\left]\right)$ is w_S[m]The autocorrelation matrix of (a);

and 8, solving the selection and rotation operation matrix T [ m ] to enable the channel capacity of the mth SU to be maximum, and comprising the following steps of:

i. computing matricesTo X^H[m]X[m]And (3) carrying out characteristic value decomposition:

<math> <mrow> <msup> <mi>X</mi> <mi>H</mi> </msup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mi>X</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>=</mo> <msub> <mi>Q</mi> <mi>xx</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msub> <mi>&Lambda;</mi> <mi>xx</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msubsup> <mi>Q</mi> <mi>xx</mi> <mi>H</mi> </msubsup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>;</mo> </mrow> </math>

wherein, <math> <mrow> <msub> <mi>Q</mi> <mi>xx</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>&Element;</mo> <msup> <mi>C</mi> <mrow> <msub> <mi>N</mi> <mi>null</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>&times;</mo> <msub> <mi>N</mi> <mi>null</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> </mrow> </msup> </mrow> </math> is a unitary matrix of the first phase, <math> <mrow> <msub> <mi>&Lambda;</mi> <mi>xx</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>&Element;</mo> <msup> <mi>C</mi> <mrow> <msub> <mi>N</mi> <mi>null</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>&times;</mo> <msub> <mi>N</mi> <mi>null</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> </mrow> </msup> </mrow> </math> is a diagonal matrix, the diagonal elements of which are matrix X^H[m]X[m]A characteristic value of (d);

ii. matrix T [ m ]]From Q_xx[m]Before D [ m ] of]Column formation, i.e. T [ m ]]＝Q_xx[m](：，1：D[m]) Wherein D [ m ]]Is the transmit dimension for SU whenWhen, D [ m ]]＝N_null[m]When is coming into contact with $N_T>\frac{(N_{\mathrm{SU}}+1)K}{K+L}$ Time D [ m ]]＝K；

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

Step 10, calculating the channel capacity of the mth SU

<math> <mrow> <mi>C</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>K</mi> <mo>+</mo> <mi>L</mi> </mrow> </mfrac> <msub> <mi>log</mi> <mn>2</mn> </msub> <mo>|</mo> <msub> <mi>I</mi> <mi>K</mi> </msub> <mo>+</mo> <mi>Q</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msub> <mi>V</mi> <mi>null</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mi>T</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mi>P</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msup> <mi>T</mi> <mi>H</mi> </msup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msubsup> <mi>V</mi> <mi>null</mi> <mi>H</mi> </msubsup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msubsup> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> <mi>H</mi> </msubsup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msup> <mrow> <mi>Q</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> </mrow> <mi>H</mi> </msup> <mo>|</mo> <mo>,</mo> </mrow> </math>

Wherein, I_KAn identity matrix representing dimensions K x K,representing the signal power distribution matrix sent to the mth SU, and obtaining Pm by water filling power algorithm]；

Step 11, adding 1 to m, and repeating the steps 6-10 until m is equal to N_SUAnd finishing the optimization design.

The invention has the beneficial effects that: the method can effectively inhibit the interference among users and simultaneously can maximize the transmission capacity of a two-layer network.

Drawings

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

FIG. 2 is N_SUITP usable dimension area and N based on BD-ZF at fixed time_TSchematic diagram of corresponding relationship of (1);

FIG. 3 shows the channel capacity of SC and the number of users N_SUA schematic diagram of the relationship of (1);

FIG. 4 shows the channel capacity of SC and the number of users N_TA schematic diagram of the relationship of (1);

fig. 5 is a diagram of the channel capacity of the SC at different signal-to-noise ratios.

Detailed Description

The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.

A system model of the two-layer cognitive network is shown in fig. 1. The cognitive network consists of a first layer of MC and a second layer of SC, wherein the MC adopts an LTE orthogonal frequency division multiple access mode for communication, and the SC adopts an MIMO-VFDM mode for communication. MC and SC share spectrum bandwidth, but MC has priority usage of shared spectrum. The MC of one-layer network comprises an MC base station (MCBaseStation, MBS) and an MC user (MCUser, MU), and the SC of the two-layer network comprises an SC base station (SCBASeStation, SBS) and N_SUAnd SC users (SCUser, SU). Assuming that all nodes can perfectly obtain the required channel state information, the system model is set as follows: MBS and all MU in the first layer network MC adopt single antenna, SBS in the second layer network SC adopts multi-antenna communication, SBS antenna number is N_TAll SUs use a single antenna. The MC adopts an OFDM transmission mode with an effective symbol length of K and a cyclic prefix length of L.

Define x in conjunction with the system model_M∈C^K×1Sending symbol vectors, y, for MBS_M∈C^K×1Is the signal vector, x, received by the MU_S[n]∈C^(K+L)×1，n＝1，2，…，N_TSignal vector, y, transmitted for the nth antenna of SBS_S[m]∈C^K×1，m＝1，2，…，N_SUFor the signal vector received by the mth SU,the overall noise signal received for all SUs. The in-layer channel matrix of the MC is H_MM∈C^K×KAnd represents the channel frequency domain response matrix from MBS to MU. The intra-layer channel matrix of the SC isRepresenting the overall channel matrix of SBS to individual SUs within the SC. The inter-layer channel matrix includes:andthe overall inter-layer channel matrices for SBS to MU and MBS to all SUs are indicated separately.

The mutual interference between SC inner users is controlled by ITP on the basis that CTP restrains the interference between layers. The present invention will be described in two parts, namely, CTP design and ITP optimization design.

Design of CTP

Let s_S∈C^J×1For SBS to send a signal vector before CTP encoding,is a CTP coding matrix, wherein J represents the largest transmission dimension of SBS. The design of the CTP matrix ensures that the transmitting signal of the SC does not interfere the communication of the MC, and the requirement is metNamely, it is

H_SMC＝0(1)

The CTP matrix satisfying formula (1) falls on matrix H_SMThe specific design scheme of CTP is as follows:

1) for channel matrix H_SMPerforming singular value decomposition to obtain <math> <mrow> <msub> <mi>H</mi> <mi>SM</mi> </msub> <mo>=</mo> <msub> <mi>U</mi> <mi>ctp</mi> </msub> <msub> <mi>&Lambda;</mi> <mi>ctp</mi> </msub> <msubsup> <mi>V</mi> <mi>ctp</mi> <mi>H</mi> </msubsup> <mo>,</mo> </mrow> </math> Wherein, U_ctp∈C^K×KAndare all unitary matrices that are used for the transmission of the signal,is a diagonal matrix with the expression of <math> <mrow> <msub> <mi>&Lambda;</mi> <mi>ctp</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>&Sigma;</mi> <mi>ctp</mi> </msub> <mo>,</mo> <msub> <mi>O</mi> <mrow> <mi>K</mi> <mo>&times;</mo> <mo>[</mo> <mrow> <mo>(</mo> <msub> <mi>N</mi> <mi>T</mi> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>K</mi> <mo>+</mo> <msub> <mi>N</mi> <mi>T</mi> </msub> <mi>L</mi> <mo>]</mo> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> Therein, sigma_ctp∈C^K×KIs a diagonal matrix with diagonal elements of H_SMThe singular value of (a).

2) For matrix V_ctpThe following segmentation is performed:

V_ctp＝(V₁，V₂)(2)

whereinEasy to prove V₂Satisfy H_SMV₂0, thus V₂Is H_SMA set of orthonormal bases of null space. Design CTP matrix C ═ V₂It can be found that J ═ N_T-1)K+N_TL。

Optimal design of ITP

The design principle of ITP is similar to CTP, with the main purpose of eliminating inter-signal interference within the SC while maximizing SC channel capacity. Equivalent channel matrix of SC layer channel matrix after CTP precodingCan be expressed asSU receives external interference term and noiseThe optimal design steps of ITP are as follows:

1) will matrixSplitting into N by row_SUK x [ (N)_T-1)K+N_TL]Sub-matrix of dimensionn＝1，…，N_SUI.e. by <math> <mrow> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <msup> <mrow> <mo>[</mo> <mn>1</mn> <mo>]</mo> </mrow> <mi>H</mi> </msup> <mo>,</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <msup> <mrow> <mo>[</mo> <mn>2</mn> <mo>]</mo> </mrow> <mi>H</mi> </msup> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <msup> <mrow> <mo>[</mo> <msub> <mi>N</mi> <mi>SU</mi> </msub> <mo>]</mo> </mrow> <mi>H</mi> </msup> <mo>)</mo> </mrow> <mi>H</mi> </msup> <mo>,</mo> </mrow> </math> WhereinByThe (n-1) th K +1 to nK rows of (a) constitute an equivalent channel matrix representing SBS to nth SU within SC.

2) Interference term w_SIs divided into N_SUA K x 1 dimensional sub-matrix w_S[i]，i＝1，…，N_SUI.e. w_S＝(w_S[1]^H，w_S[2]^H,…，w_S[N_SU]^H)^HWherein w is_s[i]From w_SThe (i-1) K +1 line to ik line elements of (i-1) represent interference terms received by the ith SU.

3) And initializing m to be 0.

4) Calculating a set of standard orthogonal bases V of a matrix null space corresponding to the ITP of the mth SU user_null[m]。

Constructing an intra-layer equivalent interference channel matrix for the mth SUThe following were used:

wherein,is a [ (N)_SU-1)K]×[(N_T-1)K+N_TL]Matrix of dimensions of at least one N_null[m]＝N_TL+(N_T-N_SU) A null space of dimension K;

iv, pairSingular value decomposition is performed to obtainZero space orthonormal basis V of_null[m]。The singular value of (a) is decomposed into:

wherein,andare all unitary matrices and are used as a matrix,is a diagonal matrix whose diagonal elements areIs (N)_SU-1) K singular values.

ThenThe set of orthonormal bases for the null space can be represented by:

V_null[m]＝V_SS[m](：，(N_SU-1)K+1：(N_T-1)K+N_TL)(5)

5) computing post-processing matrix qm]. To maximize SC channel capacity, a post-processing matrix is used at each SU receiver to align the signal vector y received by the mth SU_S[m]∈C^K×1To perform whiteningAnd eliminating interference from the MC and the noise signal. Q [ m ]]The calculation formula is as follows:

$Q\left[m\right]=R_w^{-1/2}\left[m\right]---\left(6\right)$

wherein, $R_w\left[m\right]=E\left(w_S\right[m\left]w_S^H\right[m\left]\right)$ is w_S[m]The autocorrelation matrix of (a).

6) And solving the selection and rotation operation matrix T [ m ] to enable the channel capacity of the mth SU to reach the maximum. Then the solution for T [ m ] is as follows:

calculating a matrixTo X^H[m]X[m]And (3) carrying out characteristic value decomposition:

<math> <mrow> <msup> <mi>X</mi> <mi>H</mi> </msup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mi>X</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>=</mo> <msub> <mi>Q</mi> <mi>xx</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msub> <mi>&Lambda;</mi> <mi>xx</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msubsup> <mi>Q</mi> <mi>xx</mi> <mi>H</mi> </msubsup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein,is a unitary matrix of the first phase,is a diagonal matrix, the diagonal elements of which are matrix X^H[m]X[m]The characteristic value of (2).

iii. matrix T [ m ]]From Q_xx[m]Before D [ m ] of]Column formation, i.e. T [ m ]]＝Q_xx[m](：，1：D[m]) Wherein D [ m ]]Is the sending dimension corresponding to SU, and the rule for selecting is given by fig. 2: when in useWhen, D [ m ]]＝N_null[m]When is coming into contact withTime D [ m ]]＝K。

7) Solving an optimized ITP matrix for the mth SUThe calculation formula is as follows:

$U_{\mathrm{BD}-{\mathrm{ZF}}_{\mathrm{opt}}}\left[m\right]=V_{\mathrm{null}}\left[m\right]T\left[m\right]---\left(8\right)$

8) and calculating the channel capacity C [ m ] of the mth SU according to the following calculation formula:

<math> <mrow> <mi>C</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>K</mi> <mo>+</mo> <mi>L</mi> </mrow> </mfrac> <msub> <mi>log</mi> <mn>2</mn> </msub> <mo>|</mo> <msub> <mi>I</mi> <mi>K</mi> </msub> <mo>+</mo> <mi>Q</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msub> <mi>V</mi> <mi>null</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mi>T</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mi>P</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msup> <mi>T</mi> <mi>H</mi> </msup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msubsup> <mi>V</mi> <mi>null</mi> <mi>H</mi> </msubsup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msubsup> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> <mi>H</mi> </msubsup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msup> <mrow> <mi>Q</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> </mrow> <mi>H</mi> </msup> <mo>|</mo> </mrow> </math> (9) wherein, I_KAn identity matrix representing dimensions K x K,representing the signal power distribution matrix sent to the mth SU, and obtaining Pm by water filling power algorithm]。

9) m plus 1, repeat 4) -9) until m ═ N_SUAnd finishing the optimization design.

One layer of the network of the embodiment adopts OFDM transmission with K-64, L-16 and the bandwidth of 1.92 MHz; the channel impulse responses are unchanged during the transmission of the OFDM symbols and all obey complex gaussian random distribution.

FIG. 2 shows N_SUITP usable dimension area and N based on BD-ZF for constant value_TThe relationship (2) of (c). The shaded portion in the figure represents the available transmission dimension area of SBS to the mth SU link in the case of CTP. The observation shows that: i) when in useThe dimension of the null space is equal to the upper bound of the usable dimension of the SU; ii) whenThe null-space dimension is greater than the desired dimension. Case i) requires for V_null[m]Make a certain rotation to constructA matrix for maximizing the channel capacity of the SC; case ii) requires for V_null[m]Performing selection and rotation operations to constructAnd (4) matrix. Maximizing SC channel capacity. To V_null[m]Both operations of (2) can be performed by selecting and rotating the matrix T m]And (5) realizing.

FIG. 3 shows a diagram at N_TThe channel capacity and N of SC when using optimized and non-optimized BD-ZFITP matrix under the conditions of SNR 10dB and SNR 10dB 8_SUThe corresponding relationship of (1). As can be seen from the figure, N_SULess than 9 hours, the invention provides an optimized ITP algorithmThe performance is obviously superior to that of the unoptimized ITP algorithm, N_SUThe two algorithms perform consistently when 9. It can also be observed that with N_SUThe capacity of the SC channel of the optimized ITP algorithm proposed by the present invention is not monotonically increasing, but increases first and then decreases. This means that the number of users in a cell is not as large as possible, but there is a number of users that optimizes the channel capacity of the cell.

FIG. 4 shows a diagram at N_SU2, the channel capacity and N of SC when using optimized and non-optimized BD-ZFITP matrix under the conditions of SNR 10dB and SNR 30dB_TThe corresponding relationship of (1). As can be seen from fig. 4, with the number N of transmitting antennas_TThe performance of the optimized ITP design algorithm is obviously superior to that of the unoptimized ITP design algorithm.

Fig. 5 shows the comparison result of SC transmission capacities of the optimized ITP algorithm and the unoptimized ITP algorithm at different signal-to-noise ratios. In fig. 5, the number of transmitting antennas of SBS is set to N_TThe number of SC users N is given as 8_SU4 and N_SUTwo cases are 9. As can be seen from FIG. 5, when N is_SUWhen the channel capacity performance of the optimized ITP algorithm is 4, the channel capacity performance of the optimized ITP algorithm is obviously better than that of the unoptimized ITP algorithm, and when N is equal to 4_SUAt 9, the optimized ITP design algorithm performed consistently with the unoptimized algorithm, which is consistent with the results shown in fig. 3.

Claims (1)

1. A multi-user cognitive network precoding optimization method based on MIMO-VFDM is characterized by comprising the following steps:

step 1, carrying out overall interlayer channel matrix H from SC base station SBS to MC user MU_SMPerforming singular value decomposition to obtain <math> <mrow> <msub> <mi>H</mi> <mi>SM</mi> </msub> <mo>=</mo> <msub> <mi>U</mi> <mi>ctp</mi> </msub> <msub> <mi>&Lambda;</mi> <mi>ctp</mi> </msub> <msubsup> <mi>V</mi> <mi>ctp</mi> <mi>H</mi> </msubsup> <mo>,</mo> </mrow> </math> Wherein,andare all unitary matrices that are used for the transmission of the signal,in the form of a diagonal matrix, <math> <mrow> <msub> <mi>&Lambda;</mi> <mi>ctp</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>&Sigma;</mi> <mi>ctp</mi> </msub> <mo>,</mo> <msub> <mn>0</mn> <mrow> <mi>K</mi> <mo>&times;</mo> <mo>[</mo> <mrow> <mo>(</mo> <msub> <mi>N</mi> <mi>T</mi> </msub> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>K</mi> <mo>+</mo> <msub> <mi>N</mi> <mi>T</mi> </msub> <mi>L</mi> <mo>]</mo> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> wherein,is a diagonal matrix with diagonal elements of H_SMThe singular value of (a);

step 2, partitioning the matrix V_ctp＝(V₁，V₂) Wherein V₂Is H_SMDesigning a CTP matrix C as V based on a set of standard orthogonal bases in null space₂To obtain J ═ N_T-1)K+N_TL, wherein, N_TThe number of SBS antennas is, K is the effective symbol length of MC, L is the cyclic prefix length of MC;

step 3, carrying out CTP precoding on the channel matrix in the SC layer to obtain an equivalent channel matrixSplitting into N by row_SUK x [ (N)_T-1)K+N_TL]Sub-matrix of dimensionn＝1，…，N_SU，N_SUIndicating the number of SC users, i.e. <math> <mrow> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <msup> <mrow> <mo>[</mo> <mn>1</mn> <mo>]</mo> </mrow> <mi>H</mi> </msup> <mo>,</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <msup> <mrow> <mo>[</mo> <mn>2</mn> <mo>]</mo> </mrow> <mi>H</mi> </msup> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <msup> <mrow> <mo>[</mo> <msub> <mi>N</mi> <mi>SU</mi> </msub> <mo>]</mo> </mrow> <mi>H</mi> </msup> <mo>)</mo> </mrow> <mi>H</mi> </msup> <mo>,</mo> </mrow> </math> WhereinByThe (n-1) th K +1 row to the nK row of (a) represents an equivalent channel matrix from SBS to nth SU within SC;

step 4, interference item w_SIs divided into N_SUA K x 1 dimensional sub-matrix w_S[i]，i＝1，…，N_SUI.e. w_S＝(w_S[1]^H，w_S[2]^H，…，w_S[N_SU]^H)^HWherein w is_s[i]From w_SThe (i-1) K +1 line to the iK line of (A) of (B) of (C of) of;

step 5, initializing m to be 0;

step 6, calculating a group of standard orthogonal bases V of the matrix null space corresponding to the m-th SU user ITP_null[m]The method comprises the following steps:

i. constructing an in-layer equivalent interference channel matrix of the mth SU

Wherein,is a [ (N)_SU-1)K]×[(N_T-1)K+N_TL]Matrix of dimensions of at least one N_null[m]＝N_TL+(N_T-N_SU) A null space of dimension K;

ii, toCarrying out singular valueSolution (II)To obtainZero space orthonormal basis V of_null[m]Whereinand U_SS[m]∈Are all unitary matrices and are used as a matrix,is a diagonal matrix whose diagonal elements areIs (N)_SU-1) K singular values; thenSet of orthonormal bases V of null space_null[m]＝V_SS[m](：，N_SU-1)K+1：(N_T-1)K+N_TL)；

Step 7, calculating a post-processing matrix $Q\left[m\right]=R_w^{-1/2}\left[m\right],$ Wherein, $R_w\left[m\right]=E\left(w_S\right[m\left]w_S^H\right[m\left]\right)$ is w_S[m]The autocorrelation matrix of (a);

and 8, solving the selection and rotation operation matrix T [ m ] to enable the channel capacity of the mth SU to be maximum, and comprising the following steps of:

i. computing matricesTo X^H[m]X[m]And (3) carrying out characteristic value decomposition:

<math> <mrow> <msup> <mi>X</mi> <mi>H</mi> </msup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mi>X</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>=</mo> <msub> <mi>Q</mi> <mi>xx</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msub> <mrow> <mo></mo> <mi>&Lambda;</mi> </mrow> <mi>xx</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msubsup> <mi>Q</mi> <mi>xx</mi> <mi>H</mi> </msubsup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>;</mo> </mrow> </math>

wherein,is a unitary matrix of the first phase,is a diagonal matrix, the diagonal elements of which are matrix X^H[m]X[m]A characteristic value of (d);

ii. matrix T [ m ]]From Q_xx[m]Before D [ m ] of]Column formation, i.e. T [ m ]]＝Q_xx[m](：，1：D[m]) Wherein D [ m ]]Is the transmit dimension for SU whenWhen, D [ m ]]＝N_null[m]When is coming into contact with $N_T>\frac{(N_{\mathrm{SU}}+1)K}{K+L}$ Time D [ m ]]＝K；

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

Step 10, calculating the channel capacity of the mth SU

<math> <mrow> <mi>C</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>K</mi> <mo>+</mo> <mi>L</mi> </mrow> </mfrac> <msub> <mi>log</mi> <mn>2</mn> </msub> <mo>|</mo> <msub> <mi>I</mi> <mi>K</mi> </msub> <mo>+</mo> <mi>Q</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msub> <mi>V</mi> <mi>null</mi> </msub> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mi>T</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mi>P</mi> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msup> <mi>T</mi> <mi>H</mi> </msup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msubsup> <mi>V</mi> <mi>null</mi> <mi>H</mi> </msubsup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <msubsup> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mi>SS</mi> <mi>H</mi> </msubsup> <mo>[</mo> <mi>m</mi> <mo>]</mo> <mi>Q</mi> <msup> <mrow> <mo></mo> <mo>[</mo> <mi>m</mi> <mo>]</mo> </mrow> <mi>H</mi> </msup> <mo>|</mo> <mo>,</mo> </mrow> </math>

Wherein, I_KAn identity matrix representing dimensions K x K,representing the signal power distribution matrix sent to the mth SU, and obtaining Pm by water filling power algorithm]；

Step 11, adding 1 to m, and repeating the steps 6-10 until m is equal to N_SUAnd finishing the optimization design.