CN104135451A - Pilot frequency sequence design method used in uplink multi-user MIMO (Multi-Input Multi-Output) system - Google Patents

Abstract

The present invention relates to a kind of pilot frequency sequence design methods in uplink multi-users mimo system. The present invention exists first L point is taken in unit sphere in dimension complex space, each point is one Tie up row vector. Then training matrix is formed as L row vector of training sequence with L obtained point. Training sequence is finally distributed to user. After base station receives the signal with training sequence, channel is estimated with minimum mean square error method. The accuracy of channel estimation in uplink multi-users mimo system can be improved in the case where recipient does not know channel state information in the present invention, to make the channel estimated closer to real channel, improve data transfer rate.

Description

For the pilot frequency sequence design method at uplink multi-users mimo system

Technical field

The invention belongs to wireless communication technology field, particularly radio communication multi-antenna technology field, the specifically application technology of a kind of training sequence method for designing in uplink multi-users multi-input multi-output system (MIMO).

Background technology

As everyone knows, in the situation that recipient knows channel condition information (CSI), multi-user's mimo system can provide very high message transmission rate and energy efficiency.Therefore, how to obtain CSI and seem particularly important, a kind of method that tradition obtains CSI is the channel estimating based on training sequence.Obviously, the accuracy of estimation depends on training sequence to a great extent, so devise optimum training sequence is very important and necessary.Wherein optimum a kind of design guarantees that training sequence is mutually orthogonal, for this reason, when number of users and the base station number that can produce phase mutual interference are a lot, need to spend a lot of time to send the training sequence of these quadratures, thereby affect the transfer rate of system.In fact, there are two problems here: on the one hand, training time cost is very large, and channel estimating is accurate, but has reduced message transmission rate; On the other hand, if training sequence is not quadrature, especially, when training sequence is reused, can produce Pilot Interference, the performance of channel estimating greatly declines.

Summary of the invention

The present invention is directed to the deficiencies in the prior art, proposed a kind of pilot frequency sequence design method for up many communities multi-user MIMO system.

Suppose that system has L community, there is a base station each community, and base station is furnished with M root antenna, and between community, has co-channel interference.When supposing each community, excited user number is one again.Suppose that each user sends the training sequence that length is τ, i.e. φ _l=(φ _l1, φ _l2..., φ _{l τ}), φ wherein _l1, φ _l2..., φ _{l τ}, l=1,2 ..., L be l user respectively the 1st, 2 ... the training symbol that τ sends constantly.Order for L * τ matrix, be called training matrix, subscript t represents vector or transpose of a matrix (as follows) here.

The present invention is exactly will be to Φ ₀design its method for designing is proposed.Specific as follows:

The first step: get L point in the unit sphere in τ dimension complex space, each point is a τ dimension row vector.Be designated as φ _i, i=1,2 ..., L, φ _ibuild up L * τ matrix Φ ₀, Φ ₀as training matrix.The choosing method of L point is to make following value

$\underset{1\≤i\≠j\≤L}{\max }\left|{\mathrm{\φ}}_i{\mathrm{\φ}}_j^H\right|---\left(1\right)$

The smaller the better, subscript H represents the conjugate transpose (as follows) of vector or matrix here.Concrete choosing can be in the following way: get for τ dimensional vector, each component is 1.

Order

$\begin{array}{cc}{\mathrm{\φ}}_i^t=(\mathrm{diag}{(1,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\τ}}{u}_1\right),\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\τ}}{u}_2\right),...,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\τ}}{u}_{\mathrm{\τ}-1}\right))}^{(i-1)}{\mathrm{\φ}}_0& i=\mathrm{1,2},...,L.\end{array}$

Wherein j is imaginary unit, u ₁, u ₂..., u _τ-1be and be greater than the zero positive integer that is less than τ.These integers can be according to value the smaller the better requirement obtains with calculating search.

Second step: L the row vector using the L obtaining in the first step point as training sequence, forms training matrix ${\mathrm{\Φ}}_0={({\mathrm{\φ}}_1^t,{\mathrm{\φ}}_2^t,...,{\mathrm{\φ}}_L^t)}^t.$

The 3rd step: user's transmitted signal of i base station ρ wherein ₀for sending the required gross energy of training sequence.

The 4th step: the signal Y that supposition base station receives ₀for

$Y_0=\sqrt{\frac{{\mathrm{\ρ}}_0}{\mathrm{\τ}}}\mathrm{H\; B}{\mathrm{\Φ}}_0+W_0$

Wherein H is channel matrix, and B is diagonal matrix, and on its i diagonal, i community user of element representation is to the large scale fading factor of base station.W ₀represent noise.

The 5th step: base station obtains channel estimating by following MMSE channel estimating method :

$\hat{H}=\sqrt{\frac{{\mathrm{\ρ}}_0}{\mathrm{\τ}}}{Y}_0{(I_{\mathrm{\τ}}+\frac{{\mathrm{\ρ}}_0}{\mathrm{\τ}}{\mathrm{\Φ}}_0^H{B}^2{\mathrm{\Φ}}_0)}^{-1}{\mathrm{\Φ}}_0^{H}B$

In above formula, I _τthe unit matrix that represents τ dimension.

The 6th step: matrix characteristic value be designated as τ wherein ₀=min{L, τ }.Can be according to formula calculate channel estimating variance analysis and can make corresponding estimate variance analysis chart.

Beneficial effect of the present invention: in the situation that recipient does not know channel condition information, this method for designing can improve the accuracy of channel estimating in uplink multi-users mimo system, thereby make the channel estimating closer to real channel, improve message transmission rate.

Accompanying drawing explanation

Fig. 1 is the analysis chart of training sequence estimate variance under this method for designing of τ=4 in Uplink MIMO system of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described and provide a specific embodiment:

As shown in Figure 1, initialization system has 10 reception antennas (M=10), 8 users (L=8), and training sequence length is 4 (τ=4).

According to training sequence method for designing of the present invention, obtain according to the following steps the estimate variance analysis chart of channel:

Step 1: get 8 points in the unit sphere in 4 dimension complex spaces, each point is one 4 dimension row vector.Be designated as φ _i, i=1,2 ..., 8, φ _ibuild up 8 * 4 matrix Φ ₀, Φ ₀as training matrix.The choosing method of 8 points is to make following value

$\underset{1\≤i\≠j\≤L}{\max }\left|{\mathrm{\φ}}_i{\mathrm{\φ}}_j^H\right|$

The smaller the better.Concrete choosing can be in the following way: get φ ₀=[1 11 1] ^tbe 4 dimensional vectors, each component is 1; Make u ₁=2, u ₂=4, u ₃=5, B=diag (1, β ₁, β ₂..., β ₇), β wherein _i, i=1,2 ..., the 7th, in interval (0,1), above evenly choose at random.Order

$\begin{array}{cc}{\mathrm{\φ}}_i^t={\left(\mathrm{diag}(1,\exp \left(j\frac{2\mathrm{\π}}{4}{u}_1\right),\exp \left(j\frac{2\mathrm{\π}}{4}{u}_2\right),\exp \left(j\frac{2\mathrm{\π}}{4}{u}_3\right))\right)}^{(i-1)}{\mathrm{\φ}}_0& i=\mathrm{1,2},...,8.\end{array}$

Step 2: 8 some φ that obtain by step 1 ₁, φ ₂..., φ ₈be used as 8 row vectors of training sequence, form training matrix ${\mathrm{\Φ}}_0={({\mathrm{\φ}}_1^t,{\mathrm{\φ}}_2^t,...,{\mathrm{\φ}}_L^t)}^t$

Step 3: according to training matrix Φ obtained above ₀the signal with training sequence receiving with base station the least mean-square error estimation formulas of substitution channel in, the channel that obtains estimating and by the training matrix Φ designing ₀calculate matrix eigenvalue λ ₁, λ ₂..., λ ₄.

Step 4: according to estimate variance formula

$E_H\left\{{\left|\right|H-\widehat{H|}\left|\right|}^2\right\}=M(L-{\mathrm{\τ}}_0)+M\underset{i=1}{\overset{{\mathrm{\τ}}_0}{\mathrm{\Σ}}}\frac{1}{1+{\mathrm{\ρ}}_0{\mathrm{\λ}}_i}=10\×(8-4)+10\×\underset{i=1}{\overset{4}{\mathrm{\Σ}}}\frac{1}{1+{\mathrm{\ρ}}_0{\mathrm{\λ}}_i}$

By the characteristic value substitution in step 3, obtain the analysis chart of estimate variance.

Introduce the theoretical foundation of this method for designing below.

Note real channel is H, and the signal that base station receives can be designated as

$Y_0=\sqrt{{\mathrm{\ρ}}_0}\mathrm{HB}{\mathrm{\Φ}}_0+W_0$

Wherein, Y is M * τ matrix, is illustrated in the received signal in base station in τ training process; B is the diagonal matrix of L * L, element β on diagonal _irepresent that user i is to the large scale fading factor of base station; W ₀for M * τ matrix, be illustrated in the received noise in base station in τ training process.The MMSE of channel H estimates, is designated as , for

$\hat{H}=\sqrt{{\mathrm{\ρ}}_0}{Y}_0{(I_{\mathrm{\τ}}+{\mathrm{\ρ}}_0{{\mathrm{\Φ}}_0}^H{B}^2{\mathrm{\Φ}}_0)}^{\text{-1}}{{\mathrm{\Φ}}_0}^{H}B$

Method for designing is for making estimate variance reach minimum, through can be calculated

Note matrix characteristic value be τ wherein ₀=min{L, τ }, have

$E_H\left\{{\left|\right|H-\widehat{H|}\left|\right|}^2\right\}=M(L-{\mathrm{\τ}}_0)+M\underset{i=1}{\overset{{\mathrm{\τ}}_0}{\mathrm{\Σ}}}\frac{1}{1+{\mathrm{\ρ}}_0{\mathrm{\λ}}_i}$

Estimate variance minimum is equivalent to

$\min \underset{i=1}{\overset{{\mathrm{\τ}}_0}{\mathrm{\Σ}}}\frac{1}{1+{\mathrm{\ρ}}_0{\mathrm{\λ}}_i}$

Constraints: ${\mathrm{\λ}}_1+{\mathrm{\λ}}_2+...{\mathrm{\λ}}_{{\mathrm{\τ}}_0}=\mathrm{tr}\left({\mathrm{\Φ}}_0^H{B}^2{\mathrm{\Φ}}_0\right)$

And $\mathrm{tr}\left({\mathrm{\Φ}}_0^H{B}^2{\mathrm{\Φ}}_0\right)=\mathrm{tr}\left(B^2{\mathrm{\Φ}}_0{\mathrm{\Φ}}_0^H\right)=({\mathrm{\β}}_1+{\mathrm{\β}}_2+...+{\mathrm{\β}}_{{\mathrm{\τ}}_0}),$ Note therefore, training sequence Φ ₀optimized design problem be just converted into:

$\min \underset{i=1}{\overset{{\mathrm{\τ}}_0}{\mathrm{\Σ}}}\frac{1}{1+{\mathrm{\ρ}}_0{\mathrm{\λ}}_i}$ Constraints: ${\mathrm{\λ}}_1+{\mathrm{\λ}}_2+...{\mathrm{\λ}}_{{\mathrm{\τ}}_0}={\mathrm{\β}}_0$

Obviously, the optimal solution of above-mentioned optimization problem is but in reality, can not accomplish, because require Φ ₀want and β _iindependent.But notice that optimal solution is now that the variance of these characteristic values is zero.So, can consider wherein, substitution abbreviation obtains $\underset{i=1}{\overset{{\mathrm{\τ}}_0}{\mathrm{\Σ}}}{({\mathrm{\λ}}_i-\stackrel{-}{\mathrm{\λ}})}^2=\underset{i=1}{\overset{{\mathrm{\τ}}_0}{\mathrm{\Σ}}}{\mathrm{\λ}}_i^2-{\mathrm{\τ}}_0{\stackrel{-}{\mathrm{\λ}}}^2=\underset{i=1}{\overset{{\mathrm{\τ}}_0}{\mathrm{\Σ}}}{\mathrm{\λ}}_i^2-\frac{{\mathrm{\β}}_0^2}{{\mathrm{\τ}}_0}.$

Therefore, this problem is converted into again:

$\min \underset{i=1}{\overset{{\mathrm{\τ}}_0}{\mathrm{\Σ}}}{\mathrm{\λ}}_i^2$

Constraints: ${\mathrm{\λ}}_1+{\mathrm{\λ}}_2+...{\mathrm{\λ}}_{{\mathrm{\τ}}_0}={\mathrm{\β}}_0$

Obviously, $\underset{i=1}{\overset{{\mathrm{\τ}}_0}{\mathrm{\Σ}}}{\mathrm{\λ}}_i^2=\mathrm{tr}\left({\mathrm{\Φ}}_0^H{B}^2{\mathrm{\Φ}}_0{\mathrm{\Φ}}_0^H{B}^2{\mathrm{\Φ}}_0\right)=\mathrm{tr}\left(B^2{\mathrm{\Φ}}_0{\mathrm{\Φ}}_0^H{B}^2{\mathrm{\Φ}}_0{\mathrm{\Φ}}_0^H\right)=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}\underset{j=1}{\overset{L}{\mathrm{\Σ}}}{\mathrm{\β}}_i{\mathrm{\β}}_j{\left|{\mathrm{\φ}}_i{{\mathrm{\φ}}_j}^H\right|}^2.$

So this problem is finally converted into .Therefore, final design optimal training sequence makes maximum in (i ≠ j) is the smaller the better.

Those of ordinary skill in the art will be appreciated that, above example is only for the present invention is described, and not as limitation of the invention, as long as within the scope of the invention, the variation to above embodiment, distortion all will drop on protection scope of the present invention.

Claims (1)

1. for the pilot frequency sequence design method at uplink multi-users mimo system, suppose that system has L community, there is a base station each community, and base station is furnished with M root antenna, and between community, has co-channel interference; When supposing each community, excited user number is one again, and each user sends the training sequence that length is τ, i.e. φ _l=(φ _l1, φ _l2..., φ _{l τ}), φ wherein _l1, φ _l2..., φ _{l τ}, l=1,2 ..., L be l user respectively the 1st, 2 ... the training symbol that τ sends constantly; Order for L * τ matrix, be called training matrix, it is characterized in that the method is exactly will be to Φ ₀design its method for designing is proposed, comprise the following steps:

The first step: get L point in the unit sphere in τ dimension complex space, each point is a τ dimension row vector; Be designated as φ _i, i=1,2 ..., L, φ _ibuild up L * τ matrix Φ ₀, Φ ₀as training matrix; Choosing of L point is to make following value

$\underset{1\≤i\≠j\≤L}{\max }\left|{\mathrm{\φ}}_i{\mathrm{\φ}}_j^H\right|$

The smaller the better, subscript H represents vectorial conjugate transpose here; Concrete choosing can be in the following way: get for τ dimensional vector, each component is 1, wherein the transposed matrix of subscript t representing matrix (as follows);

Order

$\begin{array}{cc}{\mathrm{\φ}}_i^t=(\mathrm{diag}{(1,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\τ}}{u}_1\right),\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\τ}}{u}_2\right),...,\exp \left(j\frac{2\mathrm{\π}}{\mathrm{\τ}}{u}_{\mathrm{\τ}-1}\right))}^{(i-1)}{\mathrm{\φ}}_0& i=\mathrm{1,2},...,L;\end{array}$

Wherein j is imaginary unit, u ₁, u ₂..., u _τ-1be and be greater than the zero positive integer that is less than τ; These integers can be according to value the smaller the better requirement obtains with calculating search;

Second step: the L obtaining by above-mentioned steps point is used as L row vector of training sequence, forms training matrix

${\mathrm{\Φ}}_0={({\mathrm{\φ}}_1^t,{\mathrm{\φ}}_2^t,...,{\mathrm{\φ}}_L^t)}^t;$

The 3rd step: the training sequence φ that aforesaid way is obtained _idistribute to user i; When base station receives after the signal with training sequence, with minimum mean square error method, estimate channel.