CN103532883A - Distributed MIMO (Multiple-Input-Multiple-Output) frequency offset and channel estimation based on SAGE (Space Alternate Generalized Expectations) at high speed - Google Patents

Abstract

The invention belongs to the technical field of wireless and mobile communication and particularly relates to a combined frequency offset and channel estimation algorithm for a distributed multiple-input-multiple-output system in a high-speed movement environment. In order to solve problems which occur when a slowly time-varying channel is pushed across a fast time-varying channel in the combined frequency offset and channel estimation for the distributed MIMO (Multiple-Input-Multiple-Output) system, a combined frequency offset and channel estimation method for the distributed MIMO system in the high-speed movement environment is provided. The combined frequency offset and channel estimation method comprises the following steps: building a system model, initiating, calculating the expectation of a hidden data space, maximizing the expectation of the hidden data space, updating a frequency offset value, updating a channel value and repeatedly iterating until an estimated value meets requirements. The influence of the high-speed movement condition on the system is analyzed from the aspect of a combined frequency offset and channel estimation algorithm for the distributed MIMO system under a slowly-varying condition, and then, influence caused by high-speed movement is overcome by a method based on SAGE (Space Alternate Generalized Expectations) iteration, so that the system can obtain better parameter estimation performance in the high-speed movement environment.

Description

Distributed MIMO frequency deviation and channel estimating based on SAGE at a high speed

Technical field

The invention belongs to wireless and mobile communication technology field, be specifically related to distributed MIMO system associating frequency deviation and channel estimation method under a kind of high-speed mobile environment.

Background technology

At following wireless communication field, MIMO (Multiple-Input Multiple-Out-put) technology that is widely used in Long Term Evolution (Long Term Evolution, LTE) receives increasing concern and research with its advantageous advantage.MIMO Signal with Distributed Transmit Antennas networking flexibility, dual-mode antenna can be set according to specific needs and higher power system capacity can be provided, thereby becoming the principal mode of MIMO technology application.In addition, along with the develop rapidly of high-speed mobile communications, significant for the key technology research of the MIMO Signal with Distributed Transmit Antennas under high velocity environment.Because transmitting antenna and reception antenna may be distributed in different geographical position, signal has experienced different transmission channels and decline, thus MIMO Signal with Distributed Transmit Antennas distich sum of fundamental frequencies partially and channel estimating have higher requirement.Especially in high-speed mobile environment, how to combine efficiently and estimate that the frequency deviation of MIMO Signal with Distributed Transmit Antennas and channel are one of core technologies of future wireless system transmission system.

Because all transmitting antennas and the reception antenna of MIMO Signal with Distributed Transmit Antennas is distributed in different geographical position separately, signal arrives reception antenna from transmitting antenna and has experienced different large scale decline and multipath fading, so it exists a plurality of different frequency deviations.The parameter Estimation of MIMO Signal with Distributed Transmit Antennas is actually multi-parameter and combines estimation.And based on maximum likelihood (Maximum Likelihood, ML) parameter Estimation of principle is the most practical estimation, but generally, the solution that multi-parameter based on maximum likelihood principle is estimated conventionally do not have closed form thereby its complexity solving higher, under MIMO Signal with Distributed Transmit Antennas environment, this problem becomes more outstanding.In the situation that maximum likelihood synchronized algorithm is difficult to obtain fully realize, the accurate maximal possibility estimation algorithm of suboptimum is a good selection, such as the multi-parameter algorithm for estimating based on relative theory.

Multiple Parameter Estimation Methods based on relative theory has been ignored the interference that many antennas bring, so the method has MSE platform, and, along with the increase of signal to noise ratio, MSE can not continue to reduce.For this problem, the associating frequency deviation based on desired conditions maximization (Expectation Conditional Maximization, ECM) iteration and channel estimation method can effectively solve correlation estimation method and with signal to noise ratio, increase the problem that produces MSE platform.But, in the algorithm based on ECM, noise profile is in whole defined complete data space, and the response of the Fisher's information of data space is larger, so its convergence rate is slack-off.

As from the foregoing, for MIMO Signal with Distributed Transmit Antennas, the method of employing based on relevant estimates frequency deviation and channel value as the initial value that carries out SAGE iteration, and then constantly iteration is until the frequency deviation estimating and channel value meet the demands, and this thinking can obtain good performance.But under high-speed mobile environment, how to adopt SAGE alternative manner to combine frequency deviation and channel estimating to MIMO Signal with Distributed Transmit Antennas, seldom have so far documents, the present invention is based on this expansion.

Summary of the invention

The object of the invention is to combine estimate the problem that run into by slow time varying channel when varying Channels pushes through in order to solve the frequency deviation of MIMO Signal with Distributed Transmit Antennas and channel, proposed the method that MIMO Signal with Distributed Transmit Antennas frequency deviation under a kind of high-speed mobile environment and channel are combined estimation.

To achieve these goals, the invention provides a kind of under high-speed mobile environment associating frequency deviation and the channel estimation method of the MIMO Signal with Distributed Transmit Antennas based on SAGE iteration, concrete steps are as follows:

S1, constructing system model:

MIMO Signal with Distributed Transmit Antennas under a high-speed mobile environment, has N _tindividual transmitting antenna and N _rindividual reception antenna, has a different frequency deviation value between every pair of dual-mode antenna, described MIMO Signal with Distributed Transmit Antennas has N _tn _rindividual different frequency deviation value, the signal that k reception antenna of described MIMO Signal with Distributed Transmit Antennas receives at moment t can be expressed as

$y_k\left(t\right)=\underset{l=1}{\overset{N_T}{\mathrm{\Σ}}}{h}_{k,l}{e}^{j{w}_{k,l}t}{s}_l\left(t\right)+n_k\left(t\right),t=\mathrm{1,2},...,N$

Wherein, s _l(t) be the training sequence of l transmission antennas transmit, h _k,l(t) be the channel coefficients between t moment l transmitting antenna and k reception antenna, w _k,lbe the frequency shift (FS) between l transmitting antenna and k reception antenna, n _k(t) represent zero-mean, independent identically distributed multiple Gaussian noise,

Definition

y _k＝[y _k(1),y _k(2),…,y _k(N)] ^T

$h_k={[h_{k,1},h_{k,2},\·\·\·{,h}_{k,N_T}]}^T$

h _k,l＝[h _k,l(1),h _k,l(2),…,h _k,l(N)] ^T

$w_k={[w_{k,1},w_{k,2},\·\·\·{,w}_{k,N_T}]}^T$

n _k＝[n _k(1),n _k(2),…,n _k(N)] ^T；

S2, initialization:

Frequency deviation in MIMO Signal with Distributed Transmit Antennas under high-speed mobile environment described in S1 and channel are carried out to initialization, obtain the initial value of frequency deviation and channel, the initial value using described initial value as SAGE iteration;

The expectation in S3, calculating hiding data space;

The expectation in S4, maximization hiding data space;

S5, renewal frequency deviation value:

Under the constant condition of fixed channel, frequency deviation is minimized to renewal;

S6, renewal channel value:

The frequency deviation value obtaining after the frequency deviation described in S5 minimizes renewal, fixing described frequency deviation value, upgrades channel coefficients;

S7, iteration until estimated value meet the demands:

The renewal value that S6 is obtained as initial value again substitution S5 and S6 carry out again iteration and upgrade, until iteration renewal value meets the demands.

The expectation of further, calculating hiding data space described in S3 comprises:

Define the training sequence of l transmission antennas transmit and the form of frequency deviation is

s _l＝[s _l(1),s _l(2),…,s _l(N)] ^T

$w_l=[e^{j{\mathrm{\ω}}_t},e^{j2{\mathrm{\ω}}_t},...,e^{\mathrm{jN}{\mathrm{\ω}}_t}]$

So receiving signal can be expressed as

Wherein, n=[n (1), n (2) ..., n (N)] ^tand n～CN (0, σ ²i _n); h _l=[h _l(1), h _l(2) ..., h _l(N)], l=1,2.Treat that estimated parameter is

θ wherein _l=[w _l, h _l] ^tfrequency deviation and channel between corresponding l transmitting antenna and reception signal.Receiving signal y is non-complete data space.Definition

hiding data space x _l=[x _l(1), x _l(2) ..., x _l(N)] ^t, and have

In the m time iteration, with y,

under known conditions, ask the expectation of the log-likelihood function in hiding data space,

$Q\left({\mathrm{\θ}}_l\right|{\widehat{\mathrm{\θ}}}^{\left[m\right]})=E\left\{\log f\left(x_l\right|{\mathrm{\θ}}_l,{\left\{{\widehat{\mathrm{\θ}}}_v^{\left[m\right]}\right\}}_{v\≠l})\right|,{\widehat{\mathrm{\θ}}}^{\left[m\right]}\}$

Concrete, have

Wherein

Further, C described in S3 ₃and C ₄to be independent of θ _ltwo constants.

The invention has the beneficial effects as follows: the associating frequency deviation channel estimation method of the MIMO Signal with Distributed Transmit Antennas from slow change condition, analyze the impact that high-speed mobile condition brings to system, then adopt the method based on SAGE iteration to overcome the impact that high-speed mobile is brought, make system under high-speed mobile environment, obtain good parameter Estimation performance.

Accompanying drawing explanation

Fig. 1 is the present invention's distributed MIMO schematic diagram used.

Fig. 2 is specific algorithm steps flow chart schematic diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described:

As shown in Figure 2,

S1: constructing system model.

MIMO Signal with Distributed Transmit Antennas under a high-speed mobile environment, has N _tindividual transmitting antenna and N _rindividual reception antenna.Between every pair of dual-mode antenna, have a different frequency deviation value, therefore described MIMO Signal with Distributed Transmit Antennas has N _tn _rindividual different frequency deviation value.The signal that k reception antenna of described MIMO Signal with Distributed Transmit Antennas receives at moment t can be expressed as

$y_k\left(t\right)=\underset{l=1}{\overset{N_T}{\mathrm{\Σ}}}{h}_{k,l}{e}^{j{w}_{k,l}t}{s}_l\left(t\right)+n_k\left(t\right),t=\mathrm{1,2},...,N---\left(1\right)$

Wherein, s _l(t) be the training sequence of l transmission antennas transmit, h _k,l(t) be the channel coefficients between t moment l transmitting antenna and k reception antenna, w _k,lbe the frequency shift (FS) between l transmitting antenna and k reception antenna, n _k(t) represent zero-mean, independent identically distributed multiple Gaussian noise.

Definition

y _k＝[y _k(1),y _k(2),…,y _k(N)] ^T (2)

$h_k={[h_{k,1},h_{k,2},...,h_{k,N_T}]}^T---\left(3\right)$

h _k,l＝[h _k,l(1),h _k,l(2),…,h _k,l(N)] ^T (4)

$w_k={[w_{k,1},w_{k,2},...,w_{k,N_T}]}^T---\left(5\right)$

n _k＝[n _k(1),n _k(2),…,n _k(N)] ^T (6)

Due to a N _t* N _rmIMO Signal with Distributed Transmit Antennas can regard equivalently N as _tthe single output of individual independently distributed many inputs (multi-input single-output, MISO) system.Therefore, in order to simplify us, can consider equivalently the DISTRIBUTED MIS O system of 2 * 1.So, at the reception signal of moment t, can be expressed as

$y_k\left(t\right)=\underset{l=1}{\overset{N_T}{\mathrm{\Σ}}}{h}_{k,l}{e}^{j{w}_{k,l}t}{s}_l\left(t\right)+n_k\left(t\right),t=\mathrm{1,2},...,N$

We define

w＝[w ₁ w ₂] ^T (8)

$\mathrm{\&Phi;}\left(w_1\right)=\mathrm{diag}\left(\begin{array}{c}\left[\begin{array}{cccc}{e}^{j{w}_1}& e^{j{2\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA0000394939520000021.png"\; state="\{\{state\}\}">w</figure-callout>}}_1}& ...& e^{j{\mathrm{Nw}}_1}\end{array}\right]\end{array}\right)---\left(9\right)$

$\mathrm{\&Phi;}\left(w_2\right)=\mathrm{diag}\left(\begin{array}{c}\left[\begin{array}{cccc}{e}^{j{w}_2}& e^{j{2w}_2}& ...& e^{j{\mathrm{Nw}}_2}\end{array}\right]\end{array}\right)---\left(10\right)$

h ₁＝diag([h ₁(1) h ₁(2)…h ₁(N)]) (11)

h ₂＝diag([h ₂(1) h ₂(2)…h ₂(N)]) (12)

We suppose that the sequence of first transmission antennas transmit is s ₁=[s ₁(1) 0 s ₁(3) ... s ₁(N-1) 0] ^t; The sequence of second transmission antennas transmit is s ₂=[0 s ₂(2) 0 ... 0 s ₂(N)] ^t.So, receiving signal can do as down conversion

$\begin{array}{c}y=\left[\begin{array}{c}\underset{l=1}{\overset{2}{\mathrm{\&Sigma;}}}{h}_l\left(1\right)e^{j{w}_1}{s}_l\left(1\right)+n\left(1\right)\\ \underset{l=1}{\overset{2}{\mathrm{\&Sigma;}}}{h}_l\left(2\right)e^{j{2w}_1}{s}_l\left(2\right)+n\left(2\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \underset{l=1}{\overset{2}{\mathrm{\&Sigma;}}}{h}_l\left(N\right)e^{j{\mathrm{Nw}}_1}{s}_l\left(N\right)+n\left(N\right)\end{array}\right]={\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HDA0000394939520000021.png"\; state="\{\{state\}\}">h</figure-callout>}}_1\mathrm{\&Phi;}\left(w_1\right){\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000394939520000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_1+h_2\mathrm{\&Phi;}\left(w_2\right)s_2+n\\ =\left[\begin{array}{c}{h}_1\left(1\right)e^{{\mathrm{jw}}_1}{s}_1\left(1\right)\\ h_2\left(2\right)e^{j2w_2}{s}_2\left(2\right)\\ h_1\left(3\right)e^{{j3w}_1}{s}_1\left(3\right)\\ .\\ .\\ .\\ h_1(N-1)e^{j(N-1)w_1}{s}_1\left(N\right)\\ h_2\left(N\right)e^{{\mathrm{jNw}}_2}{s}_2\left(N\right)\end{array}\right]+n={\mathrm{\&Phi;}}_{s}h+n\end{array}---\left(13\right)$

Wherein, ${\mathrm{\&Phi;}}_s=\mathrm{diag}\left(\begin{array}{c}\left[\begin{array}{cccccc}{s}_1\left(1\right)e^{j{w}_1}& s_2\left(2\right)e^{j2w_2}& s_1\left(3\right)e^{j3{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA0000394939520000021.png"\; state="\{\{state\}\}">w</figure-callout>}}_1}& ...& s_1(N-1)e^{j(N-1)w_2}& s_2\left(N\right)e^{\mathrm{jN}{w}_2}\end{array}\right]\end{array}\right);$ h＝[h ₁(1) h ₂(2) h ₁(3)…h ₁(N-1) h ₂(N)] ^T.

Therefore, formula (7) can be expressed as

y＝Φ _sh+n (14)

The ML of frequency deviation skew and channel estimates to realize by minimizing target function (15) formula

Λ＝||y-Φ _sh|| ² (15)

When in the situation that frequency shift (FS) is certain, can be in the hope of

h ₀＝(Φ _s ^HΦ _s) ^-1Φ _s ^Hy (16)

(16) formula is brought into (15) formula, and the multifrequency of MIMO Signal with Distributed Transmit Antennas estimates to become how (17) formula is carried out to multi-dimensional optimization partially, has

$w=\arg \underset{w}{\max }{y}^H{\mathrm{\&Phi;}}_s{\left({\mathrm{\&Phi;}}_s^H{\mathrm{\&Phi;}}_s\right)}^{-1}{\mathrm{\&Phi;}}_s^{H}y---\left(17\right)$

S2: initialization:

Receiving terminal, by receiving signal and the training sequence of l transmitting antenna being made to relevant treatment, obtains

$R_{s_t}\left(k\right)=\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{s}_l(\mathrm{kP}+p)y(\mathrm{kP}+p)---\left(18\right)$

Wherein, P is correlation length.

Remake first difference relevant, difference distance is i, obtains

$C_l\left(i\right)=E\left\{R_{s_l}\left(k\right){\left(R_{s_l}(k-i)\right)}^{*}\right\},l=\mathrm{1,2}---\left(19\right)$

Especially, when difference distance is made as 1, have

So, the skew of the frequency deviation between l transmitting antenna and first reception antenna w _{l, 1}estimation expression formula be

${\hat{w}}_{l,1}=\frac{1}{2\mathrm{\&pi;PT}}\arg \left({\hat{C}}_l\left(1\right)\right)---\left(21\right)$

Wherein, T is symbol period.

So, can obtain two transmitting antennas 1 and 2 and reception antenna between frequency deviation initial value be respectively

${\hat{w}}_1=\frac{1}{2\mathrm{\&pi;PT}}\arg \left({\hat{C}}_l\left(1\right)\right)---\left(22\right)$

${\hat{w}}_2=\frac{1}{2\mathrm{\&pi;PT}}\arg \left({\hat{C}}_2\left(1\right)\right)---\left(23\right)$

Above-mentioned two frequency deviation initial values are obtained to channel initial value and be as the known formula (16) of bringing into

$\hat{h}={\left({{\mathrm{\&Phi;}}_s}^H{\mathrm{\&Phi;}}_s\right)}^{-1}{{\mathrm{\&Phi;}}_s}^{H}y---\left(24\right)$

Using frequency deviation above and channel initial value as the initial value that carries out SAGE iteration.

S3: the expectation of calculating hiding data space.

Particularly, define the training sequence of l transmission antennas transmit and the form of frequency deviation is

s _l＝[s _l(1),s _l(2),…,s _l(N)] ^T (25)

$w_l=[e^{j{\mathrm{\&omega;}}_t},e^{j2{\mathrm{\&omega;}}_t},...,e^{\mathrm{jN}{\mathrm{\&omega;}}_t}]---\left(26\right)$

So receiving signal can be expressed as

Wherein, n=[n (1), n (2) ..., n (N)] ^tand n～CN (0, σ ²i _n); h _l=[h _l(1), h _l(2) ..., h _l(N)], l=1,2.Treat that estimated parameter is θ wherein _l=[w _l, h _l] ^tfrequency deviation and channel between corresponding l transmitting antenna and reception signal.Receiving signal y is non-complete data space.Definition

hiding data space x _l=[x _l(1), x _l(2) ..., x _l(N)] ^t, and have

Here different from ECM, SAGE allows all noises and hiding data space correlation join, thereby has reduced the Fisher's information in hiding data space, has improved convergence rate.

In the m time iteration, with y,

under known conditions, ask the expectation of the log-likelihood function in hiding data space,

$Q\left({\mathrm{\&theta;}}_l\right|{\widehat{\mathrm{\&theta;}}}^{\left[m\right]})=E\left\{\log f\left(x_l\right|{\mathrm{\&theta;}}_l,{\left\{{\widehat{\mathrm{\&theta;}}}_v^{\left[m\right]}\right\}}_{v\&NotEqual;l})\right|,{\widehat{\mathrm{\&theta;}}}^{\left[m\right]}\}---\left(29\right)$

Concrete, have

Formula (30) is brought into formula (29) can be obtained,

Wherein

And C ₃and C ₄to be independent of θ _ltwo constants.

S4: maximize the expectation in hiding data space.

The renewal value of solve for parameter θ

can be expressed as

As can be seen from the above equation, it minimizes renewal process can be divided into 2(is N _t) height minimizes renewal process,

S5: upgrade frequency deviation value.

When antithetical phrase minimization process is upgraded, SAGE algorithm handle renewal process carry out in two steps, upgrade respectively frequency deviation and channel.

Under the constant condition of fixed channel, first frequency deviation is minimized and upgraded

Wherein,

t element, t=1,2 ..., N.

S6: upgrade channel value.

After frequency deviation is upgraded, fix its value constant, then channel coefficients is upgraded, obtain channel coefficients renewal value

for

${\hat{h}}_l^{[m+1]}\left(t\right)=\frac{1}{{\left|s_l\left(t\right)\right|}^2}*\frac{{\hat{x}}_l^{\left[m\right]}\left(t\right)s_l^{*}\left(t\right)}{e^{j{\hat{w}}_l^{[m+1]}t}}t=\mathrm{1,2},...,N---\left(36\right)$

Wherein

be l transmitting antenna and the value of the channel between reception antenna when moment t that the m+1 time iteration obtains.

So far,

upgraded for the m+1 time.

S7: iteration until estimated value meet the demands.

Latest update value

as initial value substitution step 5 again and step 6, carry out again iteration renewal, until iteration renewal value meets the demands.

Claims (3)

1. distributed MIMO frequency deviation and the channel estimating based on SAGE under high velocity environment, is characterized in that, step is as follows:

S1, constructing system model:

MIMO Signal with Distributed Transmit Antennas under a high-speed mobile environment, has N _tindividual transmitting antenna and N _rindividual reception antenna, has a different frequency deviation value between every pair of dual-mode antenna, described MIMO Signal with Distributed Transmit Antennas has N _tn _rindividual different frequency deviation value, the signal that k reception antenna of described MIMO Signal with Distributed Transmit Antennas receives at moment t can be expressed as

Wherein, s _l(t) be the training sequence of l transmission antennas transmit, h _k,l(t) be the channel coefficients between t moment l transmitting antenna and k reception antenna, w _k,lbe the frequency shift (FS) between l transmitting antenna and k reception antenna, n _k(t) represent zero-mean, independent identically distributed multiple Gaussian noise,

Definition

y _k＝[y _k(1),y _k(2),…,y _k(N)] ^T

h _k,l＝[h _k,l(1),h _k,l(2),…,h _k,l(N)] ^T

n _k＝[n _k(1),n _k(2),…,n _k(N)] ^T；

S2, initialization:

Frequency deviation in MIMO Signal with Distributed Transmit Antennas under high-speed mobile environment described in S1 and channel are carried out to initialization, obtain the initial value of frequency deviation and channel, the initial value using described initial value as SAGE iteration;

The expectation in S3, calculating hiding data space;

The expectation in S4, maximization hiding data space;

S5, renewal frequency deviation value:

Under the constant condition of fixed channel, frequency deviation is minimized to renewal;

S6, renewal channel value:

The frequency deviation value obtaining after the frequency deviation described in S5 minimizes renewal, fixing described frequency deviation value, upgrades channel coefficients;

S7, iteration until estimated value meet the demands:

The renewal value that S6 is obtained as initial value again substitution S5 and S6 carry out again iteration and upgrade, until iteration renewal value meets the demands.

2. distributed MIMO frequency deviation and the channel estimating based on SAGE under a kind of high velocity environment according to claim 1, is characterized in that:

The expectation of calculating hiding data space described in S3 comprises:

Define the training sequence of l transmission antennas transmit and the form of frequency deviation is

s _l＝[s _l(1),s _l(2),…,s _l(N)] ^T

So receiving signal can be expressed as

Wherein, n=[n (1), n (2) ..., n (N)] ^tand n～CN (0, σ ²i _n); h _l=[h _l(1), h _l(2) ..., h _l(N)], l=1,2, treat that estimated parameter is

θ wherein _l=[w _l, h _l] ^tfrequency deviation and channel between corresponding l transmitting antenna and reception signal, receiving signal y is non-complete data space, definition

hiding data space x _l=[x _l(1), x _l(2) ..., x _l(N)] ^t, and have

In the m time iteration, with y,

under known conditions, ask the expectation of the log-likelihood function in hiding data space,

Concrete, have

Wherein

。

3. distributed MIMO frequency deviation and the channel estimating based on SAGE under a kind of high velocity environment according to claim 2, is characterized in that: described C ₃and C ₄to be independent of θ _ltwo constants.

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