CN103441966B - Distributed MIMO frequency deviation and channel estimation based on ECM under a kind of high speed - Google Patents
Distributed MIMO frequency deviation and channel estimation based on ECM under a kind of high speed Download PDFInfo
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Abstract
The invention belongs to wireless communication technology field, belong to wireless and mobile communication technology field, and in particular to plant distributed MIMO frequency deviation and channel estimation methods based on ECM under high speed, including：Constructing system model；Initialization；Calculate the expectation in complete data space；Maximize the expectation in complete element tool space；Update frequency deviation value；Update channel value；Iteration knows that estimate meets requirement.The joint frequency deviation channel estimation method of MIMO Signal with Distributed Transmit Antennas of the present invention under the conditions of slow become, the influence that analysis high-speed mobile condition is brought to system, then the initialization of joint frequency deviation and channel estimation is carried out using the method based on correlation and then the influence that high-speed mobile is brought is overcome using the method based on ECM iteration, system is obtained preferable parameter Estimation performance under high-speed mobile environment.
Description
Technical Field
The invention belongs to the technical field of wireless and mobile communication, and particularly relates to a joint frequency offset and channel estimation method for a distributed multi-input multi-output (MIMO) system in a high-speed mobile environment.
Background
In the field of future wireless communication, the MIMO technology widely applied to Long Term Evolution (LTE) receives more and more attention and research due to its unique advantages. The distributed MIMO system is flexible in networking, can be provided with a transmitting antenna and a receiving antenna according to specific requirements and can provide higher system capacity, so that the distributed MIMO system becomes a main form of application of the MIMO technology. In addition, with the rapid development of high-speed mobile communication, the key technology research for the distributed MIMO system in a high-speed environment has important significance. Since the transmitting antennas and the receiving antennas may be distributed in different geographical locations, and the signals experience different transmission channels and fading, the distributed MIMO system puts higher requirements on joint frequency offset and channel estimation. Especially in a high-speed mobile environment, how to efficiently and jointly estimate the frequency offset and the channel of the distributed MIMO system is one of the core technologies of a future wireless communication transmission system.
Since all transmitting antennas and receiving antennas of the distributed MIMO system are distributed at different geographical locations, signals from the transmitting antennas to the receiving antennas experience different large-scale fading and small-scale fading, and thus, a plurality of different frequency offsets exist. The parameter estimation of a distributed MIMO system is actually a multi-parameter joint estimation. While parameter estimation based on the Maximum Likelihood (ML) principle is the most practical estimation, in general, the solution of multi-parameter estimation based on the maximum likelihood principle generally has no closed form and thus the complexity of the solution is higher, and this problem becomes more prominent in the environment of a distributed MIMO system. In the case that the maximum likelihood synchronization algorithm is difficult to be fully implemented, a suboptimal quasi-maximum likelihood estimation algorithm is a good choice, such as a multi-parameter estimation algorithm based on the correlation principle.
The multi-parameter estimation method based on the correlation principle ignores the interference caused by multiple antennas, so the method has an MSE platform, namely, the MSE cannot be continuously reduced along with the increase of the signal-to-noise ratio. Aiming at the problem, the problem that the MSE platform is generated along with the increase of the signal-to-noise ratio of the correlation estimation method can be effectively solved by the combined frequency offset and channel estimation algorithm based on the ECM iteration. But these algorithms all assume that the channel is slowly varying.
Therefore, for the distributed MIMO system, the frequency offset and the channel value are estimated by adopting a correlation-based method to serve as initial values for ECM iteration, and then iteration is continuously carried out until the estimated frequency offset and the estimated channel value meet requirements, so that the thought can obtain better performance. However, in a high-speed mobile environment, how to adopt an ECM iteration method to perform joint frequency offset and channel estimation on a distributed MIMO system, the invention provides a method for joint frequency offset and channel estimation of the distributed MIMO system in the high-speed mobile environment.
Disclosure of Invention
The invention aims to solve the problem of popularization of frequency offset and channel joint estimation of a distributed MIMO system from a slow time-varying channel to a fast time-varying channel, and provides ECM-based distributed MIMO frequency offset and channel estimation at a high speed.
The purpose of the invention is realized by the following technical scheme:
s1, constructing a system model:
a distributed MIMO system in a high speed mobile environment having NTNRThe signal received by the kth receiving antenna of the distributed MIMO system at the time t can be represented as different frequency offset values
Wherein s isl(t), t is 1, 2, …, N is training sequence transmitted by the l-th transmitting antenna, hk，l(t) is the channel coefficient between the ith transmit antenna and the kth receive antenna at time t, wk，lFor the frequency offset between the l-th transmitting antenna and the k-th receiving antenna, nk(t), t is 1, 2, …, N represents zero mean, independent identically distributed complex Gaussian noise,
definition of
yk=[yk(1)，yk(2)，…，yk(N)]T
hk，l=[hk，l(1)，hk，l(2)，…，hk，l(N)]T
nk=[nk(1)，nk(2)，…，nk(N)]TDue to a single NT×NRCan be equivalently viewed as NRThus, for simplicity we can equivalently consider a 2 × 1 distributed MISO system
Definition of
w=[w1w2]T
h1=diag([h1(1) h1(2) … h1(N)])
h2=diag([h2(1) h2(2) … h2(N)])
Let the sequence transmitted by the first transmitting antenna be s1=[s1(1) 0 s1(3) … s1(N-1) 0]TThe sequence transmitted by the second transmitting antenna is s2=[0 s2(2) 0 … 0 s2(N)]TThen the received signal may be transformed as follows,
wherein,h=[h1(1) h2(2) h1(3) … h1(N-1) h2(N)]Tthen, the received signal at time t is represented as y = Φsh + n by minimizing an objective functionML estimation is carried out on frequency deviation and channel h, and h can be obtained firstly under the condition of certain frequency deviation0=(Φs HΦs)-1Φs Hy can then be obtained
S2, initialization:
the receiving end carries out correlation processing on the received signal and the training sequence of the first transmitting antenna to obtainWherein, P is the correlation length, the received signal and the training sequence of the first transmitting antenna are processed with a differential correlation again, the differential distance is i, and the correlation length is obtainedIn particular, when the differential distance is set to 1, there areThe offset w of the frequency offset between the ith transmit antenna and the first receive antennal，1Is estimated by the expressionWherein T is a symbol period, and the initial value of the frequency offset between the transmitting antenna 1 and the receiving antenna is obtained asAnd the initial value of the offset between the transmitting antenna 2 and the receiving antenna isFurther, the initial value of the channel is obtained as
S3, calculating the expectation of complete data space:
we define the training sequence transmitted by the ith transmit antenna as sl=[sl(1)，sl(2)，…，sl(N)]TDefinition ofThe frequency deviation transmitted by the transmitting antennas is in the form ofThen, the received signal is represented asn=[n(1)，n(2)，…，n(N)]TAnd n to CN (0, sigma)2IN)；hl＝[hl(1)，hl(2)，…，hl(N)]And l is 1, 2. The parameter to be estimated isWherein theta isl＝[wl，hl]TCorresponding to the frequency offset and channel between the l-th transmitting antenna and the received signal, the received signal y is an incomplete data space, however, the incomplete data space may be characterized by a complete data space, thus defining a complete data space z ═ z1，z2]TWhereinthe relationship between complete data space z and incomplete data space y can be expressed as
The total noise n is divided into two parts, i.e.,wherein n islIs independent Gaussian noise with the same distribution and zero mean value and has the variance of βlσ2IN，
Suppose βlAre equal, i.e. βl=1／NT= 1/2, the complete data space for the mth iteration is expected to be as follows:
the log-likelihood function of the complete data space may be expressed asDue to noise nlIs statistically independent, so the Probability Distribution Function (PDF) of z to θ is
Can obtain
Wherein, for complete data space expectation, due to zlAnd y obeys a joint Gaussian distribution, thenWherein,
s4, expectation of maximizing complete data space:
expectation of complete data space obtained at S3Maximizing to obtain a maximized updated value of the parameter theta to be estimated
S5, updating the frequency offset value:
according to S4Performing minimum update on the parameter theta to be estimated to obtain a minimum update value
I.e. there are 2 sub-minimization update procedures,
when updating the sub-minimization process, the ECM algorithm will updateThe updating process is carried out in two steps, namely, the frequency offset and the channel are respectively updated, and under the condition that the fixed channel is not changed, the frequency offset is firstly subjected to minimum updating
HandleIn thatIs subjected to second-order Taylor series expansion to obtainThe simulation shows that(40) Formula is always a convex function, and for wlDifferentiating and making it be 0, and resolving to obtain frequency offset updating valueIs composed of
S6, updating channel values:
after the frequency offset is updated, the value of the frequency offset is fixed to be unchanged, and then the channel coefficient is updated to obtain an updated value of the channel coefficientIs composed of
Namely, it isWherein,(t) is the first transmitting antenna and the receiving antenna obtained from the m +1 th iterationThe value of the channel in between at time t, up to this pointM +1 th this update is complete;
s7, repeating iteration until the estimated value meets the requirement:
obtained in S6And traversing S5 and S6 as initial values, and performing iterative updating again until the iterative updating value meets the requirement.
Further, S3 the βlSatisfy the requirement ofβl＞0。
Further, C at S31And C2Are two constants independent of theta.
The invention has the beneficial effects that: the method is based on a joint frequency offset channel estimation algorithm of a distributed MIMO system under a slowly varying condition, analyzes the influence of a high-speed moving condition on the system, and then adopts a correlation-based method to initialize joint frequency offset and channel estimation so as to overcome the influence of high-speed moving by adopting an ECM iteration-based method, so that the system obtains better parameter estimation performance under a high-speed moving environment.
Drawings
Fig. 1 is a schematic diagram of a distributed MIMO system used in the present invention.
FIG. 2 is a flow chart illustrating the steps of the algorithm of the present invention.
Detailed Description
The following description of the embodiments of the invention refers to the accompanying drawings:
s1: and constructing a system model.
We consider a distributed MIMO system in a high-speed mobile environment, with NTA transmitting antenna and NRA receiving antenna. There is a different frequency offset value between each pair of transmit and receive antennas, and the system considered by the present invention therefore has NTNRA different frequency offset value. The signal received by the kth receiving antenna of the system at the time t can be expressed as
Wherein S isl(t), t =1, 2, …, N being the training sequence transmitted by the l-th transmitting antenna; h isk，l(t) is the channel coefficient between the ith transmit antenna and the kth receive antenna at time t; w is ak,lIs the frequency offset between the ith transmit antenna and the kth receive antenna; n isk(t), t =1, 2, …, V representing zero-mean, independent identically distributed, complex gaussian noise.
Definition of
yk=[yk(1)，yk(2)，…，yk(N)]T(2)
hk,l=[hk,l(1)，hk,l(2)，…，hk,l(N)]T(4)
nk=[nk(1)，nk(2)，…，nk(N)]T(6)
Due to one NT×NRCan be equivalently viewed as NRThus, for simplicity we can equivalently consider a 2 × 1 distributed MISO system
We define
w=[w1w2]T(8)
h1=diag([h1(1)h1(2)…h1(N)]) (11)
h2=diag([h2(1)h2(2)…h2(N)]) (12)
Let us assume that the sequence transmitted by the first transmit antenna is s1=[s1(1) 0 s1(3) … s1(N-1)0]T(ii) a The sequence transmitted by the second transmitting antenna is s2=[0 s2(2)0…0 s2(N)]T. Then, the received signal may be transformed as follows
(13)
Wherein,
h=[h1(1) h2(2) h1(3) … h1(N-1) h2(N)]T.
therefore, the formula (7) can be expressed as
y=Φsh+n (14)
Frequency offset and ML estimation of the channel may be achieved by minimizing an objective function (15) expression
A=‖y-Φsh‖2(15)
When the frequency deviation is constant, it can be obtained
h0=(Φs HΦs)-1Φs Hy (16)
By substituting equation (16) into equation (15), the multi-frequency offset estimation of the distributed MIMO system becomes the multi-dimensional optimization of equation (17), that is
S2: and (5) initializing.
The receiving end carries out correlation processing on the received signal and the training sequence of the first transmitting antenna to obtain
Wherein P is the correlation length.
Performing a differential correlation again, wherein the differential distance is i, obtaining
(19)
In particular, when the differential distance is set to 1, there are
Then, the offset w of the frequency offset between the l-th transmitting antenna and the first receiving antennal，1Is estimated by the expression
Where T is the symbol period.
Thus, it can be obtained that the initial values of the frequency offsets between the two transmitting antennas 1 and 2 and the receiving antenna are respectively
The two frequency deviation initial values are taken as known and are substituted into a formula (16) to obtain a channel initial value of
The above frequency offset and channel initial values are used as initial values for performing ECM iterations.
S3: the expectation of a complete data space is calculated.
Specifically, we define the form of training sequence and frequency offset transmitted by the ith transmit antenna as
sl=[sl(1)，Sl(2)，…，Sl(N)]T(25)
The received signal can then be represented as
Wherein n = [ n (1), n (2), …, n (N)]TAnd n to CN (0, sigma)2IN)；hl=[hl(1)，hl(2)，…，hl(N)]L = l, 2. The parameter to be estimated isWherein thetal=[wl，hl]TCorresponding to the frequency offset and channel between the ith transmit antenna and the received signal. The received signal y is an incomplete data space, however the incomplete data space may be characterized by a complete data space, thus defining a complete data space z = [ z ]1,z2]TWherein
The relationship between complete data space z and incomplete data space y can therefore be expressed as
(29)
Dividing the total noise n into two parts, i.e.
Wherein n islIs independent Gaussian noise with the same distribution and zero mean value and has the variance of βlσ2INWherein, βlSatisfies the following conditions
(31)
Let us assume βlAre equal, i.e. βl=1／NT=1／2.
The complete data space expectation for the mth iteration is as follows:
the log-likelihood function of the complete data space may be expressed as
Due to noise nlIs statistically independent, so the Probability Distribution Function (PDF) of z to θ is
Substituting equation (33) into equation (32) may result,
(34)
wherein
(35)
In addition, C1And C2Are two constants independent of theta.
Because of zlAnd y obey a joint Gaussian distribution, obtainable from equation (29)
Wherein
Equation (34) is the expectation of a complete data space.
S4: the desire to maximize the complete data space.
Update value of parameter theta to be estimatedCan be expressed as
(38)
As can be seen from the above equation, the minimum update procedure can be divided into 2 (i.e., v)T) Sub-minimization of the update procedure, i.e.
(39)
S5: and updating the frequency offset value.
When updating the sub-minimization process, the ECM algorithm will updateThe updating process is carried out in two steps, namely, the frequency offset and the channel are respectively updated.
Under the condition of unchanging fixed channel, firstly, minimum updating is carried out on frequency deviation
HandleIn thatIs subjected to second-order Taylor series expansion to obtain
Simulations show that equation (40) is always a convex function, so equation (41) is substituted into equation (42), and for wlDifferentiating and making it be 0, and resolving to obtain frequency offset updating valueIs composed of
S6: the channel value is updated.
After the frequency offset is updated, the value of the frequency offset is fixed to be unchanged, and then the channel coefficient is updated to obtain an updated value of the channel coefficientIs composed of
Can be obtained by simplifying the above formula
WhereinThe value of the channel between the l-th transmit antenna and the receive antenna at time t obtained for the (m + 1) -th iteration.
At this point in time,m +1 th this update is completed.
S7: and repeating the iteration until the estimated value meets the requirement.
Updating the latest valueAnd substituting the initial value into the step five and the step six again to carry out iterative updating again until the iterative updating value meets the requirement.
Claims (3)
1. A distributed MIMO frequency offset and channel estimation method based on ECM under high speed is characterized in that: the steps are as follows:
s1, constructing a system model:
containing N in a high-speed moving environmentTA transmitting antenna and NRDistributed MIMO system with N receive antennasTNRThe signal received by the kth receiving antenna of the distributed MIMO system at the moment t is represented asWherein,is as followsThe training sequences transmitted by the individual transmit antennas,is at the time tChannel coefficients between the individual transmit antennas and the k-th receive antenna,is as followsFrequency offset between transmitting antenna and k-th receiving antenna, nk(t) represents zero-mean, independent, identically distributed, complex gaussian noise, where t is 1, 2, …, N is the number of training sequences, defined as:
yk＝[yk(1)，yk(2)，…，yk(N)]T
<mrow> <msub> <mi>h</mi> <mi>k</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>&lsqb;</mo> <msub> <mi>h</mi> <mrow> <mi>k</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>h</mi> <mrow> <mi>k</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>h</mi> <mrow> <mi>k</mi> <mo>,</mo> <msub> <mi>N</mi> <mi>T</mi> </msub> </mrow> </msub> <mo>&rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow>
<mrow> <msub> <mi>w</mi> <mi>k</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>&lsqb;</mo> <msub> <mi>w</mi> <mrow> <mi>k</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>w</mi> <mrow> <mi>k</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>w</mi> <mrow> <mi>k</mi> <mo>,</mo> <msub> <mi>N</mi> <mi>T</mi> </msub> </mrow> </msub> <mo>&rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow>
nk＝[nk(1)，nk(2)，…，nk(N)]T，
the reception signal of the kth reception antenna at time t isA transformation can be made as follows,
<mrow> <mi>y</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>T</mi> </msub> </munderover> <msub> <mi>h</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <msub> <mi>jw</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> </mrow> </msup> <msub> <mi>s</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>n</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>T</mi> </msub> </munderover> <msub> <mi>h</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mn>2</mn> <msub> <mi>w</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> </mrow> </msup> <msub> <mi>s</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>n</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>T</mi> </msub> </munderover> <msub> <mi>h</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <msub> <mi>jNw</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> </mrow> </msup> <msub> <mi>s</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>n</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <msub> <mi>h</mi> <mrow> <mi>k</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mi>&Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mrow> <mi>k</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>s</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>h</mi> <mrow> <mi>k</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mi>&Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mrow> <mi>k</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>s</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>...</mo> <mo>+</mo> <msub> <mi>h</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mi>&Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>l</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>s</mi> <mi>l</mi> </msub> <mo>+</mo> <mo>...</mo> <mo>+</mo> <msub> <mi>h</mi> <mrow> <mi>k</mi> <mo>,</mo> <msub> <mi>N</mi> <mi>T</mi> </msub> </mrow> </msub> <mi>&Phi;</mi> <mrow> <mo>(</mo> <msub> <mi>w</mi> <mrow> <mi>k</mi> <mo>,</mo> <msub> <mi>N</mi> <mi>T</mi> </msub> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>s</mi> <msub> <mi>N</mi> <mi>T</mi> </msub> </msub> <mo>+</mo> <mi>n</mi> <mo>=</mo> <msub> <mi>&Phi;</mi> <mi>s</mi> </msub> <mi>h</mi> <mo>+</mo> <mi>n</mi> </mrow>
wherein
Φs＝diag
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The received signal at time t is denoted as y ═ Φsh + n by minimizing the objective function Λ | y- Φsh‖2Performing ML estimation on frequency offset and a channel h, and solving h under the condition of certain frequency offset0＝(Φs HΦs)-1Φs Hy, obtaining
In the distributed MIMO system, each receiving antenna is far apart, so that the received signal of each receiving antenna can be calculated independently, and it is not necessary to distinguish the receiving antenna serial numbers, so the receiving antenna serial number k will be omitted hereinafter;
s2, initialization:
the receiving end will receive the signal and the second signalThe training sequences of the transmitting antennas are correlated to obtainWherein P is the correlation length, for the received signal and the secondThe training sequence of each transmitting antenna is subjected to differential correlation processing again, the differential distance is i, and the training sequence is obtainedThen there isThen it is firstFrequency offset between a transmitting antenna and a first receiving antennaIs estimated by the expressionWherein T is symbol period, the transmitting antenna can be obtainedWith an initial value of frequency offset from the receiving antenna ofObtain the initial value of the channel as
S3, calculating the expectation of complete data space:
definition ofThe training sequence transmitted by each transmitting antenna isDefinition ofThe frequency deviation transmitted by the transmitting antenna is in the form ofThen, the received signal is represented asn＝[n(1)，n(2)，…，n(N)]TAnd n to CN (0, sigma)2IN)；The parameter to be estimated isWhereinCorresponds to the firstFrequency offset and channel between the transmit antennas and the received signal, the received signal y being a non-complete data space, however the non-complete data space may be characterized by a complete data space, thus defining a complete data spaceWherein,the relationship between complete data space z and incomplete data space y can be expressed asDividing the total noise N into NTIn part, that is,wherein,is independent, identically distributed, zero mean Gaussian noise with variance ofIs provided withAre equal, i.e.The completeness data space expectation for the mth iteration is as follows, and the log-likelihood function of the complete data space can be expressed asDue to noiseIs statistically independent, so the Probability Distribution Function (PDF) of z to θ is
Can obtain
Wherein,is a complete data space expectation due toAnd y obeys a joint Gaussian distribution, thenWherein,
s4, expectation of maximizing complete data space:
expectation of complete data space obtained at S3Maximizing to obtain a maximized updated value of the parameter theta to be estimated
S5, updating the frequency offset value:
according to S4Performing minimum update on the parameter theta to be estimated to obtain a minimum update value When updating the sub-minimization process, the ECM algorithm will updateThe updating process is carried out in two steps, namely, the frequency offset and the channel are respectively updated, and under the condition that the fixed channel is not changed, the frequency offset is firstly subjected to minimum updating
HandleIn thatIs subjected to second-order Taylor series expansion to obtain Is a convex function, anddifferentiating and making it be 0, and resolving to obtain frequency offset updating valueIs composed of
S6, updating channel values:
after the frequency offset is updated, the value of the frequency offset is fixed to be unchanged, and then the channel coefficient is updated to obtain an updated value of the channel coefficient
Namely, it isWherein,number m +1 iterationThe value of the channel between the transmitting and receiving antennas at time t, up to this pointThe m +1 th update is completed;
and S7, repeating the iteration until the estimated value meets the requirement:
obtained in S6And traversing S5 and S6 as initial values, and performing iterative updating again until the iterative updating value meets the requirement.
2. The method of claim 1 for high speed ECM-based distributed MIMO frequency offset and channel estimation, wherein: s3 theSatisfy the requirement of
3. The method of claim 1 for high speed ECM-based distributed MIMO frequency offset and channel estimation, wherein: s3 item C1And C2Are two constants independent of theta.
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