CN103685124A - Compressed domain frequency shift estimation method - Google Patents

Abstract

The invention discloses a kind of compression domain frequency offset estimation methods, the carrier frequency synchronizations of each distinguishable path signal for wireless communication system, comprising: construction perception matrix Θ, and extract the reception signal sequence x on distinguishable path; Using the offset estimation pretreatment for receiving signal sequence x and carrying out compression domain on the path on perception matrix Θ and the distinguishable path, the pretreatment estimated value is obtained

According to pretreatment estimated value Map out offset estimation value of the distinguishable path signal in uncompressed domain

Complete Carrier frequency offset estimation when wireless system Frequency Synchronization. The present invention can greatly save processor resource.

Description

A kind of compression domain frequency offset estimation methods

Technical field

The present invention relates to a kind of frequencies of wireless communication system simultaneous techniques, refer to especially a kind of frequency shift (FS) that utilizes compressed sensing technology to carry out (carrier frequency shift is referred to as frequency deviation) method of estimation.

Background technology

In wireless communication system, carrier frequency shift (abbreviation frequency deviation) is caused by two aspects: be the unsteadiness due to oscillator on the one hand, between the local carrier of transmitter and receiver, can have frequency departure; On the other hand, the relative motion between transmitter and receiver produces Doppler frequency shift.The existence meeting of frequency deviation seriously reduces the performance of wireless communication system, as parameter Estimation performance, bit error rate performance, etc.Therefore,, before receiving signal demodulation, conventionally need to compensate frequency deviation.

As the top priority of compensate of frequency deviation, it is hot technology and Research Challenges all the time that frequency deviation is estimated.Existing frequency deviation estimating method mainly contains data householder method and the large class of non-data-aided method two, wherein, data householder method utilizes pilot frequency sequence or training sequence to carry out frequency deviation estimation, and the self-characteristic of non-data-aided method utilization reception signal carries out frequency deviation estimation.In practical wireless communication systems, the auxiliary frequency deviation estimating method of non-data is used less because of its excessive operand.Although have certain feasibility based on the auxiliary frequency deviation estimating method of data, the auxiliary frequency deviation estimating method of the data such as maximum likelihood adopting for the estimated performance obtaining still has compared with computation complexity, has taken more processor resource expense.

On the other hand, the arrival direction of different radio path signal arrival receiving terminal is normally different.Therefore, the frequency deviation of different path signals may be different.Thereby, need to the frequency deviation of each distinguishable path signal be estimated respectively and be compensated.This has further strengthened processor resource expense when frequency deviation is estimated.

The compressive sensing theory occurring is in recent years pointed out, as long as signal is sparse at certain transform domain, just can high dimensional signal be projected on lower dimensional space with compression sensing method, realizes the compression of signal and processes.Then, from a small amount of information compression, with high probability, reconstruct original signal.When wireless communication system carries out frequency deviation estimation, with respect to whole observation space, estimate that the amplitude of observed quantity only has larger range value conventionally on the Frequency point of minority.Observed quantity can be regarded as approximate sparse at observation space, utilize compressed sensing technology to carry out frequency deviation and estimate to become possibility.Therefore,, for reducing the resource overhead of wireless communication system in frequency offset estimation procedure, the present invention proposes a kind of frequency deviation estimating method based on compressed sensing technology.

Summary of the invention

Main purpose of the present invention is, a kind of novel frequency deviation estimating method is provided, operand when technical problem to be solved greatly reduces frequency deviation estimation based on compressed sensing technology, reduce the processor resource expense of wireless communication system in frequency offset estimation procedure, make it to be more suitable for practical application.

Described frequency deviation estimating method is to carry out in the situation that time synchronized completes, and has formed the starting point set S in distinguishable path.For the starting point in distinguishable path, obtain the existing a lot of mature technologies of collection approach, for example, can utilize the training sequence that receiving-transmitting sides is known, the related operation that slides is to received signal processed the correlation peak location that the range value obtaining is greater than predetermined detection thresholding, and this position is the original position of distinguishable path signal.

The inventive method comprises the steps:

A compression domain frequency offset estimation methods, the carrier frequency synchronization for each distinguishable path signal of wireless communication system, comprises the following steps:

A1, according to the original position in distinguishable path, extracts the reception burst x that on a distinguishable path, length is N * 1;

A2, the frequency deviation that the perception matrix Θ of receiving terminal utilization structure and the reception burst x on the path on described distinguishable path carry out compression domain is estimated preliminary treatment, obtains described preliminary treatment estimated value

A3, according to preliminary treatment estimated value map out the frequency deviation estimated value of described distinguishable path signal in uncompressed domain

A4 deletes element corresponding to path when pre-treatment in the starting point set S in distinguishable path; Subsequently, the frequency deviation of processing next distinguishable path not for empty set in the situation that at S is estimated; Otherwise, finish frequency offset estimation procedure.

Described method, described estimates that for compression domain frequency deviation pretreated perception matrix Θ constructs and be stored in designated memory space in advance.

Described method, described estimates that for compression domain frequency deviation the constitution step of pretreated perception matrix Θ comprises:

B1, utilizes described known training sequence A=[a ₁, a ₂..., a _n] ^tlength N, and incorporation engineering experience is set sparse grade K;

B2, the frequency deviation value according to frequency offset estimation accuracy requirement and maximum possible, arranges frequency search step delta f;

B3, calculates the search length that uncompressed domain frequency deviation is estimated

length with observed quantity in compression domain

wherein, symbol

expression is to the x computing that rounds up, described f _maxfor maximum possible frequency deviation value; Generally, M Z;

B4, the observing matrix Φ of structure M * Z;

B5, the uncompressed domain frequency deviation estimating searching matrix of Z N * N of structure

B6, each element, the uncompressed domain frequency deviation estimating searching matrix of the observing matrix Φ described in utilizing

with known training sequence A, the submatrix Θ of structure perception matrix Θ _i, i=1,2 ..., M, has ${\mathrm{\Θ}}_i={\mathrm{\φ}}_{i1}{A}^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_1\right)+{\mathrm{\φ}}_{i2}{A}^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_2\right)+\·\·\·+{\mathrm{\φ}}_{\mathrm{iZ}}{A}^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_Z\right);$ Wherein, subscript " H " represents to get conjugate transpose computing;

B7, utilizes described Θ _i, i=1,2 ..., M forms described perception matrix Θ, has $\mathrm{\Θ}=\left(\begin{array}{c}{\mathrm{\Θ}}_1\\ {\mathrm{\Θ}}_2\\ \·\\ \·\\ \·\\ {\mathrm{\Θ}}_M\end{array}\right).$

Described method, the building method of the observing matrix Φ of M * Z is: get

Described method, the uncompressed domain frequency deviation estimating searching matrix of described Z N * N

structure, described

for diagonal matrix, and have

wherein, described frequency deviation trial value ${\widetilde{\mathrm{\ν}}}_i=-f_{\max }+(i-1)\×\mathrm{\Δf},i=\mathrm{1,2},\·\·\·,Z.$

Described method, described frequency deviation estimates that preprocessing process comprises:

Utilize the submatrix Θ of described perception matrix Θ _i, i=1,2 ..., the reception burst x on M and described distinguishable path, the frequency deviation that forms compression domain is estimated preliminary treatment observed quantity set y={| Θ ₁x| ², | Θ ₂x| ²..., | Θ _mx| ², for convenience of describing, described compression domain frequency deviation is estimated to preliminary treatment observed quantity set y is expressed as y={|y (0) | ², | y (1) | ²... | y (ρ) | ², | y (ρ+1) | ²..., | y (M-1) | ²;

From described preliminary treatment observed quantity set y, find out maximum value position

? $\widehat{\mathrm{\ρ}}=\arg \underset{\mathrm{\ρ}}{\max }\left\{y\right\}=\arg \underset{\mathrm{\ρ}}{\max }\{{\left|y\left(0\right)\right|}^2,{\left|y\left(1\right)\right|}^2,\·\·\·{\left|y\left(\mathrm{\ρ}\right)\right|}^2,{\left|y(\mathrm{\ρ}+1)\right|}^2,\·\·\·,{\left|y(M-1)\right|}^2\},$ The frequency deviation that completes described compression domain is estimated pretreated handling process.

Described method, described by preliminary treatment estimated value

map out the frequency deviation estimated value in uncompressed domain processing procedure comprise:

According to described preliminary treatment estimated value

from set

middle intercepting element, forms the brachymemma set of frequency deviation trial value

wherein, described frequency deviation trial value ${\widetilde{\mathrm{\ν}}}_i=-f_{\max }+(i-1)\×\mathrm{\Δf},i=\mathrm{1,2},\·\·\·,Z;$

According to described brachymemma set β, structure observed quantity set y ₁, have

$y_1=\{{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+1}\right)x\right|}^2,{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+2}\right)x\right|}^2,\·\·\·,{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{\min (2K\widehat{\mathrm{\ρ}},Z)}\right)x\right|}^2\}.$ Wherein,

From described observed quantity set y ₁in find out the frequency offseting value that maximum element is corresponding and be frequency deviation estimated value that is to say:

$\widehat{\mathrm{\ν}}=\arg \underset{{\widetilde{\mathrm{\ν}}}_i\∈\mathrm{\β}}{\max }\left\{y_1\right\}$

$=\arg \underset{{\widetilde{\mathrm{\ν}}}_i\∈\mathrm{\β}}{\max }{\left\{\right|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+1}\right)x|}^2,{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+2}\right)x\right|}^2,\·\·\·,{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{\min (2K\widehat{\mathrm{\ρ}},Z)}\right)x\right|}^2\}.$

As can be seen from above, the frequency deviation estimating method based on compressed sensing technology that the present invention proposes, has following characteristics and advantage:

1) perception matrix Θ constructed in advance before communication process is initiated, without real-time structure.Thereby, can not take processing time and the processor resource of wireless communication system in communication process.

2) when frequency deviation is estimated, adopted compressed sensing technology to process, greatly reduce the operand while processing.Thereby reduced the processor resource expense of wireless communication system in frequency offset estimation procedure.

Accompanying drawing explanation

Fig. 1 is the frame format of the radio frames at the training sequence place that sends of the adoptable a kind of transmitter of the present invention;

Fig. 2 is the schematic flow sheet of frequency deviation estimating method according to an embodiment of the invention;

Fig. 3 is the structure flow chart of the perception matrix in frequency deviation estimating method according to an embodiment of the invention;

Fig. 4 is that frequency deviation estimating method according to an embodiment of the invention carries out frequency deviation in compression domain and estimates pretreated flow chart.

Fig. 5 is that frequency deviation estimating method according to an embodiment of the invention is mapped as compression domain estimated value the process chart of the frequency deviation estimated value in uncompressed domain.

Embodiment

Below in conjunction with specific embodiment, the present invention is described in detail.

In the embodiment of the present invention, the signal frame form schematic diagram of wireless communication system as shown in Figure 1.When carrying out frequency deviation estimation, adopt the mode based on training sequence to realize, it can be also other positions in frame that the position of its training sequence can come from frame head.

Receiving terminal reception antenna receives the Frame of transmitting terminal transmitting, and the length of establishing training sequence is N, that is to say N sampled point, receives signal length for being greater than N (a desirable 2N data are observed).

Before frequency deviation is estimated processing procedure, the present invention constructs in advance compressed sensing matrix Θ and is stored in the perception matrix stores region of appointment, thereby the processing time and the processor that do not take in practical communication process are processed resource.As shown in Figure 2, the construction process of perception matrix Θ is as follows:

Step 2.1, reads the length N of training sequence, and sparse grade K and frequency search step delta f are set.

Described training sequence A=[a ₁, a ₂..., a _n] ^tand length N is sequence and length value that receiving-transmitting sides is known, wherein subscript T represents to get transposition computing.

Described sparse grade K sets according to training sequence length N incorporation engineering experience.For example, for training sequence length N=512 situation, it is K=20 that sparse grade can be set.

The setting of described frequency search step delta f is according to the frequency deviation value f of frequency offset estimation accuracy requirement and maximum possible _maxset.For example, maximum possible frequency deviation value f _max=1000Hz, the estimated accuracy of requirement is 1Hz, and frequency search step delta f=1Hz can be set.

Step 2.2, calculates in uncompressed domain and walks inclined to one side estimating searching length according to step-size in search Δ f

according to search length Z and sparse grade K, calculate the length of observed quantity in compression domain

wherein, symbol expression is to the x computing that rounds up, f _maxfor maximum possible frequency deviation value; Generally, M Z.

Step 2.3, according to the length M of observed quantity in search length Z and compression domain, the observing matrix Φ of structure M * Z, gets

Step 2.4, according to sequence length N and frequency search step delta f.The uncompressed domain frequency deviation estimating searching matrix of Z N * N of structure $\mathrm{\Γ}\left({\widetilde{\mathrm{\ν}}}_1\right),\mathrm{\Γ}\left({\widetilde{\mathrm{\ν}}}_2\right),\·\·\·,\mathrm{\Γ}\left({\widetilde{\mathrm{\ν}}}_Z\right).$ Wherein ${\widetilde{\mathrm{\ν}}}_i=-f_{\max }+(i-1)\×\mathrm{\Δf},i=\mathrm{1,2},\·\·\·,Z,$

for diagonal matrix,

wherein,

represent plural number.

Step 2.5, each element of the observing matrix Φ of utilization structure, uncompressed domain frequency deviation estimating searching matrix

with known training sequence A=[a ₁, a ₂..., a _n] ^t, the submatrix Θ of structure perception matrix Θ _i, i=1,2 ..., M, has

${\mathrm{\Θ}}_i={\mathrm{\φ}}_{i1}{A}^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_1\right)+{\mathrm{\φ}}_{i2}{A}^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_2\right)+\·\·\·+{\mathrm{\φ}}_{\mathrm{iZ}}{A}^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_Z\right),i=\mathrm{1,2},\·\·\·,M$

Wherein, subscript " H " represents to get conjugate transpose computing.Utilize Θ _i, i=1,2 ..., M forms perception matrix Θ, has $\mathrm{\Θ}=\left(\begin{array}{c}{\mathrm{\Θ}}_1\\ {\mathrm{\Θ}}_2\\ \·\\ \·\\ \·\\ {\mathrm{\Θ}}_M\end{array}\right).$ The perception matrix of structure is put into designated storage area, thereby complete the handling process of structure perception matrix Θ.

Specifically describe frequency deviation below and estimate processing procedure, as shown in Figure 3.

Described frequency deviation estimating method is to carry out in the situation that time synchronized completes, and has formed the starting point set S in distinguishable path.For the starting point in distinguishable path, obtain the existing a lot of mature technologies of collection approach, for example, can utilize the training sequence that receiving-transmitting sides is known, the related operation that slides is to received signal processed the correlation peak location that the range value obtaining is greater than predetermined detection thresholding, and this position is the original position of distinguishable path signal.The present invention mainly pays close attention to frequency offset estimation technique, and processing procedure is:

Step 3.1, according to the original position in distinguishable path, extracts the reception burst x that on a distinguishable path, length is N * 1.

Example: as N=8, reception burst is { x ₁, x ₂..., x ₈, x ₉..., x ₁₆, the starting point set S={2 in distinguishable path, 3,5}.Thereby, can extract original position for the reception burst of " 2 " be x={x ₂, x ₃..., x ₉.

Step 3.2, utilizes the reception burst x on perception matrix Θ and this path to carry out the frequency deviation estimation preliminary treatment of compression domain, obtains described preliminary treatment estimated value concrete frequency deviation is estimated pretreatment process as shown in Figure 4, is described below:

Step 3.2.1, from perception matrix stores spatial extraction perception matrix Θ.

Step 3.2.2, utilizes the submatrix Θ of Θ _i, i=1,2 ..., M multiplies each other with x one by one, and forms the frequency deviation estimation preliminary treatment observed quantity set y={| Θ of compression domain ₁x| ², | Θ ₂x| ²..., | Θ _mx| ².

For convenience of describing, described preliminary treatment observed quantity set y is expressed as:

y＝{|y(0)| ²，|y(1)| ²，…，|y(M-1)| ²}。

Step 3.2.3 finds out maximum value position from observed quantity set y, is preliminary treatment estimated value

here, in set, explain with ρ the position of element,, ρ ∈ 0,1 ..., M-1}, has

$\widehat{\mathrm{\ρ}}=\arg \underset{\mathrm{\ρ}}{\max }\left\{y\right\}=\arg \underset{\mathrm{\ρ}}{\max }\{{\left|y\left(0\right)\right|}^2,{\left|y\left(1\right)\right|}^2,\·\·\·,{\left|y(M-1)\right|}^2\}$ Thereby the frequency deviation that completes compression domain is estimated preliminary treatment handling process.

Step 3.3, is used preliminary treatment frequency deviation estimated value

map out the frequency deviation estimated value of this distinguishable path signal in uncompressed domain

concrete mapping handling process as shown in Figure 5, is described below:

Step 3.3.1, according to preliminary treatment estimated value from set

middle intercepting element forms brachymemma frequency sets $\mathrm{\β}=\{{\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+1},{\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+2},\·\·\·,{\widetilde{\mathrm{\ν}}}_{\min (2K\widehat{\mathrm{\ρ}},Z)}\}.$ Wherein, ${\widetilde{\mathrm{\ν}}}_i=-f_{\max }+(i-1)\×\mathrm{\Δf},$ i＝1，2，…，Z。

Step 3.3.2, according to described brachymemma frequency sets β, receives burst x and and known training sequence A=[a ₁, a ₂..., a _n] ^t, structure observed quantity set y ₁:

$y_1=\{{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+1}\right)x\right|}^2,{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+2}\right)x\right|}^2,\·\·\·,{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{\min (2K\widehat{\mathrm{\ρ}},Z)}\right)x\right|}^2\}.$

Wherein, wherein, subscript " H " represents to get conjugate transpose computing,

and

Step 3.3.3, from observed quantity set y ₁in find out the frequency offseting value that maximum element is corresponding and be frequency deviation estimated value

that is to say

$\widehat{\mathrm{\ν}}=\arg \underset{{\widetilde{\mathrm{\ν}}}_i\∈\mathrm{\β}}{\max }\left\{y_1\right\}$

$=\arg \underset{{\widetilde{\mathrm{\ν}}}_i\∈\mathrm{\β}}{\max }{\left\{\right|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+1}\right)x|}^2,{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+2}\right)x\right|}^2,\·\·\·,{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{\min (2K\widehat{\mathrm{\ρ}},Z)}\right)x\right|}^2\}$

Step 3.3.4 deletes element corresponding to path when pre-treatment in the starting point set S in distinguishable path.

Example: for example, the starting point set S in distinguishable path is S={2,3,5,7}, and when the starting point corresponding to path of pre-treatment be 3, should delete the element " 3 " in S, the S set after renewal is S={2,5,7}.

Step 3.4, judges whether all distinguishable paths all finish dealing with, and that is to say and judges whether the starting point set S in distinguishable path is empty set, if empty set finishes frequency deviation and estimates flow process; Otherwise execution step 3.5.

Step 3.5 reads an element from the original position S set of distinguishable path, returns to step 3.1 and processes next distinguishable path.

Described next a distinguishable path, is element that step 3.5 reads from S set as the corresponding path of path starting point.

Below just the present invention reduce on the whole operand aspect and compare.

Conventional method, needs calculated complex multiplication NZ time, complex addition (N-1) Z, mould side's computing of plural number Z time, real number number of comparisons during search maximum Z-1 time.

The inventive method, in compression domain preliminary treatment, needs calculated complex multiplication NM time, complex addition (N-1) M, mould side's computing of plural number M time, real number number of comparisons during search maximum M-1 time.In uncompressed domain frequency deviation, estimate, in mapping, to need calculated complex multiplication 2KN time complex addition 2K (N-1), mould side's computing of plural number 2K time, real number number of comparisons during search maximum 2K-1 time.

Therefore, total complex multiplication that the present invention needs NM+2KN time, the number of times of complex addition is (N-1) M+2K (N-1), mould side's computing of plural number M+2K time, real number number of comparisons during search maximum M+2K-2 time.

For example, get N=512, according to engineering experience, can consider K=20; For guaranteeing estimated accuracy, generally, the positive integer that the value of Z is N doubly, without loss of generality, is got Z=4N=2048. contrast as shown in table 1.

Table 1

Described in above-mentioned concrete example, the inventive method, because utilizing compressed sensing technology to reduce greatly operand, has been saved processor resource.

Should be understood that, for those of ordinary skills, can be improved according to the above description or convert, and all these improvement and conversion all should belong to the protection range of claims of the present invention.

Claims (7)

1. a compression domain frequency offset estimation methods, the carrier frequency synchronization for each distinguishable path signal of wireless communication system, is characterized in that, comprises the following steps:

A1, according to the original position in distinguishable path, extracts the reception burst x that on a distinguishable path, length is N * 1;

A2, the frequency deviation that the perception matrix Θ of receiving terminal utilization structure and the reception burst x on the path on described distinguishable path carry out compression domain is estimated preliminary treatment, obtains described preliminary treatment estimated value

A3, according to preliminary treatment estimated value

map out the frequency deviation estimated value of described distinguishable path signal in uncompressed domain

A4 deletes element corresponding to path when pre-treatment in the starting point set S in distinguishable path; Subsequently, the frequency deviation of processing next distinguishable path not for empty set in the situation that at S is estimated; Otherwise, finish frequency offset estimation procedure.

2. method according to claim 1, is characterized in that, described estimates that for compression domain frequency deviation pretreated perception matrix Θ constructs and be stored in designated memory space in advance.

3. method according to claim 2, is characterized in that, described estimates that for compression domain frequency deviation the constitution step of pretreated perception matrix Θ comprises:

B1, utilizes described known training sequence A=[a ₁, a ₂..., a _n] ^tlength N, and incorporation engineering experience is set sparse grade K;

B2, the frequency deviation value according to frequency offset estimation accuracy requirement and maximum possible, arranges frequency search step delta f;

B3, calculates the search length that uncompressed domain frequency deviation is estimated

length with observed quantity in compression domain wherein, symbol

expression is to the x computing that rounds up, described f _maxfor maximum possible frequency deviation value; Generally, M Z;

B4, the observing matrix Φ of structure M * Z;

B5, the uncompressed domain frequency deviation estimating searching matrix of Z N * N of structure

B6, each element, the uncompressed domain frequency deviation estimating searching matrix of the observing matrix Φ described in utilizing

with known training sequence A, the submatrix Θ of structure perception matrix Θ _i, i=1,2 ..., M, has ${\mathrm{\Θ}}_i={\mathrm{\φ}}_{i1}{A}^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_1\right)+{\mathrm{\φ}}_{i2}{A}^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_2\right)+\·\·\·+{\mathrm{\φ}}_{\mathrm{iZ}}{A}^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_Z\right);$ Wherein, subscript " H " represents to get conjugate transpose computing;

B7, utilizes described Θ _i, i=1,2 ..., M forms described perception matrix Θ, has $\mathrm{\Θ}=\left(\begin{array}{c}{\mathrm{\Θ}}_1\\ {\mathrm{\Θ}}_2\\ \·\\ \·\\ \·\\ {\mathrm{\Θ}}_M\end{array}\right).$

4. method according to claim 3, is characterized in that, the building method of the observing matrix Φ of M * Z is: get

5. method according to claim 3, is characterized in that, the uncompressed domain frequency deviation estimating searching matrix of described Z N * N

structure, described

for diagonal matrix, and have

wherein, described frequency deviation trial value ${\widetilde{\mathrm{\ν}}}_i=-f_{\max }+(i-1)\×\mathrm{\Δf},i=\mathrm{1,2},\·\·\·,Z.$

6. method according to claim 1, is characterized in that, described frequency deviation estimates that preprocessing process comprises:

Utilize the submatrix Θ of described perception matrix Θ _i, i=1,2 ..., the reception burst x on M and described distinguishable path, the frequency deviation that forms compression domain is estimated preliminary treatment observed quantity set y={| Θ ₁x| ², | Θ ₂x| ²..., | Θ _mx| ², for convenience of describing, described compression domain frequency deviation is estimated to preliminary treatment observed quantity set y is expressed as y={|y (0) | ², | y (1) | ²... | y (ρ) | ², y (ρ+1) | ²..., | y (M-1) | ²;

From described preliminary treatment observed quantity set y, find out maximum value position

? $\widehat{\mathrm{\ρ}}=\arg \underset{\mathrm{\ρ}}{\max }\left\{y\right\}=\arg \underset{\mathrm{\ρ}}{\max }\{{\left|y\left(0\right)\right|}^2,{\left|y\left(1\right)\right|}^2,\·\·\·{\left|y\left(\mathrm{\ρ}\right)\right|}^2,{\left|y(\mathrm{\ρ}+1)\right|}^2,\·\·\·,{\left|y(M-1)\right|}^2\},$ The frequency deviation that completes described compression domain is estimated pretreated handling process.

7. method according to claim 1, is characterized in that, described by preliminary treatment estimated value

map out the frequency deviation estimated value in uncompressed domain

processing procedure comprise:

According to described preliminary treatment estimated value from set

middle intercepting element, forms the brachymemma set of frequency deviation trial value

wherein, described frequency deviation trial value ${\widetilde{\mathrm{\ν}}}_i=-f_{\max }+(i-1)\×\mathrm{\Δf},i=\mathrm{1,2},\·\·\·,Z;$

According to described brachymemma set β, structure observed quantity set y ₁, have

$y_1=\{{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+1}\right)x\right|}^2,{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+2}\right)x\right|}^2,\·\·\·,{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{\min (2K\widehat{\mathrm{\ρ}},Z)}\right)x\right|}^2\}.$ Wherein,

From described observed quantity set y ₁in find out the frequency offseting value that maximum element is corresponding and be frequency deviation estimated value

that is to say:

$\widehat{\mathrm{\ν}}=\arg \underset{{\widetilde{\mathrm{\ν}}}_i\∈\mathrm{\β}}{\max }\left\{y_1\right\}$

$=\arg \underset{{\widetilde{\mathrm{\ν}}}_i\∈\mathrm{\β}}{\max }{\left\{\right|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+1}\right)x|}^2,{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{2K(\widehat{\mathrm{\ρ}}-1)+2}\right)x\right|}^2,\·\·\·,{\left|A^H{\mathrm{\Γ}}^H\left({\widetilde{\mathrm{\ν}}}_{\min (2K\widehat{\mathrm{\ρ}},Z)}\right)x\right|}^2\}.$

Images