CN104820216B - Multipath signal direction of arrival estimation method based on array response rotational invariance - Google Patents

Abstract

The invention discloses a kind of multipath signal direction of arrival estimation method based on array response rotational invariance, for solving the technical problem of existing multipath signal direction of arrival estimation method poor practicability.Technical scheme is difference calculating observation response matrix first in the receipt signal of two different submatrixs, the output signal of the antenna oscillator of each submatrix is demodulated and low-pass filtering after, obtain baseband receiving signals, again baseband receiving signals and pseudo-random sequence are done slip related, obtain the observation impulse response of two submatrixs, by discretization is carried out to the observation impulse response of two submatrixs, extract multipath, obtain the observation impulse response vector of two submatrixs, respectively the observation impulse response vector of all antenna oscillators of two submatrixs is integrated the observed responses matrix obtaining two submatrixs；Finally utilize the direction of arrival of the rotational invariance estimation multipath signal of two submatrix receipt signal covariance matrixes.The inventive method is simple, and operation result high precision is therefore practical.

Description

Multipath signal direction of arrival estimation method based on array response rotational invariance

Technical field

The present invention relates to a kind of multipath signal direction of arrival estimation method, it is based on array response invariable rotary particularly to a kind of The multipath signal direction of arrival estimation method of property.

Background technology

Document " ESPRIT algorithm estimates performance evaluation,《Information technology》, the 3rd phase in 2011, page 100 to page 102 " in carry ESPRIT (the Estimation of Signal Parameters Via Rotational Invariance arriving Techniques) method is a kind of typical signal direction of arrival estimation method.The method divide the array into two identical Submatrix, the rotational invariance using two submatrix receipt signal covariance matrixes carries out DOA estimate.But the method exists Following problem, the method requires multipath number to be less than the oscillator number of aerial array.And the multipath number in actual channel is very big, Consider hardware cost it is difficult to realize more massive receiving antenna array, therefore ESPRIT method is difficult to be generalized to practical application.

Content of the invention

In order to overcome the shortcomings of existing multipath signal direction of arrival estimation method poor practicability, the present invention provides one kind to be based on battle array The multipath signal direction of arrival estimation method of row response rotational invariance.The method is first in the receipt signal of two different submatrixs Respectively calculating observation response matrix, the output signal of the antenna oscillator of each submatrix is demodulated and low-pass filtering after, Obtain baseband receiving signals, then by baseband receiving signals and pseudo-random sequence do slip related, obtain two submatrixs observation rush Swash response, by discretization is carried out to the observation impulse response of two submatrixs, extract multipath, obtain the observation punching of two submatrixs The observation impulse response vector of all antenna oscillators of two submatrixs is integrated the sight obtaining two submatrixs by sharp response vector respectively Survey response matrix；Finally estimate that the ripple of multipath signal reaches using the rotational invariance of two submatrix receipt signal covariance matrixes Angle.The inventive method is simple, computational complexity is low, operation result high precision is it is adaptable to carry out to a large amount of multipath signal direction of arrival Estimate, breach existing ESPRIT method for antenna shake unit restriction, practical.

The technical solution adopted for the present invention to solve the technical problems is：A kind of many based on array response rotational invariance Footpath signal direction of arrival estimation method, is characterized in comprising the following steps：

(A) definition signal.

Select the pseudo-random sequence that length is X as base-band detection signal a (t), its expression formula is

Wherein, X represents the length of pseudo-random sequence, t express time,Expression width is T_bRectangular pulse letter Number.K PN sequence forms one and detects frame u (t), and its expression formula is

Wherein, T_p=XT_b.Detecting frame u (t) is basic detectable signal, launches through antenna after the modulation of this detection frame.

For the communication environments containing L bar multipath, its space channel impulse response model h (t) is expressed as follows

Wherein, L is the multipath bar number in communication environments,Represent the channel complex response of l article of multipath, be one and often answer Number, τ_lIt is the time delay value of l article of multipath, δ (t) represents impulse function.

Receiving antenna array is one-dimensional linear aerial array, comprises M+1 antenna oscillator, wherein, M ＞ 1.This M+1 sky Linear oscillator is spaced substantially equidistant, and element spacing is expressed as d, and the directional diagram of antenna oscillator is all identical.From geometrically by antenna array Row are divided into identical two submatrixs：Submatrix Z_αWith submatrix Z_β.Wherein, submatrix Z_αBy the 1～M days in primary antenna array Linear oscillator forms, submatrix Z_βIt is made up of 2～M+1 antenna oscillator in primary antenna array.Two submatrixs all include M antenna Oscillator, is therefore all renumbered as 1～M the antenna oscillator in two submatrixs.Submatrix Z_αOn m-th antenna oscillator and submatrix Z_βOn the distance of m-th antenna oscillator be expressed as Δ.

For m-th antenna oscillator in submatrix, then its arrival bearing θ on complex response s (θ) be

Wherein, e represents the nature truth of a matter, and j represents imaginary number,Represent the wavelength of radiofrequency signal, θ represents arrival bearing.

For submatrix Z_αOn m-th antenna oscillator, according to formula (5) generate radio frequency receiving signal

Wherein, N '_mT () is the white noise of Gaussian distributed, θ_lRepresent the incident angle in l article of footpath,And τ_lFor many The complex response in footpath and time delay, u ' (t) is the detection frame after modulation.To submatrix Z_αOn all antenna oscillators, all generate corresponding Receipt signal.

For submatrix Z_βOn m-th antenna oscillator, according to formula (6) generate radio frequency receiving signal

Wherein, N '_mT () is the white noise of Gaussian distributed, θ_lRepresent the incident angle in l article of footpath,And τ_lFor many The complex response in footpath and time delay, u ' (t) is the detection frame after modulation.For submatrix Z_βOn all antenna oscillators, all generate corresponding Receipt signal.

Submatrix Z_αOn the receipt signal of m-th antenna oscillator output demodulated be expressed as

Wherein, N_mT () is the noise signal received by m-th antenna oscillator, θ_lIt is that the ripple of the l article footpath incoming signal reaches Angle, s_m(θ_l) be m-th antenna oscillator be θ to direction of arrival_lIncoming signal complex response.

Submatrix Z_βOn the receipt signal of m-th antenna oscillator output demodulated be expressed as

Wherein, e is the nature truth of a matter, and j represents imaginary number.Due to submatrix Z_βOn m-th antenna oscillator with respect to submatrix Z_αOn There is distance, delta in m-th antenna oscillator, this distance result in the wave path-difference on arrival bearing.And then be θ for angle of incidence_l's Multipath signal, submatrix Z_βReceipt signal with respect to submatrix Z_αReceipt signal occur in that phase shift ξ (θ_l).ξ(θ_l) expression formula be

Wherein,Represent the wavelength of radiofrequency signal.

(B) calculating observation impulse response matrix.

For submatrix Z_αWith submatrix Z_βOn m-th antenna oscillator, calculating observation impulse response matrix be divided into following four step Suddenly：

(B-1) output signal of antenna oscillator is demodulated, after low-pass filtering, respectively obtains baseband receiving signalsWith

(B-2) detectable signal will be received respectivelyWithSlide with local pseudo-random sequence a (t) of standard Related, you can to obtain observing impulse responseWithExpression formula is as follows respectively

Wherein,Represent spreading gain, N '_m(t) be related to local pseudo-random sequence after noise letter Number.

(B-3) impulse response will be observed respectivelyWithDiscretization.L maximum peak point of selective value, respectively It is expressed asWithWillComposition observation impulse rings Should vectorWillComposition observation impulse response vector WithMathematic(al) representation divide It is not

Wherein,Represent noise vector.

(B-4) for submatrix Z_αWith submatrix Z_βUpper 1st receipt signal to m-th reception antenna oscillator is carried out above Three steps, respectively obtain their observation impulse response vector, are expressed asWithThese are observed Impulse response vector is organized into observation impulse response matrix H according to following form_αAnd H_β

H_αIt is the matrix of M row L row, H_βIt is the matrix of M row L row, their mathematic(al) representation is

See from formula (16) and formula (17), the m row of observation impulse response matrix represents the observation punching of m-th oscillator Sharp response vector, l row represent observation impulse response on whole array for the l article footpath, referred to as array impulse response vector.

(C) estimate direction of arrival.

Space channel comprises L bar multipath, once estimates p bar therein, 1≤p≤M, specific step is as follows.

(C-1) from observation impulse response matrix H_αMiddle selection p row, this p column number is p₁,…,p_p, and constitute matrix Mathematic(al) representation be

Wherein,Represent noise vector,Represent noise matrix, A is Steering vector matrix, is defined as follows

MatrixWherein diag [] represents construction diagonal matrix.

Again from observation impulse response matrix H_βIn same position select p row, be p equally by this p column number₁,…,p_p, and Constitute matrix Expression formula as follows

Wherein,MatrixAnd matrixIt is all M × p matrix.If selected The incoming signal angle in the p bar footpath corresponding to p row selected is different, then prove matrixAnd matrixOrder be p.

Ask for matrixAnd matrixOrder, the incident letter in selected p bar footpath, if result is equal to p, is described Number direction of arrival is different, then continue executing with (C-2) step.If result is not equal to p, illustrate in selected p bar footpath at least The direction of arrival having the corresponding incoming signal in two footpaths is identical.Now the value of p is deducted 1, and re-execute this sub-step.Card Bright when p finally reduces to 1, matrixAnd matrixOrder certain be equal to 1, and during p=1, this method is still set up.Therefore originally Method must be set up.

(C-2) ask for according to formula (18) and formula (19) respectivelyWithCovariance matrixWith

Wherein,WithRepresent respectivelyWithAssociate matrix.MatrixWithIt is all M × M square Battle array.Prove, matrixWithOrder be all p.

(C-3) to matrixCarry out feature decomposition, and eigenvalue is arranged according to order from big to small, be expressed asAsk for the corresponding characteristic vector of these eigenvalues, be expressed asBuild matrix U according to formula (20)_α.

Similarly to matrixCarry out feature decomposition, and eigenvalue is arranged according to order from big to small, be expressed asAsk for the corresponding characteristic vector of these eigenvalues, be expressed asBuild matrix U according to formula (21)_β.

Matrix U_αAnd U_βIt is all the matrix of M × p.Prove, matrix U_αAnd U_βOrder be p.

(C-4) ask for matrix Ψ according to formula (22).

Ψ=(U_α)⁺U_β(25)

Wherein, ()⁺Represent and seek group inverse matrices.Matrix Ψ is the matrix of p × p.

Eigenvalue is asked for matrix Ψ, is expressed asProveIt is the diagonal of matrix Φ Element.According toThe signal direction of arrival in the corresponding p bar footpath of selected p row can be obtained.The method asked for is shown in formula (26).

Wherein, argsin () represents sine of negating, and argument of a complex number is sought in angle () expression.The signal wave completing p bar footpath reaches Angular estimation.

(C-5) go to (C-1) step, reselection p bar footpath is estimated, until all of L bar footpath all completes to estimate.

The invention has the beneficial effects as follows：The method difference calculating observation first in the receipt signal of two different submatrixs rings Answer matrix, the output signal of the antenna oscillator of each submatrix is demodulated and low-pass filtering after, obtain Baseband Receiver letter Number, then it is related that baseband receiving signals and pseudo-random sequence are done slip, obtains the observation impulse response of two submatrixs, by two The observation impulse response of individual submatrix carries out discretization, extracts multipath, obtains the observation impulse response vector of two submatrixs, respectively The observation impulse response vector of all antenna oscillators of two submatrixs is integrated the observed responses matrix obtaining two submatrixs；Finally Rotational invariance using two submatrix receipt signal covariance matrixes estimates the direction of arrival of multipath signal.Due to the inventive method In, estimate that subprocess only processes the DOA estimate of a part of multipath signal for one, substantial amounts of multipath signal can divide different Estimate that subprocess is processed.Therefore estimable multipath direction of arrival quantity is not limited by receiving antenna array scale.Due to The inventive method is not directly using sampled signal, but processes, according to sampled signal, the observation impulse response matrix obtaining and estimated Meter, the data volume therefore relating to is less.Additionally, the inventive method is not related to iteration or search, therefore operand is less.Therefore this Bright method is simple, computational complexity is low, operation result high precision it is adaptable to estimate to a large amount of multipath signal direction of arrival, dash forward Broken existing ESPRIT method for antenna shake unit restriction, practical.

Describe the present invention below in conjunction with specific embodiment in detail.

Specific embodiment

The present invention is comprised the following steps that based on the multipath signal direction of arrival estimation method of array response rotational invariance：

(A) definition signal；(B) calculating observation impulse response matrix；(C) estimate direction of arrival.

(A) definition signal.

Select the pseudo-random sequence that length is X as base-band detection signal a (t), its expression formula is

Wherein, X represents the length of pseudo-random sequence, t express time,Expression width is T_bRectangular pulse letter Number.K PN sequence forms one and detects frame u (t), and its expression formula is

Wherein T_p=XT_b.Detect the basic detectable signal that frame u (t) is in this method, send out through antenna after the modulation of this detection frame It is shot out.

For the communication environments containing L bar multipath, its space channel impulse response model h (t) is expressed as follows

Wherein, L is the multipath bar number in communication environments,Represent the channel complex response of l article of multipath, be one and often answer Number, τ_lIt is the time delay value of l article of multipath, δ (t) represents impulse function.

Receiving antenna array is one-dimensional linear aerial array, comprises M+1 antenna oscillator (M ＞ 1).This M+1 antenna shakes Son is spaced substantially equidistant, and element spacing is expressed as d, and the directional diagram of antenna oscillator is all identical.From geometrically aerial array being divided For identical two submatrixs：Submatrix Z_αWith submatrix Z_β.Wherein, submatrix Z_αShaken by the 1～M antenna in primary antenna array Son composition, submatrix Z_βIt is made up of 2～M+1 antenna oscillator in primary antenna array.Two submatrixs all include M antenna and shake Son, is therefore all renumbered as 1～M the antenna oscillator in two submatrixs.Submatrix Z_αOn m-th antenna oscillator and submatrix Z_β On the distance of m-th antenna oscillator be expressed as Δ.

For m-th antenna oscillator in submatrix, then its arrival bearing θ on complex response s (θ) be

Wherein e represents the nature truth of a matter, and j represents imaginary number,Represent the wavelength of radiofrequency signal, θ represents arrival bearing.

For submatrix Z_αOn m-th antenna oscillator, according to formula (5) generate radio frequency receiving signal

Wherein N '_mT () is the white noise of Gaussian distributed, θ_lRepresent the incident angle in l article of footpath,And τ_lFor many The complex response in footpath and time delay, u ' (t) is the detection frame after modulation.To submatrix Z_αOn all antenna oscillators, all generate corresponding Receipt signal.

For submatrix Z_βOn m-th antenna oscillator, according to formula (6) generate radio frequency receiving signal

Wherein N '_mT () is the white noise of Gaussian distributed, θ_lRepresent the incident angle in l article of footpath,And τ_lFor many The complex response in footpath and time delay, u ' (t) is the detection frame after modulation.For submatrix Z_βOn all antenna oscillators, all generate corresponding Receipt signal.

Submatrix Z_αOn the receipt signal of m-th antenna oscillator output demodulated be expressed as

Wherein, N_mT () is the noise signal received by m-th antenna oscillator, θ_lIt is that the ripple of the l article footpath incoming signal reaches Angle, s_m(θ_l) be m-th antenna oscillator be θ to direction of arrival_lIncoming signal complex response.

Submatrix Z_βOn the receipt signal of m-th antenna oscillator output demodulated be expressed as

Wherein, e is the nature truth of a matter, and j represents imaginary number.Due to submatrix Z_βOn m-th antenna oscillator with respect to submatrix Z_αOn There is distance, delta in m-th antenna oscillator, this distance result in the wave path-difference on arrival bearing.And then be θ for angle of incidence_l's Multipath signal, submatrix Z_βReceipt signal with respect to submatrix Z_αReceipt signal occur in that phase shift ξ (θ_l).ξ(θ_l) expression formula be

Wherein,Represent the wavelength of radiofrequency signal.

(B) calculating observation impulse response matrix.

For submatrix Z_αWith submatrix Z_βOn m-th antenna oscillator, calculating observation impulse response matrix be divided into following four step Suddenly：

(B-1) output signal of antenna oscillator is demodulated, after low-pass filtering, respectively obtains baseband receiving signalsWith

(B-2) detectable signal will be received respectivelyWithSlide with local pseudo-random sequence a (t) of standard Related, you can to obtain observing impulse responseWithExpression formula is as follows respectively

Wherein,Represent spreading gain, N '_m(t) be related to local pseudo-random sequence after noise letter Number.

(B-3) impulse response will be observed respectivelyWithDiscretization.L maximum peak point of selective value, respectively It is expressed asWithWillComposition observation impulse rings Should vectorWillComposition observation impulse response vector WithMathematic(al) representation divide It is not

Wherein,Represent noise vector.

(B-4) for submatrix Z_αWith submatrix Z_βUpper 1st receipt signal to m-th reception antenna oscillator is carried out above Three steps, respectively obtain their observation impulse response vector, are expressed asWithThese are observed Impulse response vector is organized into observation impulse response matrix H according to following form_αAnd H_β

H_αIt is the matrix of M row L row, H_βIt is the matrix of M row L row, their mathematic(al) representation is

See from formula (16) and formula (17), the m row of observation impulse response matrix represents the observation punching of m-th oscillator Sharp response vector, l row represent observation impulse response on whole array for the l article footpath, referred to as array impulse response vector.

(C) estimate direction of arrival.

Space channel comprises L bar multipath, and this method once estimates p bar therein (1≤p≤M), and specific step is as follows (remaining multipath second, estimate, as described in C-5 in .. for the third time ...).

(C-1) from observation impulse response matrix H_αMiddle selection p arranges (1≤p≤M), and this p column number is p₁,…,p_p, and structure Become matrix Mathematic(al) representation be

Wherein,Represent noise vector,Represent noise matrix, A is Steering vector matrix, is defined as follows

MatrixWherein diag [] represents construction diagonal matrix.

Again from observation impulse response matrix H_βIn same position select p row, be p equally by this p column number₁,…,p_p, and Constitute matrix Expression formula as follows

WhereinMatrixAnd matrixIt is all M × p matrix.If selected The incoming signal angle in the p bar footpath corresponding to p row selected is different, then prove matrixAnd matrixOrder be p.

Ask for matrixAnd matrixOrder, the incident letter in selected p bar footpath, if result is equal to p, is described Number direction of arrival is different, then continue executing with (C-2) step.If result is not equal to p, illustrate in selected p bar footpath at least The direction of arrival having the corresponding incoming signal in two footpaths is identical.Now the value of p is deducted 1, and re-execute this sub-step.Card Bright when p finally reduces to 1, matrixAnd matrixOrder certain be equal to 1, and during p=1, this method is still set up.Therefore originally Method must be set up.

(C-2) ask for according to formula (18) and formula (19) respectivelyWithCovariance matrixWith

Wherein,WithRepresent respectivelyWithAssociate matrix.MatrixWithIt is all M × M square Battle array.Prove, matrixWithOrder be all p.

(C-3) to matrixCarry out feature decomposition, and eigenvalue is arranged according to order from big to small, be expressed asAsk for the corresponding characteristic vector of these eigenvalues, be expressed asBuild matrix U according to formula (20)_α.

Similarly to matrixCarry out feature decomposition, and eigenvalue is arranged according to order from big to small, be expressed asAsk for the corresponding characteristic vector of these eigenvalues, be expressed asBuild matrix U according to formula (21)_β.

Matrix U_αAnd U_βIt is all the matrix of M × p.Prove, matrix U_αAnd U_βOrder be p.

(C-4) ask for matrix Ψ according to formula (22).

Ψ=(U_α)⁺U_β(25)

Wherein, ()⁺Represent and seek group inverse matrices.Matrix Ψ is the matrix of p × p.

Eigenvalue is asked for matrix Ψ, is expressed asProveIt is the diagonal of matrix Φ Element.According toThe signal direction of arrival in the corresponding p bar footpath of selected p row can be obtained.The method asked for is shown in formula (26).

Wherein, argsin () represents sine of negating, and argument of a complex number is sought in angle () expression.This completes p bar footpath Signal DOA estimate.

(C-5) go to (C-1) step, reselection p bar footpath is estimated, until all of L bar footpath all completes to estimate.More than Referred to as one estimation subprocess of (C-1) to (C-4) step.It should be noted that the different p value not necessarily phases estimating subprocess With.

A kind of specific simulation implementation mode introduced below.

(a) definition signal.

According to following steps definition signal.

(a-1) generate and detect frame signal.M-sequence that length be 1023 is used as pseudo-random sequence, base-band detection signal a T the bit rate of () is the T in 100 mbit, namely formula (1)_b=10ns, wherein ns represent nanosecond.One detects frame u (t) Connected by two pseudo-random sequences and form, namely K=2 in formula (2).Detect frame to modulate by BPSK, carrier frequency is 2.5GHz. Detection frame after modulation is expressed as u ' (t).

(a-2) generate multi-path information.Assume to comprise 20 multipaths in environment.The time delay of this 20 multipaths, complex response and enter It is unknown for penetrating signal angle to transmitting terminal and receiving terminal.For being emulated, by the time delay in this 20 footpaths and complex response according to table 1 It is configured.

The time delay of the different multipath of table 1 and complex response

Sequence number	Complex response	Time delay (ns)		Sequence number	Complex response	Time delay (ns)
							1	ξ	100		11	0.80ξ	200
2	0.98ξ	110		12	0.78ξ	210
							3	0.96ξ	120		13	0.76ξ	220
4	0.94ξ	130		14	0.74ξ	230
							5	0.92ξ	140		15	0.72ξ	240
6	0.90ξ	150		16	0.70ξ	250
							7	0.88ξ	160		17	0.68ξ	260
8	0.86ξ	170		18	0.66ξ	270

9	0.84ξ	180		19	0.64ξ	280
							10	0.82ξ	190		20	0.62ξ	290

Wherein, ξ is a complex constant, can freely arrange.The unit of time delay is nanosecond.The angle of incidence of this 20 multipaths can be with Machine generates, and angular resolution is 1 degree, and span is -90～90 degree.

(a-3) generate receiving antenna array.Reception antenna is wire antenna array, comprises 6 pieces of antenna oscillators, adjacent antenna The distance of oscillator is expressed as d, and d is equal to the half of radiofrequency signal wavelength, namely 6 centimetres.Then submatrix Z_αBy 1～No. 5 antenna oscillator Composition, submatrix Z_βIt is made up of 2～No. 6 antenna oscillators.By submatrix Z_αWith submatrix Z_βOn antenna oscillator be all renumbered as 1～5 Number.Then in two submatrixs, the distance of identical numbering oscillator is Δ, is apparent from Δ in the present embodiment=d=6 centimetre.

(a-4) generate submatrix Z_αWith submatrix Z_βSteering vector on different direction of arrival.Due to two submatrixs oscillator and Array structure is identical, and therefore steering vector is also identical.For m-th antenna oscillator in submatrix, then its arrival bearing θ on Complex response s (θ) be

Wherein e represents the nature truth of a matter, and j represents imaginary number,Represent the wavelength of radiofrequency signal, in this example for 12 centimetres (0.12 meter).Incoming signal to all 20 footpaths, all calculates in submatrix 1～No. 5 antenna oscillator in its incoming wave according to formula (4) θ₁..., θ₂₀On complex response s₁(θ₁),…,s₁(θ₂₀),s₂(θ₁),…,s₅(θ₂₀).

(a-5) generate submatrix relative phase shift.So-called submatrix relative phase shift, refers to that for angle of incidence be θ_lThe l article footpath enter Penetrate signal, submatrix Z_βOn oscillator with respect to submatrix Z_αPhase shift ξ (the θ of upper same numbering oscillator institute output signal_l).According to formula (9) calculate the submatrix relative phase shift ξ (θ of the incoming signal in all footpaths₁),…,ξ(θ₂₀).

(a-6) generate receipt signal.For submatrix Z_αOn m-th antenna oscillator, according to formula (5) generate radio frequency reception letter Number

Wherein N '_mT () is the white noise of Gaussian distributed, signal to noise ratio is set to 0dB.And τ_lIt is shown in table 1 The complex response in footpath and time delay.To submatrix Z_αOn all 5 pieces of antenna oscillators, all generate corresponding receipt signal.

For submatrix Z_βOn m-th antenna oscillator, according to formula (6) generate radio frequency receiving signal

For submatrix Z_βOn all 5 pieces of antenna oscillators, all generate corresponding receipt signal.

(b) calculating observation impulse response matrix.

Calculating observation impulse response matrix in accordance with the following steps.

(b-1) setting antenna oscillator sequence number m is 1.

(b-2) respectively to radio frequency receiving signalWithCarry out BPSK demodulation, low-pass filtering (filter bandwidht 100MHz), obtain base-band detection frameWith

(b-3) by base-band detection frameWith base-band detection signal a (t) do slip related, obtain observation impulse responseTry to achieveMaximum, be expressed asSetting threshold values Thr_α, its value is

Again by base-band detection frameWith base-band detection signal a (t) do slip related, obtain observation impulse responseTry to achieveMaximum, be expressed asSetting threshold values Thr_β, its value is

(b-4) from the beginning of t=0, find out satisfaction20 peak points, the value of this 20 peak points is The observation impulse response of discretization, the value of this 20 points is formed a row vector according to the form of formula (12), as observation punching Sharp response vector

Again from the beginning of t=0, find out satisfaction20 peak points, the value of this 20 peak points is as discrete The observation impulse response changed, the value of this 20 points is formed a row vector according to the form of formula (13), and as observation impulse rings Answer vector

(b-5) antenna oscillator sequence number m adds 1, rotates back into the execution of (b-2) step, until the observation punching of all 5 antenna oscillators Sharp response vector is all asked for completing

(b-6) after completing above sub-step, according to formula (14) Suo Shi submatrix Z_αThe observation impulse response vector of upper oscillator It is combined into an observation impulse response matrix, be expressed as H_α.According still further to formula (15) Suo Shi submatrix Z_βThe observation impulse of upper oscillator Response vector is combined into an observation impulse response matrix, is expressed as H_β.H in this example_αAnd H_βIt is all 5 × 20 matrix.

C () estimates direction of arrival.

Carry out the estimation of multipath signal direction of arrival in accordance with the following steps.

(c-1) represent the sequence number estimating subprocess with η, setting η is 1.The multipath signal direction of arrival number once estimated is set Amount p is set to 3.

(c-2) take out observation impulse response matrix H_α(η -1) × p+1 to η × p row.If η × p is more than 20, Take observation impulse response matrix H_α(η -1) × p+1 to the 20th row, and update p value be 20- (η -1) × p.

This p column number is 1～p.Constitute matrix according to formula (18)Further take out observation impulse response matrix H_β? ((η -1) × p+1) to (η × p) arranges, and it is 1～p that this p row are equally numbered.Constitute matrix according to formula (20)Ask for square Battle arrayOrder, be expressed as R_α, then ask for matrixOrder, be expressed as R_β.If R_αOr R_βIt is not equal to p, then the value of p is subtracted 1, Re-execute this sub-step.

(c-3) respectively according to formula (21) and formula (22) calculating matrixWithCovariance matrixWithThis example In, matrixWithIt is all 5 × 5 matrix.

(c-4) to matrixCarry out feature decomposition, and eigenvalue is arranged according to order from big to small, be expressed asSeek eigenvalue againCorresponding characteristic vector, is expressed asBuild square according to formula (23) Battle array U_α.

Similarly to matrixCarry out feature decomposition, and eigenvalue is arranged according to order from big to small, be expressed asSeek eigenvalue againCorresponding characteristic vector, is expressed asBuild square according to formula (24) Battle array U_β

(c-5) according to formula (25) calculating matrix Ψ, ask for the eigenvalue of matrix Ψ, be expressed asAccording to formula (26) obtain the signal direction of arrival in this p bar footpath respectively, be expressed asAnd preserve.

(c-6) estimate that the value of subprocess sequence number η adds 1, the value of setting p is 3, and transfers back to the execution of (c-2) step, until institute The signal direction of arrival having footpath all completes to estimate.

By all signal DOA estimate value composition set estimating subprocess output, the incident letter in as required 20 footpaths The estimation value set of number direction of arrival.

Claims (1)

1. a kind of multipath signal direction of arrival estimation method based on array response rotational invariance is it is characterised in that include following walking Suddenly：

(A) definition signal；

Select the pseudo-random sequence that length is X as base-band detection signal a (t), its expression formula is

$a\left(t\right)=\underset{n=0}{\overset{X-1}{\Σ}}{b}_n{\mathrm{rect}}_{T_b}(t-{\mathrm{nT}}_b),b_n\∈\{+1,-1\}---\left(1\right)$

Wherein, X represents the length of pseudo-random sequence, t express time,Expression width is T_bRectangular pulse signal；K Individual PN sequence forms one and detects frame u (t), and its expression formula is

$u\left(t\right)=\underset{k=0}{\overset{K-1}{\Σ}}a(t-{\mathrm{kT}}_p)---\left(2\right)$

Wherein, T_p=XT_b；Detecting frame u (t) is basic detectable signal, launches through antenna after the modulation of this detection frame；

For the communication environments containing L bar multipath, its space channel impulse response model h (t) is expressed as follows

$h\left(t\right)=\underset{l=1}{\overset{L}{\Σ}}{h}_l^{CH}\mathrm{\δ}(t-{\mathrm{\τ}}_l)---\left(3\right)$

Wherein, L is the multipath bar number in communication environments, L=20；Represent the channel complex response of l article of multipath, be one and answer Constant, τ_lIt is the time delay value of l article of multipath, δ (t) represents impulse function；

Receiving antenna array is one-dimensional linear aerial array, comprises M+1 antenna oscillator, wherein, M>1；This M+1 antenna oscillator It is spaced substantially equidistant, element spacing is expressed as d, and the directional diagram of antenna oscillator is all identical；From geometrically aerial array being divided into Identical two submatrixs：Submatrix Z_αWith submatrix Z_β；Wherein, submatrix Z_αBy the 1～M antenna oscillator in primary antenna array Composition, submatrix Z_βIt is made up of 2～M+1 antenna oscillator in primary antenna array；Two submatrixs all include M antenna oscillator, Therefore the antenna oscillator in two submatrixs is all renumbered as 1～M；Submatrix Z_αOn m-th antenna oscillator and submatrix Z_βOn The distance of m-th antenna oscillator is expressed as Δ；

For m-th antenna oscillator in submatrix, then its arrival bearing θ on complex response s (θ) be

Wherein, e represents the nature truth of a matter, and j represents imaginary number,Represent the wavelength of radiofrequency signal, θ represents arrival bearing；

For submatrix Z_αOn m-th antenna oscillator, according to formula (5) generate radio frequency receiving signal

$y_{{\mathrm{\α}}_m}^{\′}\left(t\right)=\underset{l=1}{\overset{20}{\Σ}}{h}_l^{CH}{s}_m\left({\mathrm{\θ}}_l\right)u^{\′}(t-{\mathrm{\τ}}_l)+N_m^{\′}\left(t\right)---\left(5\right)$ Wherein, N '_mT () is to obey Gauss to divide The white noise of cloth, θ_lRepresent the incident angle in l article of footpath,And τ_lComplex response for multipath and time delay, after u ' (t) is modulation Detect frame；To submatrix Z_αOn all antenna oscillators, all generate corresponding receipt signal；

For submatrix Z_βOn m-th antenna oscillator, according to formula (6) generate radio frequency receiving signal

$y_{{\mathrm{\β}}_m}^{\′}\left(t\right)=\underset{l=1}{\overset{20}{\Σ}}{h}_l^{CH}{s}_m\left({\mathrm{\θ}}_l\right)e^{j\mathrm{\ξ}\left({\mathrm{\θ}}_l\right)}{u}^{\′}(t-{\mathrm{\τ}}_l)+N_m^{\′}\left(t\right)---\left(6\right)$

Wherein, N '_mT () is the white noise of Gaussian distributed, θ_lRepresent the incident angle in l article of footpath,And τ_lFor multipath Complex response and time delay, u ' (t) is the detection frame after modulation；For submatrix Z_βOn all antenna oscillators, all generate and connect accordingly The collection of letters number；

Submatrix Z_αOn the receipt signal of m-th antenna oscillator output demodulated be expressed as

$y_{{\mathrm{\α}}_m}\left(t\right)=\underset{l=1}{\overset{L}{\Σ}}{h}_l^{CH}{s}_m\left({\mathrm{\θ}}_l\right)u(t-{\mathrm{\τ}}_l)+N_m\left(t\right)---\left(7\right)$

Wherein, N_mT () is the noise signal received by m-th antenna oscillator, θ_lIt is the direction of arrival of the l article footpath incoming signal, s_m (θ_l) be m-th antenna oscillator be θ to direction of arrival_lIncoming signal complex response；

Submatrix Z_βOn the receipt signal of m-th antenna oscillator output demodulated be expressed as

$y_{{\mathrm{\β}}_m}\left(t\right)=\underset{l=1}{\overset{L}{\Σ}}{h}_l^{CH}{s}_m\left({\mathrm{\θ}}_l\right)e^{j\mathrm{\ξ}\left({\mathrm{\θ}}_l\right)}u(t-{\mathrm{\τ}}_l)+N_m\left(t\right)---\left(8\right)$

Wherein, e is the nature truth of a matter, and j represents imaginary number；Due to submatrix Z_βOn m-th antenna oscillator with respect to submatrix Z_αOn m There is distance, delta in individual antenna oscillator, this distance result in the wave path-difference on arrival bearing；And then be θ for angle of incidence_lMany Footpath signal, submatrix Z_βReceipt signal with respect to submatrix Z_αReceipt signal occur in that phase shift ξ (θ_l)；ξ(θ_l) expression formula be

Wherein,Represent the wavelength of radiofrequency signal；

(B) calculating observation impulse response matrix；

For submatrix Z_αWith submatrix Z_βOn m-th antenna oscillator, calculating observation impulse response matrix is divided into following four steps：

(B-1) output signal of antenna oscillator is demodulated, after low-pass filtering, respectively obtains baseband receiving signalsWith

(B-2) detectable signal will be received respectivelyWithTo local pseudo-random sequence a (t) of standard do slip related, Can obtain observing impulse responseWithExpression formula is as follows respectively

${\tilde{h}}_{{\mathrm{\α}}_m}\left(t\right)=\underset{l=1}{\overset{L}{\Σ}}{\mathrm{\ρh}}_l^{CH}{s}_m\left({\mathrm{\θ}}_l\right)\mathrm{\δ}(t-{\mathrm{\τ}}_l)+N_m^{\′}\left(t\right)---\left(10\right)$

${\tilde{h}}_{{\mathrm{\β}}_m}\left(t\right)=\underset{l=1}{\overset{L}{\Σ}}{\mathrm{\ρh}}_l^{CH}{s}_m\left({\mathrm{\θ}}_l\right)e^{j\mathrm{\ξ}\left({\mathrm{\θ}}_l\right)}\mathrm{\δ}(t-{\mathrm{\τ}}_l)+N_m^{\′}\left(t\right)---\left(11\right)$

Wherein,Represent spreading gain, N '_m(t) be related to local pseudo-random sequence after noise signal；

(B-3) impulse response will be observed respectivelyWithDiscretization；L maximum peak point of selective value, represents respectively ForWithWillComposition observation impulse response to AmountWillComposition observation impulse response vector WithMathematic(al) representation be respectively

$\begin{array}{c}{\tilde{a}}_{{\mathrm{\α}}_m}=\[\begin{array}{ccc}{\tilde{h}}_{{\mathrm{\α}}_m}\left({\mathrm{\τ}}_1\right)& \mathrm{...}& {\tilde{h}}_{{\mathrm{\α}}_m}\left({\mathrm{\τ}}_L\right)\end{array}\]\\ =\mathrm{\ρ}\[\begin{array}{ccc}{h}_1^{CH}{s}_m\left({\mathrm{\θ}}_1\right)& \mathrm{...}& h_L^{CH}{s}_m\left({\mathrm{\θ}}_L\right)\end{array}\]+{\tilde{N}}_m^{\′}\end{array}---\left(12\right)$

$\begin{array}{c}{\tilde{a}}_{{\mathrm{\β}}_m}=\[\begin{array}{ccc}{\tilde{h}}_{{\mathrm{\β}}_m}\left({\mathrm{\τ}}_1\right)& \mathrm{...}& {\tilde{h}}_{{\mathrm{\β}}_m}\left({\mathrm{\τ}}_L\right)\end{array}\]\\ =\mathrm{\ρ}\[\begin{array}{ccc}{h}_1^{CH}{s}_m\left({\mathrm{\θ}}_1\right)e^{j\mathrm{\ξ}\left({\mathrm{\θ}}_1\right)}& \mathrm{...}& h_L^{CH}{s}_m\left({\mathrm{\θ}}_L\right)e^{j\mathrm{\ξ}\left({\mathrm{\θ}}_L\right)}\end{array}\]+{\tilde{N}}_m^{\′}\end{array}---\left(13\right)$

Wherein,Represent noise vector；

(B-4) for submatrix Z_αWith submatrix Z_βUpper 1st receipt signal to m-th reception antenna oscillator is carried out three above Step, respectively obtains their observation impulse response vector, is expressed asWithThese are observed impulse Response vector is organized into observation impulse response matrix H according to following form_αAnd H_β

$H_{\mathrm{\α}}=\left[\begin{array}{c}{\tilde{a}}_{{\mathrm{\α}}_1}\\ .\\ .\\ .\\ {\tilde{a}}_{{\mathrm{\α}}_M}\end{array}\right]---\left(14\right)$

$H_{\mathrm{\β}}=\left[\begin{array}{c}{\tilde{a}}_{{\mathrm{\β}}_1}\\ .\\ .\\ .\\ {\tilde{a}}_{{\mathrm{\β}}_M}\end{array}\right]---\left(15\right)$

H_αIt is the matrix of M row L row, H_βIt is the matrix of M row L row, their mathematic(al) representation is

See from formula (16) and formula (17), the m row of observation impulse response matrix represents the observation impulse sound of m-th oscillator Should be vectorial, l row represent observation impulse response on whole array for the l article footpath, referred to as array impulse response vector；

(C) estimate direction of arrival；

Space channel comprises L bar multipath, once estimates p bar therein, 1≤p≤M, specific step is as follows；

(C-1) from observation impulse response matrix H_αMiddle selection p row, this p column number is p₁,…,p_p, and constitute matrix Mathematic(al) representation be

Wherein,Represent noise vector,Represent noise matrix, A is guiding arrow Moment matrix, is defined as follows

MatrixWherein diag [] represents construction diagonal matrix；

Again from observation impulse response matrix H_βIn same position select p row, be p equally by this p column number₁,…,p_p, and constitute Matrix Expression formula as follows

Wherein,MatrixAnd matrixIt is all M × p matrix；If selected p The incoming signal angle in the corresponding p bar footpath of row is different, then prove matrixAnd matrixOrder be p；

Ask for matrixAnd matrixOrder, if result is equal to p, illustrate that the incoming signal ripple in selected p bar footpath reaches Angle is different, then continue executing with (C-2) step；If result is not equal to p, illustrate at least two in selected p bar footpath The direction of arrival of the corresponding incoming signal in footpath is identical；Now the value of p is deducted 1, and re-execute this sub-step；Prove to work as p When finally reducing to 1, matrixAnd matrixOrder certain be equal to 1, and during p=1, this method is still set up；Therefore this method must Set up；

(C-2) ask for according to formula (21) and formula (22) respectivelyWithCovariance matrixWith

${\tilde{C}}_{\mathrm{\α}}={\hat{H}}_{\mathrm{\α}}{\hat{H}}_{\mathrm{\α}}^H---\left(21\right)$

${\tilde{C}}_{\mathrm{\β}}={\hat{H}}_{\mathrm{\β}}{\hat{H}}_{\mathrm{\β}}^H---\left(22\right)$

Wherein,WithRepresent respectivelyWithAssociate matrix；MatrixWithIt is all M × Metzler matrix；Prove, MatrixWithOrder be all p；

(C-3) to matrixCarry out feature decomposition, and eigenvalue is arranged according to order from big to small, be expressed as Ask for the corresponding characteristic vector of these eigenvalues, be expressed asBuild matrix U according to formula (23)_α；

$U_{\mathrm{\α}}=\left[\begin{array}{ccc}{u}_{{\mathrm{\α}}_1}& \mathrm{...}& u_{{\mathrm{\α}}_p}\end{array}\right]---\left(23\right)$

Similarly to matrixCarry out feature decomposition, and eigenvalue is arranged according to order from big to small, be expressed asAsk for the corresponding characteristic vector of these eigenvalues, be expressed asBuild matrix U according to formula (24)_β；

$U_{\mathrm{\β}}=\left[\begin{array}{ccc}{u}_{{\mathrm{\β}}_1}& \mathrm{...}& u_{{\mathrm{\β}}_p}\end{array}\right]---\left(24\right)$

Matrix U_αAnd U_βIt is all the matrix of M × p；Prove, matrix U_αAnd U_βOrder be p；

(C-4) ask for matrix Ψ according to formula (25)；

Ψ=(U_α)⁺U_β(25)

Wherein, ()⁺Represent and seek group inverse matrices；Matrix Ψ is the matrix of p × p；

Eigenvalue is asked for matrix Ψ, is expressed asProveIt is the diagonal element of matrix Φ； According toThe signal direction of arrival in the corresponding p bar footpath of selected p row can be obtained；The method asked for is shown in formula (26)；

Wherein, argsin () represents sine of negating, and argument of a complex number is sought in angle () expression；The signal direction of arrival completing p bar footpath is estimated Meter；

(C-5) go to (C-1) step, reselection p bar footpath is estimated, until all of L bar footpath all completes to estimate.