CN103220240A - Compressed sensing-based high-resolution signal time-of-arrival estimation method - Google Patents

Abstract

The invention discloses a compressed sensing-based high-resolution signal time-of-arrival (TOA) estimation method, which belongs to the technical field of wireless communication. According to the method, the shortest time delay path is determined by using a signal total energy-based decision method on the basis of a channel impulse response estimation value through high-resolution estimation on channel impulse response, and further the estimated value of the TOA is given. In a process ofperforming high-resolution estimation on the channel impulse response, an observation matrix in a system model is processed to meet the conditions for restoring a sparse signal based on the compressed sensing, and then the channel impulse response is estimated by using a reconstruction method of the compressed sensing. The method has higher resolution, stronger anti-noise performance and higher accuracy in judgment of the shortest time delay path.

Description

A kind of high-resolution signal method of estimation time of advent based on compressed sensing

Technical field

The invention belongs to wireless communication technology field, be specifically related to based on compressed sensing (Compressed Sensing, high-resolution signal time of advent CS) (Time Of Arrival, TOA) method of estimation.

Background technology

Along with popularizing and the raising of disposal ability of intelligent wireless terminal, location-based service (LBS:location based service) more and more receives cellular carrier and service provider's concern.Therefore, location technology has become a hot issue in the signal processing research.Except traditional navigation feature, positional information can be integrated in the communication equipment, thereby makes communication system can distribute frequency spectrum resource more effectively.Present location technology can be divided into two classes substantially: a kind of localization method that is based on distance, another kind is based on other information, as the localization method of received power.For the latter, need obtain received signal intensity indicator diagram (Received Signal Strength Indication map, RSSI map) in advance, and the structure of RSSI map need spend great amount of manpower.

Realize location by the measurement target position to the distance of known location based on the localization method of distance, thereby without any need for the positional information of priori.The measurement of distance can be summed up as the problem of a channel estimating under the multi-path environment, as traditional relevant peaks detection method based on spread spectrum system.In practice, because the restriction of bandwidth, can only be accurate to chip (chip) level to the estimation of time delay.Promptly being lower than the two-way received signal of 1 chip duration at interval can't differentiate, and cause the accuracy of these class methods lower.For example, for the spread spectrum system of 1.2288MCPS, obscure the error that two footpaths that are spaced apart 1/4chip will cause 61m.Also have the signal processing method of a class a operation in Array Signal Processing, by handling correlation function to detect the signal path that arrives the earliest.This class methods utilization method for processing signals reaches the effect of accurate estimation channel delay, the super-resolution that is otherwise known as (Super Resolution) algorithm is as MUSIC(MUltip Signal Classification) and ESPRIT(Estimation of Signal Parameters via Rotation Invariance Technique).These class methods estimate to be converted into the Frequency Estimation of frequency domain with the time delay of time domain, and its resolution does not rely on bandwidth.Yet its operand is bigger usually, and the general time that needs the precognition signal to arrive.

The compressed sensing theory of Ti Chuing is pointed out in recent years, can original signal be recovered out by a spot of sampled point through noise pollution, and this provides new possibility for TOA estimation accurately.Particularly, suppose to attempt to recover the signal y of a p dimension with n measured value, i.e. y=X β+z, wherein X is a n * p matrix; β ∈ R ^pBe the object that to estimate, have S to be non-0 value in its p sample value at the most; The sample value z of noise vector _iBe i.d.d.N (0, σ ²).For this problem, people such as Candes have proposed the restoration methods of a kind of Dantzig of being called Selector (DS), and are specific as follows:

$\underset{\widetilde{\mathrm{\&beta;}}\&Element;R^p}{\min }{\left|\right|\widetilde{\mathrm{\&beta;}}\left|\right|}_{{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002966590900012.png"\; state="\{\{state\}\}">l</figure-callout>}}_1}\mathrm{subjectto}{\left|\right|X^{H}r\left|\right|}_{l_{\&infin;}}\&le;{\mathrm{\&lambda;}}_p\mathrm{\&sigma;}$

Residual error amount wherein

λ _pIt is a constant relevant with p.DS can be converted into optimization problem linear program (Liner Programming) and find the solution.

Summary of the invention

The present invention proposes a kind of high-resolution signal method of estimation time of advent based on compressed sensing, estimate by high-resolution channel impulse response, on the basis of channel impulse response estimation value, take a kind of decision method to determine to prolong the most in short-term the path, and then provide the estimated value of TOA based on the signal gross energy.In high-resolution estimation procedure to channel impulse response, the observing matrix in the system model is handled, make it satisfy the condition of recovering sparse signal based on compressed sensing, utilize the reconstructing method of compressed sensing to carry out channel impulse response estimation then.

Technical solution of the present invention is as follows:

A kind of high-resolution signal method of estimation time of advent based on compressed sensing as shown in Figure 1, may further comprise the steps:

Step 1: transmitting terminal sends periodic spread-spectrum signal s (t), and then the spread-spectrum signal s (t) in the periodic unit can be expressed as

E wherein _cAnd T _cBe respectively the energy and the cycle of a chip in the frequency expansion sequence, c[n] { 1,1} is a n chip of frequency expansion sequence to ∈, and N is the length of frequency expansion sequence, and ω (t) is that base band sends waveform.

Because send to send out and the recipient in the scene of low-speed motion, can think that multipath channel only has frequency selectivity, and not change in time that then received signal r (t) can be expressed as

$r\left(t\right)=\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{p}s(t-{\mathrm{\&tau;}}_p)+n\left(t\right)$

α wherein _pAnd τ _pBe respectively the decay and the time delay of signal on the p transmission paths, n (t) is a white Gaussian noise.

Step 2: receiving terminal is to the transmission signal s in the periodic unit ₀(t) carry out the reference signal x[n that M over-sampling doubly obtains dispersing], be designated as x[n]={ x ₁, x ₂..., x _K, K=MN wherein.

Step 3: receiving terminal r (t) to received signal carries out sample frequency f _s=M/T _cOver-sampling, the received signal r[n that obtains dispersing].R[n] can regard that s (t) is through f as _sThe signal s[n that obtains of sampling] with the sampling interval be T _cThe convolution of the channel impulse response h of/M [n], promptly

$r\left[n\right]=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}s[n-l]\&CenterDot;h\left[l\right]+n\left[n\right]$

At r[n] in intercepted length be the one-period section of K=MN, be designated as y[n], y[n then] can be expressed as

y[n]=X·h+n[n]

Wherein

Be step 2 gained reference signal x[n] vectorial determined circular matrix.

Step 4: structural matrix Σ ^-1U, wherein U is K rank discrete Fourier transform (DFT) matrix, Σ ^-1Be diagonal matrix Σ=UXU ^HInverse matrix, U ^HThe associate matrix of expression U.

Step 5: to the vectorial y[n of step 3 gained] premultiplication matrix Σ ^-1U obtains

y'[n]=Σ ^-1U·y[n]=Uh+Σ ^-1U·n[n]

Step 6: with Σ ^-1The vector formed of diagonal entry be designated as b, then can determine sub-subscript collection by b

J={i∈G||b(i)|≤1}

G={1 wherein, 2 ..., K} is total subscript collection.

Step 7: the pairing y'[n of subscript collection J] in the vector formed of element be designated as y' _{| J|}, the submatrix that the corresponding line of the corresponding U of J is formed is designated as U _{| J|}Reconstructing method (using Dantzig Selector here, i.e. the DS restoration methods) by compressed sensing is found the solution following sparse equation:

y' _|J|=U _|J|h+n' _|J|

Step 8: establish step 7 and find the solution the estimated value that obtains channel impulse response h by the reconstructing method of compressed sensing and be

Determine the value of time of arrival (toa) (TOA) by following steps:

Step 8-1: will

In element arrange from big to small according to absolute value, obtain vector

Step 8-2: find out the q that satisfies the following formula minimum

$\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{\left|\right|{\hat{h}}_D\left(i\right)\left|\right|}^2\&GreaterEqual;0.95\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|\hat{h}\left(i\right)\left|\right|}^2$

Wherein || || ²Mould two norms of expression vector " ".

Step 8-3: keep Q element of middle absolute value maximum, remaining is changed to 0, and the vector that obtains is designated as

If

In be designated as λ under first non-0 element, then the estimated value of time of arrival (toa) TOA is λ/f _s

For realizing that the channel impulse response high-resolution is estimated, the present invention adopts and carries out M times of over-sampling to received signal at receiving terminal, and regarding received signal as time delay spacing is T _CThe K of/M (K=MN) sends the stack of signal copy after decay.Send the form that process that signal obtains received signal by channel can be regarded as matrix multiple.In the broadband system of reality,, thereby can utilize the reconstructing method of compressed sensing to carry out channel impulse response estimation because channel impulse response h [n] has sparse property.The present invention has utilized these characteristics of channel impulse response just, by the observing matrix in the system model is handled, make it satisfy the condition of recovering sparse signal based on compressed sensing, utilize the reconstructing method of compressed sensing to carry out channel impulse response estimation then, and then adopt and determine to prolong the most in short-term the path, and provide the estimated value of TOA based on the decision method of signal gross energy.

Owing to utilized the sparse property of wireless channel inherence, to find the solution by compressed sensing and obtain sparse channel impulse response, this programme possesses very strong noiseproof feature.In addition, over-sampling makes the discrete impulse response of the channel in the model have higher resolution, and no longer is subject to bandwidth.In a word, high-resolution, noiseproof feature are by force the outstanding features of this programme.

Description of drawings

Fig. 1 is the schematic flow sheet of the high-resolution signal method of estimation time of advent based on compressed sensing provided by the invention.

The performance comparison diagram that Fig. 2 estimates channel for the channel estimation scheme and the least square method of the present invention's proposition.

The TOA estimation scheme that Fig. 3 the present invention proposes and the performance comparison diagram of existing TOA estimation technique (relevant peaks detection).

Embodiment

A kind of high-resolution signal method of estimation time of advent based on compressed sensing as shown in Figure 1, may further comprise the steps:

Step 1: transmitting terminal sends periodic spread-spectrum signal s (t), and then the spread-spectrum signal s (t) in the periodic unit can be expressed as

E wherein _cAnd T _cBe respectively the energy and the cycle of a chip in the frequency expansion sequence, c[n] { 1,1} is a n chip of frequency expansion sequence to ∈, and N is the length of frequency expansion sequence, and ω (t) is that base band sends waveform.

Because send to send out and the recipient in the scene of low-speed motion, can think that multipath channel only has frequency selectivity, and not change in time that then received signal r (t) can be expressed as

$r\left(t\right)=\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{p}s(t-{\mathrm{\&tau;}}_p)+n\left(t\right)$

α wherein _pAnd τ _pBe respectively the decay and the time delay of signal on the p transmission paths, n (t) is a white Gaussian noise.

Step 2: receiving terminal is to the transmission signal s in the periodic unit ₀(t) carry out the reference signal x[n that M over-sampling doubly obtains dispersing], be designated as x[n]={ x ₁, x ₂..., x _K, K=MN wherein.

Step 3: receiving terminal r (t) to received signal carries out sample frequency f _s=M/T _cOver-sampling, the received signal r[n that obtains dispersing].R[n] can regard that s (t) is through f as _sThe signal s[n that obtains of sampling] with the sampling interval be T _cThe convolution of the channel impulse response h of/M [n], promptly

$r\left[n\right]=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}s[n-l]\&CenterDot;h\left[l\right]+n\left[n\right]$

At r[n] in intercepted length be the one-period section of K=MN, be designated as y[n], y[n then] can be expressed as

y[n]=X·h+n[n]

Wherein

Be step 2 gained reference signal x[n] vectorial determined circular matrix.

Step 4: structural matrix Σ ^-1U, wherein U is K rank discrete Fourier transform (DFT) matrix, Σ ^-1Be diagonal matrix Σ=UXU ^HInverse matrix, U ^HThe associate matrix of expression U.

Step 5: to the vectorial y[n of step 3 gained] premultiplication matrix Σ ^-1U obtains

y'[n]=Σ ^-1U·y[n]=Uh+Σ ^-1U·n[n]

Step 6: with Σ ^-1The vector formed of diagonal entry be designated as b, then can determine sub-subscript collection by b

J={i∈G||b(i)≤1}

G={1 wherein, 2 ..., K} is total subscript collection.

Step 7: the pairing y'[n of subscript collection J] in the vector formed of element be designated as y' _{| J|}, the submatrix that the corresponding line of the corresponding U of J is formed is designated as U _{| J|}Reconstructing method by compressed sensing (use Dantzig Selector here, DS) find the solution following sparse equation:

y' _|J|=U _|J|h+n' _|J|

Step 8: establish step 7 and find the solution the estimated value that obtains channel impulse response h by the reconstructing method of compressed sensing and be

Determine the value of time of arrival (toa) (TOA) by following steps:

Step 8-1: will

In element arrange from big to small according to absolute value, obtain vector

Step 8-2: find out the q that satisfies the following formula minimum

$\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{\left|\right|{\hat{h}}_D\left(i\right)\left|\right|}^2\&GreaterEqual;0.95\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|\hat{h}\left(i\right)\left|\right|}^2$

Wherein || || ²Mould two norms of expression vector " ".

Step 8-3: keep

Q element of middle absolute value maximum, remaining is changed to 0, and the vector that obtains is designated as

If

In be designated as λ under first non-0 element, then the estimated value of time of arrival (toa) TOA is λ/f _s

Fig. 2 is to be under the 10dB in signal to noise ratio, and channel estimation scheme of the present invention and least square method (that is: will

As separating of equation y=Xh+n) the performance comparison figure of estimated channel impulse response.In emulation, our channel is set to comprise 2 multipaths that amplitude is identical, and two multipaths be spaced apart 1/2 chip.As we can see from the figure, the estimated result that least square method provides is not sparse, and error is bigger under The noise.Comparatively speaking, the channel estimation value that the present invention provides is comparatively accurate, has stronger noise resisting ability.

Fig. 3 is the comparison diagram that the performance of the present invention program and other TOA methods of estimation changes with signal to noise ratio.In emulation, our channel is set to exist 4 multipaths, and preceding two multipaths be spaced apart 1/4 chip; The whose amplitude obeys rayleigh distributed of each bar multipath.Transmitting terminal uses 31 m sequence as frequency expansion sequence, and the sample rate of receiving terminal is f _s=4/T _c(being M=4).Traditional method principle that detects based on relevant peaks is: produce in this locality one with the identical reference signal of transmission signal, reference signal and received signal are carried out relevant, detect the position at relevant output result's the peak (being first peak value) that arrives first then.The pairing time delay of the peak value of Dao Daing is just as the estimated value of TOA first.We have also compared the method for using this programme to estimate channel and have obtained after the estimated value of channel impulse response, by determine the performance of TOA based on the criterion of amplitude (that is: with the path of amplitude maximum as prolonging the path the most in short-term).As we can see from the figure, even signal to noise ratio increases, relevant peaks detects because latent defect can't be differentiated the multipath that is spaced apart 1/4 chip.Because the influence of Rayleigh fading is prolonged the path the most in short-term and is not necessarily had maximum amplitude, so bigger based on the judgment criterion error of amplitude.And the scheme that the present invention proposes can be differentiated at interval less than T _cMultipath, and have stronger noiseproof feature; In addition, judge that the accuracy of prolonging the path the most in short-term is also higher.

Those of ordinary skill in the art will appreciate that embodiment described here is in order to help reader understanding's principle of the present invention, should to be understood that protection scope of the present invention is not limited to such special statement and embodiment.Those of ordinary skill in the art can make various other various concrete distortion and combinations that do not break away from essence of the present invention according to these technology enlightenments disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.

Claims (2)

1. the high-resolution signal method of estimation time of advent based on compressed sensing may further comprise the steps:

Step 1: transmitting terminal sends periodic spread-spectrum signal s (t), and then the spread-spectrum signal s (t) in the periodic unit can be expressed as

E wherein _cAnd T _cBe respectively the energy and the cycle of a chip in the frequency expansion sequence, c[n] { 1,1} is a n chip of frequency expansion sequence to ∈, and N is the length of frequency expansion sequence, and ω (t) is that base band sends waveform;

Because send to send out and the recipient in the scene of low-speed motion, can think that multipath channel only has frequency selectivity, and not change in time that then received signal r (t) can be expressed as

$r\left(t\right)=\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{p}s(t-{\mathrm{\&tau;}}_p)+n\left(t\right)$

α wherein _pAnd τ _pBe respectively the decay and the time delay of signal on the p transmission paths, n (t) is a white Gaussian noise;

Step 2: receiving terminal is to the transmission signal s in the periodic unit ₀(t) carry out the reference signal x[n that M over-sampling doubly obtains dispersing], be designated as x[n]={ x ₁, x ₂..., x _K, K=MN wherein;

Step 3: receiving terminal r (t) to received signal carries out sample frequency f _s=M/T _cOver-sampling, the received signal r[n that obtains dispersing]; R[n] can regard that s (t) is through f as _sThe signal s[n that obtains of sampling] with the sampling interval be T _cThe convolution of the channel impulse response h of/M [n], promptly

$r\left[n\right]=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}s[n-l]\&CenterDot;h\left[l\right]+n\left[n\right]$

At r[n] in intercepted length be the one-period section of K=MN, be designated as y[n], y[n then] can be expressed as

y[n]=X·h+n[n]

Wherein Be step 2 gained reference signal x[n] vectorial determined circular matrix;

Step 4: structural matrix Σ ^-1U, wherein U is K rank discrete Fourier transform (DFT) matrix, Σ ^-1Be diagonal matrix Σ=UXU ^HInverse matrix, U ^HThe associate matrix of expression U;

Step 5: to the vectorial y[n of step 3 gained] premultiplication matrix Σ ^-1U obtains

y'[n]=Σ ^-1U·y[n]=Uh+Σ ^-1U·n[n]

Step 6: with Σ ^-1The vector formed of diagonal entry be designated as b, then can determine sub-subscript collection by b

J={i∈G||b(i)≤1}

G={1 wherein, 2 ..., K} is total subscript collection;

Step 7: the pairing y'[n of subscript collection J] in the vector formed of element be designated as y' _{| J|}, the submatrix that the corresponding line of the corresponding U of J is formed is designated as U _{| J|}Find the solution following sparse equation by the reconstructing method of compressed sensing:

y' _|J|=U _|J|h+n' _|J|

Step 8: establish step 7 and find the solution the estimated value that obtains channel impulse response h by the reconstructing method of compressed sensing and be

Determine the value of time of arrival (toa) TOA by following steps:

Step 8-1: will

In element arrange from big to small according to absolute value, obtain vector

Step 8-2: find out the q that satisfies the following formula minimum

$\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{\left|\right|{\hat{h}}_D\left(i\right)\left|\right|}^2\&GreaterEqual;0.95\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|\hat{h}\left(i\right)\left|\right|}^2$

Wherein || || ²Mould two norms of expression vector " ";

Step 8-3: keep

Q element of middle absolute value maximum, remaining is changed to 0, and the vector that obtains is designated as

If

In be designated as λ under first non-0 element, then the estimated value of time of arrival (toa) TOA is λ/f _s

2. the high-resolution signal method of estimation time of advent based on compressed sensing according to claim 1 is characterized in that the reconstructing method of compressed sensing described in the step 8 is Dantzig Selector, i.e. the DS restoration methods.

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