CN105245474A - Ultra-wideband channel estimation method - Google Patents

Abstract

The invention discloses an ultra-wideband channel estimation method. The method comprises the steps that A, an ultra-wideband pulse training signal is transmitted, and down-sampling is carried out on a received ultra-wideband signal to acquire observation data; B, based on the transmitted ultra-wideband pulse training signal and a down-sampling rate, an observation matrix is generated; and C, the acquired observation data and observation matrix are used as the input of GAMP reconstruction, and a GAMP reconstruction algorithm is applied to ultra-wideband channel impulse response to give the specific method of the GAMP reconstruction algorithm in ultra-wideband channel estimation. According to the invention, the GAMP reconstruction algorithm can be well applied to ultra-wideband channel estimation; the ADC sampling rate of an ultra-wideband receiving end is greatly reduced; and a great channel estimation performance is acquired at low signal to noise ratio.

Description

Ultra-wideband channel estimation method

Technical Field

The invention relates to the technical field of wireless communication, in particular to an ultra wide-Band (UWB) wireless channel estimation method based on Compressed Sensing (CS) theory.

Background

Channel estimation is an important research direction in wireless communication, and the quality of channel estimation directly affects the performance of an ultra-wideband communication system. In addition, adaptive modulation, multiuser scheduling, and the like of a wireless communication system require a system receiving end to know Channel State Information (CSI). The acquisition of CSI also requires channel estimation techniques to be done.

In the existing narrow-band wireless communication system, channel estimation is a relatively mature technology and is widely applied to mobile communication systems. For the ultra-wideband wireless communication system, the estimation of the channel is still in the starting stage, most methods are still in the simple simulation stage, and many problems need to be solved if the method is applied to the actual system.

The UWB technology is a new wireless communication technology, and it uses very narrow pulses (nanosecond or even picosecond pulses) to transmit data, so it has many advantages such as high speed, low power consumption, low interception rate, low cost, high multipath resistance, and can coexist with the existing wireless communication system, and the UWB has received wide attention from all sides under increasingly tense spectrum resources.

UWB signals adopt a narrow pulse transmission mode, the duration of pulses is short, and according to the Nyquist sampling law, extremely high sampling frequency is needed in digital processing of a receiver, and the requirement of hardware manufacturing process for reaching the sampling rate is difficult at present. In addition, the ultra-wideband channel environment is very complex, multipath components in the received signal are extremely rich, but a large number of experiments show that most of path energy is zero or close to zero, so that the channel has strong sparsity. At present, most of the ultra-wideband channel estimation methods proposed by researchers apply the conventional channel estimation method to the UWB field. These methods not only require extremely high sampling rates, but also often ignore sparsity of the ultra-wideband channel, resulting in many meaningless zero-valued tap estimates, increasing the complexity of the algorithm while reducing the estimation accuracy.

Disclosure of Invention

The technical problem to be solved by the invention is to provide an ultra-wideband channel estimation method, which reduces the requirement of ultra-wideband channel estimation on the sampling rate and reduces the complexity of the ultra-wideband channel estimation method.

The ultra-wide channel estimation method comprises the following steps:

step A, transmitting an ultra-wideband pulse training signal, and down-sampling the received ultra-wideband signal to obtain observation data;

b, generating an observation matrix according to the transmitted ultra-wideband pulse training signal and the down-sampling rate;

and C, the observation data and the observation matrix are used for reconstructing impulse response of the ultra-wideband channel.

Further, the step C is configured to reconstruct an impulse response of the ultra-wideband channel, specifically, use the observation data and the observation matrix as input of a Generalized Approximate Message Passing (GAMP) reconstruction algorithm for sparse signal reconstruction, where an applicable signal model is y ═ Ax + w, where x ∈ R is^L×1Is a sparse signal vector, y ∈ R^N×1Is an observation vector, A ∈ R^N×LIs an observation matrix, w ∈ R^L×1Is Additive White Gaussian Noise (AWGN); the GAMP reconstruction algorithm converts the estimation problem of x into solution $\hat{x}=\arg \min \mathrm{\λ}\left|\right|y-Ax|{|}^2+\underset{l=1}{\overset{L}{\Σ}}{\mathrm{\γ}}_l{\left|x_l\right|}^2+\underset{l=1}{\overset{L}{\Σ}}\frac{1}{{\mathrm{\γ}}_l}+\frac{1}{\mathrm{\λ}}.$

Further, the process of the GAMP reconstruction algorithm is,

initializing Vp, S, lambda, x and gamma in the process 1;

scheme 2 according to formulaSolving Vq;

scheme 3 according to formulaSolving q;

scheme 4 according to formulaSolving Vx;

scheme 5 according to formulaUpdating x;

scheme 6 according to formulaUpdating gamma;

scheme 7 according to formulaUpdating Vp;

equation 8, according toSolving for

Scheme 9 according to formulaUpdating the S;

scheme 10 according to formulaSolving Vb;

scheme 11 according to formulaSolving for

Scheme 12 according to formulaUpdating the lambda;

computingRepeating the iteration until theta is smaller than the set threshold value, so that the current value isIs the final

Further, the estimation method is applied to an ultra-wideband channel, and particularly,

the initialization is that i and L are defined as integers, i is more than or equal to 1 and is more than or equal to N, L is more than or equal to 1 and is less than or equal to L, lambda is 1, h is an L × 1 vector, and the element h of h is_lAll 1, Vp is the N × 1 vector, element of VpIs a 1 × N vector with elements of 0, gamma is a 1 × L vector, and gamma is an element ofA＝Φ；

Updating h: solving Vq, q and Vx according to GAMP reconstruction algorithm flow 2, 3 and 4, and then updating by using formula of reconstruction algorithm flow 5

Update parameters γ, Vp and S: updating the parameter gamma according to the reconstruction algorithm flow 6, updating the parameter Vp according to the reconstruction algorithm flow 7, solving P according to the reconstruction algorithm flow 8, and updating S according to the reconstruction algorithm flow 9;

updating the parameter lambda: solving Vb according to a reconstruction algorithm flow 10, solving b according to a reconstruction algorithm flow 11, and updating a parameter lambda according to a reconstruction algorithm flow 12;

judging whether to continue the iterative loop: calculating theta according to the reconstruction algorithm flow 13, and when theta is smaller than a set threshold, h obtained by iterative updating at this time is the finally estimated ultra-wideband channel impulse response; otherwise, continuing to update h according to the updated parameters until theta is smaller than the set threshold.

The GAMP ultra-wideband channel estimation method based on the compressed sensing reconstruction algorithm combines the compressed sensing theory and the ultra-wideband channel estimation problem, and converts a signal transmission convolution model into a sparse vector reconstruction model in the compressed sensing theory. And a receiving end uses a sampling device with a lower speed to carry out undersampling on the received signal, and then a GAMP reconstruction algorithm is utilized to accurately reconstruct a sparse channel, thereby reducing the requirement of ultra-wideband channel estimation on the sampling speed. Meanwhile, the method makes full use of the sparsity of the ultra-wideband channel, avoids meaningless zero tap estimation and reduces the algorithm complexity.

Drawings

FIG. 1 is a flow chart of ultra-wideband channel estimation based on compressed sensing;

FIG. 2 is a graph comparing an original channel with an estimated channel at a signal-to-noise ratio of 30 dB;

FIG. 3 is a graph of a comparison of reconstructed errors in Mean Squared Error (MSE);

detailed description of the invention

The invention relates to a novel CS reconstruction algorithm, and provides a UWB channel estimation method based on the reconstruction algorithm, which can accurately estimate a sparse channel model of UWB by undersampling a received signal on the premise of ensuring the accuracy of a measurement matrix.

The signal model applicable to the invention is y ═ Ax + w, wherein x ∈ R^L×1Is a sparse signal vector, y ∈ R^N×1Is an observation vector, A ∈ R^N×LIs an observation matrix, w ∈ R^L×1Is an additive white gaussian noise AWGN vector. The invention converts the estimation problem of x into solution:

$\hat{x}=\arg \min \mathrm{\λ}\left|\right|y-Ax|{|}^2+\underset{l=1}{\overset{L}{\Σ}}{\mathrm{\γ}}_l{\left|x_l\right|}^2+\underset{l=1}{\overset{L}{\Σ}}\frac{1}{{\mathrm{\γ}}_l}+\frac{1}{\mathrm{\λ}}---\left(1\right)$

the reconstruction algorithm flow comprises the following steps:

1) initializing Vp, S, lambda, x and gamma;

2) according to the formulaSolving Vq;

3) according to the formulaSolving q;

4) according to the formulaSolving Vx;

5) according to the formulaUpdating x;

6) according to the formulaUpdating gamma;

7) according to the formulaUpdating Vp;

8) according to the formulaSolving for

9) According to the formulaUpdating the S;

10) according to the formulaSolving Vb;

11) according to the formulaSolving for

12) According to the formulaUpdating the lambda;

13) and (3) calculating:repeating the iteration until theta is smaller than the set threshold value, so that the current value isIs the final

CS is a new data acquisition theory, and is a technology in which sampling and compression are performed simultaneously. The essence of the theory is that the sparse signal is sampled at a rate far lower than the nyquist sampling rate, and the receiving end can still accurately recover the original signal. Under the framework of the CS theory, the data acquisition can greatly break through the limitation of the Nyquist sampling law, and great convenience is brought to the data processing.

The central problem of compressed sensing is the reconstruction of sparse vector x ∈ R by the following measurement model^N:

b＝Ax:||x||₀≤K

Wherein | · | purple sweet₀Representing the number of non-zero elements in the vector, A being a known M x N measurement matrix, b ∈ R^MThe elements in (a) are in turn the inner product of each row in a and x, i.e. each row in a corresponds to one measurement value. When M is<<And N, the problem is that the ill-conditioned problem is difficult to solve. And the compressed sensing theory shows that when K is<M<<N, the sparse vector x can be accurately reconstructed from the linear measurement b and the matrix a. The accuracy and stability of the reconstruction depends on whether matrix a satisfies the constrained isometric property (RIP). The definition of constrained isovolumetric properties was first proposed by CANDESE, romberg and TAOT and is the most widely used tool for discriminating compressed sensing measurement matrices.

The channel estimation problem also belongs to the signal reconstruction problem to a great extent, and currently commonly used CS reconstruction algorithms can be divided into two categories: an Orthogonal Matching Pursuit (OMP) algorithm among a Base Pursuit (BP) algorithm and a greedy pursuit algorithm.

Because the impulse response of the ultra-wideband channel has the characteristic of sparse clusters, if the ultra-wideband channel is regarded as a sparse vector, and the channel output is regarded as the measurement of the channel after the training sequence is sent, the problem of channel estimation can be converted into the problem of sparse vector reconstruction in the compressive sensing theory. Only a small number of measured values are collected by undersampling at a receiving end, and then the sparse channel can be reconstructed by using a compressed sensing reconstruction algorithm, so that channel estimation is completed.

The present invention will be described in further detail below with reference to the accompanying drawings. As shown in fig. 1, this example describes a specific embodiment of the present invention in detail, specifically: in the ultra-wideband impulse radio system, an ultra-wideband training signal is designed according to the IEEE802.15.4a protocol to implement the GAMP-based ultra-wideband channel estimation method.

The transmitting end transmits the ultra-wideband signal by using an impulse radio technology, and uses a second derivative of a Gaussian pulse as a pulse waveform:

$\mathrm{\&omega;}\left(t\right)=(1-4\mathrm{\&pi;}\frac{t^2}{{\mathrm{\&alpha;}}^2}){\exp }^{-\frac{2{\mathrm{\&pi;t}}^2}{{\mathrm{\&alpha;}}^2}}---\left(2\right)$

wherein, α²For the pulse forming factor, the waveform, i.e. the width of the pulse, is changed by adjusting the pulse forming factor.

According to the ieee802.15.4a protocol, an ultra-wideband training signal designed for ultra-wideband channel estimation is:

$x\left(t\right)=\underset{n=0}{\overset{Nc-1}{\&Sigma;}}{C}_i\mathrm{\&omega;}(t-{\mathrm{nLT}}_c)---\left(3\right)$

wherein,is a ternary sequence and N_cIs the length of the ternary sequence, T_cFor chip time, L is the length of the discrete Delta function.

The ultra-wideband channel impulse response may be expressed as:

$h\left(t\right)=\underset{l=0}{\overset{L}{\&Sigma;}}\underset{k=0}{\overset{K}{\&Sigma;}}{\mathrm{\&alpha;}}_{k,l}\mathrm{\&delta;}(t-T_l-{\mathrm{\&tau;}}_{k,l})---\left(4\right)$

in the formula, α_k,lAttenuation coefficient for multipath, T_lTime delay of the ith cluster, τ_k,lIs represented by T_lAs a reference, the time delay of the kth multipath component of the ith cluster.

In noisy environments, the received signal may be expressed as:

r(t)＝x(t)*h(t)+w(t)，t∈[0,T_cMN_c+τ_max](5)

in the formula, τ_maxFor maximum delay spread of an ultra-wideband channel, w (t) is white gaussian noise.

Under the set system resolution, the actual channel is approximated by the discrete form h of h (t), and according to the characteristic that the ultra-wideband channel is sparse in the time domain, a received signal r (t) can be obtained in timeSampling with an analog to digital converter (ADC) at low speed to obtain a sequence r [ n ]]And can be regarded as the observation of h, then r [ n ]]The compressive sensing model can be used to represent:

r＝Φh(6)

wherein, h dimension is L multiplied by 1, phi is a perception matrix of N multiplied by L dimension.

Constructing a Toeplitz (Toeplitz) matrix by a training sequence x, extracting a plurality of rows at equal intervals to form a quasi-Toeplitz matrix, and filtering out rows with all zero elements to ensure that information of original signals is not lost in an observation process, wherein r represents L measurements (L < < N), and the dimension is L multiplied by 1.

According to equation (6), the channel estimation is converted into the reconstruction of the channel vector h (as shown in fig. 1) by using the compressed sensing theory, i.e. the rarest solution of equation (6) is obtained, and the estimation problem of h is converted into the solution according to equation (1):

$\hat{h}=\arg \min \mathrm{\&lambda;}\left|\right|r-\mathrm{\&Phi;}h|{|}^2+\underset{l=1}{\overset{L}{\&Sigma;}}{\mathrm{\&gamma;}}_l{\left|h_l\right|}^2+\underset{l=1}{\overset{L}{\&Sigma;}}\frac{1}{{\mathrm{\&gamma;}}_l}+\frac{1}{\mathrm{\&lambda;}}.$

in this embodiment, r and Φ are known, and the specific implementation of the channel estimation method based on the GAMP is as follows:

the initialization is that i and L are defined as integers, i is more than or equal to 1 and is more than or equal to N, L is more than or equal to 1 and is less than or equal to L, lambda is 1, h is an L × 1 vector, and the element h of h is_lAll 1, Vp is the N × 1 vector, element of VpS is a 1 × N vector with all elements 0, gamma is a 1 × L vector, and gamma is an elementA＝Φ；

Updating h: solving Vq, q and Vx according to GAMP algorithm flow 2, 3 and 4, and then updating by using formula of algorithm flow 5

Update parameters γ, Vp and S: updating the parameter gamma according to the algorithm flow 6, updating the parameter Vp according to the algorithm flow 7, solving P according to 8, and updating S according to 9;

updating the parameter lambda: solving Vb according to the algorithm flow 10, solving b according to the algorithm flow 11, and updating the parameter lambda according to the algorithm flow 12;

judging whether to continue the iterative loop: calculating theta according to the algorithm process 13, and when theta is smaller than a set threshold, h obtained by iterative updating at this time is the finally estimated ultra-wideband channel impulse response; otherwise, continuing to update h according to the updated parameters until theta is smaller than the set threshold.

The channel estimation method can be applied to information demodulation of a related receiver of the ultra-wideband communication system:

the ultra-wideband channel impulse response h estimated by the channel estimation method is used for generating a relevant received reference template signal C_tmp, $C_{tmp}\left(t\right)=\mathrm{\&omega;}*\hat{h}\left(t\right);$

Generated reference template signal C_tmpPerforms a piecewise integration with the received signal r (t) to determine the polarity of the transmitted symbol, ${\hat{b}}_i=\mathrm{sgn}\&lsqb;{\&Integral;}_{iLTc}^{\left(i+1\right)LTc}r\left(t\right)C_{tmp}\left(t-{\mathrm{iLT}}_c\right)dt\&rsqb;;$

the accurate channel estimation enables the reference template of the relevant receiving to be more accurate, and therefore the error rate of information demodulation can be reduced.

To further illustrate the beneficial effects of the present invention, the following description of the simulation process and results of the present invention is made, the simulation uses the CM1 channel model, and the system parameters are set to set the resolution of the system to 50 picoseconds and the pulse shaping factor α²＝0.25e-9，C_i{1,1,0,0,1,0,0, -1, -1, -1,1, -1,0,1,1, -1,0,0,0,1,0,1,0, -1,1,0,1,0, 1,0,0,0,0} is a ternary sequence, the length N of which is the length of the ternary sequence_cChip time T of 31_c2e-9 seconds, the length L of the discrete Delta function is 4. The length of the selected channel impulse response is 100ns, and the dimensionality reduction ratio is 0.2.

As can be seen from fig. 2, in a noisy environment, the GAMP algorithm can recover the main multipath of the ultra-wideband channel, and only a small amplitude difference exists; as can be seen from fig. 3, compared with the OMP, LASSO, FOCUSS algorithm, the GAMP reconstruction algorithm has smaller reconstruction error at low snr, and has better performance, and the performance is not lower than that of the conventional reconstruction method at high snr. In general, the impulse response of the ultra-wideband channel estimated by the GAMP algorithm reserves the main characteristics of the ultra-wideband channel, can reflect the real channel state information CSI, has more outstanding performance at low signal-to-noise ratio compared with the traditional reconstruction methods, and is more suitable for the ultra-wideband communication system which needs to meet the requirement of radiation masking.

The invention has the advantages that a novel CS reconstruction algorithm is provided, and meanwhile, the reconstruction algorithm is applied to UWB channel estimation.

Claims (4)

1. An ultra-wideband channel estimation method, characterized by comprising the steps of:

step A, transmitting an ultra-wideband pulse training signal, and down-sampling the received ultra-wideband signal to obtain observation data;

b, generating an observation matrix according to the transmitted ultra-wideband pulse training signal and the down-sampling rate;

and C, the observation data and the observation matrix are used for reconstructing impulse response of the ultra-wideband channel.

2. The estimation method according to claim 1, characterized in that said step C is used for reconstructing impulse response of ultra-wideband channel, in particular for sparse signal reconstruction using said observation data and observation matrix as input to GAMP reconstruction algorithm, applicable signal model is y-Ax + w, where x ∈ R is^L×1Is a sparse signal vector, y ∈ R^N×1Is an observation vector, A ∈ R^N×LIs an observation matrix, w ∈ R^L×1Is an AWGN vector; the GAMP reconstruction algorithm converts the estimation problem of x into solution $\hat{x}=\mathrm{argmin}\mathrm{\&lambda;}\left|\right|y-Ax|{|}^2+\underset{l=1}{\overset{L}{\&Sigma;}}{\mathrm{\&gamma;}}_l|x_l{|}^2+\underset{l=1}{\overset{L}{\&Sigma;}}\frac{1}{{\mathrm{\&gamma;}}_l}+\frac{1}{\mathrm{\&lambda;}}.$

3. The estimation method according to claim 2, characterized in that: the process of the GAMP reconstruction algorithm is as follows,

initializing Vp, S, lambda, x and gamma in the process 1;

scheme 2 according to formula ${\mathrm{Vq}}_l={\left(\underset{i=1}{\overset{N}{\&Sigma;}}\frac{|A_{il}{|}^2}{{\left(\widehat{\mathrm{\&lambda;}}\right)}^{-1}+{\mathrm{Vp}}_i}\right)}^{-1},$ Solving Vq;

scheme 3 according to formula ${\hat{q}}_l={\mathrm{Vq}}_l\underset{i=1}{\overset{N}{\&Sigma;}}{S}_i{A}_{il}+{\hat{x}}_l,$ Solving q;

scheme 4 according to formula ${\mathrm{Vx}}_l={(\frac{1}{{\mathrm{Vq}}_l}+{\mathrm{\&gamma;}}_l)}^{-1},$ Solving Vx;

scheme 5 according to formula ${\hat{x}}_l=\frac{{\mathrm{Vx}}_l{\hat{q}}_l}{{\mathrm{Vq}}_l},$ Updating x;

scheme 6 according to formula ${\mathrm{\&gamma;}}_l=\frac{1}{{\mathrm{Vx}}_l+|{\hat{x}}_l{|}^2},$ Updating gamma;

scheme 7 according to formula ${\mathrm{Vp}}_i=\underset{l=1}{\overset{L}{\&Sigma;}}|A_{il}{|}^2{\mathrm{Vx}}_l,$ Updating Vp;

scheme 8 according to formula ${\hat{P}}_i=\underset{l=1}{\overset{L}{\&Sigma;}}{A}_{il}{\hat{x}}_l,$ Solving for

Scheme 9 according to formula $S_i=\frac{y_i-{\hat{P}}_i}{{\widehat{\mathrm{\&lambda;}}}^{-1}+{\mathrm{Vp}}_i},$ Updating the S;

scheme 10 according to formula ${\mathrm{Vb}}_i={(\widehat{\mathrm{\&lambda;}}+\frac{1}{{\mathrm{Vp}}_i})}^{-1},$ Solving Vb;

scheme 11 according to formula ${\hat{b}}_i={\mathrm{Vb}}_i(y_i\widehat{\mathrm{\&lambda;}}+\frac{{\hat{P}}_i}{V_{pi}}),$ Solving for

Scheme 12 according to formula $\widehat{\mathrm{\&lambda;}}=\frac{N}{\underset{i=1}{\overset{N}{\&Sigma;}}|y_i-{\hat{b}}_i{|}^2+{\mathrm{Vb}}_i},$ Updating the lambda;

computingRepeating the iteration until theta is smaller than the set threshold value, so that the current value isIs the final

4. The estimation method according to claim 3, applied to an ultra-wideband channel, in particular,

the initialization is that i and L are defined as integers, i is more than or equal to 1 and is more than or equal to N, L is more than or equal to 1 and is less than or equal to L, lambda is 1, h is an L × 1 vector, and the element h of h is_lAll 1, Vp is the N × 1 vector, element of VpIs a 1 × N vector with elements of 0, gamma is a 1 × L vector, and gamma is an element ofA＝Φ；

Updating h: solving Vq, q and Vx according to GAMP reconstruction algorithm flow 2, 3 and 4, and then utilizingThe formula of the flow 5 of the reconstruction algorithm can be updated

Update parameters γ, Vp and S: updating the parameter gamma according to the reconstruction algorithm flow 6, updating the parameter Vp according to the reconstruction algorithm flow 7, solving P according to the reconstruction algorithm flow 8, and updating S according to the reconstruction algorithm flow 9;

updating the parameter lambda: solving Vb according to a reconstruction algorithm flow 10, solving b according to a reconstruction algorithm flow 11, and updating a parameter lambda according to a reconstruction algorithm flow 12;

judging whether to continue the iterative loop: calculating theta according to the reconstruction algorithm flow 13, and when theta is smaller than a set threshold, h obtained by iterative updating at this time is the finally estimated ultra-wideband channel impulse response; otherwise, continuing to update h according to the updated parameters until theta is smaller than the set threshold.