CN105681240A - High-precision frequency offset estimation method suitable for low signal-to-noise ratio environment - Google Patents

Abstract

The invention relates to a high-precision frequency offset estimation method suitable for a low signal-to-noise ratio environment. The high-precision frequency offset estimation method suitable for the low signal-to-noise ratio environment comprises the following steps: multiplying a received signal by a corresponding synchronization code, thereby obtaining a pseudo code information canceling sequence; performing an autocorrelation preprocessing on the pseudo code information canceling sequence to increase the signal-to-noise ratio of the sequence; performing computation on the preprocessed sequence, thereby obtaining all-order difference accumulation signals, and obtaining multi-order carrier frequency offset signals; estimating a frequency offset by utilizing multi-order carrier phase information based on a minimum mean square error. The high-precision frequency offset estimation method suitable for the low signal-to-noise ratio environment is applicable to a communication scenario with the ultra-low receiving sensitivity.

Description

A kind of high accuracy frequency deviation estimating method being adapted under low signal-to-noise ratio environment

Technical field

The present invention relates to wireless communication technology field, particularly relate to a kind of high accuracy frequency deviation estimating method being adapted under low signal-to-noise ratio environment.

Background technology

Carrier frequency synchronization is the key technical problem of wireless communication field research, particularly having the application such as wireless sensor network of burst communication feature, lacks synchronizing channel or priori subcarrier Frequency Synchronization. Simultaneously as cost restriction, the common crystals that general selecting frequency accuracy is poor, frequency departure is up to more than 40PPM. The existence of carrier wave frequency deviation can reduce the transmission performance of system greatly. Therefore, frequency deviation is estimated to have become the key technology that wireless communication system is indispensable.

For the performance of frequency excursion algorithm, mainly assess from estimated accuracy, estimation range, signal-to-noise ratio (SNR) estimation thresholding and algorithm complex. For the Nonlinear Transformation in Frequency Offset Estimation of burst communication pattern, existing part achievement in research outside Present Domestic. Wherein, the performance based on the fft algorithm of maximal possibility estimation theory is counted relevant to FFT, counts more many, estimates more accurate, and resource overhead is also more big, and fft analysis frequency deviation also exists fence effect simultaneously. Kay proposes based on the method for estimation of signal differential phase place, when signal to noise ratio is higher close to CRLB lower limit, but when signal to noise ratio is reduced to a certain degree performance high progression, namely the method signal-to-noise ratio (SNR) estimation thresholding is higher, inapplicable low signal-to-noise ratio application scenarios.

Currently also there is the part achievement in research low signal-to-noise ratio frequency deviation Estimation Study for DSSS communication system, such as L&R algorithm: based on maximal possibility estimation, there is relatively low signal-noise ratio threshold, but, signal to noise ratio very long in spread spectrum code length non-normally low time estimate degradation, frequency offset estimation range is narrow simultaneously. Fitz utilizes the argument of auto-correlation function on average to estimate frequency deviation, has a relatively low signal-to-noise ratio (SNR) estimation thresholding, but estimation range is subject to the restriction of auto-correlation exponent number, and is still unable to reach the estimated accuracy of needs when signal to noise ratio is low again. Qi proposes a kind of method of phase expansion on Fitz algorithm basis, expands estimation range, but has also raised signal-noise ratio threshold simultaneously. Mengali and Morelli (M&M) proposes the method for estimation of a kind of difference based on auto-correlation function argument, has relatively low signal-noise ratio threshold and bigger estimation range when frequency is less, but when frequency is bigger, signal-noise ratio threshold is quickly raised.Additionally Lanante and Hai et al. is for the unbalanced characteristic of IQ, it is proposed that be applicable to process the method for estimation of zero intermediate frequency reciver, but inapplicable in low signal-to-noise ratio situation.

Summary of the invention

The technical problem to be solved is to provide a kind of high accuracy frequency deviation estimating method being adapted under low signal-to-noise ratio environment, is adapted to overlength distance transmission application.

The technical solution adopted for the present invention to solve the technical problems is: provides a kind of high accuracy frequency deviation estimating method being adapted under low signal-to-noise ratio environment, comprises the following steps:

(1) reception signal is multiplied with corresponding synchronization code word, the sequence of the pseudo-code that is eliminated information;

(2) sequence eliminating pseudo-code information is done auto-correlation pretreatment, promote sequence signal to noise ratio;

(3) calculating of pretreated sequence is obtained each jump and divide cumulative signal, it is thus achieved that multistage carrier wave frequency deviation signal;

(4) utilize multistage carrier phase information, based on least mean-square error, estimate frequency deviation.

Reception signal in described step (1) is expressed asWherein a (k) is pseudo-code signal, and Δ ω is frequency deviation, and T represents the sampling period, and θ is local phase place, and n (k) is white Gaussian noise, and Es represents sampled point power, and k represents the sequence number of discretization; The sequence eliminating pseudo-code information is $t\left(k\right)=\sqrt{Es}\·a\left(k\right)\×a^{*}\left(k\right)\×e^{j(\mathrm{\Δ}\mathrm{\ω}kT+\mathrm{\θ})}+a^{*}\left(k\right)\×n\left(k\right)=\sqrt{Es}{e}^{j(\mathrm{\Δ}\mathrm{\ω}kT+\mathrm{\θ})}+n^{*}\left(k\right),$ Wherein | a (k) |²=1, n^*K () is white complex gaussian noise, orderRepresentation signal component.

In described step (2), pretreated sequence is:

$R_{xx}\left(0\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{\left|x_i\right|}^2=Es$

$R_{xx}\left(1\right)=\frac{1}{N-1}\underset{i=1}{\overset{N-1}{\Σ}}{x}_{i+1}{x}_i^{*}=Es\·e^{j\mathrm{\Δ}\mathrm{\ω}T}$

$R_{xx}\left(2\right)=\frac{1}{N-2}\underset{i=1}{\overset{N-2}{\Σ}}{x}_{i+2}{x}_i^{*}=Es\·e^{j2\mathrm{\Δ}\mathrm{\ω}T}$

...

$R_{xx}(N-1)=x_N{x}_1^{*}=Es\·e^{j(N-1)\mathrm{\Δ}\mathrm{\ω}T}$

Wherein, x_iFor eliminating the reception signal of pseudo-code, N represents spread spectrum code length, and Es represents sampled point power, and Δ ω is frequency deviation, and T represents the sampling period; The mean-Gaussian noise power of sequence after pretreatmentWherein γ=0.5772 is Euler's constant.

The each jump point accumulation calculating of described step (3) is:

$R\left(1\right)=\frac{1}{N-1}\underset{k=2}{\overset{N}{\Σ}}{\mathrm{Es}}^2\·e^{j\mathrm{\Δ}\mathrm{\ω}Tk}\×e^{-j\mathrm{\Δ}\mathrm{\ω}T(k-1)}+n^{\′}={\mathrm{Es}}^2\·e^{j\mathrm{\Δ}\mathrm{\ω}T}+n^{\′}$

R (2)=Es²·e^j2ΔωT+n'

…

R (M)=Es²·e^jMΔωT+n'

Wherein, Es represents sampled point power, and Δ ω is frequency deviation, and T represents the sampling period, n' be multinomial noise and, M is autocorrelation value exponent number, M arrange according to system exist maximum frequency deviation and determine, it is ensured that the performance degradation that R (M) is caused by maximum frequency deviation is less.

In described step (4), the mode of carrier wave frequency deviation is: calculate the argument of autocorrelation value, and the formula that the argument calculating obtained each exponent sheet autocorrelation value substitutes into least mean-square error calculates the frequency offseting value that can obtain optimized correspondence.

Described step (2) and step (3) iteration repeatedly, promote signal to noise ratio further.

Beneficial effect

Owing to have employed above-mentioned technical scheme, the present invention is compared with prior art, have the following advantages that and good effect: the present invention is relative to tradition frequency excursion algorithm, there is estimated accuracy more accurately under low signal-to-noise ratio, it is adapted to very much the communications applications scene of ultralow receiving sensitivity, it is possible to be applied to IEEE802.15.4k standard overlength code word, ultralow signal to noise ratio, telecommunication application. The present invention, when calculating argument, has carried out pretreatment, has improve the signal to noise ratio of pending sequence so that frequency deviation estimates that can carry out high accuracy under very low signal-to-noise ratio environment estimates. The present invention promotes requirement based on signal to noise ratio, optional implementation successive ignition pretreatment, and each iteration all can promote the signal to noise ratio of pending sequence, meets the high accuracy frequency deviation under Arctic ice area environment and estimates.

Accompanying drawing explanation

Fig. 1 is the flow chart of the high accuracy frequency deviation being adapted under the low signal-to-noise ratio environment estimation of the present invention.

Detailed description of the invention

Below in conjunction with specific embodiment, the present invention is expanded on further. Should be understood that these embodiments are merely to illustrate the present invention rather than restriction the scope of the present invention.In addition, it is to be understood that after having read the content that the present invention lectures, the present invention can be made various changes or modifications by those skilled in the art, and these equivalent form of values fall within the application appended claims limited range equally.

The present invention provides a kind of high accuracy frequency deviation estimating method being adapted under low signal-to-noise ratio environment, below with reference to about accompanying drawing, a specific embodiment in DSSS system communication is described in detail.

After down coversion, the reception signal with carrier wave frequency deviation is:

$s\left(k\right)=\sqrt{Es}\·a\left(k\right)\×e^{j(\mathrm{\Δ}\mathrm{\ω}kT+\mathrm{\θ})}+n\left(k\right)---\left(1\right)$

Wherein a (k) is pseudo-code signal, and Δ ω is frequency deviation, and T represents the sampling period, and θ is local phase place, and n (k) is white Gaussian noise, and Es represents sampled point power, and k represents the sequence number of discretization.

Being multiplied receiving signal with synchronization pseudo-code, the sequence eliminating pseudo-code information is $t\left(k\right)=\sqrt{Es}\·a\left(k\right)\×a^{*}\left(k\right)\×e^{j(\mathrm{\Δ}\mathrm{\ω}kT+\mathrm{\θ})}+a^{*}\left(k\right)\×n\left(k\right)=\sqrt{Es}{e}^{j(\mathrm{\Δ}\mathrm{\ω}kT+\mathrm{\θ})}+n^{*}\left(k\right)---\left(2\right)$

Wherein | a (k) |²=1, n^*K () is white complex gaussian noise, orderRepresentation signal component.

T (k) has eliminated pseudo-code information, only retains carrier wave frequency deviation phase information, t (k) is done pretreatment, seeks auto-correlation, obtain each data autocorrelative

$R_{xx}\left(0\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{\left|x_i\right|}^2=Es$

$R_{xx}\left(1\right)=\frac{1}{N-1}\underset{i=1}{\overset{N-1}{\Σ}}{x}_{i+1}{x}_i^{*}=Es\·e^{j\mathrm{\Δ}\mathrm{\ω}T}$

$R_{xx}\left(2\right)=\frac{1}{N-2}\underset{i=1}{\overset{N-2}{\Σ}}{x}_{i+2}{x}_i^{*}=Es\·e^{j2\mathrm{\Δ}\mathrm{\ω}T}$

...

$R_{xx}(N-1)=x_N{x}_1^{*}=Es\·e^{j(N-1)\mathrm{\Δ}\mathrm{\ω}T}---\left(3\right)$

Pretreated mean-Gaussian noise $noise\_power=\frac{1}{N}(1+\frac{1}{2}+\frac{1}{3}+...\frac{1}{N-1}+\frac{1}{N}){\mathrm{\σ}}^4=\frac{1}{N}\left(\ln \right(N+1)+\mathrm{\γ}){\mathrm{\σ}}^4---\left(4\right)$

Wherein γ=0.5772 is Euler's constant.

Sequence after auto-correlation pretreatment can be expressed as:

T'(k)=R_xx(k)+noise(5)

For improving signal to noise ratio further, it is possible to the method adopting successive ignition, to t'(k) carry out successive ignition auto-correlation pretreatment. For the sake of simplicity, the implementation case only does a pretreatment. Sequence after pretreatment has improve signal to noise ratio, and this sequence is done difference accumulating operation, it is thus achieved that each rank frequency deviation phase information.

$R\left(1\right)=\frac{1}{N-1}\underset{k=2}{\overset{N}{\Σ}}{\mathrm{Es}}^2\·e^{j\mathrm{\Δ}\mathrm{\ω}Tk}\×e^{-j\mathrm{\Δ}\mathrm{\ω}T(k-1)}+n^{\′}={\mathrm{Es}}^2\·e^{j\mathrm{\Δ}\mathrm{\ω}T}+n^{\′}$

R (2)=Es²·e^j2ΔωT+n'(6)

…

R (M)=Es²·e^jMΔωT+n'

M is autocorrelation value exponent number, and M arranges the maximum frequency deviation existed according to system and determine, it is ensured that the performance degradation that R (M) is caused by maximum frequency deviation is less, n' be multinomial noise with.

After obtaining each rank frequency deviation phase information, the mode calculating carrier wave frequency deviation is: calculate argument phi (the n)=arg{R (n) of each exponent sheet autocorrelation value first respectively }, the formula that then argument calculating obtained each exponent sheet autocorrelation value substitutes into least mean-square error calculates, and can obtain the frequency offseting value of optimized correspondence.

$\widehat{\mathrm{\ω}}=\frac{1}{2{\mathrm{\πT}}_s}\frac{\underset{1}{\overset{M}{\Σ}}\mathrm{\φ}\left(n\right)}{\underset{1}{\overset{M}{\Σ}}{n}^2}=\frac{6\underset{1}{\overset{M}{\Σ}}\mathrm{\φ}\left(n\right)}{M(M+1)(2M+1)}---\left(7\right)$

In sum, set forth herein a kind of high accuracy frequency deviation estimating method being applicable to very under low signal-to-noise ratio environment. First the signal that receives synchronized is multiplied by the method with corresponding code word, eliminates the impact of pseudo-code information; Secondly the sequence eliminating pseudo-code information is done auto-correlation pretreatment, improve the signal to noise ratio of pending sequence; Then pretreated sequence is calculated and obtain each jump sub-signal; The phase argument high accuracy being finally based on differential signal estimates frequency deviation value. As can be seen here, this method, relative to tradition frequency excursion algorithm, has estimated accuracy more accurately under low signal-to-noise ratio, is adapted to very much the communications applications scene of ultralow receiving sensitivity. The method can apply to IEEE802.15.4k standard overlength code word, ultralow signal to noise ratio, telecommunication application.

Claims (6)

1. the high accuracy frequency deviation estimating method that a kind is adapted under low signal-to-noise ratio environment, it is characterised in that comprise the following steps:

(1) reception signal is multiplied with corresponding synchronization code word, the sequence of the pseudo-code that is eliminated information;

(2) sequence eliminating pseudo-code information is done auto-correlation pretreatment, promote sequence signal to noise ratio;

(3) calculating of pretreated sequence is obtained each jump and divide cumulative signal, it is thus achieved that multistage carrier wave frequency deviation signal;

(4) utilize multistage carrier phase information, based on least mean-square error, estimate frequency deviation.

2. the high accuracy frequency deviation estimating method being adapted under low signal-to-noise ratio environment according to claim 1, it is characterised in that the reception signal in described step (1) is expressed asWherein a (k) is pseudo-code signal, and Δ ω is frequency deviation, and T represents the sampling period, and θ is local phase place, and n (k) is white Gaussian noise, and Es represents sampled point power, and k represents the sequence number of discretization;The sequence eliminating pseudo-code information is $t\left(k\right)=\sqrt{Es}\·a\left(k\right)\×a^{*}\left(k\right)\×e^{j(\mathrm{\Δ}\mathrm{\ω}kT+\mathrm{\θ})}+a^{*}\left(k\right)\×n\left(k\right)=\sqrt{Es}{e}^{j(\mathrm{\Δ}\mathrm{\ω}kT+\mathrm{\θ})}+n^{*}\left(k\right),$ Wherein | a (k) |²=1, n^*K () is white complex gaussian noise, orderRepresentation signal component.

3. the high accuracy frequency deviation estimating method being adapted under low signal-to-noise ratio environment according to claim 1, it is characterised in that it is characterized in that, in described step (2), pretreated sequence is:

$R_{xx}\left(0\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\Σ}}{\left|x_i\right|}^2=Es$

$R_{xx}\left(1\right)=\frac{1}{N-1}\underset{i=1}{\overset{N-1}{\Σ}}{x}_{i+1}{x}_i^{*}=Es\·e^{j\mathrm{\Δ}\mathrm{\ω}T}$

$R_{xx}\left(2\right)=\frac{1}{N-2}\underset{i=1}{\overset{N-2}{\Σ}}{x}_{i+2}{x}_i^{*}=Es\·e^{j2\mathrm{\Δ}\mathrm{\ω}T}$

...

$R_{xx}(N-1)=x_N{x}_1^{*}=Es\·e^{j(N-1)\mathrm{\Δ}\mathrm{\ω}T}$

Wherein, x_iFor eliminating the reception signal of pseudo-code, N represents spread spectrum code length, and Es represents sampled point power, and Δ ω is frequency deviation, and T represents the sampling period; The mean-Gaussian noise power of sequence after pretreatment $noise\_power=\frac{1}{N}\left(ln\right(N+1)+\mathrm{\γ}){\mathrm{\σ}}^4,$ Wherein γ=0.5772 is Euler's constant.

4. the high accuracy frequency deviation estimating method being adapted under low signal-to-noise ratio environment according to claim 1, it is characterised in that each jump point accumulation calculating of described step (3) is:

$R\left(1\right)=\frac{1}{N-1}\underset{k=2}{\overset{N}{\Σ}}{\mathrm{Es}}^2\·e^{j\mathrm{\Δ}\mathrm{\ω}Tk}\×e^{-j\mathrm{\Δ}\mathrm{\ω}T(k-1)}+n^{\′}={\mathrm{Es}}^2\·e^{j\mathrm{\Δ}\mathrm{\ω}T}+n^{\′}$

R (2)=Es²·e^j2ΔωT+n'

…

R (M)=Es²·e^jMΔωT+n'

Wherein, Es represents sampled point power, and Δ ω is frequency deviation, and T represents the sampling period, n' be multinomial noise and, M is autocorrelation value exponent number, M arrange according to system exist maximum frequency deviation and determine, it is ensured that the performance degradation that R (M) is caused by maximum frequency deviation is less.

5. the high accuracy frequency deviation estimating method being adapted under low signal-to-noise ratio environment according to claim 1, it is characterized in that, in described step (4), the mode of carrier wave frequency deviation is: calculate the argument of autocorrelation value, and the formula that the argument calculating obtained each exponent sheet autocorrelation value substitutes into least mean-square error calculates the frequency offseting value that can obtain optimized correspondence.

6. the high accuracy frequency deviation estimating method being adapted under low signal-to-noise ratio environment according to claim 1, it is characterised in that described step (2) and step (3) iteration repeatedly, promote signal to noise ratio further.