CN101383629B - UWB receiver error rate performance optimizing method by noncoherent energy detection - Google Patents

Abstract

The invention provides an error rate performance optimizing method of a noncoherent energy detecting UWB receiver, comprising the following steps: the outside band noise of a received signal is filtered via a bandpass filter; the signal is processed by a square-law detector, and after the synchronism process, the SNR estimation is carried out; an energy window is optimized; and an optimized threshold is selected based on a least square fitting correction gauss approximate threshold. The error rate performance optimizing method of a noncoherent energy detecting UWB receiver enables the receiver performance to be greatly improved by the combined optimization of the judgment threshold of the receiver and an energy integral window.

Description

UWB receiver error rate performance optimizing method by noncoherent energy detection

Technical field

The present invention relates to wireless ultra wideband communications receiver field, particularly a kind of UWB receiver error rate performance optimizing method by noncoherent energy detection.

Background technology

Pulse ultra-broad band (IR-UWB) is the radiotechnics that adopts ultra-narrow pulse direct radiation mode to transmit; Because simple, characteristics such as volume is little, low-power consumption, low cost that it is realized; In middle low-speed wireless data application facet; Like location, control, sensor network etc., have a good application prospect.The incoherent reception mode of the UWB system that detects based on energy integral since avoided complicated channel estimating and and undemanding synchronous requirement, greatly reduce the complexity of receiver, become the ideal scheme that real system is realized.The energy integral scheme adopts simple OOK modulation system collocation usually, but because the inherent defect of OOK modulation system itself adds that the selection of UWB receiver integration window is improper, will cause the receiver error performance not high.At present; Optimization problem to the energy integral receiver in some documents has been carried out certain research; As the UWB-OOK signal is carried out weighted, utilize the way of Monte-Carlo emulation to provide the proof of optimal energy integration window existence and utilized Gaussian distribution to be similar to x ²The method that distributes obtains the analytical expression of optimization threshold, but all fails the energy integral length of window is carried out further theory analysis, and for the processing of thresholding also not than the better way of Gaussian approximation.

Summary of the invention

The present invention is in order to overcome the deficiency of above-mentioned prior art, and the present invention provides a kind of ultra broadband energy measuring receiver that can make to reach the UWB receiver error rate performance optimizing method by noncoherent energy detection of more performance.

The technical solution adopted for the present invention to solve the technical problems is: a kind of UWB receiver error rate performance optimizing method by noncoherent energy detection is provided, may further comprise the steps:

S1: with the signal process band pass filter filtering out-of-band noise that receives;

S2: signal is handled through square-law detector;

S3: signal carries out SNR estimation through after synchronous;

S4: optimize energy window;

S5:, select optimization threshold based on the match correction Gaussian approximation thresholding of least square.

The scheme that the present invention solves further technical problem is: among the said step S1, the signal of this moment has pre-set frame format, and the frame format that configures comprises synchronous head, training sequence and data.

The scheme that the present invention solves further technical problem is: among the said step S3, the average of bit is respectively:

$\left\{\begin{array}{cc}{\mathrm{\μ}}_1={\mathrm{MN}}_0+E_{\mathrm{eff}}& b_i=1\\ {\mathrm{\μ}}_0={\mathrm{MN}}_0& b_i=0\end{array}\right.$

Defined variable γ is following

γ＝μ ₁/μ ₀＝1+E _eff/MN ₀

Then the effective signal-to-noise ratio approximate evaluation of signal is:

E _eff/N ₀＝M(γ-1)。

The scheme that the present invention solves further technical problem is: among the described step S4, and given thresholding η _C, optimize energy integral window M and E _Eff/ N ₀Make error rate P _eMinimum, corresponding different M and E _Eff/ N ₀, the lowest bit error rate of system is different.

The scheme that the present invention solves further technical problem is: work as E _Eff/ N ₀Necessarily, P _eWith the M monotonic increase; When M certain, P _eWith E _Eff/ N ₀Monotone decreasing.

The scheme that the present invention solves further technical problem is: the error rate expression formula of said system: P _e=(P ₀+ P ₁)/2 wherein, P0, P1 does

$P_0={\∫}_{{\mathrm{\η}}_C}^{+\∞}{f}_0\left(x\right)\mathrm{dx}=\exp (-\frac{{\mathrm{\η}}_C}{2})\underset{k=0}{\overset{M-1}{\mathrm{\Σ}}}\frac{{({\mathrm{\η}}_C/2)}^k}{k!},$

$P_1={\∫}_0^{{\mathrm{\η}}_C}{f}_1\left(x\right)\mathrm{dx}=1-Q_M(\sqrt{\mathrm{\λ}},\sqrt{{\mathrm{\η}}_C}).$

The scheme that the present invention solves further technical problem is: the absolute value of given logarithm error rate difference is as standard, need match interval as follows:

(M，E _eff/N ₀)∈{(M，E _eff/N ₀)：|log(Pe _C)-log(Pe _G)|≥0.5}

The match form of utilizing least square method to obtain is multinomial

$o(M,\mathrm{\λ})={\mathrm{\Σ}}_{j=1}^p{\mathrm{\Σ}}_{i=1}^q{a}_{i,j}{M}^p{\mathrm{\λ}}^q$

Accurately the approximate solution of thresholding does ${\mathrm{\η}}_C=\frac{N_0}{2}\·o(M,\mathrm{\λ})+{\mathrm{\η}}_G.$

The scheme that the present invention solves further technical problem is: the signal that will pass through behind the square-law detector carries out a step preliminary treatment, makes that the variance of signal is 1:

$(s_j+n_j)/\sqrt{N_0/2}~N(s_j,1)$

Relation between new judgement amount and the original judgment amount does $y=\underset{j=1}{\overset{2M}{\mathrm{\Σ}}}{\left(\frac{s_j+n_j}{\sqrt{N_0/2}}\right)}^2=\frac{2}{N_0}x.$

The scheme that the present invention solves further technical problem is: the receiver that this method was directed against comprises the BPF unit that connects successively, square-law detector, lock unit, SNR estimation unit, thresholding and decision unit.

Compared to prior art, thereby UWB receiver error rate performance optimizing method by noncoherent energy detection of the present invention makes receiver obtain very big performance boost through the combined optimization to receiver decision threshold and energy integral window.

Description of drawings

Fig. 1 is the structural representation of the receiver that is directed against of UWB receiver error rate performance optimizing method by noncoherent energy detection of the present invention.

Fig. 2 is the schematic flow sheet of UWB receiver error rate performance optimizing method by noncoherent energy detection of the present invention.

Fig. 3 is the schematic flow sheet of UWB receiver error rate performance optimizing method by noncoherent energy detection of the present invention.

Fig. 4 is the q and the P of UWB receiver error rate performance optimizing method by noncoherent energy detection of the present invention _eCorresponding relation function sketch map.

Embodiment

Following content is to combine concrete preferred implementation to the further explain that the present invention did, and can not assert that practical implementation of the present invention is confined to these explanations.For the those of ordinary skill of technical field under the present invention, under the prerequisite that does not break away from the present invention's design, can also make some simple deduction or replace, all should be regarded as belonging to protection scope of the present invention.

The present invention provides a kind of UWB receiver error rate performance optimizing method by noncoherent energy detection, and the structure of described receiver is as shown in Figure 1, and it comprises the BPF unit that connects successively; Square-law detector; Lock unit, SNR estimation unit, thresholding and decision unit.

As shown in Figure 2, UWB receiver error rate performance optimizing method by noncoherent energy detection of the present invention comprises the steps:

S1: with the signal process band pass filter filtering out-of-band noise that receives

The signal of this moment should have pre-set frame format, and is as shown in Figure 2:

The frame format that configures comprises: synchronous head, training sequence and data.

Wherein:

Synchronous head: be used for carrying out signal Synchronization, will consume at synchronous phase;

Training sequence: be used for estimating the signal to noise ratio of present frame, will consume in the SNR estimation stage;

Data: user's useful information.

S2: signal is handled through square-law detector

The signal form that obtains is:

$x={\mathrm{\Σ}}_{j=1}^{2M}{(s_j+n_j)}^2$

Here 2M representes x ²The degree of freedom that distributes, 2M=BT+1, T representes the time of integration, because s _jBe to confirm signal, so s _j+ n _j～N (s _j, N ₀/ 2).

S3: signal carries out SNR estimation through after synchronous

Estimation principles is following:

The average of bit is respectively:

Average:

$\left\{\begin{array}{cc}{\mathrm{\μ}}_1={\mathrm{MN}}_0+E_{\mathrm{eff}}& b_i=1\\ {\mathrm{\μ}}_0={\mathrm{MN}}_0& b_i=0\end{array}\right.$

Defined variable γ is following

γ＝μ ₁/μ ₀＝1+E _eff/MN ₀

Then the effective signal-to-noise ratio of signal can approximate evaluation be:

E _eff/N ₀＝M(γ-1)

S4: optimize energy window

In theory, the signal that will pass through behind the square-law detector carries out a step preliminary treatment, makes that the variance of signal is 1:

$(s_j+n_j)/\sqrt{N_0/2}~N(s_j,1)$

Relation between new judgement amount and the original judgment amount does

$y=\underset{j=1}{\overset{2M}{\mathrm{\Σ}}}{\left(\frac{s_j+n_j}{\sqrt{N_0/2}}\right)}^2=\frac{2}{N_0}x$

Therefore, the form of signal meets x fully ²The form that distributes.

In following formula, x ²The degree of freedom that distributes is 2M, x ²The expression-form of the non-centrality parameter that distributes does

$\mathrm{\λ}=\underset{j=1}{\overset{2M}{\mathrm{\Σ}}}{\left(\frac{{2s}_j}{N_0}\right)}^2=\frac{2E_{\mathrm{eff}}}{N_0}$

Probability density to following formula is carried out the Laplace conversion, and its characteristic equation does

$F_1\left(s\right)=\frac{1}{{(1+2s)}^M}\exp (-\frac{\mathrm{s\λ}}{1+2s}),s>0,$

Following formula is asked the Laplace inverse transformation, can know that the probability density of variable x does

$f_1\left(x\right)=\frac{1}{2}{\left(\frac{x}{\mathrm{\λ}}\right)}^{\frac{M-1}{2}}\exp (-\frac{1}{2}(x+\mathrm{\λ}))I_{M-1}\left(\sqrt{\mathrm{\λx}}\right),x>0;---\left(7\right)$

Wherein

$I_r\left(u\right)=\frac{{\left(\frac{1}{2}u\right)}^2}{\sqrt{\mathrm{\π}}\mathrm{\Γ}(r+\frac{1}{2})}{\∫}_0^{\mathrm{\π}}\exp \left(u\cos \mathrm{\θ}\right){\sin }^{2r}\mathrm{\θd\θ}$

Bei Saier function for the correction of first kind r rank.

If there is not signal to exist, λ=0, probability density does

$f_0\left(x\right)=\frac{1}{2^M\mathrm{\Γ}\left(M\right)}{x}^{M-1}\exp (-\frac{1}{2}x)---\left(8\right)$

The error rate expression formula of system:

P _e＝(P ₀+P ₁)/2 (9)

Wherein, P0, P1 does

$P_0={\∫}_{{\mathrm{\η}}_C}^{+\∞}{f}_0\left(x\right)\mathrm{dx}=\exp (-\frac{{\mathrm{\η}}_C}{2})\underset{k=0}{\overset{M-1}{\mathrm{\Σ}}}\frac{{({\mathrm{\η}}_C/2)}^k}{k!},$

$P_1={\∫}_0^{{\mathrm{\η}}_C}{f}_1\left(x\right)\mathrm{dx}=1-Q_M(\sqrt{\mathrm{\λ}},\sqrt{{\mathrm{\η}}_C})$

Wherein,

is the Marcum-Q function.

Can know given thresholding η by error rate expression formula _C, optimize M and E _Eff/ N ₀Can make P _eMinimum, corresponding different M and E _Eff/ N ₀, the lowest bit error rate of system is different.Trend from figure can be found out, works as E _Eff/ N ₀Necessarily, P _eWith the M monotonic increase; When M certain, P _eWith E _Eff/ N ₀Monotone decreasing promptly should exist one group of (M, E in the system _Eff/ N ₀) make that the bit error rate performance of system is best.Can know E again by following formula _Eff/ N ₀Be the function that changes along with M,, make the error rate of system performance best so necessarily there is unique energy integral window M in the system.

In order to optimize error rate P _e, defined variable:

$q=\frac{\sqrt{M+2E_{\mathrm{eff}}/N_0}-\sqrt{M}}{2}---\left(10\right)$

Making q is the monotonic decreasing function of M, is E _Eff/ N ₀Monotonically increasing function, q and P _eBe monotonic relationshi.Therefore, can make P through seeking the extreme value of q _eMinimum.Q and P _eRelation as shown in Figure 4, wherein transverse axis is represented q, its numerical value by left-to-right be respectively 0,1...7, the longitudinal axis is represented P _e, its numerical value have go up under be respectively

According to the signal-noise ratio estimation method that the front provides,, seek (M, the E that make q maximum through continuous change M (change length of window) _Eff/ N ₀), thereby reach the purpose of optimizing window.

S5:, select optimization threshold based on the match correction Gaussian approximation thresholding of least square

Behind selected window, carry out the optimization of thresholding then.

At first carry out Gaussian approximation: can get according to central-limit theorem, a large amount of independent identically distributed stochastic variables with convergence in (with)probability in Gaussian random variable.The average of signal is provided by (14) formula, and variance can be expressed as following form:

${\mathrm{\σ}}_0^2=D\left\{x\right|H_0\}={{\mathrm{MN}}_0}^2---\left(18\right)$

${\mathrm{\σ}}_1^2=D\left\{x\right|H_1\}={{\mathrm{MN}}_0}^2+2E_{\mathrm{eff}}{N}_0---\left(19\right)$

According to the minimum error probability criterion, work as P ₀During=P

The optimum gate of Gaussian approximation is limited to

η _Gopt＝(σ ₀μ ₁+σ ₁μ ₀)/(σ ₀+σ ₁)，

Corresponding minimum bit-error rate Pe=Q (q); Wherein, q defines suc as formula (10).

Can prove that Gauss estimates optimum thresholding and x ²The difference of accurate thresholding of distributing is about M and E _Eff/ N ₀Function, expression formula is following:

${\mathrm{\η}}_C-{\mathrm{\η}}_G=\frac{N_0}{2}\·\mathrm{\ϵ}(M,E_{\mathrm{eff}}/N_0)---\left(20\right)$

The error term of approximate thresholding that obtains of expression Gauss thresholding and accurate thresholding, wherein ε (M, E _Eff/ N ₀) be about (M, E _Eff/ N ₀) binary function, by (M, E _Eff/ N ₀) unite definite.But because x ²The thresholding analytical expression that distributes is difficult to provide, so ε (M, E _Eff/ N ₀) the function analytical expression also be difficult to accurately obtain.This further analyzes Gaussian approximation and x to us ²The difference that distributes is brought difficulty.

For being reduced in the algorithm complex under certain precision, UWB receiver error rate performance optimizing method by noncoherent energy detection of the present invention adopts local least square fitting, and the absolute value of given logarithm error rate difference is as standard, need match interval as follows:

(M，E _eff/N ₀)∈{(M，E _eff/N ₀)：|log(Pe _C)-log(Pe _G)|≥0.5}

The match form of utilizing least square method to obtain is multinomial

$o(M,\mathrm{\λ})={\mathrm{\Σ}}_{j=1}^p{\mathrm{\Σ}}_{i=1}^q{a}_{i,j}{M}^p{\mathrm{\λ}}^q---\left(21\right)$

Accurately the approximate solution of thresholding does

${\mathrm{\η}}_C=\frac{N_0}{2}\·o(M,\mathrm{\λ})+{\mathrm{\η}}_G---\left(22\right)$

Multinomial coefficient after error curved surface after the least square fitting (the normalization minimum mean-square error the is 0.0343) match is as shown in the table:

?

y6

y5

y4

y3

y2

y1

y0

x5

5.2292e-12

-1.3583e-9

1.2866e-7

-5.5213e-6

1.2358e-4

-6.8911e-4

0.0117

x4

-1.6149e-1 0

3.7491e-8

-2.9524e-6

8.7315e-5

-0.0017

0

0

x3

1.7418e-9

-3.5010e-7

2.0968e-5

1.3596e-5

0

0

0

x2

-7.9522e-9

1.4956e-6

-1.2458e-4

0

0

0

0

x1

-5.6422e

4.9606e-6

0

0

0

0

0

Thereby UWB receiver error rate performance optimizing method by noncoherent energy detection of the present invention makes receiver obtain very big performance boost through the combined optimization to receiver decision threshold and energy integral window.

Claims (4)

1. UWB receiver error rate performance optimizing method by noncoherent energy detection, it is characterized in that: this method may further comprise the steps:

S1: with the signal process band pass filter filtering out-of-band noise that receives;

S2: signal is handled through square-law detector;

S3: signal carries out SNR estimation through after synchronous, and the average of bit is respectively:

Defined variable γ is following

γ＝μ ₁/μ ₀＝1+E _eff/MN ₀

Then the effective signal-to-noise ratio approximate evaluation of signal is:

E _eff/N ₀＝M(γ-1)；

S4: optimize energy window, given thresholding η _C, optimize energy integral window M and E _Eff/ N ₀Make error rate P _eMinimum, corresponding different M and E _Eff/ N ₀, the lowest bit error rate of system is different, works as E _Eff/ N ₀Necessarily, P _eWith the M monotonic increase; When M certain, P _eWith E _Eff/ N ₀Monotone decreasing;

The error rate expression formula of said system: P _e=(P ₀+ P ₁)/2, wherein P ₀, P ₁For

S5: based on the match correction Gaussian approximation thresholding of least square, select optimization threshold,

The absolute value of given logarithm error rate difference is as standard, need match interval as follows:

(M，E _eff/N ₀)∈{(M，E _eff/N ₀):|log(Pe _C)-log(Pe _G)|≥0.5}

The match form of utilizing least square method to obtain is multinomial

Accurately the approximate solution and the relation between the exact solution of thresholding are

2. UWB receiver error rate performance optimizing method by noncoherent energy detection according to claim 1; It is characterized in that: among the said step S1; The signal of this moment has pre-set frame format, and the frame format that configures comprises synchronous head, training sequence and data.

3. UWB receiver error rate performance optimizing method by noncoherent energy detection according to claim 1 is characterized in that: the signal that will pass through behind the square-law detector carries out a step preliminary treatment, makes that the variance of signal is 1:

Relation between new judgement amount and the original judgment amount is

4. UWB receiver error rate performance optimizing method by noncoherent energy detection according to claim 1; It is characterized in that: the receiver that this method was directed against comprises the BPF unit that connects successively, square-law detector, lock unit; SNR estimation unit, thresholding and decision unit.

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