CN101047677B - Low complexity, high performance GFSK signal multi-bit demodulation method - Google Patents

Abstract

This invention provides a multi-bit demodulation method for GFSK signals including the following steps: 1, converting the frequency change form when modulating to a phase change form, 2, using the DPSK modem method in the GFSK demodulation, 3, making parameters concrete to carry out iterative judgment to get the demodulation result.

Description

A kind of GFSK signal multi-bit demodulation method

Technical field

The present invention relates to a kind of demodulation method of signal, relate in particular to a kind of GFSK signal multi-bit demodulation method.

Background technology

GFSK Gaussian Frequency Shift Keying (GFSK) modulation is a kind of digital modulation technique of saving bandwidth, is applied to widely in the various low-cost transmission standards, like Bluetooth [1] and DECT.In the engineering, GFSK generally is modulated into the form of continuous phase (CPFSK), can effectively reduce secondary lobe like this and reveal.

Developed at present the demodulation method that multiple GFSK signal.Common have difference phase demodulation (Phase-Shift Discriminator), integrated detected (Quadrature Detector), frequency feedback (frequency feedback), a zero passage detection (Zero-Crossing) etc.But because the GFSK signal is a partial response signal, intersymbol interference is more serious, and compares with BPSK modulation signals such as (two-phase PSKs), and the intersymbol distance is little, so performance is relatively poor relatively.Considered the influence of intersymbol interference in some receivers, the intersymbol interference that last signal is introduced compensates, and has improved performance.Yet this compensation also is limited.However, above-mentioned algorithm all has simple advantage.

Maximum likelihood algorithm also makes the amount of calculation exponentially increase when the performance with receiver improves greatly, and hardware is realized it being unacceptable.Vitebi and matched filter array (matched filter bank) are the implementations of two kinds of maximum likelihood algorithms.The former will pass through long convergence time-delay, and the latter's operand is still very big.

Nineteen ninety-five, Harry Leib has delivered on IEEE from the maximum likelihood algorithm development, is used for the algorithm of DPSK (differential phase shift modulation) signal demodulation: Data-Aided Noncoherent Demodulation of DPSK.The author starts with from the most basic judgment variables of signal optimum receiver, and receiving N of hypothesis has under the individual known situation of L (training sequence or decision-feedback) that judgment variables is simplified in the signal.Then, Harry makes L=N-1, thereby has obtained carrying out to received signal the method for recurrence judgement.Concrete recurrence variable and judgment variables are expressed as:

Z(n-1)＝exp[jc(n-1)]Z(n-2)+y(n-1)；

$A_i(n,n-1)=2\cos [\widehat{\mathrm{\φ}}\left(n\right)-{\mathrm{\α}}_i\left(n\right)]\left|y\left(n\right)Z^{*}(n-1)\right|;$

Wherein, The phase place of

, c (n-1) is the phase place that obtains after last position demodulating data is modulated again.Y (n-1) is the sampled signal that receives:

$y\left(n\right)=\underset{(n-1)T}{\overset{\mathrm{nT}}{\∫}}\tilde{r}\left(t\right)\mathrm{dt}$

α _i(n) represent the phase place that data possibly transferred to.α for DQPSK (four-phase DPSK) _i(n) there are 4, for 8DPSK (8 phase differential phase keying (DPSK)), α _i(n) there are 8.

With different α _i(n) bring A into _i(n n-1), works as A _i(n, α when n-1) obtaining maximum _i(n) pairing modulated data are exactly demodulation result.Obviously, because cosine function is a decreasing function,

Near which α _i(n), demodulation result is exactly that α _i(n) pairing modulating data.

Summary of the invention

Technical problem to be solved by this invention provides a kind of data at dpsk signal and assists development on the basis of irrelevant demodulation (Data-aided Noncoherent demodulation) algorithm and next low complex degree, high performance GFSK signal multi-bit demodulation method

In order to solve the problems of the technologies described above, the technical scheme that the present invention adopted is:

A kind of GFSK signal multi-bit demodulation method comprises the steps:

Step 1, the frequency change form during with frequency modulation(FM) change into the phase change form;

Step 2, be applied to the DPSK modulation-demo-demodulation method in the GFSK demodulation;

Step 3, parameter is specific is carried out the iteration judgement, thereby obtains demodulation result;

The concrete grammar that frequency change form in the said step 1 during with frequency modulation(FM) changes into the phase change form is: $\mathrm{\φ}\left(\mathrm{NT}\right)=\mathrm{\π\; h}\underset{i=-\∞}{\overset{n-2}{\mathrm{\Σ}}}{\mathrm{\α}}_i\left(n\right)+{\mathrm{\δ}}_{\mathrm{\Δ}}$

$\left|{\mathrm{\δ}}_{\mathrm{\Δ}}\right|=\left\{\begin{array}{cc}0;& ({\mathrm{\α}}_i(n-1)\·{\mathrm{\α}}_i(n-2)=1)\\ 4\mathrm{\πhq}\left(T\right)\≈0.21\mathrm{\πh};& ({\mathrm{\α}}_i(n-1)\·{\mathrm{\α}}_i(n-2)=-1)\end{array}\right.$

Wherein, φ (nT) is illustrated in the GFSK signal and is accumulated by the caused equivalent phase of frequency change, and h is the index of modulation of GFSK signal, α _i(n) ∈ 1 ,+1}, q (t) represents the phase impulse waveform,

Be equivalent to the form of the accumulative total phase place of DPSK modulation signal, δ _ΔRepresentative

Between deviation; Carrying out the method that iteration declares in the said step 3 is specially:

Z(n-3)＝exp[jk(n-3)]Z(n-4)+y(n-1)；

$\widehat{\mathrm{\φ}}\left(n\right)=\∠\left[y\left(n\right)Z^{*}(n-3)\right];$

$d(n-2)=\mathrm{sign}[\mathrm{sign}\left(\widehat{\mathrm{\φ}}\left(n\right)\right)+1];$

$k(n-2)=\mathrm{\πh}\×\mathrm{sign}\left[\widehat{\mathrm{\φ}}\left(n\right)\right];$

Wherein, Z (n) representes iteration variable,

The expression judgment variables, d (n) represent court verdict, i.e. demodulating data, k (n) representes an auxiliary iteration variable, y (n) representes the sampled signal that receives, α _i(n) represent the phase place that data possibly transferred to.

Method of the present invention has than difference phase demodulation, integrated detected, zero passage detection and frequency feedback scheduling algorithm more performance, and operand and complexity are significantly less than the matched filter Array Method again.

Description of drawings

Fig. 1 has shown that under the simulated environment of a Bluetooth performance of many bit demodulation method and other demodulation methods relatively.

Embodiment

Low complex degree of the present invention, high performance GFSK signal multi-bit demodulation method comprise the steps: at first, and the frequency change form during with frequency modulation(FM) changes into the phase change form:

In the time of the GFSK modulation, bitstream data { d _i, d _i{ 0,1} changes the nonreturn to zero code that the duration is T into to ∈, then is shaped as baseband signal through Gaussian filter.The shape of Gaussian response is relevant with index of modulation BT.Coefficient (as in bluetooth) commonly used is 0.5.Baseband waveform can be expressed as formula (1):

$s\left(t\right)=\sqrt{\frac{2E_b}{T}}\exp \left(\mathrm{j\φ}\left(t\right)\right)$

$\mathrm{\&phi;}\left(t\right)=2\mathrm{\&pi;h}\underset{i=-\&infin;}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i\left(n\right)q(t-\mathrm{iT}),\mathrm{nT}<t<(n+1)T---\left(1\right)$

E wherein _bBe the energy of every bit, α _i∈ 1 ,+1}. phase impulse q (t) is relevant with the frequency response g (t) of Gaussian filter:

$q\left(t\right)={\&Integral;}_{-\&infin;}^{t}g\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;},---\left(2\right),g\left(t\right)=g(\mathrm{LT}-t),---\left(3\right)$ ${\&Integral;}_0^{\mathrm{LT}}g\left(\mathrm{\&tau;}\right)\mathrm{d\&tau;}=q\left(\mathrm{LT}\right)=\frac{1}{2}---\left(4\right)$

L is the bit length of the pulse persistance of Gaussian response.Formula (2), (3) and (4) substitution formula 1 can be got:

$\mathrm{\&phi;}\left(t\right)=2\mathrm{\&pi;h}\underset{i=n-L+1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i\left(n\right)q(t-\mathrm{iT})+\mathrm{\&pi;h}\underset{i=-\&infin;}{\overset{n-L}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i\left(n\right),\mathrm{nT}\&le;t<(n+1)T---\left(5\right)$

When the index of modulation was 0.5, the Gaussian response length L can be taken as 3, i.e. intersymbol interference only occurs between the adjacent bit.As adopt frequency the same with data frequency, and promptly there is not over-sampling, formula has t=nT in (5).Further, notice g (t) about the t=LT/2 symmetry, then formula (5) can be simplified as follows:

$\mathrm{\&phi;}\left(\mathrm{nT}\right)=2\mathrm{\&pi;h}\underset{i=n-2}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i\left(n\right)q(\mathrm{nT}-\mathrm{iT})+\mathrm{\&pi;h}\underset{i=-\&infin;}{\overset{n-3}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i\left(n\right)$

$=\mathrm{\&pi;h}\underset{i=-\&infin;}{\overset{n-3}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i\left(n\right)+2\mathrm{\&pi;h}{\mathrm{\&alpha;}}_i(n-2)q\left(2T\right)+2\mathrm{\&pi;h}{\mathrm{\&alpha;}}_i(n-1)q\left(T\right)+2\mathrm{\&pi;h}{\mathrm{\&alpha;}}_i\left(n\right)q\left(0\right)$

$=\mathrm{\&pi;h}\underset{i=-\&infin;}{\overset{n-2}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i\left(n\right)-2\mathrm{\&pi;h}{\mathrm{\&alpha;}}_i(n-2)q\left(T\right)+2\mathrm{\&pi;h}{\mathrm{\&alpha;}}_i(n-1)q\left(T\right)---\left(6\right)$

$=\mathrm{\&pi;h}\underset{i=-\&infin;}{\overset{n-2}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i\left(n\right)+2\mathrm{\&pi;hq}\left(T\right)({\mathrm{\&alpha;}}_i(n-2)-{\mathrm{\&alpha;}}_i(n-2))$

$=\mathrm{\&pi;h}\underset{i=-\&infin;}{\overset{n-2}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i\left(n\right)+{\mathrm{\&delta;}}_{\mathrm{\&Delta;}}$

$\left|{\mathrm{\&delta;}}_{\mathrm{\&Delta;}}\right|=\left\{\begin{array}{cc}0;& ({\mathrm{\&alpha;}}_i(n-1)\&CenterDot;{\mathrm{\&alpha;}}_i(n-2)=1)\\ 4\mathrm{\&pi;hq}\left(T\right)\&ap;0.21\mathrm{\&pi;h};& ({\mathrm{\&alpha;}}_i(n-1)\&CenterDot;{\mathrm{\&alpha;}}_i(n-2)=-1)\end{array}\right.$

Wherein, φ (nT) is illustrated in the GFSK signal and is accumulated by the caused equivalent phase of frequency change, and h is the index of modulation α of GFSK signal _i(n) ∈ 1 ,+1}, q (t) represents the phase impulse waveform,

Be equivalent to the form of the accumulative total phase place of DPSK modulation signal, δ _ΔRepresent φ (nT) with

Between deviation.If ignore the influence of δ Δ, (6) formula equivalence is an incoherent dpsk signal.

Like this, just can be applied to the DPSK modulation-demo-demodulation method in the GFSK demodulation.Above-mentioned signal can be expressed as through the signal behind the white Gaussian noise:

wherein n (t) represent average be 0 white noise,

is the constant phase variation of channel introducing.The phase place that has demodulated is applied to the parameter Z and the judgment variables A of dpsk signal demodulation with k (n) expression _iThis can be applied to equally.

Z(n-1)＝exp[jk(n-1)]Z(n-2)+y(n-1)； (7)

$A_i(n,n-1)=2\cos [\widehat{\mathrm{\&phi;}}\left(n\right)-\mathrm{\&pi;h}{\mathrm{\&alpha;}}_i\left(n\right)]\left|y\left(n\right)Z^{*}(n-1)\right|;---\left(8\right)$

Wherein

Represent plural y (n) Z ^*(n-1) angle, the sampled signal that y (n) representative receives

$y\left(n\right)=\underset{(n-1)T}{\overset{\mathrm{nT}}{\&Integral;}}\tilde{r}\left(t\right)\mathrm{dt},---\left(9\right)$

When $2\mathrm{Cos}[\widehat{\mathrm{\&phi;}}\left(n\right)-\mathrm{\&pi;\; h}{\mathrm{\&alpha;}}_i\left(n\right)]\left|y\left(n\right)Z^{*}(n-3)\right|=\mathrm{Max}\left[A_i(n-2,n-3)\right]$ The time, d (n)=α _i(n).In a symbol period | y (n) Z ^*(n-3) | be constant;

At last, parameter is specialized, carried out the iteration judgement, thereby obtain demodulation result.

α in the GFSK signal _i(n) ∈ 1 ,+1}, d (n) can be expressed as more intuitively:

Z(n-3)＝exp[jk(n-3)]Z(n-4)+y(n-1)；

$\widehat{\mathrm{\&phi;}}\left(n\right)=\mathrm{angle}\left[y\left(n\right)Z^{*}(n-3)\right];$ (10)

$d(n-2)=\mathrm{sign}[\mathrm{sign}\left(\widehat{\mathrm{\&phi;}}\left(n\right)\right)+1];$

$k(n-2)=\mathrm{\&pi;h}\&times;\mathrm{sign}\left[\widehat{\mathrm{\&phi;}}\left(n\right)\right];$

Wherein, Wherein, Z (n) representes iteration variable, represent judgment variables; D (n) represents court verdict; Be demodulating data, k (n) representes an auxiliary iteration variable, the sampled signal that y (n) expression receives.Demodulation will realize with the mode of this iteration.When concrete the realization, the lasting stack of Z (n) will be introduced the memory cell that a length can not be estimated.And after drift or process fading channel took place carrier frequency, the signal that receives no longer had

such simple form.The influence of the mistaken verdict that therefore causes also can be along with all judgements after the overlaying influence of Z (n).Therefore, generally can introduce one and forget the coefficient w influence of signal at a distance that decays.Promptly have:

Z(n-3)＝w·exp[jk(n-3)]Z(n-4)+y(n-1)；

The present invention is the universal method that is used for the demodulation of GFSK signal, can be used for all indexes of modulation more than or equal to 0.5 GFSK modulating system, like Bluetooth and DECT technology etc.When the index of modulation was too little, the influence of intersymbol interference was extended to outside the adjacent Baud Length significantly, and above-mentioned analysis and method are no longer suitable.Yet, in practical application, the index of modulation generally all near 0.5 or more than.Therefore many bits algorithm has very wide range of application.

Fig. 1 has shown that under the simulated environment of a Bluetooth performance of many bit demodulation method and other demodulation methods relatively.Here the parameter that adopts is: BT=0.5, h=0.32, w=0.7.Signal only passes through additive white Gaussian noise channel, and sample frequency equates with data frequency.

7 simulation curves of Fig. 1 have been represented difference phase demodulation method from top to bottom successively; The difference phase demodulation method that has decision-feedback phase compensation; Overlay length is the matched filter Array Method of 3 bits; Overlay length is the matched filter Array Method of 5 bits, and many bit demodulation method and overlay length are the matched filter Array Method of 7 bits.Can find out that therefrom the performance of many bit demodulation method is superior to simple difference phase demodulation method (having improved 3dB) greatly, be the matched filter Array Method of 7 bits near overlay length.

Yet the amount of calculation of many bit demodulation method is significantly smaller than the matched filter array of equal performance.Prior art has provided the evaluation method of amount of calculation of the matched filter array of different overlay lengths, is standard with the number of real multiplications: 2 ^L+2N+2 ^K+3Wherein L is the bit length that impulse response continues, and is 3 corresponding to the situation of GFSK; N is that over-sampling is counted, and is 1 corresponding to present example, and K is the length that array covers.So, but the estimation abbreviation of amount of calculation is min (K2 ^K+2, 2 ⁵N+2 ^K+3).Table 1 has been listed the performance and the amount of calculation of various algorithms among Fig. 1.Therefrom we are clear that, for reaching identical performance, the amount of calculation of matched filter Array Method is 132 times of many bits method.

The performance of several kinds of GFSK signals of table 1 demodulating algorithm and amount of calculation size

Claims (3)

1. a GFSK signal multi-bit demodulation method is characterized in that, comprises the steps:

Step 1, the frequency change form during with frequency modulation(FM) change into the phase change form;

Step 2, be applied to the DPSK modulation-demo-demodulation method in the GFSK demodulation;

Step 3, parameter is specific is carried out the iteration judgement, thereby obtains demodulation result;

The concrete grammar that frequency change form in the said step 1 during with frequency modulation(FM) changes into the phase change form is: $\mathrm{\&phi;}\left(\mathrm{NT}\right)=\mathrm{\&pi;\; h}\underset{i=-\&infin;}{\overset{n-2}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i\left(n\right)+{\mathrm{\&delta;}}_{\mathrm{\&Delta;}}$

$\left|{\mathrm{\&delta;}}_{\mathrm{\&Delta;}}\right|=\left\{\begin{array}{cc}0;& ({\mathrm{\&alpha;}}_i(n-1)\&CenterDot;{\mathrm{\&alpha;}}_i(n-2)=1)\\ 4\mathrm{\&pi;hq}\left(T\right)\&ap;0.21\mathrm{\&pi;h};& ({\mathrm{\&alpha;}}_i(n-1)\&CenterDot;{\mathrm{\&alpha;}}_i(n-2)=-1)\end{array}\right.$

Wherein, φ (nT) is illustrated in the GFSK signal and is accumulated by the caused equivalent phase of frequency change, and h is the index of modulation of GFSK signal, α _i(n) ∈ 1 ,+1}, q (t) represents the phase impulse waveform, Be equivalent to the form of the accumulative total phase place of DPSK modulation signal, δ _ΔRepresent φ (nT) with Between deviation; The method of carrying out the iteration judgement in the said step 3 is specially:

Z(n-3)＝exp[jk(n-3)]Z(n-4)+y(n-1)；

$\widehat{\mathrm{\&phi;}}\left(n\right)=\&angle;\left[y\left(n\right)Z^{*}(n-3)\right];$

$d(n-2)=\mathrm{sign}[\mathrm{sign}\left(\widehat{\mathrm{\&phi;}}\left(n\right)\right)+1];$

$k(n-2)=\mathrm{\&pi;h}\&times;\mathrm{sign}\left[\widehat{\mathrm{\&phi;}}\left(n\right)\right];$

Wherein, Z (n) representes iteration variable, The expression judgment variables, d (n) represent court verdict, i.e. demodulating data, k (n) representes an auxiliary iteration variable, y (n) representes the sampled signal that receives, α _i(n) represent the phase place that data possibly transferred to.

2. GFSK signal multi-bit demodulation method according to claim 1, the parameter in the said step 3 are specialized and are meant α in the GFSK signal _i(n) ∈ 1 ,+1}.

3. GFSK signal multi-bit demodulation method according to claim 1 is characterized in that, introduces one and forgets the coefficient W influence of signal at a distance that decays carrying out iteration when judgement, that is:

Z(n-3)＝w·exp[jk(n-3)]Z(n-4)+y(n-1)。

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