CN101388877A - A non-coherent demodulation method based on Chirp spread spectrum technology based on fractional Fourier transform - Google Patents

Abstract

The invention belongs to the field of signal processing and is used for the demodulation of Chirp spread spectrum technology. The non-coherent demodulation method can reduce the influence of phase shift error, multipath time delay error and Doppler frequency shift, and can be used in multipath fading channels and IEEE802 .15.4a has better performance under the S-V standard channel. The basic principle is that a Chirp signal is expressed as an impulse function in an appropriate fractional Fourier domain, that is, the Fractional Fourier transform has good focus on the Chirp signal emitted by the CCS system. Using the advantages of fractional Fourier transform to process Chirp signals, the fractional Fourier transform can be used in CSS spread spectrum technology to realize the demodulation of Chirp signals with different modulation frequencies. In the CSS system, by performing fractional Fourier transform on the received baseband data and detecting the peak value of the focusing order to perform symbol judgment and complete CCS system demodulation, this method reduces the requirement for frequency synchronization and does not require phase synchronization , which has better performance in multipath frequency selective fading channel.

Description

A non-coherent demodulation method based on Chirp spread spectrum technology based on fractional Fourier transform

technical field

The invention relates to a non-coherent demodulation method of Chirp spread spectrum technology, belongs to the field of signal processing, and is used for demodulation of Chirp spread spectrum technology.

Background technique

Broadband Chirp Spread Spectrum (CSS) technology is a spread spectrum technology that uses the modulation frequency of the Chirp signal to carry information. The CSS system has the advantages of both the DSSS system and the UWB system. CSS physical layer technology has been adopted by IEEE802.15.4a standard in August 2007. This standard is a revised version of IEEE802.15.4, which aims to provide a new physical layer alternative for wireless personal area networks (WPANs) in low-to-medium rate and low-power transmission applications such as industrial control, medical monitoring, and wireless sensor networks. , is one of the core standards of WPANs. The CSS system works in the 2450MHz unlicensed frequency band, supports data transmission rates of 250kbps, 1Mbps and 2Mbps, and the indoor transmission distance is 60m, and the outdoor transmission distance is 900m. In addition to providing reliable communication functions, it also provides high-precision ranging and positioning functions (accuracy is less than 1m).

The CSS system is a binary transmission (BOK) system. In principle, the system uses modulation frequency to carry information and realize digital signal modulation. A certain modulation frequency μ ₁ of the real LFM signal is used to represent "1", and a modulation frequency μ ₀ is used to represent "0", that is:

When the code is "1", the carrier signal is:

When the code is "0", the carrier signal is:

The basic principle block diagram of the CSS system is shown in Figure 1. In Figure 1, the classic CSS system uses two Chirp signals whose modulation frequencies are opposite numbers as the carrier, namely: μ ₁ =-μ ₀ ; the demodulation part utilizes the pulse compression characteristic of the Chirp signal, which is widely used Used in radar systems. To perform pulse compression on the Chirp signal is to pass the Chirp signal through a matched filter. The impulse response of the filter is also a chirp signal whose modulation frequency is the opposite number, and the pulse compression waveform obtained after the matched filter is used for judgment detection. After derivation, it can be concluded that the theoretical bit error rate of CSS spread spectrum technology is:

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; \&ap;</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; (</span>\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

The matched filter demodulation described above is a kind of coherent demodulation. Although it has a good bit error rate performance, it needs strict phase synchronization during demodulation, which has high requirements on the system, especially when there are common signals in the wireless channel. When phase shift error, multipath delay error and Doppler frequency shift occur, the bit error rate performance of matched demodulation deteriorates significantly.

The present invention proposes a non-coherent demodulation method based on Fractional Fourier Transform (FRFT). The demodulation method utilizes the good focus of the Chirp signal by Fractional Fourier Transform, and detects the peak value of the focus order. By performing symbol judgment, it can better resist intersymbol interference and have better bit error rate performance in multipath frequency selective fading channels. At the same time, it reduces the difficulty of system implementation to a certain extent.

In order to better understand the present invention, the fractional Fourier transform is briefly introduced below:

In recent years, as a new time-frequency analysis tool, fractional Fourier transform has been widely used in the field of signal processing, and has attracted widespread attention in the field of signal processing. Fractional Fourier transform was originally widely used in the field of optics. In 1993, Almeida interpreted fractional Fourier transform as the rotation of signals in the time-frequency plane, which was an extension of classical Fourier transform. In 1996, Ozaktas, a Turk, proposed a method with FFT calculation speed After the equivalent discrete sampling algorithm, the fractional Fourier transform began to be applied in the field of signal processing. The fractional Fourier transform can be regarded as a unified time-frequency transform, which reflects the information of the signal in the time and frequency domains at the same time. It is different from the commonly used quadratic time-frequency distribution in that it uses a single variable to represent the time-frequency information, and There is no cross-term trouble. Compared with the traditional Fourier transform (actually a special case of fractional Fourier transform), it is suitable for dealing with non-stationary signals, especially Chirp signals, and has one more free parameter (transformation order a), Therefore, under certain conditions, the fractional Fourier transform can often obtain the effect that the traditional time-frequency distribution or Fourier transform cannot obtain, and because it has a relatively mature fast discrete algorithm, it does not need to pay too much while getting better results. Much computational cost.

Using fractional Fourier transform to process Chirp signals is the most typical and effective method, because the basis function of fractional Fourier transform is a set of orthogonal Chirp bases on the fractional Fourier domain. For a given Chirp signal, in a specific The fractional Fourier domain has energy aggregation characteristics, so the fractional Fourier transform is especially suitable for processing Chirp signals.

The fractional Fourier transform of a signal x(t) is defined as:

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}^{<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them: p=2·α/π is the order of the fractional Fourier transform, α is the rotation angle, F _p [·] is the operator symbol of the fractional Fourier transform, K _p (t, u) is the fractional Fourier transform Transform kernel:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="t"\; filenames="A200810226068E00143.png,A200810226068E00151.png"\; state="\{\{state\}\}">t</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; csc</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; n\&pi;</span>}\\ \mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; n\&pi;</span>}\\ \mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; \&PlusMinus;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

The inverse transform of the fractional Fourier transform is:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}^{<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; du</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In practical applications, the discrete form of Fractional Fourier Transform (DFRFT) is required. Currently, there are several different types of fast algorithms for discrete fractional Fourier transform, with different accuracy and computational complexity. Different from the usual decomposed fast algorithm, this paper chooses the discrete fractional Fourier transform fast algorithm proposed by Soo-Chang Pei et al. in 2000, which directly samples the input and output. In the case of keeping the transformation accuracy and complexity of the same decomposition type fast algorithm (the calculation complexity is (O(Nlog ₂ N), N is the number of sampling points), by limiting the sampling interval of input and output, the discrete fractional order The transformation kernel of the Fourier transform maintains orthogonality, so that the original sequence can be restored through the inverse discrete transformation at the output end more accurately.

The input and output of the fractional Fourier transform are sampled at intervals Δt and Δu respectively. When the number of sampling points M of the output of the fractional Fourier domain is greater than or equal to the number of sampling points N of the time domain input, and the sampling interval satisfies

Δu·Δt＝|S|·2π·sinα/M                  

Where |S| is an integer that is relatively prime to M (often taken as 1), and the discrete fractional Fourier transform can be expressed as:

in $A_{\mathrm{\&alpha;}}=\sqrt{\frac{\sin \mathrm{\&alpha;}-j\&Center\; Dot;\cos \mathrm{\&alpha;}}{N}},$ D is an integer.

Contents of the invention

The purpose of the present invention is to propose a non-coherent demodulation method based on fractional Fourier transform for the CSS physical layer technology in the IEEE802.15.4a standard, by performing fractional Fourier transform on the received baseband data to detect the focus order The peak value is used to judge the symbol and complete the demodulation of the CCS system. This method reduces the requirement for frequency synchronization and does not require phase synchronization. It has better performance in multipath frequency selective fading channels.

The basic principle of the present invention is that a Chirp signal is expressed as an impulse function in an appropriate fractional Fourier domain, that is, the Fractional Fourier transform has good focus on the Chirp signal emitted by the CCS system. Using the advantages of fractional Fourier transform to process Chirp signals, the fractional Fourier transform can be used in CSS spread spectrum technology to realize the demodulation of Chirp signals with different modulation frequencies.

The present invention is achieved through the following technical solutions.

The non-coherent demodulation method based on fractional Fourier transform that the present invention proposes comprises the following five steps:

(1) Band-pass filter the intermediate frequency signal of the Chirp spread spectrum system received by the receiver, and mix it with the local oscillator to obtain the baseband signal;

(2) The baseband signal of the Chirp spread spectrum system is low-pass filtered to complete the digital down-conversion;

(3) Perform p ₀ order fractional Fourier transform on the low-pass filtered baseband data (where p ₀ is the peak focusing order of the first Chirp carrier in the fractional Fourier transform domain, p ₀ =-2 arc cot(μ ₀ )/π, μ ₀ is the modulation frequency of the first Chirp carrier signal), then find the modulus value of u _m0 position after the fractional Fourier transform (u _m0 is the p ₀ order fractional Fourier transform of the first Chirp carrier signal The position corresponding to the maximum modulus value, u _m0 =f ₀ ·sinα ₀ , where α ₀ =-arc cotμ ₀ );

(4) Perform p ₁ order fractional Fourier transform on the baseband data of the Chirp spread spectrum system (where p ₁ is the peak focusing order of the second Chirp carrier in the fractional Fourier transform domain, p ₁ =-2 arc cot(μ ₁ )/π, μ ₁ is the modulation frequency of the second road Chirp carrier signal), then find the modulus value of the u _m1 position after the fractional Fourier transform ( _um1 is the p ₁ order fractional Fourier transform of the second road Chirp carrier signal The position corresponding to the maximum modulus value, u _m1 =f ₁ ·sin α ₁ , where α ₁ =-arc cotμ ₁ );

(5) Carry out larger judgment on the two modulus values obtained in step (3) and step (4), and output symbol information.

Provide principle analysis and theoretical derivation process of the present invention below:

(1) Principle of fractional Fourier transform demodulation method

The basis function of the fractional Fourier transform is a set of orthogonal Chirp bases in the fractional frequency domain. A Chirp signal will appear as an impulse function in the appropriate fractional Fourier domain, that is, the fractional Fourier transform is in a certain fractional order The Fourier domain has the best energy focusing characteristics for a given Chirp signal. This focusing characteristic is widely used in Chirp signal detection and parameter estimation. It is precisely the advantage of using FRFT to process Chirp signals that the fractional Fourier transform can be used in CSS spread spectrum technology to realize the demodulation of Chirp signals with different modulation frequencies. According to the properties of fractional Fourier transform, when the transformation order is p∈(0,1), there is the following corresponding relationship between the Chirp signal modulation frequency μ and the focusing order p: μ=-cot(p·π/2).

The following is a theoretical analysis of the focusing characteristics of the Chirp signal in the corresponding fractional Fourier domain. Let the Chirp signal be:

Substituting the above formula into the theoretical formula (3) of fractional-order Fourier transform, then its p-order fractional-order Fourier transform is shown in the following formula, where p=α·2/π:

When μ=-cotα, f _m ＝u cscα, the fractional Fourier magnitude spectrum (fractional Fourier transform module square) of g(t) gets a peak value, and the peak value is:

${{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; csc</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T"\; filenames="A200810226068E00143.png,A200810226068E00151.png"\; state="\{\{state\}\}">T</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

According to the modulation frequency μ ₀ and μ ₁ proposed by the CSS spread spectrum technology modulation carrier scheme, it can be obtained by making p ₀ and p ₁ order respectively at the receiving end (p ₀ =-2·arc cot(μ ₀ )/π, p ₁ = The fractional Fourier transform of -2·arc cot(μ ₁ )/π) can judge the transmitted symbol by the order of the peak value.

At the same time, the sampling positions u _m0 and u _m1 of the two carriers in their respective fractional Fourier domain peaks can be calculated by the initial frequency: u _m0 = f ₀ · sinα ₀ , where α ₀ = -arc cotμ ₀ ; u _m1 = f ₁ • sin α ₁ , where α ₁ =-arc cot μ ₁ . Therefore, after performing p ₀ and p ₁ order fractional Fourier transform on the received signal, compare the modulus square of the position u _m0 of the p ₀ order fractional order Fourier transform result with the modulus of the position u _m1 of the p ₁ order fractional order Fourier transform result The size of the square, the decision output. The principle block diagram of fractional-order Fourier transform demodulation is shown in Fig. 2 .

(2) Theoretical performance analysis of fractional Fourier transform demodulation method.

Let the chirp signal modulation frequency corresponding to the "1" code be μ, and the corresponding fractional Fourier transform order be p order; then the "0" code corresponds to -μ and -p. According to formula (9), it can be known that the amplitude of the peak point of the Chirp signal with the modulation frequency μ after p-order fractional Fourier transform is:

$\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T"\; filenames="A200810226068E00143.png,A200810226068E00151.png"\; state="\{\{state\}\}">T</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

However, after performing -p-order fractional Fourier transform (order mismatch), the output amplitude at the corresponding frequency point is approximately 0.

For the noise signal, suppose the noise introduced from the channel is n ₀ (t), and the power spectral density is N ₀ , then after down-conversion, it is n(t)=n _I (t)+j·n _Q (t), where The power spectral densities of n _I (t) and n _Q (t) are N ₀ . For the fractional Fourier transform, it can be regarded as a linear filter. White noise is still white noise after passing through the linear filter, and the spectral density becomes N ₀ |H(f)| ² at this time. So the power spectral density of n _I (t) and n _Q (t) after fractional Fourier transform is:

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="N"\; filenames="A200810226068E00151.png"\; state="\{\{state\}\}">N</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="N"\; filenames="A200810226068E00151.png"\; state="\{\{state\}\}">N</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

The power spectral density of the IQ two-way combined into complex noise is:

$\frac{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="N"\; filenames="A200810226068E00151.png"\; state="\{\{state\}\}">N</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

So the theoretical bit error rate performance of fractional Fourier demodulation is:

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; (</span>\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="E.\; b"\; filenames="A200810226068E00143.png,A200810226068E00151.png"\; state="\{\{state\}\}">E.</figure-callout></span><figure-callout\; id="2"\; label="E.\; b"\; filenames="A200810226068E00143.png,A200810226068E00151.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

(3) Performance analysis of fractional Fourier transform demodulation method in multipath channel.

In a wireless channel, due to the refraction, scattering or reflection of obstacles, there is always more than one signal propagation path. The signal arriving at the receiver on each path has different phase shifts, time delays, and power fading (large-scale fading and small-scale fading) compared to the received signal of the direct wave path. The following is an analysis of the performance analysis of the fractional Fourier transform demodulation of the CSS system in the presence of multipath phase error, multipath delay error and Doppler frequency shift respectively, and the typical multipath frequency of DVB-T standard channel Taking selective fading channel as an example, the performance of fractional Fourier transform demodulation is analyzed.

a. Multipath phase shift error

的Chirp信号可以表示为：Fractional Fourier transform demodulation is non-coherent demodulation, which is adaptable to phase changes, while traditional coherent demodulation, such as matched demodulation, is sensitive to phase shift errors. The performance of Chirp signals with phase shift errors is as follows. analyze. There is a phase shift error

The Chirp signal can be expressed as:

According to the fractional Fourier transform formula (3) of the Chirp signal, it can be known that its predicted peak formula in the fractional Fourier domain is:

${<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; csc</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="T"\; filenames="A200810226068E00143.png,A200810226068E00151.png"\; state="\{\{state\}\}">T</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

It can be seen from the above formula that the peak amplitude is the same as the Chirp signal without phase shift error. Fractional order demodulation only utilizes the amplitude, modulation frequency and initial frequency information of the signal, but does not utilize the phase information. Therefore, the phase shift error will not affect the focusing order, peak position and size of the fractional Fourier transform, thus will not affect the demodulation result. For traditional matched demodulation, it is a coherent demodulation that requires strict phase synchronization, and the impact of phase shift error has a greater impact on the peak value.

b. Multipath delay error

In a multipath channel, since each path arrives at the receiver at different times, the signal received by the receiver includes multiple path components with time delay. In the following analysis, the performance of fractional-order Fourier transform demodulation exists in the presence of multipath time delay errors. Assuming that there is a multipath delay error τ, the Chirp signal can be expressed as:

In the above discussion, the peak formula of fractional Fourier demodulation under ideal conditions is proposed. Substituting the above formula into the fractional Fourier transform formula (3), the formula of the sampling value at the predetermined peak position in the presence of time delay τ is obtained:

${<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cot</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; csc</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; \&pi;\&mu;\&tau;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

c. Multipath frequency offset error (Doppler frequency shift)

If there is a Doppler shift with a frequency shift of f _d , the Chirp signal can be expressed as:

It can be seen that the frequency shift only causes the change of the initial frequency f _m . According to the peak calculation formula proposed above, it can be concluded that the change of the initial frequency f _m only moves the peak position, but does not change the peak amplitude. Therefore, according to the fractional order sampling theorem, for fractional order demodulation, as long as f _d is not It is so large that the baseband signal is undersampled in the fractional Fourier domain, that is, the initial frequency of g'(t) is not greater than the repetition period |sinα|/Δt in the fractional Fourier domain after signal sampling, so theoretically it will not affect its demodulation effect. But the matched filter has no adaptability to the Doppler frequency shift, even if the search is performed, the performance will be deteriorated due to the adaptation. Therefore, the demodulation performance of the fractional Fourier transform demodulation is not affected after using the peak search method of the corresponding fractional Fourier domain; while the matched demodulation has a greater impact on the Doppler frequency shift, and the performance deteriorates seriously.

d. Performance under multipath channel model

Sections a, b, and c analyze several errors that often occur in CSS systems in wireless channels. Fractional Fourier transform demodulation has little influence on phase error and delay error caused by multipath, and is different from traditional matched demodulation Compared with has the advantage. The following analyzes the performance of the CSS system based on fractional Fourier transform demodulation under a specific multipath time-delay channel model.

Intersymbol interference (ISI) caused by multipath delay spread is the most serious interference problem that any communication system can encounter, and it has a great impact on demodulation performance. There are different phase shifts, time delays and power fading between the signal arriving at the receiver on each path and the received signal on the direct wave path. The following takes the channel model given by the European digital television standard (DVB-T) as an example for actual analysis. This model is a standard multipath channel model, which is mainly divided into two cases: mobile reception and fixed reception. Distinguished by the presence or absence of a Line of Sight (LOS) channel. The specific formula is as follows:

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{\sqrt{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$

In the above formula, _ρ0 is the attenuation of the line-of-sight transmission path; N is the number of reflection paths (equal to 20); _φi is the phase shift of each multipath; _ρi is the attenuation of each multipath; _τi is The delay of each multipath. It can be seen from formula (20) that the channel model is a typical multipath fading channel composed of time delay, phase shift and fading.

S-V channel performance of e.IEEE802.15.4a

The S-V channel is a standard channel model defined in IEEE802.15.4a. In this channel model, large-scale fading (shadow fading) obeys a classical logarithmic distribution, and small-scale fading (flat time fading) obeys Nakagami-m distribution. At the same time, the definition of arrival time of multipath and number of multipath clusters in this model obeys the standard Poisson distribution. According to the above definition, different parameters can divide the S-V model into the following types: residential environment, office environment, outdoor environment, industrial environment and outdoor open environment. Each type is divided into line-of-sight path (LOS) type and non-line-of-sight path (NLOS) type. The specific parameters of each channel will not be described in detail here. In this paper, the CM7 model of LOS and the CM8 model of NLOS in the industrial environment are taken as examples to analyze the demodulation performance of fractional Fourier transform. For specific results, please refer to the detailed description.

The non-coherent demodulation method based on fractional Fourier transform proposed by the present invention has the beneficial effects of:

(1) Compared with the matched filter demodulation method, the non-coherent demodulation method based on fractional Fourier transform proposed by the present invention reduces the difficulty of system implementation. Matched filter demodulation is a kind of coherent demodulation method, which requires strict carrier synchronization and phase synchronization, and requires the receiver to generate a Chirp signal that completely matches the transmission carrier. The method of the present invention is a non-coherent demodulation method that does not require strict frequency Synchronization, phase synchronization is not required, which reduces the difficulty of system implementation.

(2) The non-coherent demodulation method based on fractional Fourier transform proposed by the present invention is less affected by phase shift error, multipath time delay error and Doppler frequency shift, while traditional matching demodulation has little effect on the above three kinds of errors more sensitive.

(3) The non-coherent demodulation method based on fractional Fourier transform proposed by the present invention has better performance than traditional matching demodulation under multipath channel model and IEEE802.15.4a standard channel—S-V channel.

(4) The non-coherent demodulation method based on fractional Fourier transform proposed by the present invention is supported by a fast algorithm of discrete fractional Fourier transform, the calculation amount is equivalent to FFT, and the implementation is simple and easy.

Description of drawings

Figure 1--The basic principle block diagram of the CSS system;

Fig. 2--the present invention realizes principle block diagram;

Fig. 3--the present invention and traditional method performance comparison under the phase shift error;

Fig. 4--the performance comparison of the present invention and the traditional method under time delay error;

Figure 5--DVB-T standard channel fixed receiving channel and mobile receiving channel frequency response;

The present invention compares with traditional method performance under Fig. 6--DVB-T multipath channel;

Figure 7--The standard channel model S-V channel defined by IEEE802.15.4a in the industrial environment LOS channel and NLOS channel impulse response;

Fig. 8 - Performance comparison between the present invention and the traditional method under the standard channel model S-V channel defined by IEEE802.15.4a.

Detailed ways

The content of the invention will be described in detail below in conjunction with accompanying drawings 1 and 2 and the FPGA embodiment.

The present invention relates to a kind of non-coherent demodulation method based on fractional Fourier transform, its principle is shown in accompanying drawing 1, and the algorithm flow of realization is shown in Figure 2, and the whole flow is decomposed into the following five steps to complete:

(1) Band-pass filter the intermediate frequency signal of the Chirp spread spectrum system received by the receiver, and mix it with the local oscillator to obtain the baseband signal;

(2) The baseband signal of the Chirp spread spectrum system is low-pass filtered to complete the digital down-conversion;

(3) Carry out p ₀ order fractional Fourier transform (wherein p ₀ =-2·arc cot(μ ₀ )/π) to the baseband data of the Chirp spread spectrum system, calculate the modulus value, and calculate the peak sampling value at the u _m0 position ( u _m0 =f ₀ ·sinα ₀ , where α ₀ =-arc cotμ ₀ );

(4) Carry out p ₁ order fractional Fourier transform (where p ₁ =-2 arc cot(μ ₁ )/π) to the baseband data of the Chirp spread spectrum system, calculate the modulus value, and calculate the peak sampling value at u _m1 position ( u _m1 =f ₁ ·sin α ₁ , where α ₁ =-arc cot μ ₁ );

(5) Compare the peak sampling value of p _0th order fractional Fourier transform at u _m0 with the peak sampling value of _p1 order fractional Fourier transform at u _m1 position, and output the symbol information.

Below in conjunction with above-mentioned 5 steps, provide this algorithm and be used for FPGA implementation method, according to Fig. 2, when FPGA realizes the inventive method, comprise following several modules: mixer, DDC, two fractional order Fourier transform modules, ratio large Judgment module. Among them, the mixer and DDC are realized by traditional design methods; the fractional-order Fourier transform module is two fixed-order transforms, so only two FFT modules and a small amount of RAM are needed to realize it; the final ratio decision module When implementing, replace the modulus module with the square sum module to reduce the implementation complexity. The entire FPGA implementation uses pipeline processing to improve timing, and due to reduced complexity, less resource consumption, and good real-time performance.

Attached Figure 3 is the Monte Carlo simulation of two demodulation methods in the case of different phase shift errors in the CSS system. The solid line represents fractional demodulation, and the dotted line represents matching demodulation. The phase errors are: π/10, π/ 6, π/5, π/4, π/3, π/4, π/5, under different phase shift errors, the demodulation performance of fractional Fourier transform tends to the same bit error rate curve; while the matching demodulation effect Larger, especially when the phase shift exceeds π/2, the bit error rate performance deteriorates sharply. The specific simulation parameters are: the symbol rate is 62.5kbits/s, the time-width bandwidth product is 20 (spreading gain is about 13dB), and the transmission bandwidth is 1.25MHz.

Accompanying drawing 4 shows the Monte Carlo simulation under the condition that the CSS system has different multipath time delays. The solid line represents fractional order demodulation, the dotted line represents matching demodulation, and the multipath delay errors from bottom to top are: 0.2μs, 0.4μs, 0.6μs, 0.8μs, 1.0μs, 1.2μs, as can be seen from the figure , the performance of fractional-order demodulation gradually degrades when the delay is from 0 μs to 1 μs, and the performance deteriorates only when the delay is above 1 μs; while for matched demodulation, when the synchronization error is above 0.6 μs , the performance of matching demodulation has seriously deteriorated. Therefore, the impact of multipath delay error on the performance of fractional demodulation is smaller than that of matched demodulation.

Accompanying drawing 5 is the channel frequency response of DVB-T standard, wherein the left picture is the channel frequency response of fixed reception, the right picture is the channel frequency response of mobile reception.

Accompanying drawing 6 is the Monte Carlo simulation of the CSS system using fractional Fourier transform demodulation and traditional matched filter demodulation respectively under the above two channels. The solid line represents fractional demodulation, the dotted line represents matched demodulation, the asterisk represents fixed reception, and the circle represents mobile reception. It can be seen from the figure that the fractional-order Fourier transform demodulation has an advantage in the ability to resist intersymbol interference compared with the matched filter demodulation. The main reason is also based on the phase error and time delay error caused by multipath discussed above have little influence on fractional order demodulation. Although matched filter demodulation has good anti-noise performance, it requires very strict phase synchronization and symbol Synchronization, so the performance deteriorates severely in the presence of intersymbol interference.

Figure 7 is the simulation of the discrete impulse response h(n) of the LOS channel and the NLOS channel in the industrial environment respectively. Under the above two typical LOS channels and NLOS channels, the Monte Carlo simulation is carried out to verify the bit error rate performance of the CSS spread spectrum transmission system using fractional Fourier transform demodulation and traditional matched filter demodulation respectively. The specific CSS spread spectrum simulation parameters are: the transmission symbol rate is 250Kb/s, the time-width bandwidth product is 20 (the spread spectrum gain is 13dB), and the bandwidth of the Chirp signal is 5MHz. The specific bit error rate performance is shown in Figure 8. It can be seen from the figure that under the CM7 (ie: LOS path) model, the performance of pulse pressure (matching) demodulation is slightly better than that of fractional Fourier transform demodulation, but the difference in performance is not large, and can basically be achieved below 10dB. 10 ^-4 bit error rate. In the CM8 model of the NLOS path, since there is no line-of-sight path, it has a serious impact on the performance of traditional matched demodulation, while the impact of fractional Fourier transform demodulation is much smaller. It can be clearly seen from the bit error rate curve that the performance of fractional Fourier transform demodulation is better than that of traditional matching demodulation.

The specific description above further elaborates the purpose, technical solution and beneficial effect of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not used to limit the protection of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims (1)

1. Chirp spread spectrum non-coherent demodulation method based on fraction Fourier conversion is characterized in that the specific implementation step is as follows:

(1) the Chirp spread spectrum system intermediate-freuqncy signal that receiver is received is carried out bandpass filtering, carries out mixing with local oscillator, obtains baseband signal;

(2) baseband signal of Chirp spread spectrum system is carried out low-pass filtering, finish Digital Down Convert;

(3) base band data after the low-pass filtering is carried out p ₀Rank fraction Fourier conversion, wherein p ₀For first via Chirp carrier wave at fraction Fourier conversion territory peak focus order, p ₀=-2arccot (μ ₀)/π, μ ₀Be the frequency modulation rate of first via Chirp carrier signal, then ask u behind the fraction Fourier conversion _M0The mould value of position, wherein u _M0P for first via Chirp carrier signal ₀The pairing position of fraction Fourier conversion mould value maximum, rank, u _M0=f ₀Sin α ₀, α wherein ₀=-arccot μ ₀

(4) base band data to the Chirp spread spectrum system carries out p ₁Rank fraction Fourier conversion, wherein p ₁Be that the second road Chirp carrier wave is at fraction Fourier conversion territory peak focus order, p ₁=-2arccot (μ ₁)/π, μ ₁Be the frequency modulation rate of the second road Chirp carrier signal, then ask u behind the fraction Fourier conversion _M1The mould value of position, wherein u _M1Be the p of the second road Chirp carrier signal ₁The pairing position of fraction Fourier conversion mould value maximum, rank, u _M1=f ₁Sin α ₁, α wherein ₁=-arccot μ ₁

(5) two mould values that step (3) and step (4) are tried to achieve are carried out than big judgement output symbol information.

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