CN114338297B - Combined timing synchronization and frequency offset estimation method under incoherent LoRa system - Google Patents

Abstract

The invention provides a combined timing synchronization and frequency offset estimation method under an incoherent LoRa system, which comprises the steps of establishing a data frame structure, sequentially carrying out de-modulation operation, de-chirp operation, discrete Fourier transform operation, modulus taking operation, maximum taking operation, amplitude taking operation and the like on a received pilot signal to obtain a combined offset estimation quantity related to time delay and Doppler frequency shift, and compensating the combined offset estimation quantity into the received data signal, thereby realizing reliable estimation of large transmission time delay and Doppler frequency shift under extremely low signal-to-noise ratio. The invention supports reliable satellite Internet of things communication under extremely low signal-to-noise ratio, large transmission delay and Doppler frequency shift, and has lower processing complexity and implementation complexity compared with the existing estimation algorithm.

Description

A Joint Timing Synchronization and Frequency Offset Estimation Method for Incoherent LoRa System

technical field

The invention relates to the technical field of Internet of Things communication, in particular to a joint timing synchronization and frequency offset estimation method under a non-coherent LoRa system.

Background technique

For satellite IoT transmission, its transmission link usually has the following three disadvantages:

(1) The power of the received signal is low: In free space propagation, the amplitude attenuation of the received signal is proportional to the square of the transmission distance. The distance between the satellite terminal and the user or ground control station is relatively far away, which will cause the signal power received by the receiving end to become very low. This requires that the designed receiver synchronization scheme can work well under extremely low signal-to-noise ratio;

(2) Large Doppler frequency shift: Take the carrier frequency of 4GHz (S-band), the short distance between the satellite and the user or ground control station of 200km, and the relative speed of Mach 10 (1 Mach is calculated as 340m/s) as an example, according to Doppler The calculation formula of Le frequency shift f _d =f _c vcosθ/c (where f _c is the carrier frequency, v is the relative velocity, and θ is the angle with the horizontal direction of the ground) can obtain the maximum Doppler frequency shift (ie θ=0 ) is about 45kHz. This will limit the design of the receiver synchronization scheme in terms of estimation accuracy and estimation range;

(3) The deviation between the timing and the remaining carrier is large: the satellite-to-earth transmission delay of low-orbit satellites is 30ms, which will cause the closed-loop control cycle to be much longer than that of ground mobile communications, thus degrading the performance of timing synchronization and frequency offset estimation using closed-loop control. Therefore, large timing errors and residual frequency offsets will remain during the closed-loop control period.

In fact, IoT transmission including satellite IoT belongs to short data packet transmission, so the available pilot resources become very limited. Moreover, the large Doppler frequency shift and transmission delay will bring severe challenges to the communication system based on LoRa technology. This requires research on the receiver synchronization scheme of LoRa technology. For the research on the receiver synchronization scheme under LoRa technology, Tapparel J et al. described the software definition of LoRa transceiver in the article "An open-source LoRa physical layer prototype on GNU radio" (2020 IEEE SPAWC,2020:1-5) The radio is implemented, and the estimation module of carrier frequency deviation and sampling time deviation is also designed. Colavolpe G et al. In "Reception of LoRa signals from LEO satellites" (IEEE Transactions on Aerospace and Electronic Systems, 2019, 55(6): 3587-3602) for Doppler frequency shift, Doppler rate and transmission delay These carrier parameters provide a joint parameter estimation scheme based on Fast Fourier Transformation (FFT). Bernier C et al. proposed a low-complexity LoRa frame synchronization in the article "Low complexity LoRaframe synchronization for ultra-low power software-defined radios" (IEEETransactions on Communications, 2020, 68(5): 3140-3152) scheme, designed to be applicable to the recently proposed ultra-low power software-defined radio system. Xhonneux M et al. claimed in the article "A low-complexity synchronization scheme for LoRa end nodes" (https://arxiv.org/abs/1912.11344v1, 2019) to propose a low-complexity synchronization scheme for LoRa end nodes , can estimate and correct carrier frequency offset and sampling time offset. However, these synchronization schemes all require a relatively complex process, and none of them consider the characteristics of non-coherent LoRa systems.

Contents of the invention

Aiming at the shortcomings of low received signal power, large Doppler frequency shift, large deviation between timing and remaining carrier in satellite Internet of Things communication, and the technical problems that the processing process of the synchronization scheme based on LoRa technology is relatively complicated in the prior art, the present invention proposes A joint timing synchronization and frequency offset estimation method under the non-coherent LoRa system, which supports reliable satellite Internet of Things communication with extremely low signal-to-noise ratio, large transmission delay and Doppler frequency shift, and has low processing complexity and Achieve complexity.

In order to solve the above-mentioned technical problems, the present invention adopts the following technical solutions: a joint timing synchronization and frequency offset estimation method under a non-coherent LoRa system, comprising the following steps:

Step S1: Establish a data frame structure, the data frame structure includes receiving pilot signals and receiving data signals;

Step S2: performing a demodulation operation on the received pilot signal in the data frame structure to obtain a demodulated signal;

Step S3: performing a de-chirp operation on the de-modulated signal to obtain a de-chirp signal;

Step S4: performing discrete Fourier transform on the dechirped signal to obtain a frequency domain signal;

Step S5: Perform a modulo operation on the frequency domain signal to obtain the corresponding amplitude;

Step S6: Perform the maximum value and argument operation on the obtained amplitude to obtain the corresponding maximum value index, and use the maximum value index as the estimated value of the joint offset of the transmission delay and Doppler frequency shift;

Step S7: Use the estimated value of the joint offset to perform a compensation operation on the received data signal in the data frame structure to obtain a corrected data signal, and realize reliable estimation of large transmission delay and Doppler frequency shift under extremely low signal-to-noise ratio .

The method for establishing the data frame structure in the step S1 is:

Step S1.1: Given a pilot block with a length of L _p and a data block with a length of L _d ;

Step S1.2: Insert the pilot block of length L _p into the head of the data block of length L _d , and obtain the data frame structure F.

The method for obtaining the demodulated signal in the step S2 is:

Step S2.1: first obtain the received pilot signal in the data frame structure F, the data frame structure F traverses through the sampling time k to obtain the sampling time set κ _p ={k:0≤k≤L _p corresponding to the pilot block -1} and the set of sampling moments corresponding to the data block κ _d = {k: L _p ≤ k ≤ L _p + L _d -1}; then the set of sampling moments κ _p corresponding to the pilot block passes through the sampling moment k one by one Extract the received pilot signal of the l-th chirp:

为虚数单位；In the formula: B is the transmission bandwidth, M=2 ^SF is the number of orthogonal chirps, SF is the spreading factor, τ, f _d and θ are the transmission delay, Doppler frequency shift and phase deviation respectively, n _k (l ) is a complex Gaussian random variable with a mean of 0 and a variance of ^σ2 , s _k (l-τ) is a LoRa modulated signal with a transmission delay τ added,

is an imaginary unit;

Step S2.2: Finally, perform a demodulation operation on the received pilot signal r _k (l) _p to obtain a demodulated signal:

In the formula: d _k is the transmission pilot symbol.

In the step S3, the de-chirp operation is performed on the demodulated signal r' _k (l) _p to obtain the de-chirp signal:

In the step S4, the discrete Fourier transform (DFT) operation is carried out to the dechirped signal z _k (l) to obtain the frequency domain signal:

In the formula: q represents the frequency index of DFT.

In the step S5, the frequency domain signal Z(q) is subjected to a modulo operation to obtain the corresponding amplitude:

进行取最大值和幅角操作得到相应的最大值索引，即联合偏移量的估计值：In the step S6, for the amplitude

Perform the maximum value and argument operation to obtain the corresponding maximum value index, that is, the estimated value of the joint offset:

The method for obtaining the correction data signal in the step S7 is:

Step S7.1: first obtain the received data signal in the data frame structure F, and extract the sampling time set κ _d corresponding to the data block one by one through the sampling time k to obtain the received data signal of the l-th chirp:

对接收数据信号r_k(l)_d进行补偿操作得到校正数据信号：Step S7.2: Then use the estimate of the joint offset

Compensation operation is performed on the received data signal r _k (l) _d to obtain the corrected data signal:

The beneficial effects of the present invention are:

1. Compared with existing estimation algorithms, the present invention has lower processing complexity. Because the estimation method in the present invention does not need to estimate the transmission time delay and the Doppler frequency shift separately, but instead estimates the joint offset of the transmission time delay and the Doppler frequency shift.

2. In actual operation, the Discrete Fourier Transform (DFT) operation based on joint timing synchronization and frequency offset estimation method proposed by the present invention can be replaced by an efficient Fast Fourier Transform (FFT) operation, so it also has comparative advantages Low implementation complexity.

3. The present invention finally obtains a joint offset estimator about time delay and Doppler frequency shift by performing a series of operations on the received pilot signal, and then compensates the joint offset estimator into the received data signal , so as to achieve reliable estimation of large transmission delay and Doppler shift at extremely low SNR.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

Fig. 1 is a data frame structure diagram of the present invention;

Fig. 2 is a schematic flow sheet of the present invention;

Fig. 3 is the uncoded non-coherent LoRa system performance of the present invention based on joint timing synchronization and frequency offset estimation method under spreading factor SF=12;

Fig. 4 is the uncoded non-coherent LoRa system performance of the present invention based on joint timing synchronization and frequency offset estimation method under spreading factor SF=14;

Fig. 5 is the performance of the Turbo coded non-coherent LoRa system based on joint timing synchronization and frequency offset estimation method of the present invention under spreading factor SF=12;

FIG. 6 shows the performance of the Turbo coded non-coherent LoRa system based on the method of joint timing synchronization and frequency offset estimation in the present invention under the spreading factor SF=14.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

In order to support reliable satellite IoT communication under extremely low signal-to-noise ratio, large transmission delay and Doppler frequency shift, the present invention provides a joint timing synchronization and frequency offset estimation method under the non-coherent LoRa system. The received signal is separated into the received data signal and the received pilot signal by the demultiplexer, and then the received pilot signal is demodulated and de-chirped to obtain the de-chirped signal, and the obtained de-chirped signal is subjected to discrete Fourier transform The frequency domain signal is obtained by calculation, the corresponding amplitude is obtained by taking the modulus operation on the obtained frequency domain signal, and the maximum value and the argument angle operation are performed on the amplitude to obtain the maximum value index, and then the transmission delay and Doppler The estimator of the joint offset of the Doppler frequency shift, and finally compensate the estimator of the joint offset into the received data signal, so as to realize the reliable estimation of the Doppler frequency shift and transmission delay under extremely low signal-to-noise ratio . The specific implementation steps include:

Step S1: first establish the data frame structure.

The method for establishing the data frame structure is as follows:

Step S1.1: Given a pilot block with a length of L _p and a data block with a length of L _d ;

Step S1.2: Insert the pilot block of length L _p into the head of the data block of length L _d , that is, obtain the data frame structure F shown in FIG. 1 .

Then, the received pilot signal in the data frame structure F is correspondingly processed to obtain an estimated value of the joint offset of the transmission delay and the Doppler frequency shift. The specific operation process is shown in Figure 2, including:

Step S2: Demodulate the received pilot signal in the data frame structure F to obtain the demodulated signal. The specific operation is:

Step S2.1: first obtain the received pilot signal in the data frame structure F, the data frame structure F traverses through the sampling time k to obtain the sampling time set κ _p ={k:0≤k≤L _p corresponding to the pilot block -1} and the set of sampling moments corresponding to the data block κ _d = {k: L _p ≤ k ≤ L _p + L _d -1}; then the set of sampling moments κ _p corresponding to the pilot block passes through the sampling moment k one by one Extract the received pilot signal r _k (l) _p of the l-th chirp:

为虚数单位，/>

称作一个关于传输时延和多普勒频移的联合偏移量。In the formula: B is the transmission bandwidth, M=2 ^SF is the number of orthogonal chirps, SF is the spreading factor, τ, f _d and θ are the transmission delay, Doppler frequency shift and phase deviation respectively, and d _k is the transmission Pilot symbol, n _k (l) is a complex Gaussian random variable with mean value 0 and variance σ ² , s _k (l-τ) is a LoRa modulated signal with transmission delay τ added,

is the imaginary unit, />

is called a joint offset with respect to transmission delay and Doppler shift.

Step S2.2: Finally, perform a demodulation operation on the received pilot signal r _k (l) _p to obtain a demodulated signal r′ _k (l) _p :

为高斯噪声。In the formula:

is Gaussian noise.

Step S3: Perform a de-chirp operation on the obtained demodulated signal r′ _k (l) _p to obtain a de-chirped signal z _k (l):

为高斯噪声。In the formula:

is Gaussian noise.

Step S4: Perform discrete Fourier transform (DFT) operation on the obtained de-chirped signal z _k (l) to obtain its frequency domain signal Z(q):

是噪声项n″_k(l)的DFT结果，/>

为N₁(q)的随机翻转结果，/>

为联合偏移量S(τ,f_d)的近似值，round(·)函数表示四舍五入运算的取整操作，q表示DFT的频率索引。In the formula: δ( ) is the Dirac function,

is the DFT result of the noise term n″ _k (l), />

is the random flip result of N ₁ (q), />

is the approximate value of the joint offset S(τ,f _d ), the round(·) function represents the rounding operation of the rounding operation, and q represents the frequency index of the DFT.

Step S5: Perform a modulo operation on the obtained frequency domain signal Z(q) to obtain the corresponding amplitude

为N₂(q)的一个旋转结果。In the formula:

is a rotation result of N ₂ (q).

进行取最大值和幅角操作得到相应的最大值索引q^*，即联合偏移量的估计值/>

Step S6: For the obtained amplitude

Perform the maximum value and argument operation to obtain the corresponding maximum value index q ^* , that is, the estimated value of the joint offset />

对数据帧结构F中的接收数据信号r_k(l)_d进行补偿操作得到校正数据信号/>

具体操作为：Step S7: Utilize the estimated value of the joint offset

Compensate the received data signal r _k (l) _d in the data frame structure F to obtain the corrected data signal />

The specific operation is:

Step S7.1: first obtain the received data signal in the data frame structure F, and extract the sampling time set κ _d corresponding to the data block one by one through the sampling time k to obtain the l-th chirped received data signal r _k (l) _d :

对接收数据信号r_k(l)_d进行补偿操作得到校正数据信号/>

Step S7.2: Then use the estimate of the joint offset

Perform a compensation operation on the received data signal r _k (l) _d to obtain a corrected data signal />

也是均值为0、方差为σ²的复高斯随机变量。In the formula:

is also a complex Gaussian random variable with mean 0 and variance ^σ2 .

In this embodiment, the received signal is separated into a data signal and a pilot signal through a demultiplexer, and the received pilot signal is sequentially subjected to a demodulation operation, a dechirping operation, a DFT operation, a modulo value operation, and a maximum value and Argument operation etc. get a joint offset estimator about time delay and Doppler frequency shift, and then compensate this joint offset estimator to the received data signal, so as to realize the Doppler frequency shift estimation under extremely low signal-to-noise ratio Reliable estimation of Le frequency shift and transmission delay.

In order to further illustrate the beneficial effects of the present invention, in the present embodiment, a comparison is made through a simulation experiment, specifically as follows:

Simulation 1:

1.1 Simulation conditions

The transmission bandwidth B=20MHz, the spreading factors SF are 12 and 14, and the corresponding adjacent chirp intervals Δf are 488Hz and 122Hz respectively. It is further assumed that the transmission time delay τ=256 chirps, the maximum Doppler frequency shift f _d =45 kHz>>Δf and the random phase deviation θ∈[-π,π). For the LoRa modulated signal, the non-coherent demodulation method proposed by Fabregas AG I and Grant AJ in "Capacity approaching codes for non-coherent orthogonal modulation" (IEEE Transactions on Wireless Communications, 2007, 6(11): 4004-4013) is used.

1.2 Simulation results and analysis

Take pilot symbol length L _p =4 and data symbol length L _d =60 as an example. The pilot overhead at this time is about 0.067. In fact, for spreading factors SF=12 and SF=14, the corresponding transmission data sequence lengths are 720 bits and 840 bits respectively.

Figure 3 and Figure 4 respectively show the bit error rate (Bit error rate, BER) performance of the uncoded non-coherent LoRa system based on the joint timing synchronization and frequency offset estimation method under these two spreading factors. Among them, the curve marked with a diamond in Figure 3 represents the performance of the uncoded non-coherent LoRa system based on the joint timing synchronization and frequency offset estimation method under the conditions of the uncoded LoRa system, SF = 12, f _d = 45 kHz, τ = 256 chirps . The curve marked with a square in Fig. 3 represents the performance of the uncoded non-coherent LoRa system based on the method of joint timing synchronization and frequency offset estimation under the conditions of uncoded LoRa system, SF = 12, _fd = 0, τ = 0. The diamond-shaped curve in Figure 4 represents the performance of the uncoded non-coherent LoRa system based on the joint timing synchronization and frequency offset estimation method under the conditions of the uncoded LoRa system, SF = 14, f _d = 45 kHz, τ = 256 chirps. The curve marked with a square in Fig. 4 represents the performance of the uncoded non-coherent LoRa system based on the joint timing synchronization and frequency offset estimation method under the condition of uncoded LoRa system, SF = 14, f _d = 0, τ = 0.

From the simulation results in Fig. 3 and Fig. 4, it can be seen that no matter the spreading factor SF is 12 or 14, the non-coherent LoRa modulation system based on the proposed synchronization method is close to the ideal situation (that is, f _d = 0 and τ = 0) BER performance. Specifically, when BER=10 ^-4 , for SF=12 and SF=14, the performance of the non-coherent LoRa system based on the proposed synchronization scheme is 0.4dB and 0.2dB worse than the ideal performance, respectively. These results demonstrate the effectiveness of the proposed joint timing synchronization and frequency offset estimation method. In addition, it can also be found that the spreading gain brought by the large spreading factor is very considerable.

Simulation 2:

2.1 Simulation conditions

(/>

表示向上取整，可以通过对码字补零实现)，对应的导频开销分别约为0.063和0.073。Take a Turbo code with a code rate of 0.5 and an information bit length of 384 as an example. The inner and outer interleavers used are both quadratic permutation polynomial interleavers, and the decoding algorithm used is the modified Max-Log-MAP algorithm; the pilot symbol length L _p =4 used, for SF=12 and SF=14, The transmitted data symbol length L _d is 768/12=64 and

(/>

Indicates rounding up, which can be realized by padding the codeword with zeros), and the corresponding pilot overheads are about 0.063 and 0.073 respectively.

2.2 Simulation results and analysis

Figure 5 and Figure 6 respectively show the performance of the Turbo coded non-coherent LoRa system based on the joint timing synchronization and frequency offset estimation method under these two spreading factors. Among them, the curve marked with a diamond in Fig. 5 indicates that under the conditions of Turbo coded non-coherent LoRa system, SF=12, f _d =45kHz, τ=256chirps, L _p =4, the method based on joint timing synchronization and frequency offset estimation is adopted. Turbo coded non-coherent LoRa system performance. The curve marked with a square in Figure 5 represents the performance of the Turbo-coded non-coherent LoRa system based on the joint timing synchronization and frequency offset estimation method under the conditions of the Turbo-coded non-coherent LoRa system, SF=12, _fd =0, and τ=0 . The curve marked with a diamond in Fig. 6 shows that under the conditions of Turbo coded non-coherent LoRa system, SF=14, f _d =45kHz, τ=256chirps, L _P =4, using Turbo code based on joint timing synchronization and frequency offset estimation method Non-coherent LoRa system performance. The curve marked with a square in Figure 6 represents the performance of the Turbo-coded non-coherent LoRa system based on the joint timing synchronization and frequency offset estimation method under the conditions of the Turbo-coded non-coherent LoRa system, SF=14, _fd =0, and τ=0 .

From the simulation results in Figure 5 and Figure 6, it can be found that no matter the spreading factor SF is 12 or 14, the Turbo coded non-coherent LoRa system based on the proposed synchronization method has achieved a BER performance very close to the ideal situation. Specifically, when the BER is in the range of 10 ^-4 to 10 ^-5 , the performance difference between the two does not exceed 0.1 dB.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of the present invention. within the scope of protection.

Claims (4)

1. A combined timing synchronization and frequency offset estimation method under an incoherent LoRa system is characterized by comprising the following steps:

step S1: establishing a data frame structure, wherein the data frame structure comprises a received pilot signal and a received data signal;

step S2: performing de-modulation operation on the received pilot signal in the data frame structure to obtain a de-modulated signal;

the method for obtaining the demodulation signal in the step S2 is as follows:

step S2.1: firstly, a received pilot signal in a data frame structure F is obtained, and the data frame structure F is traversed through sampling time k to obtain a sampling time set kappa corresponding to a pilot block _p ＝{k:0≤k≤L _p -1 and a set of sample moments k corresponding to a data block _d ＝{k:L _p ≤k≤L _p +L _d -1}，L _p For the length of the pilot block, L _d Is the length of the data block; then the sampling time set kappa corresponding to the pilot block is collected _p Extracting the first chirp received pilot signal one by one through sampling time k:

wherein: b is the transmission bandwidth, m=2 ^SF Is orthogonal chirp number, SF is spreading factor, τ, f _d And θ are respectively transmission delay, doppler shift and phase offset, n _k (l) Is the mean value is 0 and the variance is sigma ² Complex gaussian random variable s _k (l-tau) is the LoRa modulated signal with the transmission delay tau attached,

is an imaginary unit;

step S2.2: finally butt jointReceiving pilot signal r _k (l) _p Performing a de-modulation operation to obtain a de-modulated signal:

wherein: d, d _k For transmitting pilot symbols;

step S3: carrying out de-chirp operation on the de-modulated signal to obtain a de-chirp signal;

in the step S3, the de-modulated signal r _k ′(l) _p And performing a de-chirp operation to obtain a de-chirp signal:

step S4: performing discrete Fourier transform on the de-chirped signal to obtain a frequency domain signal;

step S5: performing a modulus operation on the frequency domain signal to obtain a corresponding amplitude;

step S6: performing maximum value and amplitude angle operation on the obtained amplitude value to obtain a corresponding maximum value index, and taking the maximum value index as an estimated value of the joint offset of the transmission delay and the Doppler frequency shift;

in the step S6, the amplitude is calculated

And performing maximum value and amplitude angle taking operation to obtain corresponding maximum value indexes, namely estimated values of the joint offset:

step S7: performing compensation operation on the received data signals in the data frame structure by using the estimated value of the joint offset to obtain corrected data signals, so as to realize reliable estimation of large transmission delay and Doppler frequency shift under extremely low signal-to-noise ratio;

the method for obtaining the correction data signal in the step S7 is as follows:

step S7.1: first, the received data signal in the data frame structure F is obtained, and the sampling time set kappa corresponding to the data block is collected _d And extracting the first chirp received data signal one by one through the sampling time k:

step S7.2: then use the estimate of the joint offset

Receiving a data signal r _k (l) _d Performing compensation operation to obtain a corrected data signal:

2. the method for jointly timing synchronization and frequency offset estimation in an incoherent LoRa system according to claim 1, wherein the method for establishing a data frame structure in step S1 is as follows:

step S1.1: given a length L _p Pilot block and length L _d Is a data block of (a);

step S1.2: will have a length of L _p Insertion of pilot block of length L _d The header of the data block of (2) to obtain a data frame structure F.

3. The method for joint timing synchronization and frequency offset estimation in incoherent LoRa system according to claim 2, wherein in step S4, the de-chirp signal z is de-chirped _k (l) Performing discrete Fourier transform operation to obtain a frequency domain signal:

wherein: q represents the frequency index of the DFT.

4. The method for joint timing synchronization and frequency offset estimation in incoherent LoRa system according to claim 3, wherein in step S5, the frequency domain signal Z (q) is subjected to a modulo operation to obtain a corresponding amplitude value:

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