CN114338297B - Combined timing synchronization and frequency offset estimation method under incoherent LoRa system - Google Patents
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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
Technical Field
The invention relates to the technical field of communication of the Internet of things, in particular to a combined timing synchronization and frequency offset estimation method under an incoherent LoRa system.
Background
For satellite internet of things transmission, its transmission link generally has the following three disadvantages:
(1) The received signal power is low: in free space propagation, the amplitude fading of the received signal is proportional to the square of the transmission distance. The satellite terminals are relatively far from the user or ground control station, which can result in the signal power received at the receiving end becoming very low. This requires that the designed receiver synchronization scheme work well at very low signal to noise ratios;
(2) The Doppler shift is large: taking carrier frequency of 4GHz (S band), short distance of satellite to user or ground control station of 200km and relative speed of Mach 10 (Mach 1 is calculated according to 340 m/S) as examples, according to calculation formula f of Doppler frequency shift d ＝f c vcos θ/c (where f c The maximum obtainable doppler shift (i.e., θ=0) is about 45kHz for the carrier frequency, v is the relative velocity, θ is the angle with the ground horizontal. This will limit the design of the receiver synchronization scheme both in terms of estimation accuracy and estimation range;
(3) The timing and remaining carrier deviation is large: the low-rail satellite ground transmission delay is 30ms, which can lead to the closed-loop control period being far longer than that of ground mobile communication, so that the performance of timing synchronization and frequency offset estimation adopting closed-loop control is reduced. And therefore a larger timing error and residual frequency offset remain during closed loop control.
In fact, internet of things transmissions, including satellite internet of things, belong to short packet transmissions, so the available pilot resources become very limited. And the larger doppler shift and propagation delay can lead to serious challenges for a communication system based on the LoRa technology. This requires a study of the receiver synchronization scheme with respect to the LoRa technique. For studies of receiver synchronization schemes under LoRa technology, tapprel J et al, in the article "An open-source LoRa physical layer prototype on GNU radio" (2020 IEEE SPAWC,2020:1-5), describes a software defined radio implementation of LoRa transceivers, while also designing An estimation module for carrier frequency offset and sampling time offset. Colavolpe G et al, in "Reception of LoRa signals from LEO satellites" (IEEE Transactions on Aerospace and Electronic Systems,2019,55 (6): 3587-3602), herein, describe a joint parameter estimation scheme based on a fast Fourier transform (Fast Fourier transformation, FFT) for carrier parameters such as Doppler shift, doppler rate and transmission delay. Bernier C et al, in the text, "Low complexity LoRa frame synchronization for ultra-low power software-defined radios" (IEEE Transactions on Communications,2020,68 (5): 3140-3152), propose a low complexity LoRa frame synchronization scheme intended for use in the recently proposed ultra-low power consumption software defined radio systems. Xhonneux M et al, in the text, "A low-complexity synchronization scheme for LoRa end nodes" (https:// arxiv. Org/abs/1912.11344v1, 2019), states that a low complexity synchronization scheme for LoRa end nodes is proposed that can estimate and correct carrier offset versus sampling time. However, these synchronization schemes require a relatively complex process and do not take into account the characteristics of the incoherent LoRa system.
Disclosure of Invention
Aiming at the defects of low received signal power, large Doppler frequency shift, large deviation between timing and residual carrier and the like in satellite Internet of things communication and the technical problem that the processing process of a synchronous scheme based on the LoRa technology in the prior art is complex, the invention provides a combined timing synchronization and frequency offset estimation method under an incoherent 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 lower processing complexity and implementation complexity.
In order to solve the technical problems, the invention adopts the following technical scheme: a joint timing synchronization and frequency offset estimation method under an incoherent LoRa system comprises 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;
step S3: carrying out de-chirp operation on the de-modulated signal 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;
step S7: and compensating the received data signals in the data frame structure by using the estimated value of the joint offset to obtain corrected data signals, and realizing 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 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 Number of (2)And obtaining a data frame structure F according to the head of the block.
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}; 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 receives the 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.
In the step S3, the de-modulated signal r' k (l) p And performing a de-chirp operation to obtain a de-chirp signal:
in the step S4 of the above-mentioned process,for de-chirp signal z k (l) Performing Discrete Fourier Transform (DFT) operation to obtain a frequency domain signal:
wherein: q represents the frequency index of the DFT.
In the step S5, the frequency domain signal Z (q) is subjected to a modulus operation to obtain a corresponding amplitude value:
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:
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:
the beneficial effects of the invention are as follows:
1. compared with the existing estimation algorithm, the method has lower processing complexity. Because the estimation method of the present invention does not require separate estimation of the transmission delay and the doppler shift, instead, a joint offset is estimated for the transmission delay and the doppler shift.
2. In actual operation, the Discrete Fourier Transform (DFT) operation in the method based on the joint timing synchronization and frequency offset estimation can be replaced by high-efficiency Fast Fourier Transform (FFT) operation, so that the method has lower implementation complexity.
3. The invention finally obtains a joint offset estimation quantity related to delay and Doppler frequency shift through a series of operation processing on the received pilot signal, and then compensates the joint offset estimation quantity into the received data signal, thereby realizing reliable estimation of large transmission delay and Doppler frequency shift under extremely low signal-to-noise ratio.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a block diagram of a data frame according to the present invention;
FIG. 2 is a schematic flow chart of the present invention;
fig. 3 is an uncoded incoherent LoRa system performance based on a joint timing synchronization and frequency offset estimation method at spreading factor sf=12 according to the present invention;
fig. 4 shows the performance of an uncoded incoherent LoRa system of the present invention based on a joint timing synchronization and frequency offset estimation method at a spreading factor sf=14;
fig. 5 shows performance of a Turbo coding incoherent LoRa system based on a joint timing synchronization and frequency offset estimation method under a spreading factor sf=12;
fig. 6 shows performance of a Turbo coding incoherent LoRa system based on a joint timing synchronization and frequency offset estimation method under the spreading factor sf=14.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without any inventive effort, are intended to be within the scope of the invention.
In order to support reliable satellite Internet of things communication under extremely low signal-to-noise ratio, large transmission delay and Doppler frequency shift, the invention provides a joint timing synchronization and frequency shift estimation method under an incoherent LoRa system. The specific implementation steps comprise:
step S1: first a data frame structure is established.
The method for establishing the data frame structure comprises the following steps:
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 (a) is the data frame structure F shown in fig. 1.
The received pilot signal in the data frame structure F is then processed accordingly to obtain an estimate of the joint offset for the propagation delay and doppler shift. The specific operation process is shown in fig. 2, and comprises the following steps:
step S2: the method comprises the following specific operations of performing a de-modulation operation on a received pilot signal in a data frame structure F to obtain a de-modulated signal:
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}; then the sampling time set kappa corresponding to the pilot block is collected p The receiving pilot signal r of the first chirp is extracted one by one through the sampling time k k (l) p ：
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, d k To transmit pilot symbols, 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 imaginary unit, ++>
Referred to as a joint offset for transmission delay and doppler shift.
Step S2.2: finally receives the pilot signal r k (l) p Performing de-modulation operation to obtain a de-modulated signal r' k (l) p ：
Wherein:
is gaussian noise.
Step S3: for the obtained de-modulated signal r' k (l) p Performing the de-chirp operation to obtain a de-chirp signal z k (l)：
Wherein:
is gaussian noise.
Step S4: for the obtained de-chirp signal z k (l) Performing Discrete Fourier Transform (DFT) operation to obtain a frequency domain signal Z (q):
wherein: delta (·) is the dirac function,
is the noise term n k (l) DFT results of->
Is N 1 (q) random inversion result, +.>
For 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: performing a modulus operation on the obtained frequency domain signal Z (q) to obtain a corresponding amplitude value
Wherein:
is N 2 One rotation result of (q).
Step S6: for the obtained amplitude
Performing maximum value taking and amplitude angle taking operations to obtain corresponding maximum value index q * I.e. estimate of joint offset +.>
Step S7: using estimates of joint offsets
For the received data signal r in the data frame structure F k (l) d Performing compensation operation to obtain corrected data signal +.>
The specific operation 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 The first chirp received data signal r is obtained by extracting one by one through the sampling time k k (l) d ：
Step S7.2: then use the estimate of the joint offset
Receiving a data signal r k (l) d Performing compensation operation to obtain correctionData signal->
Wherein:
also the mean value is 0 and the variance is sigma 2 Is a complex gaussian random variable of (c).
In this embodiment, the received signal is separated into a data signal and a pilot signal by a demultiplexer, and the received pilot signal is sequentially subjected to a demodulation operation, a chirp removal operation, a DFT operation, a modulus taking operation, a maximum taking operation, an amplitude angle taking operation, and the like to obtain a joint offset estimation amount related to delay and doppler shift, and then the joint offset estimation amount is compensated into the received data signal, so as to realize reliable estimation of large doppler shift and transmission delay under extremely low signal-to-noise ratio.
In order to further illustrate the beneficial effects of the present invention, in this embodiment, a comparison is performed through a simulation experiment, which is specifically as follows:
simulation 1:
1.1 simulation conditions
The transmission bandwidth b=20 MHz, the spreading factor SF is 12 and 14, and the corresponding adjacent chirp intervals Δf are 488Hz and 122Hz, respectively. Assuming again a transmission delay τ=256 chips, maximum doppler shift f d =45 kHz > Δf and random phase bias θ∈ [ -pi, pi). For LoRa modulated signals, the incoherent demodulation method proposed in "Capacity approaching codes for non-coherent orthogonal modulation" (IEEE Transactions on Wireless Communications,2007,6 (11): 4004-4013) by Fabregas AG I and Grant AJ is used.
1.2 simulation results and analysis
With pilot symbol length L p =4 and data symbol length L d And=60 is an example. The pilot overhead at this time is about 0.067. In practice, for spreading factors sf=12 and sf=14, forThe corresponding transmission data sequences are 720 bits and 840 bits in length, respectively.
Fig. 3 and fig. 4 show Bit Error Rate (BER) performance of an uncoded incoherent LoRa system based on a joint timing synchronization and frequency offset estimation method under these two spreading factors, respectively. Wherein the diamond marked curves in fig. 3 are shown in the uncoded LoRa system, sf=12, f d Under the conditions of=45 kHz and τ=256 chirp, the uncoded incoherent LoRa system performance based on the joint timing synchronization and frequency offset estimation method is adopted. The curve marked with square in fig. 3 shows the results in an uncoded LoRa system, sf=12, f d And under the conditions of=0 and τ=0, adopting an uncoded incoherent LoRa system performance based on a joint timing synchronization and frequency offset estimation method. The diamond marked curves in fig. 4 are shown in uncoded LoRa system, sf=14, f d Under the conditions of=45 kHz and τ=256 chirp, the uncoded incoherent LoRa system performance based on the joint timing synchronization and frequency offset estimation method is adopted. The curve marked with square in fig. 4 shows the results in an uncoded LoRa system, sf=14, f d And under the conditions of=0 and τ=0, adopting an uncoded incoherent LoRa system performance based on a joint timing synchronization and frequency offset estimation method.
As can be seen from the simulation results of fig. 3 and 4, the incoherent LoRa modulation system based on the proposed synchronization method achieves near-ideal conditions (i.e., f, no matter whether the spreading factor SF is 12 or 14 d =0 and τ=0). Specifically, when ber=10 -4 When for sf=12 and sf=14, the incoherent LoRa system performance based on the proposed synchronization scheme is 0.4dB and 0.2dB worse than the ideal case, respectively. These results demonstrate the effectiveness of the proposed joint timing synchronization and frequency offset estimation method. In addition, the spreading gain from a large spreading factor can be found to be very substantial.
Simulation 2:
2.1 simulation conditions
Take a Turbo code with a code rate of 0.5 and an information bit length of 384 as an example. The adopted inner and outer interleavers are both quadratic permutation polynomial interleavers, and the adopted decoding algorithm is a modified Max-Log-MAP algorithm; pilot symbol length L used p =4, for sf=12 and sf=14, the transmitted data symbol length L d 768/12=64 and respectively
(/>
The representation is rounded up, which may be achieved by zero padding the codeword), the corresponding pilot overhead is approximately 0.063 and 0.073, respectively.
2.2 simulation results and analysis
Fig. 5 and fig. 6 show the performance of the Turbo coding incoherent LoRa system based on the joint timing synchronization and frequency offset estimation method under the two spreading factors, respectively. Wherein, the curve marked with diamond in fig. 5 represents the non-coherent LoRa system, sf=12, f in Turbo coding d ＝45kHz、τ＝256chirps、L p And under the condition of=4, the performance of the non-coherent LoRa system of Turbo coding based on the joint timing synchronization and frequency offset estimation method is adopted. The curve marked with square in fig. 5 shows the result of coding incoherent LoRa system in Turbo, sf=12, f d And under the conditions of=0 and τ=0, the performance of the Turbo coding incoherent LoRa system based on the joint timing synchronization and frequency offset estimation method is adopted. The curve marked with diamond in fig. 6 shows the result of coding incoherent LoRa system in Turbo, sf=14, f d ＝45kHz、τ＝256chirps、L P And under the condition of=4, the performance of the non-coherent LoRa system of Turbo coding based on the joint timing synchronization and frequency offset estimation method is adopted. The curve marked with square in fig. 6 shows the result of coding incoherent LoRa system in Turbo, sf=14, f d And under the conditions of=0 and τ=0, the performance of the Turbo coding incoherent LoRa system based on the joint timing synchronization and frequency offset estimation method is adopted.
From the simulation results of fig. 5 and fig. 6, it can be found that the Turbo coding incoherent LoRa system based on the proposed synchronization method achieves BER performance very close to the ideal case, regardless of whether the spreading factor SF is 12 or 14. Specifically, when ber=10 -4 ～10 -5 When the range is in the range, the performance difference of the two is not more than 0.1dB.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
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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