Blind Frequency Offset Estimation Method for OQPSK Signals Based on Differential Constellation Trajectory Diagram

Abstract

The present invention discloses a blind frequency offset estimation method for OQPSK signals based on differential constellation trajectory diagrams. This method includes three parts: differential constellation trajectory diagram generation, symmetry axis estimation, and frequency offset estimation. The receiving end knows the symbol rate of the signal, performs even multiple oversampling, and does not require information such as training sequences for synchronization processing. The receiving end performs specific non-linear processing on the received signal, then performs differential processing at a certain differential interval, and projects it onto the complex plane to generate several differential constellation trajectory diagrams. Then, the receiving end estimates the symmetry axis and measures the symmetry of each differential constellation trajectory diagram, and selects the symmetry axis of the differential constellation trajectory diagram with the best symmetry as the final symmetry axis estimation result. Finally, the receiving end obtains the blindly estimated frequency offset value based on the specific relationship between the symmetry axis and the frequency offset, the differential interval, and the sampling rate. The invention can be used for frequency deviation estimation of systems adopting OQPSK modulation methods such as IEEE 802.15.4.

Description

Technical Field

[0001] This application relates to the field of communications, and particularly to a method for obtaining the frequency deviation of an OQPSK modulation communication system. In addition, this application can also be used in a target recognition system that needs to obtain the radio frequency fingerprint features of an OQPSK communication system. Background Art

[0002] OQPSK modulation is a constant envelope digital modulation technology developed on the basis of QPSK. It offsets the code streams of the in-phase and quadrature branches by half a symbol period in time. Due to the offset of the half symbol period of the two branches, only one branch may have a polarity reversal at a time, and there will be no phenomenon of simultaneous polarity reversal of the two branch symbols. Therefore, the phase of the OQPSK signal can only jump by 0°, ±90°, and there will be no 180° phase jump existing in QPSK modulation.

[0003] The IEEE 802.15.4 standard, namely Zigbee, describes the physical layer and media access control protocol of a low-rate wireless personal area network, and is applicable to low-power and low-rate wireless coverage within a short distance. Among them, the modulation method used by the IEEE 802.15.4 standard in the 2.4 GHz and 868 / 915 MHz frequency bands is direct sequence spread spectrum OQPSK modulation, and a half-sine shaping filter is adopted. Since the IEEE 802.15.4 standard is oriented to low-cost and low-power consumption applications, the receiving end designed based on its standard uses a non-coherent demodulation method, and the circuits of its hardware design generally also select components with better economy, and the deviation of the components themselves is relatively large, and certain frequency offsets will be generated between the transmitter and the receiver.

[0004] Carrier frequency offset is not only an important feature of the radio frequency fingerprint, but also accurate estimation and compensation of the frequency offset are required to obtain other radio frequency fingerprint features. Traditional frequency offset estimation algorithms usually achieve this through preambles or training sequences, and frequency offset search and pre-compensation are also required when the frequency offset is large, with high complexity and relatively poor real-time performance. However, passive radio frequency fingerprint recognition systems sometimes need to work in blind scenarios, that is, only a few parameter details of the transmitter are known, and the frequency offset range of the target device is large and the real-time performance requirement is high. Therefore, a pure blind and highly real-time method is needed to estimate the carrier frequency offset. Based on the symmetry of the differential constellation trajectory diagram, the present invention proposes a method for blindly estimating the frequency offset by estimating the angle of the symmetry axis of the differential constellation trajectory diagram, which greatly improves the range and real-time performance of frequency offset estimation. Summary of the Invention

[0005] The main purpose of this application is to provide a blind frequency offset estimation method for OQPSK signals based on differential constellation trajectory diagrams. Since the partial differential constellation trajectory diagrams of OQPSK signals have symmetry, and there is a specific relationship between the axis of symmetry and the signal frequency offset. Therefore, by estimating the axis of symmetry of a specific differential constellation trajectory diagram, the frequency offset of the signal can be effectively estimated without a synchronization sequence and without frequency search, which will improve the speed and range of the system's frequency offset estimation.

[0006] This application proposes a blind frequency offset estimation method for OQPSK signals based on differential constellation trajectory diagrams, including the following steps:

[0007] Step A is specifically to receive the baseband OQPSK signal after down-conversion at the receiving end where S(n) = Ae jθ(n) represents the transmitted OQPSK symbol sample point, A represents the constant phase of the OQPSK symbol, l(n) ∈ {0, 1, 2, 3} represents the phase corresponding to the transmitted symbol, where l(n) satisfies |l(n) - l(n - M)| ≠ 2 representing no phase mutation of π between adjacent symbols, M is a non-zero integer, representing the receiving end sampling rate f s is 2M times the target signal symbol rate f sym Δf represents the frequency offset to be estimated between the transmitter and the receiver, T s = 1 / f s represents the receiving end sampling time interval, ψ represents the phase offset between the transmitter and the receiver, and v(n) represents the channel noise.

[0008] Step B is specifically to perform a non-linear processing of multiplying the phase of the received baseband OQPSK signal by 4 to eliminate part of the OQPSK modulation, where ρ(n) and represent the amplitude and phase of the received baseband signal respectively, and n represents the index of the sampling point.

[0009] Step C is specifically to perform a differential processing with a differential interval of k on the non-linearly processed signal x(n) to generate M differential signals where the differential interval k is a non-zero integer multiple of M. The receiving end projects these M differential signals onto the complex plane to generate the corresponding M differential constellation trajectory diagrams DCTF t ; i represents the differential signal index, i ∈ {0, 1,..., M - 1}, m represents the index of the differential signal sampling point, the differential interval k is required to be a non-zero integer multiple of M, M is a non-zero integer, representing the receiving end sampling rate f s is 2M times the target signal symbol rate f sym of.

[0010] Step D specifically is that the receiving end estimates the axis of symmetry passing through the origin for each differential constellation trajectory diagram DCTF i by using an iterative algorithm. The iterative algorithm specifically is to initialize the axis of symmetry angle α i (0) = 0, and the iteration count j = 0; the iterative update rule is where angle(·) represents the phase-taking operation, and ToPi(·) represents mapping any angle to the interval (-π, π]; when the iteration count exceeds the maximum iteration count t max or the updated value of the symmetry angle is less than the set threshold ε, stop the iteration to obtain the estimated axis of symmetry angle α i .

[0011] Step E specifically is that the receiving end measures the symmetry of each differential constellation trajectory diagram DCTF i based on the estimated axis of symmetry angle α i to obtain the symmetry dispersion where var{·} represents the variance-taking operation.

[0012] Step F specifically is that the receiving end selects the axis of symmetry angle of the differential constellation trajectory diagram with the minimum symmetry dispersion as the final axis of symmetry angle

[0013] Step G specifically is that the receiving end, according to the relationship between the axis of symmetry angle and the frequency offset, differential interval, and sampling interval α = -8πfΔfT s k, uses the estimated axis of symmetry angle to estimate the frequency offset of the OQPSK signal as

[0014] The present invention has the following beneficial effects:

[0015] The present invention uses a data-aided-free blind frequency offset estimation method to estimate the frequency offset of the OQPSK signal, without the need to know the specific parameters of the synchronization sequence and shaping filter.

[0016] The present invention first removes part of the modulation information through non-linear processing, and then, by using the differential constellation trajectory diagram generated with a specific differential interval having good symmetry, estimates the frequency offset by estimating the axis of symmetry angle. The frequency offset estimation range is (-f sym / 8, f sym / 8).

[0017] In addition, the frequency offset estimation process of the present invention uses a fully digital implementation method, without the need to use frequency offset step search and pre-compensation, and can be quickly implemented in an actual system. Through Matlab simulation in an AWGN channel, it can be obtained that the blind frequency offset estimation method of the OQPSK signal based on the differential constellation trajectory diagram of the present invention has excellent performance at medium and high signal-to-noise ratios. Description of the Drawings

[0018] Figure 1 It is the overall block diagram for system implementation

[0019] Figure 2 It is one of the differential constellation trajectory diagrams and the symmetry axis generated under a 20 dB signal-to-noise ratio

[0020] Figure 3 It is the performance comparison of the method of the present invention under an AWGN channel for simulation Detailed Implementation Manner

[0021] The overall block diagram of the blind frequency offset estimation method for OQPSK signals based on differential constellation trajectory diagrams proposed by the present invention is as shown in the attached drawings of the specification Figure 1 Shown. Its processing mainly includes baseband signal acquisition, non-linear processing to remove partial modulation, differential constellation trajectory diagram generation, symmetry measurement and symmetry axis estimation, and frequency offset estimation based on the symmetry axis. Below, for the OQPSK spread spectrum signal modulation based on the Ti's CC2530 module, the detailed implementation manner will be described for each part:

[0022] (1) Baseband signal acquisition

[0023] In this specific implementation, the baseband signal r(n) is the baseband spread spectrum chip signal of the OQPSK modulation signal transmitted by the CC2530 module at the 2.4 GHz frequency band received by the receiving end, which complies with the IEEE 802.15.4 standard, that is

[0024]

[0025] where S(n) = Ae jθ(n) represents the transmitted OQPSK symbol sample point, A represents the constant phase of the OQPSK symbol, l(n) ∈ {0, 1, 2, 3} represents the phase corresponding to the transmitted symbol, where l(n) satisfies |l(n) - l(n - M)| ≠ 2, indicating that there is no phase mutation of π between adjacent symbols.

[0026] In this specific implementation, the symbol rate f sym of the ZigBee module = 1 Msamples / s, and the sampling rate f s of the receiving end = 10 Msamples / s. Therefore, the sampling rate of the receiving end is 10 times the symbol rate of the target signal, that is, M = 5. Δf represents the frequency offset to be estimated between the transmitting end and the receiving end, represents the receiving - end sampling time interval, ψ represents the phase deviation between the transmitting - end and the receiving - end. v(n) represents the channel noise. In this specific implementation, only Gaussian white noise is considered, that is, v(n) is a white Gaussian complex - noise sequence independent of S(n), with a mean of zero and a variance of

[0027] (2) Non - linear processing to remove part of the modulation

[0028] In this specific implementation, the receiving - end performs non - linear processing on the received base - band OQPSK signal by multiplying the phase by 4 to eliminate part of the OQPSK modulation, while keeping the amplitude part unchanged, obtaining:

[0029]

[0030] where ρ(n) and represent the amplitude and phase of the received base - band signal respectively.

[0031] (3) Differential constellation trajectory diagram generation

[0032] In this specific implementation, the receiving - end performs differential processing with a differential interval of k = 5 on the non - linearly processed signal x(n) to generate 5 differential signals:

[0033]

[0034] where the differential interval k is required to be a non - zero integer multiple of M. In this specific implementation, k = M. The receiving - end projects these 5 differential signals onto the complex plane to generate 5 corresponding differential constellation trajectory diagrams DCTF0, DCTF1, DCTF2, DCTF3, DCTF4. A typical differential constellation trajectory diagram is as shown in the appendix of the specification Figure 2 shown.

[0035] (4) Differential constellation trajectory diagram symmetry - axis estimation

[0036] In this specific implementation, the receiving - end estimates the symmetry axis passing through the origin for each differential constellation trajectory diagram DCTF t by an iterative algorithm. The iterative algorithm is as follows:

[0037] (4 - 1) First, initialize the symmetry - axis angle α i (0)=0, and the iteration number j = 0;

[0038] (4 - 2) Keep iterating according to the following iterative update rule:

[0039]

[0040] where angle(·) represents the phase extraction operation, and ToPi(·) represents mapping any angle to the interval (-π, π].

[0041] (4-3) When the number of iterations exceeds the maximum number of iterations t max = 10 or the symmetric angle update value is less than the set threshold ε = 0.001, stop the iteration and obtain the estimated axis of symmetry angle α i .

[0042] (5) Symmetry metric of the differential constellation trajectory diagram

[0043] In this specific implementation, the receiver selects the symmetric dispersion to measure the symmetry of each differential constellation trajectory diagram DCTF i The calculation method of the symmetric dispersion is as follows: i

[0044]

[0045] where var{·} represents the variance extraction operation.

[0046] (6) Axis of symmetry angle selection

[0047] In this specific implementation, the receiver selects the axis of symmetry angle of the differential constellation trajectory diagram with the minimum symmetric dispersion as the final axis of symmetry angle That is

[0048]

[0049] (7) Frequency offset estimation

[0050] In this specific implementation, according to the relationship between the axis of symmetry angle and the frequency offset, differential interval, and sampling interval α = -40πΔfT s , using the estimated axis of symmetry angle the frequency offset of the OQPSK signal can be estimated as

[0051]

[0052] Through Matlab simulation in the AWGN channel, the performance of using this method to estimate the frequency offset of the received signal is as shown in the accompanying instructions Figure 3As shown. When using this method to estimate the frequency offset of the received signal, a frequency offset of 100 KHz was added to the simulation system, and the number of sampling points N = 100. It can be seen from the simulation results that when the signal-to-noise ratio is medium to high (greater than 13 dB), the normalized mean square error of the frequency offset estimation by the frequency offset estimation method of the present invention is about twice higher than the modified Cramer-Rao bound derived in the literature "On the use of Cramer-Rao-like bounds in the presence of random nuisance parameters". At low signal-to-noise ratios, there is a threshold for the normalized mean square error result of the method of the present invention. When the signal-to-noise ratio is low to a certain extent, the noise blurs the differential constellation trajectory diagram, resulting in insufficient symmetry or excessive symmetric dispersion, leading to inaccurate estimation of the symmetry axis.

[0053] In summary, the receiving end of a communication system using the OQPSK modulation method can blindly estimate the frequency offset by estimating the angle of the symmetry axis passing through the origin of the differential constellation trajectory diagram with the best symmetry. It can accurately estimate the frequency deviation of the OQPSK system in scenarios without prior knowledge such as training sequences and shaping filters at medium to high signal-to-noise ratios, so that the system performance close to the case without frequency offset can be obtained through accurate frequency offset estimation and compensation in the case of a large frequency offset in the system, or conditions can be provided for obtaining the radio frequency fingerprint characteristics of the OQPSK modulation communication system.

[0054] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A blind frequency offset estimation method for OQPSK signals based on differential constellation trajectory diagrams, characterized in that: It includes the following steps: Step A, the receiving end samples at a sampling rate f s to obtain the baseband OQPSK signal r(n); Step B: The receiving end performs a non-linear processing of multiplying the phase of the received baseband OQPSK signal r(n) by 4 to eliminate part of the OQPSK modulation to obtain x(n), where n represents the index of the sampling point; Step C: The receiver performs differential processing on the non-linearly processed signal x(n) with a differential interval of k to generate M differential signals and the corresponding differential constellation trajectory diagram DCTF i , where i represents the differential signal index, i ∈ {0, 1,..., M−1}, m represents the index of the differential signal sampling point, the differential interval k is required to be a non-zero integer multiple of M, M is a non-zero integer, and the receiver sampling rate f s is 2M times the target signal symbol rate f sym ; Step D, the receiver estimates each differential constellation trajectory figure DCTF i The symmetry axis angle α passing through the origin i ; Step E, the receiving end performs symmetry measurement on each differential constellation trajectory diagram DCTF according to the estimated symmetry axis angle α i for each differential constellation trajectory diagram DCTF i to perform symmetry measurement; Step F, the receiving end selects the symmetry axis angle of the differential constellation trajectory diagram with the best symmetry as the final symmetry axis angle Step G, the receiving end estimates the frequency offset based on the estimated axis of symmetry angle differential interval k and sampling rate f s to obtain the frequency offset estimation result of the OQPSK signal 2. The blind frequency offset estimation method for OQPSK signals based on differential constellation trajectory diagrams according to claim 1, wherein The sampling rate f described in step A s is an even multiple of the OQPSK symbol rate, including directly setting even multiple sampling at the receiving end and resampling to an even number after non-even multiple sampling. n represents the index of the sampling point.

3. The blind frequency offset estimation method for OQPSK signals based on differential constellation trajectory diagrams according to claim 1, characterized in that The differential signal described in step C is i represents the differential signal index, i ∈ {0, 1, ..., M-1}, and m represents the index of the differential signal sampling point. represents the complex conjugate of the signal. The differential interval k is required to be a non-zero integer multiple of M, where M is a non-zero integer, and the receiving end sampling rate f s is 2M times the target signal symbol rate f sym of.

4. The blind frequency offset estimation method for OQPSK signals based on differential constellation trajectory diagrams according to claim 1, characterized in that, The differential constellation trajectory figure DCTF described in step C i is generated by projecting the differential signal onto the complex plane.

5. The blind frequency offset estimation method for OQPSK signals based on differential constellation trajectory diagram according to claim 1, wherein, The symmetry axis angle estimation algorithms described in Step D include the iterative estimation method and the minimum asymmetric energy term method.

6. The blind frequency offset estimation method for OQPSK signals based on the differential constellation trajectory diagram according to claim 1, characterized in that The symmetry measurement method described in step E includes symmetric dispersion where var{·} represents the variance operation and angle(·) represents the phase operation.

7. The blind frequency offset estimation method for OQPSK signals based on the differential constellation trajectory diagram according to claim 6, characterized in that The selection of the final axis of symmetry angle described in step F includes selecting the axis of symmetry angle of the differential constellation trajectory diagram with the smallest symmetry dispersion 8. The blind frequency offset estimation method for OQPSK signals based on differential constellation trajectory diagrams according to claim 1, wherein The frequency offset estimation formula described in step G is 9. The blind frequency offset estimation method for OQPSK signals based on differential constellation trajectory diagram according to claim 1, wherein The method can be used for communication systems compatible with the IEEE 802.15.4 standard and other communication systems using the OQPSK modulation method.

Images