A GMSK receiving method based on blind equalization

Abstract

The present invention discloses a GMSK receiving method based on blind equalization, comprising the following steps: down-converting the received GMSK signal to baseband; low-pass filtering the GMSK baseband waveform; capturing and synchronizing the received signal based on the pseudo-random sequence in the frame header; equalizing the received GMSK signal using a CMA constant modulus algorithm; derotating the equalized signal; estimating the phase offset of the derotated signal and performing phase compensation; demodulating the soft information, extracting the real part, and making a decision. This method effectively solves the inter-symbol interference problem caused by multipath channels in the current GMSK system, achieving a low-complexity equalization and receiving method suitable for high-speed GMSK transmission.

Description

Technical Field

[0001] The present invention relates to the field of wireless communications, and in particular to a GMSK receiving method based on blind equalization. Background Art

[0002] Gaussian Minimum Shift Keying (GMSK) is a continuous phase modulation method that features a constant envelope, low out-of-band radiation, good power spectrum characteristics, and robust interference resistance. Consequently, many communications standards, such as the Global System for Mobile Communication (GSM), use GMSK.

[0003] Most existing GMSK systems use the Maximum Likelihood Sequence Estimation (MLSE) equalization method. MLSE is optimal in terms of minimizing the probability of sequence re-errors. MLSE receiver architectures are typically implemented using the Viterbi algorithm. In GSM systems, GMSK operates at a relatively low symbol rate of 270.833 kbit / s. The multipath delay in typical urban environments is approximately 5 µs, generally within the timeframe of five GMSK symbols. GSM provides eight 26-bit training sequences. The middle 16 bits of each training sequence exhibit good correlation characteristics. The five bits preceding and following each sequence serve as the cyclic prefix and suffix of the middle sequence. Their autocorrelation functions exhibit the following characteristics:

[0004]

[0005] Therefore, when the maximum channel delay spread is less than or equal to 5 symbol periods, the autocorrelation function of the training sequence is the unit matrix. The received signal is represented as y and the training sequence matrix is ​​represented as M:

[0006]

[0007] Where P is the bit length with good autocorrelation in the training sequence, which is 16 here; L is the length of the cyclic prefix and cyclic suffix, which is 5 here. According to the LS channel estimation method, the channel can be obtained:

[0008]

[0009] Since MHM is a diagonal matrix, the above formula can be simplified to That is, the channel estimation can be obtained simply by correlating the received signal with the training sequence. The number of taps obtained by the channel estimation is L=5.

[0010] For any sequence of GMSK signals, there will be a state transition path that matches it. The GMSK signal demodulation principle based on the Viterbi algorithm is to sequentially search the network and find the best sequence that maximizes the likelihood function among all sequences. Any node in a GMSK signal has only two corresponding paths in the next cycle: 1 or -1. Therefore, for a signal with a correlation length of L = 5, there are a total of 2L-1 = 16 paths. However, when the GMSK symbol rate increases to Mbps, the number of channel taps increases, and the complexity of the Viterbi algorithm increases. For example, when the symbol rate is 10 Mbps, the channel requires at least 50 tap coefficients and at least 249 states, which cannot be achieved by the MLSE equalization algorithm. Therefore, a low-complexity equalization method and reception method suitable for high-speed GMSK transmission is needed. Summary of the Invention

[0011] In order to solve the inter-symbol interference problem caused by the multipath channel under the GMSK system, in a first aspect, the present invention provides a GMSK receiving method based on blind equalization, comprising the following steps:

[0012] Step S1: down-converting the received GMSK signal to baseband;

[0013] Step S2: performing waveform low-pass filtering on the down-converted GMKS signal;

[0014] Step S3: Capture and synchronize the filtered GMSK signal according to the pseudo-random sequence of the frame header;

[0015] Step S4: using a CMA constant modulus algorithm to equalize the captured and synchronized GMSK signal;

[0016] Step S5: Derotate the equalized GMSK signal;

[0017] Step S6: estimating the phase offset of the derotated GMSK signal and performing phase compensation;

[0018] Step S7: demodulate the phase-compensated GMSK signal to obtain the real part of the soft information and make a decision.

[0019] Furthermore, in step S2, a raised cosine filter is used as a low-pass filter for filtering.

[0020] Furthermore, in step S3, the locally stored pseudo-random sequence is used for sliding correlation with the received signal, and the frame header is captured and the bit is synchronized for the GMSK signal according to the set threshold value.

[0021] Furthermore, in step S4, an equalizer is used to equalize the GMSK signal, and the tap coefficients of the equalizer are obtained by the steepest descent method, as shown in the following expression:

[0022] f(k+1)=f(k)-μy * (k)e(k)

[0023] =f(k)-μy(k) * z(k)[R p -z(k) 2 ].

[0024] Where f(k) is a vector representing the tap coefficient of the previous equalizer, f(k+1) represents the tap coefficient of the current iteration; μ is a sufficiently small step size factor; y(k) is the received signal vector; () * Represents the conjugate transpose of a vector; R p is a positive constant representing the modulus of the received signal and is used to control the amplitude of the equalizer output; e(k) is the error between the square of the modulus of the received signal vector and the square of the GMSK theoretical modulus.

[0025] Furthermore, in step S5, the derotation is to multiply the received k-th sample by a rotation factor, and a new sequence can be obtained after the derotation:

[0026]

[0027] Among them, z(k) is the GMSK sequence after CMA equalization, z(k) can be further expanded as, I n is the information codeword, C 0k-n is the impulse response, n k is Gaussian white noise, j -k is the rotation factor.

[0028] Furthermore, in step S6, estimating the phase offset includes: erasing the modulated signal using a simple square demodulation algorithm, summing and averaging N adjacent symbols, and applying an acrtan function to the accumulated symbols to return a fixed phase offset value.

[0029] On the other hand, the present invention also provides a GMSK receiving system based on blind equalization, the system comprising the following modules:

[0030] A down-conversion module, used for down-converting the received GMSK signal to baseband;

[0031] A low-pass filter module is used to perform waveform low-pass filtering on the down-converted GMSK signal;

[0032] Capture bit synchronization module, used to capture and synchronize the filtered GMSK signal according to the pseudo-random sequence of the frame header;

[0033] Blind equalization module, used to equalize the GMSK signal after capture and synchronization using CMA constant modulus algorithm;

[0034] A derotation module is used to derotate the equalized GMSK signal;

[0035] The phase offset compensation module is used to estimate the phase offset of the derotated GMSK signal and perform phase compensation.

[0036] The decision module is used to obtain the real part of the phase-compensated GMSK signal and make a decision.

[0037] In another aspect, the present invention further provides an electronic device, wherein the electronic device comprises:

[0038] a memory for storing instructions; and

[0039] The processor is configured to call the instructions stored in the memory to execute the GMSK receiving method based on blind equalization.

[0040] On the other hand, the present invention further provides a computer-readable storage medium storing instructions, which, when executed by a processor, executes the GMSK receiving method based on blind equalization.

[0041] Beneficial Effects: The GMSK demodulation method provided by the present invention can correct GMSK signal distortion caused by multipath fading under high-speed transmission conditions, helping the receiver to perform subsequent correct demodulation. Compared with existing Viterbi equalization techniques, this method has lower algorithm complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Shown is a schematic diagram of the process of the present invention;

[0043] Figure 2 Shown is a structural diagram of the equalizer of the present invention;

[0044] Figure 3 shows a block diagram of the phase deviation estimation algorithm;

[0045] Figure 4 The signal constellation diagram obtained by GMSK signal bit synchronization in the embodiment is shown.

[0046] Figure 5 Cost function convergence curve in the blind equalization process in the embodiment

[0047] Figure 6 is a signal constellation diagram obtained after blind equalization in the embodiment;

[0048] Figure 7 is the signal constellation diagram obtained after derotation in the embodiment;

[0049] Figure 8 is a signal constellation diagram obtained after compensating for phase deviation in the embodiment;

[0050] Figure 9 , which is the soft signal constellation diagram finally obtained by demodulation in the embodiment. DETAILED DESCRIPTION

[0051] The present invention will now be discussed with reference to several exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the present invention, rather than to imply any limitation on the scope of the present invention.

[0052] As used herein, the term "including" and variations thereof are to be interpreted as open-ended terms meaning "including, but not limited to." The term "based on" is to be interpreted as "based, at least in part, on." The terms "one embodiment" and "an embodiment" are to be interpreted as meaning "at least one embodiment." The term "another embodiment" is to be interpreted as meaning "at least one other embodiment."

[0053] Example 1

[0054] like Figure 1 As shown, the present invention provides a receiving method based on blind equalization, comprising the following steps: down-converting the received GMSK signal to baseband; low-pass filtering the GMSK baseband waveform to remove noise and high-frequency components; capturing and synchronizing the received signal according to the pseudo-random sequence of the frame header, and extracting it to a rate of one times the Rs; then using the CMA constant modulus algorithm to equalize the received GMSK signal to eliminate inter-symbol interference caused by the multipath channel; derotating the equalized signal; performing phase offset and phase compensation on the derotated signal, and finally demodulating the soft information and making a judgment, as follows:

[0055] The transmitted sequence is denoted as b(n). The information sequence is precoded at the transmitter to obtain the codeword I(n). The transmitted waveform is denoted as s(t), the channel impulse response is denoted as h(t), and the noise is denoted as n(t). The received signal after downconversion can be expressed as:

[0056] y(t)=s(t)*h(t)+n(t)

[0057] The received signal is sampled to obtain y(n), and a raised cosine filter is used as a low-pass filter to filter the received GMSK channel, removing high-frequency components and out-of-band noise without introducing inter-symbol interference. Due to the non-causal nature of the raised cosine filter, a truncation process is performed on it. In this embodiment, a truncation coefficient of 6 is selected. Subsequently, a locally stored pseudo-random sequence is used to slide correlate with the received signal, and the frame header and bit synchronization of the received signal are performed according to the set threshold value. Figure 4As shown, the signal constellation diagram obtained by GMSK signal bit synchronization is obtained.

[0058] The signal after bit synchronization is then equalized to correct the signal distortion caused by multipath fading, helping the receiver to demodulate correctly. The blind equalization algorithm does not need to add additional pilot sequences, and can adaptively equalize the signal using only the received signal sequence. At the same time, blind equalization is robust to frequency offset and phase offset, so the correction of frequency offset and phase offset can be completed after equalization. Figure 2 As shown, the equalizer is an FIR filter with a length of N = 2L + 1, and the tap coefficients of the filter are expressed as:

[0059] f(k)=[f(kL),…f(k-1),f(k),f(k+1),…f(k+L)]

[0060] Before the equalizer converges, the filter tap coefficients are continuously updated, and the equalizer output z(k) can be calculated as follows:

[0061]

[0062] Define the cost function J(k) as:

[0063]

[0064] Where Y[z(k)] is a nonlinear function of the output sequence z(k). Since the GMSK system is a constant envelope signal, this system uses the constant modulus algorithm (CMA), and the cost function of the algorithm is:

[0065]

[0066] Where Rp is the modulus of the received signal. Define the error function e(k) as the gradient of Y[z(k)] with respect to z(k), that is:

[0067]

[0068] The error function e(k) represents the error between the statistics of the equalizer output sequence z(k) and the statistics of the expected signal. When the error function e(k) approaches zero, the cost function approaches the minimum value, such as Figure 5 As shown in Figure 1, it is the convergence curve of the cost function during the blind equalization process.

[0069] The equalizer tap coefficient update process is defined as:

[0070]

[0071] Updating the tap coefficients is an iterative process, with the iterative step size being the gradient of the cost function with respect to the tap weight vector multiplied by a step size factor, μ. The condition for tap coefficient convergence is that the cost function reaches its minimum, which is the same condition as the error function approaching zero. Therefore, the convergence of the equalization algorithm is the process of bringing the equalizer output sequence closer to the desired optimal sequence. The step size factor, μ, affects the convergence speed of the equalization algorithm and the residual error after convergence.

[0072] The output sequence z(k) of the equalizer can be expressed as:

[0073] z(k)=f(k-1)y(k)

[0074] Substituting the above formula into the equalizer tap coefficient update process, the equalizer tap coefficient update expression can be obtained:

[0075] f(k+1)=f(k)-μy * (k)e(k)

[0076] =f(k)-μy(k) * z(k)[R p -z(k) 2 ]

[0077] Where f(k) is a vector representing the tap coefficient of the previous equalizer, f(k+1) represents the tap coefficient of the current iteration; μ is a sufficiently small step size factor; y(k) is the received signal vector; () * Represents the conjugate transpose of a vector; R p is a positive constant representing the modulus of the received signal and is used to control the amplitude of the equalizer output; e(k) is the error between the square of the modulus of the received signal vector and the square of the GMSK theoretical modulus.

[0078] It can be seen from the equalizer weight vector update formula that the constant modulus algorithm has low computational complexity, is simple and easy to operate.

[0079] After blind equalization, Figure 6 As shown, the signal constellation diagram after blind equalization is obtained, and the sequence z(k) can be considered as the transmitted signal obtained through a channel with no multipath and only one phase angle deflection, and can be demodulated.

[0080] GMSK modulation is a nonlinear modulation with a constant envelope. Laurent's decomposition theorem shows that a binary CPM signal with any modulation index can be viewed as a linear combination of Q time-limited PAM signals. The Q pulse signals are denoted by C0 to CQ-1, and Ik is the codeword obtained by precoding the information sequence. The GMSK signal can be expressed as:

[0081]

[0082] When BT>0.25, most of the GMSK energy is concentrated in the impulse response C0, so the linear approximate expression of the GMSK signal is:

[0083]

[0084] The formula shows that the GMSK signal can be considered as the data sequence Ikjk after the impulse response is C0. Therefore, after CMA equalization, the GMSK has the following form:

[0085]

[0086] In the formula, jk is equivalent to rotating the signal In on the constellation diagram. Multiplying the sequence by jk will give a new sequence:

[0087]

[0088] The derotation operation is as shown above, multiplying the received k-th sample by a rotation factor jk, such as Figure 7 As shown in Figure 1, the derotated signal constellation is obtained. From the perspective of hardware implementation, derotation can be achieved by simply changing the sign and exchanging the real and imaginary parts, requiring relatively little hardware overhead.

[0089] Since C0 has the largest information weight at the current moment, and due to the existence of jn-k, the weights of the adjacent previous and next code elements to the sequence at the current moment differ by 90°, and the weights of the remaining code elements to the current moment are small and can be ignored. Therefore, if z(k) obtained by blind equalization has no phase bias, the transmitted sequence In can be deciphered by directly taking the real part of u(k); however, since z(k) obtained by blind equalization often has a fixed phase bias, derotation cannot eliminate this fixed phase bias. Therefore, this fixed phase bias needs to be estimated and compensated after derotation. To estimate the phase bias, the sequence u(k) needs to be demodulated, and a simple square demodulation algorithm is used to demodulate the sequence u(k) and erase the modulation signal. Then the N adjacent symbols are summed and averaged to reduce the influence of additive Gaussian noise. Finally, the accumulated symbols are used through the acrtan function to return the fixed phase bias value, thereby obtaining an estimated value of the phase bias. Finally, the phase offset is compensated on the sequence u(k), as Figure 8 As shown in , the signal constellation diagram after phase offset compensation is obtained, and the real part is taken to obtain the final soft information, as shown in Figure 9 As shown in FIG, the final signal constellation diagram is obtained, and the final result can be obtained by judging the soft information.

[0090] Example 2

[0091] The present invention also provides a GMSK receiving system based on blind equalization, the system comprising the following modules:

[0092] A down-conversion module, used for down-converting the received GMSK signal to baseband;

[0093] A low-pass filter module is used to perform waveform low-pass filtering on the down-converted GMSK signal;

[0094] Capture bit synchronization module, used to capture and synchronize the filtered GMSK signal according to the pseudo-random sequence of the frame header;

[0095] Blind equalization module, used to equalize the GMSK signal after capture and synchronization using CMA constant modulus algorithm;

[0096] A derotation module is used to derotate the equalized GMSK signal;

[0097] The phase offset compensation module is used to estimate the phase offset of the derotated GMSK signal and perform phase compensation.

[0098] The decision module is used to obtain the real part of the phase-compensated GMSK signal and make a decision.

[0099] Example 3

[0100] The present invention further provides an electronic device, wherein the electronic device comprises:

[0101] a memory for storing instructions; and

[0102] The processor is configured to call the instructions stored in the memory to execute the GMSK receiving method based on blind equalization.

[0103] Example 4

[0104] The present invention also provides a computer-readable storage medium, in which instructions are stored. When the instructions are executed by a processor, the GMSK receiving method based on blind equalization is executed.

[0105] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the embodiments. Those skilled in the art will readily appreciate that other variations or modifications based on the above descriptions are possible. It is not necessary and impossible to enumerate all embodiments here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A GMSK receiving method based on blind equalization, characterized in that: The following steps are involved: Step S1: down-converting the received GMSK signal to baseband; Step S2: performing waveform low-pass filtering on the down-converted GMSK signal; Step S3: Capture and synchronize the filtered GMSK signal according to the pseudo-random sequence of the frame header; Step S4: using a CMA constant modulus algorithm to equalize the captured and synchronized GMSK signal; Step S5: Derotate the equalized GMSK signal; Step S6: estimating the phase offset of the derotated GMSK signal and performing phase compensation; Step S7: demodulate the phase-compensated GMSK signal to obtain the real part of the soft information and make a decision; In step S4, an equalizer is used to equalize the GMSK signal. The tap coefficients of the equalizer are obtained by the steepest descent method, as shown in the following expression: f(k+1)=f(k)-μy * (k)e(k) =f(k)-μy(k) * z(k)[R p -|z(k)| 2 ] Where f(k) is a vector representing the tap coefficient of the previous equalizer, f(k+1) represents the tap coefficient of the current iteration; μ is a sufficiently small step size factor; y(k) is the received signal vector; () * Represents the conjugate transpose of a vector; R p is a positive constant representing the modulus of the received signal, which is used to control the amplitude of the equalizer output; e(k) is the error between the square modulus of the received signal vector and the square modulus of the GMSK theoretical vector; z(k) is the GMSK sequence after CMA equalization; In step S5, the derotation is to multiply the received k-th sample by a rotation factor, and a new sequence can be obtained after the derotation: Among them, I n is the information codeword, C 0k-n is the impulse response, n k is Gaussian white noise, j -k is the rotation factor.

2. The GMSK receiving method based on blind equalization according to claim 1, wherein In step S2, a raised cosine filter is used as a low-pass filter to perform filtering.

3. The GMSK receiving method based on blind equalization according to claim 1, wherein in step S3, a locally stored pseudo-random sequence is slidingly correlated with the received signal, and frame header capture and bit synchronization are performed on the filtered GMSK signal according to a set threshold value.

4. The GMSK receiving method based on blind equalization according to claim 1, wherein in step S6, estimating the phase offset comprises: A simple square demodulation algorithm is used to erase the modulated signal, and the N adjacent symbols are summed and averaged. The accumulated symbols are then passed through the acrtan function to return a fixed phase offset value.

5. A GMSK receiving system based on blind equalization, the system comprising the following modules: A down-conversion module, used for down-converting the received GMSK signal to baseband; A low-pass filter module is used to perform waveform low-pass filtering on the down-converted GMSK signal; Capture bit synchronization module, used to capture and synchronize the filtered GMSK signal according to the pseudo-random sequence of the frame header; Blind equalization module, used to equalize the GMSK signal after capture and synchronization using CMA constant modulus algorithm; A derotation module is used to derotate the equalized GMSK signal; Phase offset compensation module, used to estimate the phase offset of the derotated GMSK signal and perform phase compensation; A decision module is used to obtain the real part of the phase-compensated GMSK signal and make a decision; The blind equalization module uses an equalizer to equalize the GMSK signal. The tap coefficient of the equalizer is obtained by the steepest descent method, as shown in the following expression: f(k+1)=f(k)-μy * (k)e(k) =f(k)-μy(k) * z(k)[R p -|z(k)| 2 ] Where f(k) is a vector representing the tap coefficient of the previous equalizer, f(k+1) represents the tap coefficient of the current iteration; μ is a sufficiently small step size factor; y(k) is the received signal vector; () * Represents the conjugate transpose of a vector; R p is a positive constant representing the modulus of the received signal, which is used to control the amplitude of the equalizer output; e(k) is the error between the square modulus of the received signal vector and the square modulus of the GMSK theoretical vector; z(k) is the GMSK sequence after CMA equalization; In the derotation module, the derotation is to multiply the received k-th sample by a rotation factor, and a new sequence can be obtained after the derotation: Among them, I n is the information codeword, C 0k-n is the impulse response, n k is Gaussian white noise, j -k is the rotation factor.

6. An electronic device, wherein: The electronic device comprises: a memory for storing instructions; and A processor, configured to call the instructions stored in the memory to execute the GMSK receiving method based on blind equalization according to any one of claims 1 to 4.

7. A computer-readable storage medium storing instructions, wherein when the instructions are executed by a processor, the GMSK receiving method based on blind equalization according to any one of claims 1 to 4 is executed.

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