A Demodulation Method for GFSK Signals of a Bluetooth Comprehensive Tester

Abstract

The present invention discloses a demodulation method for GFSK signals of a Bluetooth comprehensive tester, which includes clarifying the modulation method of GFSK signals, defining the wireless channel model of the Bluetooth comprehensive tester, defining the maximum likelihood probability calculation method for the signals of the Bluetooth comprehensive tester based on the maximum likelihood probability theory, calculating the conditional probability of segmented received signals, and demodulation based on the viterbi search algorithm and probability scale calculation. By establishing the maximum likelihood probability of Bluetooth signals 0 and 1, and making group decisions according to the magnitude of the received signals and the magnitude of the probabilities, the present invention provides a basis for soft demodulation decisions for the demodulation of received signals, improving the demodulation correctness of the 0 and 1 bit streams; the present invention uses Bluetooth soft decisions to avoid decision errors due to a strong interference environment; in addition, the present invention combines the maximum likelihood probability and the viterbi search algorithm, and uses the demodulation outputs of soft decisions 0 and 1 to correctly demodulate GFSK signals.

Description

Technical Field

[0001] The present invention relates to a method for demodulating signals, specifically a method for demodulating GFSK signals of a Bluetooth comprehensive tester that combines the maximum likelihood probability and the viterbi search algorithm, belonging to the technical field of wireless communication signal processing. Background Art

[0002] Bluetooth devices are widely used in smartphones and other wireless communication-related devices. With the rapid development of wireless communication technology, people's requirements for Bluetooth technology are also getting higher and higher. A Bluetooth comprehensive tester is a high-tech device that can perform various function tests on Bluetooth devices. The Bluetooth comprehensive tester can help manufacturers and developers ensure that their products meet the Bluetooth standards and operate properly. Therefore, a high-performance, convenient and efficient Bluetooth comprehensive tester has become an increasingly urgent development tool.

[0003] A high-performance and efficient Bluetooth comprehensive tester requires reliable support from Bluetooth physical layer algorithms. For Bluetooth physical layer algorithms, GFSK demodulation at the receiving end is one of the key technologies. Although various mature solutions have been proposed for the GFSK demodulation algorithm of Bluetooth signals, such as the widely used phase difference decision method and a method, device, system and electronic device for demodulating Bluetooth GFSK signals disclosed in the publication number CN115941409A. However, the development of Bluetooth comprehensive testers under various unpredictable test environments poses higher requirements for GFSK demodulation. Especially during the product implementation process, the GFSK demodulation of the physical layer of the Bluetooth comprehensive tester is affected by unknown sudden interferences, which brings certain difficulties to the GFSK demodulation of Bluetooth signals. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for demodulating GFSK signals of a Bluetooth comprehensive tester that combines the maximum likelihood probability and the viterbi search algorithm to solve at least one of the above technical problems. It aims at the GFSK demodulation of Bluetooth signals under various interference conditions and proposes a technology for GFSK demodulation of Bluetooth frame signals during the development process of Bluetooth comprehensive testers, which can correctly demodulate Bluetooth signals, thus laying a solid foundation for the Bluetooth comprehensive tester to correctly parse the signal frame header and payload information.

[0005] The present invention achieves the above purpose through the following technical solutions: A method for demodulating GFSK signals of a Bluetooth comprehensive tester, the demodulation method includes the following steps:

[0006] Step 1. Define the modulation method of the Bluetooth GFSK signal: According to the Bluetooth protocol, the modulation of the GFSK signal of the Bluetooth synthesizer tester needs to pass through a Gaussian filter. The bandwidth of the Gaussian filter affects the spectrum of the GFSK signal. The product BT of the 3dB bandwidth of the Gaussian filter and the binary symbol period T is the main parameter of the Gaussian filter. The smaller the value of BT, the longer the duration of the impulse response;

[0007] Step 2. Define the wireless channel model of the Bluetooth synthesizer tester;

[0008] Step 3. Define the maximum likelihood probability calculation method of the Bluetooth synthesizer tester signal based on the maximum likelihood probability theory;

[0009] Step 4. Calculate the conditional probability of the received signal in segments;

[0010] Step 5. Demodulation based on the viterbi search algorithm and probability scale calculation.

[0011] As a further solution of the present invention: In Step 1, the impulse response expression of the Gaussian filter is:

[0012]

[0013] In the formula: t represents time, h(t) represents the channel impulse response, T is the signal period size, and σ is the signal variance;

[0014]

[0015] In the formula: is the signal variance, B is the signal modulation coefficient, and T is the signal period size.

[0016] As a further solution of the present invention: In Step 1, if the input signal x(t) is a bipolar square wave corresponding to the binary data to be transmitted, the output after the bipolar square wave passes through the Gaussian filter is:

[0017]

[0018] In the formula: m(t; T) represents a pulse with a period of T, t is the time variable, and g(t) represents a rectangular pulse after transmission through the channel h(t);

[0019] The rectangular pulse is defined as:

[0020]

[0021] After derivation, the expression is obtained:

[0022]

[0023] Where: g(t) is the pulse signal after Gaussian modulation, T is the period size, Q(t) is the Gaussian function, B is the modulation coefficient, and t is the time variable;

[0024]

[0025] Where: Q(t) is the Gaussian function and t is the time variable.

[0026] As a further solution of the present invention: in step one, assuming that the sequence x(n) is the discrete-time sampling of the input signal x(t) and is a bipolar non-return-to-zero code, the phase expression after GFSK signal modulation is:

[0027]

[0028] Where: g(tau-nT) is the pulse signal after Gaussian modulation;

[0029] The expression of the GFSK signal after modulation at the carrier frequency of f c is:

[0030]

[0031] Where: s(t) is the signal after GFSK modulation, B is the modulation coefficient, phi(t) is the signal phase, and phi0 is the initial phase.

[0032] As a further solution of the present invention: in step two, it specifically includes:

[0033] The transmitting-end signal s(t) is transmitted through the wireless channel n(t), and the receiving-end signal R(t) is expressed as:

[0034] R(t) = s(t) + n(t)

[0035] Where: s(t) is the transmitting-end signal; n(t) is Gaussian white noise, and the probability distribution it satisfies is:

[0036]

[0037] Where: μ is the mean, σ 2 is the variance, p(n) is the probability distribution function, and N0 is the signal length.

[0038] As a further solution of the present invention: in step three, when the receiving-end signal is R(t), the binary bit stream b m , is described using the maximum likelihood probability as P(b m |R(t)), that is, it satisfies the Bayesian probability:

[0039]

[0040] When b0 is 0, the value of the GFSK signal modulation is 0 or -1. At this time, for the received signal R(t), the conditional probability that the carried information b0 is 0 is:

[0041]

[0042] In the formula: real() represents taking the real part of the complex signal;

[0043] For the received signal R(t), the conditional probability that the carried information b0 is 1 is:

[0044]

[0045] When b0 = 1, if the following conditions are met:

[0046]

[0047] Then the likelihood probability ratio for b0 is:

[0048]

[0049] In the formula: real() represents taking the real part of the complex signal.

[0050] As a further solution of the present invention: In step four, it specifically includes: Based on the modulation structure of the GFSK signal, when real ( R(t) ) ≤ -1, the likelihood probability ratio is:

[0051]

[0052] Taking the logarithm operation on both sides of the above formula gives:

[0053]

[0054] In the formula: ln() represents the logarithm operation with the natural exponential e as the base;

[0055] When -1 ≤ real( R(t) ) <0 , 0 ≤ real( R(t) ) <1 , the likelihood probability ratio is:

[0056]

[0057] Taking the logarithm on both sides of the above formula gives:

[0058]

[0059] When real (R(t) ) ≥1 , the likelihood probability ratio is:

[0060]

[0061] Taking the logarithm of both sides of the above formula gives:

[0062]

[0063] As a further solution of the present invention: Step Five, use the viterbi search algorithm for the demodulation algorithm:

[0064] Construct a trellis grid diagram;

[0065] Perform iterative estimation based on the received IQ complex data to be 0 or 1 to achieve demodulation;

[0066] Then calculate the branch metric values one by one for the received IQ complex data, select the minimum path at each level, discard other paths, and continue until the minimum path is selected and the demodulated bit stream is obtained by backtracking.

[0067] As a further solution of the present invention: The scale calculation of path search uses the maximum likelihood probability measurement, that is:

[0068]

[0069] The beneficial effects of the present invention are:

[0070] 1) By establishing the maximum likelihood probability of Bluetooth signals 0 and 1, the present invention makes a grouped decision based on the magnitude and probability of the received signal, providing a soft demodulation decision basis for the demodulation of the received signal and improving the demodulation correctness of the 0 and 1 bit streams;

[0071] 2) The present invention combines the viterbi search algorithm and searches for the optimal decision path based on different ranges of the received signal, and further uses Bluetooth soft decision to avoid decision errors caused by a strong interference environment;

[0072] 3) The present invention combines the maximum likelihood probability and the viterbi search algorithm, and uses the demodulation output of soft decision 0 and 1, which ensures the correct demodulation of GFSK signals;

[0073] 4) The method in the present invention has strong robustness for the parameter tests of a Bluetooth comprehensive tester for GFSK demodulation in an environment with strong noise interference. Description of the Drawings

[0074] Figure 1 It is the demodulation flowchart of the present invention combining the maximum likelihood probability and the viterbi search algorithm;

[0075] Figure 2 Schematic diagram of path search for the grid graph of the present invention;

[0076] Figure 3 GFSK modulation waveform with 64 sampling points in one symbol period of the present invention;

[0077] Figure 4 Graph showing the change of GFSK demodulation bit error rate with SNR of the present invention. Detailed implementation manners

[0078] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0079] Embodiment, the present invention provides a method for demodulating the GFSK signal of a Bluetooth comprehensive tester by combining the maximum likelihood probability and the viterbi search algorithm. The demodulation is performed by combining the maximum likelihood probability of the Bluetooth signal and the viterbi search algorithm. For the GFSK signal demodulation of a Bluetooth comprehensive tester, the grouping of the received signal is judged by using the method of maximum likelihood probability, so as to facilitate the grouping and path division of the viterbi search algorithm. The method of using the maximum likelihood probability for grouping judgment here is a soft decision calculation method, which avoids the wrong judgment of hard decision. This method is particularly suitable for the comprehensive test environment with strong interference intensity. In the viterbi search process, the calculation of the path weight size also uses the method of conditional probability, which also plays a role in more accurately judging the possibility of 0 and 1.

[0080] As Figure 1 shown, the specific steps of this demodulation method include:

[0081] First: It is necessary to clarify the modulation method of the GFSK signal of the Bluetooth comprehensive tester: According to the Bluetooth protocol, the modulation of the GFSK signal of the Bluetooth comprehensive tester needs to pass through a Gaussian filter. The bandwidth of the Gaussian filter affects the modulation spectrum of the GFSK signal. Therefore, the product BT of the 3dB bandwidth of the Gaussian filter and the binary symbol period T is the main parameter of the Gaussian filter. The smaller the value of BT, the longer the pulse response duration.

[0082] In actual design, the pulse response duration is usually truncated as needed. The impulse response expression of the Gaussian filter is:

[0083]

[0084] Where: t represents time, h(t) represents the channel impulse response, T is the signal period size, and σ is the signal variance;

[0085]

[0086] Where: is the signal variance, B is the signal modulation coefficient, and T is the signal period size.

[0087] Assume that the input signal x(t) is a bipolar square wave corresponding to the binary data to be transmitted. The output after passing through a Gaussian filter is:

[0088]

[0089] Where: m(t; T) represents a pulse with a period of T, t is the time variable, and g(t) represents a rectangular pulse after transmission through the channel h(t);

[0090] The rectangular pulse is defined as:

[0091]

[0092] After derivation, the expression is obtained:

[0093]

[0094] Where: g(t) is the pulse signal after Gaussian modulation, T is the period size, Q(t) is the Gaussian function, B is the modulation coefficient, and t is the time variable;

[0095]

[0096] Where: Q(t) is the Gaussian function and t is the time variable.

[0097] Assume that the sequence x(n) is the discrete-time sampling of the input signal x(t). If it is a bipolar non-return-to-zero code, the phase expression after GFSK signal modulation is:

[0098]

[0099] Where: g(tau - nT) is the pulse signal after Gaussian modulation;

[0100] The expression of the GFSK signal after modulation at the carrier frequency of f c is:

[0101]

[0102] Where: s(t) is the signal after GFSK modulation, B is the modulation coefficient, phi(t) is the signal phase, and phi0 is the initial phase.

[0103] The time-domain waveform diagram of GFSK signal modulation is as follows Figure 3 shown.

[0104] Second: In this embodiment, it is necessary to define the wireless channel model of the Bluetooth comprehensive tester.

[0105] The signal s(t) at the transmitter is transmitted through the wireless channel n(t), and the received signal R(t) is expressed as:

[0106] R(t) = s(t) + n(t)

[0107] Here, s(t) is the signal at the transmitter; n(t) is Gaussian white noise, which satisfies the following probability distribution:

[0108]

[0109] In the formula: μ is the mean, σ 2 is the variance, p(n) is the probability distribution function, and N0 is the signal length.

[0110] Third: Based on the maximum likelihood probability theory, define the calculation method of the maximum likelihood probability of the Bluetooth comprehensive tester signal.

[0111] For the received signal R(t), the purpose is to recover the binary bit stream b m , which is described by the maximum likelihood probability as P(b m |R(t)), that is, it satisfies the Bayesian probability:

[0112]

[0113] When b0 is 0, the value of GFSK signal modulation is 0 or -1. At this time, for the received signal R(t), the conditional probability that the carried information b0 is 0 is:

[0114]

[0115] In the formula: real() represents taking the real part of the complex signal;

[0116] For the received signal R(t), the conditional probability that the carried information b0 is 1 is:

[0117]

[0118] When b0 = 1, if the following conditions are satisfied:

[0119]

[0120] Then the likelihood probability ratio for b0 is:

[0121]

[0122] In the formula: real() represents taking the real part of a complex signal.

[0123] Fourth: Calculation of the conditional probability of the received signal in segments.

[0124] Based on the modulation structure of the GFSK signal, when real ( R(t) ) ≤ -1, the likelihood probability ratio is:

[0125]

[0126] In the formula: real() represents taking the real part of a complex signal;

[0127] Taking the logarithm of both sides of the above formula gives:

[0128]

[0129] In the formula: ln() represents the logarithmic operation with the natural exponent e as the base;

[0130] When -1 ≤ real( R(t) ) <0 , 0 ≤ real( R(t) ) <1 , the likelihood probability ratio is:

[0131]

[0132] Taking the logarithm of both sides of the above formula gives:

[0133]

[0134] When real ( R(t) ) ≥1 , the likelihood probability ratio is:

[0135]

[0136] Taking the logarithm of both sides of the above formula gives:

[0137]

[0138] The above is for the size decision of the received signal R ( t ) is a decision of whether it is between 0 and 1, or between -1 and 0, or greater than 1, or less than -1. Based on the above likelihood probability representation, the size range and decision of the received signal R ( t ) are 0 and 1, and the present invention creatively uses the viterbi algorithm to search for the decision.

[0139] Fifth: Demodulation based on the Viterbi search algorithm and probability scale calculation.

[0140] The demodulation algorithm uses the Viterbi search algorithm: construct a trellis grid diagram; perform iterative estimation based on the received IQ complex data to be 0 or 1 to achieve demodulation; the schematic diagram of the demodulation path search is as follows Figure 2 As shown, calculate the branch metric values for each of the received IQ complex data one by one, select the minimum path at each level, discard other paths, and continue until the minimum path is selected. By backtracking, the demodulated bit stream can be obtained.

[0141] The scale calculation for path search uses the maximum likelihood probability measurement above, that is:

[0142]

[0143] The demodulation of this embodiment is as Figure 4 shown, where the modulation coefficient is 0.5, and the demodulation error rate is statistically calculated for one symbol period length under different signal-to-noise ratios. From Figure 4 the display, when the signal-to-noise ratio is about 12 dB, the error rate drops to 0.

[0144] Working principle: Use the maximum likelihood probability of the received signal to determine the symbol range, determine the grouping of the received signal according to the conditional probability, and combine with the Viterbi search algorithm. Use the maximum likelihood probability to calculate the scale variable, backtrack the best search path, and finally determine the demodulated bit stream, and finally achieve the demodulation of GFSK.

[0145] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and without departing from the spirit or basic characteristics of the present invention, the present invention can be implemented in other specific forms. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention. Any reference signs in the claims should not be regarded as limiting the claims involved.

[0146] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A demodulation method for GFSK signals of a Bluetooth comprehensive tester, characterized in that The demodulation method includes the following steps: Step 1: Determine the modulation method of the GFSK signal of the Bluetooth comprehensive tester: According to the Bluetooth protocol, the GFSK signal of the Bluetooth comprehensive tester is modulated through a Gaussian filter. The bandwidth of the Gaussian filter affects the spectrum of the GFSK signal. The product BT of the 3dB bandwidth of the Gaussian filter and the binary symbol period T is a parameter of the Gaussian filter. The smaller the value of BT, the longer the pulse response duration. Step 2: Define the wireless channel model of the Bluetooth comprehensive tester; Step 3: Define the maximum likelihood probability calculation method of the Bluetooth comprehensive tester signal based on the maximum likelihood probability theory; Step 4: Calculate the conditional probability of the received signal in segments; Step 5: Demodulation based on the viterbi search algorithm and probability scale calculation; Specifically included in the above Step 2: The transmitted signal s(t) is transmitted through the wireless channel n(t), and the received signal R(t) is expressed as: R(t) = s(t) + n(t) In the formula, s(t) is the transmitted signal; n(t) is Gaussian white noise, and the probability distribution it satisfies is: where μ is the mean, σ 2 is the variance, p(n) is the probability distribution function, and N0 is the signal length; In the above Step 3: The received signal is R(t), and the recovered binary bit stream is b m , which is described using the maximum likelihood probability as P(b m |R(t)), that is, it satisfies the Bayesian probability: When b0 is 0, the value modulated by the GFSK signal is 0 or -1. At this time, for the received signal R(t), the conditional probability that the carried information b0 is 0 is: In the formula: real() represents taking the real part of the complex signal; For the received signal R(t), the conditional probability that the carried information b0 is 1 is: When b0 = 1, if the following conditions are satisfied: Then the likelihood probability ratio for b0 is: In the formula: real() represents taking the real part of the complex signal; Specifically included in the above Step 4: Based on the modulation structure of GFSK signals, when real ( R(t) ) ≤-1 , the likelihood probability ratio is: In the formula: real() represents taking the real part of the complex signal; Taking the logarithm operation on both sides of the above formula gives: In the formula: ln() represents the logarithm operation with the natural exponent e as the base; When -1≤real ( R(t) ) <0,0≤real ( R(t) ) <1 , the likelihood probability ratio is: Taking the logarithm on both sides of the above formula gives: When real ( R(t) ) ≥1 , the likelihood probability ratio is: Taking the logarithm on both sides of the above formula gives:

2. The demodulation method according to claim 1, wherein: In the above Step 1, The impulse response expression of the Gaussian filter is: In the formula: t represents time, h(t) represents the channel impulse response, T is the signal period size, and σ is the signal variance; In the formula: B is the signal modulation coefficient, and T is the signal period size.

3. The demodulation method according to claim 2, wherein In the above Step 1: If the input signal x(t) is a bipolar square wave corresponding to the binary data to be sent, the output after the bipolar square wave passes through the Gaussian filter is: In the formula: m(t; T) represents a pulse with a period of T, t is the time variable, and g(t) represents a rectangular pulse after transmission through the channel h(t); The rectangular pulse is defined as: After derivation, the expression is obtained as: In the formula: g(t) is the pulse signal after Gaussian modulation, T is the period size, Q(t) is the Gaussian function, B is the modulation coefficient, and t is the time variable; In the formula: Q(t) is the Gaussian function, and t is the time variable.

4. The demodulation method according to claim 2, wherein In the above Step 1: Assume that the sequence x(n) is the discrete-time sampling of the input signal x(t), which is a bipolar non-return-to-zero code. Then the phase expression after GFSK signal modulation is: In the formula: g(tau - nT) is the pulse signal after Gaussian modulation; The expression of the GFSK signal after modulation at a carrier frequency of f c is as follows: In the formula: s(t) is the signal after GFSK modulation, B is the modulation coefficient, phi(t) is the signal phase, and phi0 is the initial phase.

5. The demodulation method according to claim 1, wherein In the fifth step, the viterbi search algorithm is used for the demodulation algorithm: Construct a trellis diagram; Perform iterative estimation based on the received IQ complex data to be 0 or 1 for demodulation; Calculate the branch metric values one by one for the received IQ complex data, select the minimum path at each level, discard other paths, and continue until the minimum path is selected and the demodulated bit stream is obtained by backtracking.

6. The demodulation method according to claim 5, characterized in that: The scale calculation for path search uses the maximum likelihood probability measure, that is:

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