RU2722001C1 - Digital simulator of random signals - Google Patents

Abstract

FIELD: radio engineering; measuring equipment.

SUBSTANCE: digital simulator of random signals, which includes reference frequency generator, memory unit, digital-to-analogue converter, generator of equiprobable pseudorandom numbers and register, also comprises digital comparator, first input of which is connected to output of equiprobable pseudorandom number generator, second input is to output of memory unit, successive approximation register, clock input of which is connected to third output of reference frequency generator, control input is to output of digital comparator, and output is parallel connected to first address input of memory unit and input of register, and buffer register, output of buffer register is digital output of simulator, and output of digital-to-analogue converter is analogue output of simulator.

EFFECT: technical result consists in reduction of required capacity of memory unit when generating binary random numbers.

1 cl, 6 dwg, 1 tbl

Description

The invention relates to the fields of radio engineering and measuring equipment and can be used to simulate signals and interference when testing radio communication equipment and control systems.

Known digital chaotic signal generator [1] based on a shift register and an analog noise source, generating a "truly random" digital signal with equally probable samples, in which there is no possibility of changing the statistical characteristics of the signal.

Known digital generators [2] of pseudo-random binary sequences (for example, M-sequences, Gould, Kassami, etc.) formed using shift registers with linear or nonlinear feedbacks. Known [3] is a random number sensor with a uniform probability distribution, which uses random numbers recorded in a memory block that are “mixed” using binary counters, improving the quality of matching the generated numbers with a theoretical uniform probability distribution law. Their disadvantage is the lack of the possibility of forming pseudo-random numbers with different laws of probability distribution.

A known radio signal simulator [4], comprising a reference frequency generator, a memory unit, a data reader, a digital-to-analog converter. The device imitates arbitrary signals represented by model data files or digital records of signals that are previously recorded in the memory unit and read during the simulation. Its disadvantage is the limited duration of the reproduced implementation, which is especially important for high-frequency data reading.

Closest to the technical nature of the proposed device is a digital random signal simulator [5], containing a reference frequency generator, a memory unit, a digital-to-analog converter, an equiprobable pseudorandom number generator and a register.

The objective of the proposed technical solution is to reduce the required capacity of the memory block when generating binary random numbers.

The problem is solved in that a digital random signal simulator containing a reference frequency generator, a memory unit, a digital-to-analog converter, an equiprobable pseudorandom number generator and a register further comprises a digital comparator, the first input of which is connected to the output of the equiprobable pseudorandom number generator, the second input is to the output a memory block, a sequential approximation register, the clock input of which is connected to the third output of the reference frequency generator, the control input is connected to the output of the digital comparator, and the output is connected in parallel with the first address input of the memory block and the register input, and a buffer register, the input of which is connected to the register output successive approximations, and the output is to the input of the digital-to-analog converter, the register output is connected to the second address input of the memory block, and its clock input is connected to the second output of the reference frequency generator, the clock input of the equally probable pseudorandom number generator is connected to the first the output of the reference frequency generator, the output of the buffer register is the digital output of the simulator, and the output of the digital-to-analog converter is the analog output of the simulator.

The proposed technical solution is illustrated by drawings.

In FIG. 1 shows a structural diagram of the proposed device, in FIG. 2 is three-dimensional diagrams of the transition probability matrices of a Gaussian random process with different correlation coefficients, FIG. 3 is their three-dimensional diagrams of the probability distribution functions of a Gaussian random process with various correlation coefficients, FIG. 4 - simulation results of a Gaussian random signal simulator, FIG. 5 - terms of the criterion χ ² , and in FIG. 6 - dependence of χ ² on the bit depth of the pseudo-random number generator.

The reference frequency generator (G) 1 at the first output generates clock pulses (TI1), according to which the pseudorandom number generator (PRNG) 2 generates a D-bit equiprobable binary code received at the first input of a digital comparator (CC) 3, with which D- the binary code of the probability distribution function F _ij , a Markov model of the simulated process, recorded in the memory unit 4. pre-calculated from the given two-dimensional probability density 4. The register (WG) 5 contains the m-bit binary value of the random signal i obtained at the previous simulation step , which is written to it by the clock pulse TI2 at the second output of G 1. At the clock input of the register of successive approximations (RPP) 6, a packet of (m + 1) pulses of TI3 from the third output of G 1 is received. The first of TI3 sets code 10 in RPP 6 ... 0, arriving at the first address input 7 of BP 4, while at the second address input 8 of BP 4 there is a code i from the output of WP 5, and at the output of BP 4 a D-bit double appears Decimal code 9 of the value F _ij . Codes from GPRS 2 and BP 4 are compared in CC 3, which forms the control bit for RPP 6. The second pulse of TI3 from G 1 in RPP 6 is written code 110 ... 0, if the code at the output of PRNG 2 is greater than the code at output 9 of BP 4, Otherwise, in RPP 6, the code 010 ... 0 is generated. The control is carried out by the signal from the output of the CC 3 at the control input of RPP 6. Next, the process is repeated until the least significant m-th pulse of TI3 generates the least significant bit of code in RPP 6, and then the last (m + 1) -th pulse of TI3 m- bit code j from RPP 6 is written into the register of WP 5 and into the buffer register of BR 10, forming a code of a simulated pseudo-random number. The output code of the BR 10 is transmitted to the input of the digital-to-analog converter of the DAC 11 and to the digital output of the simulator 12, the output analog voltage of the DAC 11 is supplied to the analog output of the simulator 13. After the next pulse T1, the process is repeated.

The device operates as follows.

Based on a given two-dimensional probability density w (x ₁ , x ₂ ) of the simulated signal, a homogeneous Markov model is formed [6-8], described by a matrix of transition probabilities

where P _ij is the probability of a discrete signal transition from the value z _n = i,

М=2^m (m- число разрядов двоичного кода отсчета) в момент времени t_n к значению z_n+1=j,

в следующий момент времени t_n+1; n - номер отсчета имитируемого сигнала.

M = 2 ^m (m is the number of bits of the binary reference code) at time t _n to the value z _{n + 1} = j,

at the next time t _{n + 1} ; n is the reference number of the simulated signal.

Based on the transition probability matrix [P _ij ] (1), a matrix of a two-dimensional probability distribution function is formed

For a stationary Gaussian random process x (t), considered at time t ₁ , t ₂ , the two-dimensional probability density has the form [8]

- коэффициент корреляции процесса x(t).where x _cf is the average value, σ ² is the variance,

is the correlation coefficient of the process x (t).

If we choose the quantization step in terms of the level d = (6 ÷ 10) σ / M and the values of the quantization levels

then for transition probabilities we get

The matrices [P _ij ] and [F _ij ] are conveniently represented graphically in three-dimensional coordinates. For the considered two-dimensional Gaussian distribution with x _cp = 0, σ = 1, M = 32 (m = 5) and various correlation coefficients r of the diagram [P _ij ] are shown in FIG. 2, and diagrams [F _ij ] in FIG. 3. For FIG. 2a and 3a, the correlation coefficient is 0, for FIG. 2b and 3b, the correlation coefficient is 0.8, for FIG. 2c and 3c, the correlation coefficient is 0.8.

переходов соседних отсчетов сигнала от z_n=i к z_n+1=j. Тогда при большом объеме выборки N»М² получим оценкиA similar Markov model can be constructed from the experimental implementation of a signal of a sufficiently large volume N. To estimate P _ij , the numbers

transitions of neighboring samples of the signal from z _n = i to z _{n + 1} = j. Then with a large sample size N »M ² we get the estimates

целесообразно добавить константу, например, 1.To eliminate the possible uncertainty of estimates (2) to the values

it is advisable to add a constant, for example, 1.

The probabilities F _ij for any i with increasing j vary from F _i1 = 0 to F _iM = 1. Each value of F _ij is represented by a binary D-bit code G _ij = d _D-1 d _{D-2 ...} d ₀ (from 00 ... 0 to 11 ... 1) and is written to the memory block in D-bit cells with addresses A = i2 ^m + j A = i⋅2 ^m + j (where m is the width of the output samples of the simulator).

The source of equally probable random (pseudo-random) numbers of PRNG 2 can be implemented as a noise generator [1], or, for example, as an M-sequence generator [2] based on a multi-bit shift register. It generates binary D-bit codes U = u _D-1 and u _D-2 ... u ₀ . With a shift register width of R = 43, the period of the M-sequence is 2 ^R -1 = 8.796⋅10 ¹² , and at R = 6l it is already 2 ^R -1 = 2.306⋅10 ¹⁸ , which is quite enough for the formation of realizations of a random signal of long duration. If a noise generator is used, the simulator will generate “truly” random numbers.

According to the clock pulse TI1 GPRS 2 generates the code U = u_D-1 u_D-2... u₀received at the first input of the CC 3. In the register of the WP 5 is recorded the value of i reference obtained at the previous cycle of the simulator (its initial state can be any). After TI1, the first pulse of TI3 in the RPP records the code 10 ... 0 (the average value of the m-bit reference code j) and from the memory block BP 4 at its output 9 appears the code G_ij= d_D-1d_D-2 ... d₀received at the second input of the CC 3. The digital comparator of the CC 3 is a binary code subtractor. If in BP 4 write additional codes of numbers G_ij, then as a CC 3, you can use a binary adder.

Sign digit CK 3 controls the operation of the RPP 6. If the U code from the PRNG 2 is greater than the G code_ij= d_D-1d_D-2... d₀, then the second pulse TI3 in RPP 6 records the code 110 ... 0, otherwise the code 010 ... 0. Further, the process continues in a similar fashion until m-bit code is formed in RPM 6 after m pulses of TI3.

The register of successive approximations is described in [9]. Based on it, analog-to-digital converters of successive approximations are constructed, which in practice can be implemented using a separate integrated circuit RPP K155IR17.

With a TI2 clock pulse, the code j received in RPP 6 is recorded in the RG 5 register, becoming the previous sample i, and in the BR 10 buffer register, from the output of which random signal samples are output to digital output 12, and through DAC 11 to analog output 13.

In order to check the operability and efficiency of the proposed generator, its operation was simulated when generating samples of a random Gaussian signal with parameters x _cp = 0, σ = 1, M = 32 and a correlation coefficient between two adjacent samples r = 0.8. On figb and 3b shows the Markov model of the simulated process: three-dimensional diagrams of the matrix of transition probabilities P _ij and probability distribution functions F _ij . In FIG. 4a shows the time diagram of the signal samples x _n generated by the simulator (where n is the reference number), in FIG. 4b is a histogram of the generated sample (where also the dotted line shows the corresponding theoretical probability density of the Gaussian distribution), and in FIG. 4c shows the dependence of the correlation coefficient r _k = 〈x (t ₁ ) x (t _k )〉 on the offset of the samples k (where the theoretical dependence r _{k is} plotted in dashed lines).

For a given bit depth m of simulated random numbers, the accuracy of the probability characteristics depends on the bit depth D of the codes G_ij= d_D-1d_D-2... d₀ and U = u_D-1u_D-2... u₀. To quantify the accuracy of the simulation of probability characteristics, we use the agreement criterion χ² (Pearson) [10]:

Where

n _k is the number of values x _k = k samples in a sample of volume N (its histogram),

P _k - theoretical value of the probability of occurrence x _k (one-dimensional probability distribution). Values w _k (3) characterize the deviation of the histogram from the theoretical value for the k-th value of the reference. In FIG. Figure 5 shows the dependences of w _k obtained as a result of statistical simulation for (k-1) at M = 64, N = 2 ²⁰ ≈10 ⁶ and different bit depths D of the code of values F _ij . FIG. 5a corresponds to D = 11 (χ ² = 219), FIG. 5b - D = 14 (χ ² = 71). As can be seen, w _k increase in the region of unlikely values and decrease with increasing D.

и, если

то эмпирическое распределение вероятностей соответствует теоретическому.The value of χ ² characterizes the reliability of the hypothesis about the correspondence of the empirical estimates of probabilities to a given distribution. For a given value a of the Nyquist criterion, the boundary value is calculated

and if

then the empirical probability distribution corresponds to the theoretical one.

соответственно. При М=2¹⁰=1024 значение

достигается уже при D=11. Таким образом, при m=6 необходимо выбрать D=14, при m=8-D=13, а при m=10-D=11, соответственно. При m≥16 можно принять D=m.In FIG. 6, solid lines show the dependences of χ ² on D at M = 2 ⁶ = 64 (Fig. 6a) and M = 2 ⁸ = 256 (Fig. 6b). Here, the dashed lines with significance α = 0.01 indicate the values

respectively. With M = 2 ¹⁰ = 1024, the value

achieved already at D = 11. Thus, for m = 6, it is necessary to choose D = 14, for m = 8-D = 13, and for m = 10-D = 11, respectively. When m≥16, you can take D = m.

For storing G codes_ij= d_D-1d_D-2... d₀ in the proposed simulator, the volume of the PSU memory block is V1 = 2^2m D bit. In turn, for the implementation of the prototype of the invention [5] the required amount of memory PSU V2 = 2^{m + D} m bits. Thus, the value V2 / V1 characterizes the gain in capacity of the memory block in the proposed technical solution compared to the prototype. The indicated values are given in the table.

From the obtained results it follows that the proposed simulator with high accuracy generates a random signal whose two-dimensional statistical properties are determined by a given Markov model, and for m≤10 it provides a significant gain in the required volume of the memory block.

Literature

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Claims (1)

A digital random signal simulator containing a reference frequency generator, a memory unit, a digital-to-analog converter, an equiprobable pseudorandom number generator and a register, further comprises a digital comparator, the first input of which is connected to the output of an equiprobable pseudorandom number, the second input is to the output of a memory block, a sequence approximation register , the clock input of which is connected to the third output of the reference frequency generator, the control input is connected to the output of the digital comparator, and the output is connected in parallel with the first address input of the memory block and the register input, and the buffer register, the input of which is connected to the output of the sequential approximation register, and the output is to the input of the digital-analog converter, the register output is connected to the second address input of the memory unit, and its clock input is connected to the second output of the reference frequency generator, the clock input of the equally probable pseudorandom number generator is connected to the first output of the reference frequency generator, output The buffer register is the digital output of the simulator, and the output of the digital-to-analog converter is the analog output of the simulator.

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