CN105045561A - Pseudo-random number generating method - Google Patents

Abstract

The present invention discloses a pseudo-random number generating method which is a method for carrying out operation on more than two pseudo-random number generators to generate high-speed pseudo-random numbers with long sequence periods, wherein generation of each pseudo-random number is based on a parallel structure longest linear feedback shift register circuit; the pseudo-random numbers generated by the pseudo-random number generators which are requested to participate in operation are not related mutually; the uniformly distributed pseudo-random numbers with a plurality of data bits can be generated in real time, the pseudo-random numbers which are of other distribution structures also can be generated, and digital white noise signals with wide bands also can be generated; and parameters of the pseudo-random numbers, such as a mean value, variances and the like, are adjustable.

Description

A kind of pseudo random number production method

Technical field

The present invention relates to signal and field, specifically a kind of pseudo random number production method occur.

Background technology

The power spectral density function of desirable white noise signal is a constant in all frequencies, and its power is infinitely great, therefore can not physics realization.A noise signal its power spectral density function in interested frequency range is approximately a constant, is called as bandlimited white noise acoustical signal, physically can realizes.The character of bandlimited white noise acoustical signal and desirable white noise signal is similar.The bandwidth of side circuit system is limited, as long as the frequency range of the bandlimited white noise acoustical signal produced is wider than the bandwidth of side circuit, it is identical on the impact of the desirable white noise signal that the impact of signal system distributes with same spectrum density, equal probabilities.After the voltage digital of simulating the white noise signal, ideal random number can be formed.

Noise signal is physically based deformation technology traditionally.Such as, utilize the radioactivity of radiomaterial, use detector to produce random number to its counting.The electric discharge of gas-discharge tube is utilized to produce noise signal.At the seventies in last century six, gas-discharge tube was at home and abroad once widely used as noise criteria.The method and technology complexity, the security that more than produce noise are not high, the solid-state noise generation techniques be therefore born again based on circuit noise.Such as, utilize the thermonoise of resistance or the noise of semiconductor devices, can produce broadband noise signal, its theory diagram as shown in Figure 1.

Charge carrier result of random thermal motion in conductor and the fluctuation noise produced are thermonoise, and thermal noise voltage is relevant with temperature, and its mean square value is:

V ²＝4kTBR

Wherein R is the resistance of conductor, and B is the bandwidth of circuit, and k is Boltzmann constant, and T is absolute temperature.Because thermonoise originates from the motion of majority carrier, so it is the Gaussian distribution of zero that its instantaneous amplitude obeys average, when temperature and resistance one timing, the spectral density of thermal noise voltage and frequency have nothing to do, and therefore, the thermonoise of resistance is the white noise of Gaussian.

A semiconductor diode reverse bias operation, in avalanche breakdown state, in avalanche region, produces snowslide Johnson noise because electron-hole pair produces the random fluctuation character of speed.Under certain avalanche frequency, snowslide Johnson noise is similar to white noise, and its noise power spectral density is uniformly distributed.Therefore, reverse operation can become a comparatively ideal noise source in the diode of avalanche breakdown state.Utilize the avalanche breakdown of Zener diode or PIN diode to produce noise signal, then through wide-band amplify, can broadband noise signal be produced.

Solid state noise generator frequency range is wider, can be covered to microwave frequency band, and the probability density of output signal meets Gaussian distribution, belongs to white Gaussian noise signal.The shortcoming of conventional noise signal generator is that the probability distribution outputed signal can not adjust, spectral density adjustment difficulty.In practical application, often need random number or the noise signal of numeric type.By the output quantization of solid state noise generator, the noise signal of numeric type can be produced.

Set forth the method that physically based deformation technology produces true random number below.Utilize the noise that the avalanche breakdown of Zener diode produces, warp is every straight and wide-band amplify, and can produce the broadband white noise signal of simulation, this noise signal is Gaussian distribution.Use A/D converter at a high speed by analogue noise signal digital, can produce the digital noise signal of Gaussian distribution, theory diagram as shown in Figure 2.In figure, Vcc is direct voltage source, and R is current-limiting resistance, is operated in avalanche breakdown region to make diode D.L provides DC channel, isolates AC signal simultaneously, and C is partiting dc capacitor, and simultaneously by noise signal coupling output, N is amplifying circuit.The noise signal quantized compares with numerical value 0 again, if numerical value is more than or equal to 0 just export 1, if be less than 0 just export 0, create an equally distributed scale-of-two random number in this way, theory diagram as shown in Figure 3.Analog comparator at a high speed can certainly be used to convert analogue noise signal to binary digital noise signal.

The limited random number of sequence period is called pseudo random number, and the limited random signal of sequence period is called pseudo random signal.The sequence period of pseudo random number is longer, and its statistical property is better, more close to true random number.Because the generation circuit of true random number is comparatively complicated, in engineering, the normal pseudo random number that uses replaces true random number, because its mathematical property is similar, can meet requirement of engineering.

Utilize computing machine to produce easily and be uniformly distributed pseudo random number.The method producing pseudo random number has middle square method, multiplicative congruential method, linear congruent algorithm.Middle square method, multiplicative congruential method produce the of low quality of pseudo random number.On computers, conventional linear congruent algorithm produces pseudo random number.Linear congruential method recursion formula is:

rand(n)＝(rand(n-1)*mult+inc)modM

Wherein rand (n) is current random number, and rand (n-1) is previous moment random number, and mult is multiplier factor, M=2 ^lfor modulus value.Inc is increment, under normal circumstances the desirable odd number being less than M.In C language compiler, function rand () can produce the random integers between 0 ~ 32767.The formula producing pseudo random number in VC is:

rand(n)＝((rand(n-1)*214013+2531011)mod65536)&0x7fff

The formula producing pseudo random number in BC is:

rand(n)＝((rand(n-1)*22695477+1)mod65536)&0x7fff

Utilize digital technology, produce after being uniformly distributed pseudo random number, other distribution pseudo random number can be produced easily, the pseudorandom number white noise signal that such as Gaussian distribution pseudo-random sequence, and average, variance, spectral density are adjustable.

M sequence, also known as longest linear feedback shift register sequence, is a kind of binary pseudo-random sequence studying more deep.Be usually used in the fields such as spread spectrum communication, range finding, circuit test.It is produced by the shift register with linear feedback, as shown in Figure 4.The state a of single place shift register in figure _irepresent, a _i=0 or a _i=1, i is integer.The connection status C of feedback line _irepresent, C _i=0 represents that this feedback line disconnects, C _i=1 represents that feedback exists.

Under control of the clock signal, be outwards shifted shift register output step by step.Due to the existence of feedback, if original state is complete " 0 ", then what obtain after displacement is still complete " 0 ", therefore should avoid occurring complete " 0 " state; Again because n level shifting memory has 2 ⁿplant possible different conditions, except complete " 0 " state, remaining 2 ⁿ-a kind of state can be used.Often be shifted once, just occur a kind of state, after displacement several times, one repeats front a certain state surely, and process thereafter is is just gone round and begun again, and that is, output signal must be periodic signal.To there are the different sequences of different cycles in feedback line position difference, it is desirable to find suitable linear feedback logic, the sequence that shift register can be made to produce is the longest, namely reaches cycle M=2 ⁿ-1.By line relation in figure, the input that shift register group left end obtains can be written as:

a _n＝c ₁a _n-1⊕c ₂a _n-2⊕c ₃a _n-3⊕...⊕c _n-1a ₁⊕c _na ₀

In formula, ⊕ is xor operator.When selecting suitable linear feedback logic, output sequence is exactly one-period is 2 ⁿthe m sequence of-1.

C _ivalue determine the feedback link of concrete shift register, sequential structure and cycle, for ease of expressing C _istate, introduce polynomial expression:

f(x)＝c ₀+c ₁x+c ₂x ²+...+c _n-1x ^n-1+c _nx ⁿ

This formula is called proper polynomial.When knowing the proper polynomial of a linear feedback shift register, the structure of linear feedback shift register just can be determined.Verified, if the proper polynomial of linear feedback shift register is primitive polynomial, then this linear feedback shift register can produce m sequence.This is the sufficient and necessary condition that linear feedback shift register produces m sequence.In actual applications, need according to data bits the length first determining m sequence, then by the feedback logic that just can obtain m sequencer easily of tabling look-up.The linear feedback shift register of certain length, has a lot of primitive polynomials, corresponding different m sequences.Conventional primitive polynomial, forefathers provide in table form.Such as, as n=31, f (x)=1+x ³+ x ³¹for primitive polynomial, m sequence can be produced.C in corresponding formula ₀=1, C ₃=1, C ₃₁=1.Sequence period is 2 ³¹-1, be a Mersenne Prime just.M sequence has following character:

(1) equilibrium response.In each 2 of m sequence ⁿin-1 cycle, the number that " 1 " code element occurs is 2 ^n-1secondary, the number that " 0 " code element occurs is 2 ^n-1-1 time, i.e. the number of " 0 " always fewer than the number of " 1 ", this shows, serial mean is minimum.

(2) Run length property.The distance of swimming refers to being collectively referred to as of continuously arranged in a sequence period and the code element that value is identical, and the number of the code element in a distance of swimming is run length.2 are had in m sequence ^n-1the individual distance of swimming.Wherein length is that the distance of swimming number of k (1≤k≤n-2) accounts for 2 of total number of runs ^-k, length is the number of runs of the company " 0 " of n-1 is 1, and length is company " 1 " number of runs of n is 1.

(3) shifter-adder characteristic.A m sequence { a _nrear another the different sequence { a produced that is shifted is postponed any time from it _n+kexclusive-OR, the delay shift sequence being still this m sequence obtained.As, 01001l1 moves to right and produces another sequence 1010011 for 1 time, and the sequence after exclusive-OR is 1l10100, is equivalent to former sequence and moves to right the sequence obtained after 3 times.

(4) m sequence has excellent autocorrelation performance, its autocorrelation function:

$R\left(\mathrm{\τ}\right)=\left\{\begin{array}{cc}1& \mathrm{\τ}=0\\ -1/M& \mathrm{\τ}\≠0\end{array}\right.$

Usually there are a lot of m sequences in longest linear feedback shift register.There are 2 m sequences in the longest linear feedback shift register of such as 3, there are 2 m sequences in the longest linear feedback shift register of 4, there are 6 m sequences in the longest linear feedback shift register of 5, there are 6 m sequences in the longest linear feedback shift register of 6, there are 18 m sequences in the longest linear feedback shift register of 7, there are 16 m sequences in the longest linear feedback shift register of 8, there are 48 m sequences in the longest linear feedback shift register of 9, there are 60 m sequences in the longest linear feedback shift register of 10, there are 176 m sequences in the longest linear feedback shift register of 11, there are 144 m sequences in the longest linear feedback shift register of 12, there are 630 m sequences in the longest linear feedback shift register of 13, there are 756 m sequences in the longest linear feedback shift register of 14, there are 1800 m sequences in the longest linear feedback shift register of 15.Along with the increase of longest linear feedback shift register figure place, the number of m sequence increases sharply.

Coefficient is that 19 longest linear feedback shift registers of 5 exist 158 m sequences.Its primitive polynomial is 1+x+x ²+ x ⁵+ x ¹⁹, 1+x+x ²+ x ⁶+ x ¹⁹, 1+x+x ⁴+ x ⁶+ x ¹⁹, 1+x ³+ x ⁴+ x ⁶+ x ¹⁹, 1+x+x ⁵+ x ⁶+ x ¹⁹, 1+x+x ⁴+ x ⁷+ x ¹⁹, 1+x ⁵+ x ⁶+ x ⁷+ x ¹⁹, 1+x+x ⁶+ x ⁸+ x ¹⁹..., 1+x ¹³+ x ¹⁷+ x ¹⁸+ x ¹⁹, 1+x ¹⁴+ x ¹⁷+ x ¹⁸+ x ¹⁹.Coefficient is that 25 longest linear feedback shift registers of 3 exist 4 m sequences.Its primitive polynomial is 1+x ³+ x ²⁵, 1+x ⁷+ x ²⁵, 1+x ¹⁸+ x ²⁵, 1+x ²²+ x ²⁵.Usually there is a mirror image primitive polynomial in a primitive polynomial, the number of these two primitive polynomial coefficients is identical, and the exponent number of coefficient is symmetrical with the figure place of longest linear feedback shift register.Such as 19 rank primitive polynomial 1+x+x ²+ x ⁵+ x ¹⁹with 1+x ¹⁴+ x ¹⁷+ x ¹⁸+ x ¹⁹mirror image, 1+x+x ²+ x ⁶+ x ¹⁹with 1+x ¹³+ x ¹⁷+ x ¹⁸+ x ¹⁹mirror image.25 rank primitive polynomial 1+x ³+ x ²⁵with 1+x ²²+ x ²⁵mirror image, 1+x ⁷+ x ²⁵with 1+x ¹⁸+ x ²⁵mirror image.The m sequence that the primitive polynomial of two mirror images generates has stronger correlativity.The cross correlation function of the m sequence not having the primitive polynomial of mirror to generate is almost nil, can think incoherent.Such as primitive polynomial 1+x+x ²+ x ⁵+ x ¹⁹, 1+x+x ²+ x ⁶+ x ¹⁹, 1+x+x ⁴+ x ⁶+ x ¹⁹, 1+x ³+ x ⁴+ x ⁶+ x ¹⁹, 1+x+x ⁵+ x ⁶+ x ¹⁹, 1+x+x ⁴+ x ⁷+ x ¹⁹, 1+x ⁵+ x ⁶+ x ⁷+ x ¹⁹, 1+x+x ⁶+ x ⁸+ x ¹⁹, 1+x ³+ x ²⁵, 1+x ⁷+ x ²⁵between uncorrelated mutually.

The pseudo-randomness of m sequence is fine, but it can only export one at every turn.Want the pseudo random number of generation data bit more than, very natural idea directly extracts several from longest linear feedback shift register, obtains the random number of a multidigit.Fig. 5 is the circuit diagram obtaining 4 pseudo random numbers the longest linear feedback shift register of from 8.The primitive polynomial that its linear feedback logical circuit is corresponding can select 1+x ²+ x ³+ x ⁴+ x ⁸, the feedback line that namely a6, a5, a4, a0 data bit is corresponding is in connection status.But this method is bad, because the pseudo random number that this moment exports, the pseudo random number exported with subsequent time, except a data bit is newly-generated, other several data bit is identical, and only position offset by one.The pseudo random number that this moment exports, the pseudo random number exported with next subsequent time, except two data bit are newly-generated, other two data bit are identical, and only position offset by two.The like.That is have stronger correlativity between before and after the pseudo random number generated in this way, therefore its quality is good not.

Summary of the invention

The object of this invention is to provide a kind of pseudo random number production method, to solve prior art Problems existing.

In order to achieve the above object, the technical solution adopted in the present invention is:

A kind of pseudo random number production method, is characterized in that: based on the N of parallel organization longest linear feedback shift register _aposition pseudorandom number generator A, what generate m position is uniformly distributed pseudo random number, is designated as A [k], take binary representation as A _m-1[k] A _m-2[k] ... A ₁[k] A ₀[k]; Based on the N of parallel organization _bthe pseudorandom number generator B of position longest linear feedback shift register, what generate m position is uniformly distributed pseudo random number, is designated as B [k], take binary representation as B _m-1[k] B _m-2[k] ... B ₁[k] B ₀[k]; Pseudo random number A [k] carries out XOR with corresponding data position in pseudo random number B [k], and generating pseudo random number D [k], take binary representation as D _m-1[k] D _m-2[k] ... D ₁[k] D ₀[k]; The pseudo random number B [k] that the pseudo random number A [k] requiring pseudorandom number generator A to generate and pseudorandom number generator B generate is uncorrelated, namely the primitive polynomial of pseudorandom number generator A and the primitive polynomial of pseudorandom number generator B can not be mirror image primitive polynomials, due to uncorrelated between pseudorandom number generator A and pseudorandom number generator B, each in the pseudo random number D [k] generated is equally distributed, and therefore D [k] is that m position is uniformly distributed pseudo random number.

The present invention carries out computing for a kind of to two or more pseudorandom number generator, produces the method for long sequence period high speed pseudo random number; Wherein the generation of each pseudo random number is based on parallel organization longest linear feedback shift register circuit; Require that the pseudo random number that the pseudorandom number generator participating in computing produces is uncorrelated mutually.What the present invention can produce multiple data bit in real time is uniformly distributed pseudo random number, also can produce the pseudo random number of other distribution, can also produce wide band digital white noise signal, and its Parameter adjustable such as average, variance saves.

Accompanying drawing explanation

The solid-state noise signal generator theory diagram of Fig. 1.

Fig. 2 Gaussian distribution digital noise signal generator theory diagram.

Fig. 3 scale-of-two is uniformly distributed digital noise signal generator theory diagram.

Fig. 4 longest linear feedback shift register theory diagram.

Fig. 5 extracts the theory diagram of 4 figure places from 8 longest linear feedback shift registers.

Fig. 6 parallel organization pseudo random number circuit for generating theory diagram.

The long sequence period high speed circuit for producing pseudorandom number theory diagram of Fig. 7 invention.

Fig. 8 has the high speed circuit for producing pseudorandom number theory diagram of three circuit units.

Fig. 9 different distributions circuit for producing pseudorandom number theory diagram.

Specifically implement theory diagram for one of Figure 10 circuit for producing pseudorandom number.

Another of Figure 11 circuit for producing pseudorandom number specifically implements theory diagram.

Figure 12 Gaussian distribution pseudo random number probability density curve.

Figure 13 Gaussian distribution pseudo random number cumulative distribution function curve.

Numerical curve when Figure 14 produces Gaussian distribution pseudo random number in look-up table.

Figure 158 position pseudorandom number generator schematic diagram.

Figure 16 model selection control circuit.

Embodiment

Extracting from longest linear feedback shift register in the method for a few figure place has partial data position to be identical between adjacent pseudo random number, and only position offsets to some extent, and the pseudo random number poor quality of generation, needs to make improvement.

For the longest linear feedback shift register of n position, the value of internal register illustrates the state of circuit { Q [k] }, and the value of current time register is designated as Q _n-1[k], Q _n-2[k], Q _n-3[k] ... Q ₁[k], Q ₀[k], Q _n[k] is

Q _n[k]＝c ₁Q _n-1[k]⊕c ₂Q _n-2[k]⊕c ₃Q _n-3[k]⊕...⊕c _n-1Q ₁[k]⊕c _nQ ₀[k]

The state of lower moment circuit is designated as { Q [k+1] }, and the value of register is Q _n-1[k+1], Q _n-2[k+1], Q _n-3[k+1] ... Q ₁[k+1], Q ₀[k+1], then

Q _n-1[k+1]＝Q _n[k]

Q _n-2[k+1]＝Q _n-1[k]

Q _n-3[k+1]＝Q _n-2[k]

...

Q ₁[k+1]＝Q ₂[k]

Q ₀[k+1]＝Q ₁[k]

Q _n[k+1]＝c ₁Q _n-1[k+1]⊕c ₂Q _n-2[k+1]⊕c ₃Q _n-3[k+1]⊕...⊕c _n-1Q ₁[k+1]⊕c _nQ ₀[k+1]

The state of circuit of lower lower moment is designated as { Q [k+2] }, and the value of register is Q _n-1[k+2], Q _n-2[k+2], Q _n-3[k+2] ... Q ₁[k+2], Q ₀[k+2], then

Q _n-1[k+2]＝Q _n[k+1]

Q _n-2[k+2]＝Q _n-1[k+1]

Q _n-3[k+2]＝Q _n-2[k+1]

...

Q ₁[k+2]＝Q ₂[k+1]

Q ₀[k+2]＝Q ₁[k+1]

Q _n[k+2]＝c ₁Q _n-1[k+2]⊕c ₂Q _n-2[k+2]⊕c ₃Q _n-3[k+2]⊕...⊕c _n-1Q ₁[k+2]⊕c _nQ ₀[k+2]

The like.If prepare the binary data of parallel output m position, generate the shortcoming of pseudo random number to overcome preceding method, need to come m clock, the state of circuit become { Q [k+m] } from { Q [k] }, the value of register is Q _n-1[k+m], Q _n-2[k+m], Q _n-3[k+m] ... Q ₁[k+m], Q ₀[k+m].The binary data of the m position generated in this way is Q _m-1[k+m], Q _m-2[k+m] ..., Q ₁[k+m], Q ₀[k+m].Be identical without any data bit between before and after the m position pseudo random number of such generation, the correlativity overcome between data well, the quality of pseudo random number obtains very big improvement.Because every bit " 0 " is identical with the probability of " 1 " code element, the pseudo random number of the m position therefore generated is equally distributed.When the pseudo random number of m position regards complement code as, numerical range is [-2 ^m-1, 2 ^m-1-1].When the pseudo random number of m position regards unsigned number as, numerical range is [0,2 ^m-1].

The shortcoming of said method often carrys out m clock, just can obtain a pseudo random number, and therefore the speed of circuit evolving pseudo random number have dropped m doubly.If to state { Q [the k] } recursion of foregoing circuit, obtain successively { Q [k+1] } ... { Q [k+m] }, the Logical Deriving of circuit state { Q [k+m] } is derived the state only depending on { Q [k] }, the longest linear feedback shift register so designed often carrys out a clock, just can export the pseudo random number of a m position, the speed generating pseudo random number is greatly improved, and its internal state is equivalent to the state that original longest linear feedback shift register changes m time.The longest linear feedback shift register theory diagram of this parallel organization as shown in Figure 6.

The present invention proposes a kind of being combined with more than one parallel organization longest linear feedback shift register by a parallel organization longest linear feedback shift register and produce the method for long sequence period pseudo random number, theory diagram as shown in Figure 7.

If based on the N of parallel organization longest linear feedback shift register _aposition pseudorandom number generator A, what generate m position is uniformly distributed pseudo random number, is designated as A [k], take binary representation as A _m-1[k] A _m-2[k] ... A ₁[k] A ₀[k].Based on the N of parallel organization _bthe pseudorandom number generator B of position longest linear feedback shift register, what generate m position is uniformly distributed pseudo random number, is designated as B [k], take binary representation as B _m-1[k] B _m-2[k] ... B ₁[k] B ₀[k].Pseudo random number A [k] carries out XOR with corresponding data position in pseudo random number B [k], and generating pseudo random number D [k], take binary representation as D _m-1[k] D _m-2[k] ... D ₁[k] D ₀[k].The pseudo random number B [k] that the pseudo random number A [k] requiring pseudorandom number generator A to generate and pseudorandom number generator B generate is uncorrelated, and namely the primitive polynomial of pseudorandom number generator A and the primitive polynomial of pseudorandom number generator B can not be mirror image primitive polynomials.Due to uncorrelated between pseudorandom number generator A and pseudorandom number generator B, each in the pseudo random number D [k] of generation is equally distributed, and therefore D [k] is that m position is uniformly distributed pseudo random number.

When m is even number, the sequence period of parallel organization pseudorandom number generator A is 2 ^nathe sequence period of-1, parallel organization pseudorandom number generator B is 2 ^nb-1.The sequence period of pseudo random number D [k] is the lowest common multiple of pseudorandom number generator A and B sequence period.Therefore the sequence period of pseudo random number D [k] obtains very big expansion.

When adopting three grades of pseudorandom number generator circuit structures, theory diagram as shown in Figure 8.Based on the N of parallel organization longest linear feedback shift register _aposition pseudorandom number generator A, what generate m position is uniformly distributed pseudo random number, is designated as A [k].Based on the N of parallel organization longest linear feedback shift register _bposition pseudorandom number generator B, what generate m position is uniformly distributed pseudo random number, is designated as B [k].Based on the N of parallel organization longest linear feedback shift register _cposition pseudorandom number generator C, what generate m position is uniformly distributed pseudo random number, is designated as C [k].A [k] carries out XOR with B [k] and C [k], and what generate m position is uniformly distributed pseudo random number D [k].Require that pseudorandom number generator A and pseudorandom number generator B and pseudorandom number generator C is uncorrelated mutually.

When m is even number, the sequence period of parallel organization pseudorandom number generator A is 2 ^nathe sequence period of-1, parallel organization pseudorandom number generator B is 2 ^nbthe sequence period of-1, parallel organization pseudorandom number generator C is 2 ^nc-1.The sequence period of pseudo random number D [k] is the lowest common multiple of pseudorandom number generator A and B and C sequence period.Therefore the sequence period of pseudo random number D [k] obtains very big expansion.

The pseudorandom number generator of more multicircuit unit can be designed with.Such as can be designed with the pseudorandom number generator of four parallel organization longest linear feedback shift registers, XOR is carried out in the output of these four pseudorandom number generators, generate have multiple data bit be uniformly distributed pseudo random number.Require that these four pseudorandom number generators are uncorrelated mutually.The sequence period generating pseudo random number is the lowest common multiple of these four pseudorandom number generator sequence periods.

After generating equally distributed pseudo random number, just easily generate the pseudo random number of various distribution and noise signal.Such as can produce be uniformly distributed, Gaussian distribution, other pseudo random number that distributes, also can produce be uniformly distributed, Gaussian distribution, other distributed digital loop white noise signal, its average, variance, spectral density are adjustable.The circuit block diagram of other distribution pseudo random number is converted to as shown in Figure 9 by being uniformly distributed pseudo random number.When generating other distribution pseudo random number, be uniformly distributed pseudo random number becomes required distribution pseudo random number through look-up table conversion.Change the numerical value in look-up table, the distribution of pseudo random number, average, variance can be changed.Also the pseudorandom number white noise signal of required distribution, average, variance, spectral density can be generated.When generating pseudorandom number white noise signal, the highest half being about circuit clock frequency of digital noise signal bandwidth of output.

Specific embodiment:

Generate 8 pseudo random numbers for 32 longest linear feedback shift registers, the specific implementation of the high speed pseudo-random number generation method used in the present invention is described.Get primitive polynomial 1+x ²+ x ⁶+ x ⁷+ x ³², the circuit state of current time k is { Q [k] }, and its register value is Q ₃₁[k], Q ₃₀[k] ..., Q ₁[k], Q ₀[k], Q ₃₂[k] is

Q ₃₂[k]＝Q ₃₀[k]⊕Q ₂₆[k]⊕Q ₂₅[k]⊕Q ₀[k]

Then in stepping type, the circuit state { Q [k+8] } in k+8 moment is

Q ₀[k+8]＝Q ₈[k]

Q ₁[k+8]＝Q ₉[k]

...

Q ₂₃[k+8]＝Q ₃₁[k]

Q ₂₄[k+8]＝Q ₃₂[k]＝Q ₃₀[k]⊕Q ₂₆[k]⊕Q ₂₅[k]⊕Q ₀[k]

Q ₂₅[k+8]＝Q ₃₂[k+1]＝Q ₃₀[k+1]⊕Q ₂₆[k+1]⊕Q ₂₅[k+1]⊕Q ₀[k+1]

＝Q ₃₁[k]⊕Q ₂₇[k]⊕Q ₂₆[k]⊕Q ₁[k]

Q ₂₆[k+8]＝Q ₃₂[k+2]＝Q ₃₀[k+2]⊕Q ₂₆[k+2]⊕Q ₂₅[k+2]⊕Q ₀[k+2]

＝Q ₃₂[k]⊕Q ₂₈[k]⊕Q ₂₇[k]⊕Q ₂[k]

＝Q ₃₀[k]⊕Q ₂₈[k]⊕Q ₂₇[k]⊕Q ₂₆[k]⊕Q ₂₅[k]⊕Q ₂[k]⊕Q ₀[k]

Q ₂₇[k+8]＝Q ₃₂[k+3]＝Q ₃₀[k+3]⊕Q ₂₆[k+3]⊕Q ₂₅[k+3]⊕Q ₀[k+3]

＝Q ₃₂[k+1]⊕Q ₂₉[k]⊕Q ₂₈[k]⊕Q ₃[k]

＝Q ₃₁[k]⊕Q ₂₉[k]⊕Q ₂₈[k]⊕Q ₂₇[k]⊕Q ₂₆[k]⊕Q ₃[k]⊕Q ₁[k]

Q ₂₈[k+8]＝Q ₃₂[k+4]＝Q ₃₀[k+4]⊕Q ₂₆[k+4]⊕Q ₂₅[k+4]⊕Q ₀[k+4]

＝Q ₃₂[k+2]⊕Q ₃₀[k]⊕Q ₂₉[k]⊕Q ₄[k]＝Q ₃₀[k]⊕Q ₂₈[k]⊕Q ₂₇[k]

⊕Q ₂₆[k]⊕Q ₂₅[k]⊕Q ₂[k]⊕Q ₀[k]⊕Q ₃₀[k]⊕Q ₂₉[k]⊕Q ₄[k]

＝Q ₂₉[k]⊕Q ₂₈[k]⊕Q ₂₇[k]⊕Q ₂₆[k]⊕Q ₂₅[k]⊕Q ₄[k]⊕Q ₂[k]⊕Q ₀[k]

Q ₂₉[k+8]＝Q ₃₂[k+5]＝Q ₃₀[k+5]⊕Q ₂₆[k+5]⊕Q ₂₅[k+5]⊕Q ₀[k+5]

＝Q ₃₂[k+3]⊕Q ₃₁[k]⊕Q ₃₀[k]⊕Q ₅[k]

＝Q ₃₀[k]⊕Q ₂₉[k]⊕Q ₂₈[k]⊕Q ₂₇[k]⊕Q ₂₆[k]⊕Q ₅[k]⊕Q ₃[k]⊕Q ₁[k]

Q ₃₀[k+8]＝Q ₃₂[k+6]＝Q ₃₀[k+6]⊕Q ₂₆[k+6]⊕Q ₂₅[k+6]⊕Q ₀[k+6]

＝Q ₃₂[k+4]⊕Q ₃₂[k]⊕Q ₃₁[k]⊕Q ₆[k]＝Q ₂₉[k]⊕Q ₂₈[k]⊕Q ₂₇[k]

⊕Q ₂₆[k]⊕Q ₂₅[k]⊕Q ₄[k]⊕Q ₂[k]⊕Q ₀[k]⊕Q ₃₀[k]⊕Q ₂₆[k]

⊕Q ₂₅[k]⊕Q ₀[k]⊕Q ₃₁[k]⊕Q ₆[k]

＝Q ₃₁[k]⊕Q ₃₀[k]⊕Q ₂₉[k]⊕Q ₂₈[k]⊕Q ₂₇[k]⊕Q ₆[k]⊕Q ₄[k]⊕Q ₂[k]

Q ₃₁[k+8]＝Q ₃₂[k+7]＝Q ₃₀[k+7]⊕Q ₂₆[k+7]⊕Q ₂₅[k+7]⊕Q ₀[k+7]

＝Q ₃₀[k+7]⊕Q ₂₆[k+7]⊕Q ₂₅[k+7]⊕Q ₀[k+7]＝Q ₃₂[k+5]⊕Q ₃₂[k+1]

⊕Q ₃₂[k]⊕Q ₇[k]＝Q ₃₀[k]⊕Q ₂₉[k]⊕Q ₂₈[k]⊕Q ₂₇[k]⊕Q ₂₆[k]

⊕Q ₅[k]⊕Q ₃[k]⊕Q ₁[k]⊕Q ₃₁[k]⊕Q ₂₇[k]⊕Q ₂₆[k]⊕Q ₁[k]

⊕Q ₃₀[k]⊕Q ₂₆[k]⊕Q ₂₅[k]⊕Q ₀[k]⊕Q ₇[k]

＝Q ₃₁[k]⊕Q ₂₉[k]⊕Q ₂₈[k]⊕Q ₂₆[k]⊕Q ₂₅[k]⊕Q ₇[k]⊕Q ₅[k]⊕Q ₃[k]

⊕Q ₀[k]

Q ₃₂[k+8]＝Q ₃₀[k+8]⊕Q ₂₆[k+8]⊕Q ₂₅[k+8]⊕Q ₀[k+8]

Derive above-mentioned various in, the circuit state in k+8 moment only depends on the circuit state in k moment.The parallel organization longest linear feedback shift register designed in this way often carrys out a clock, the internal state being just equivalent to original longest linear feedback shift register changes 8 times, the pseudo random number of 18 can be exported, improve the slow-footed shortcoming of Serial output method.Because 32 longest linear feedback shift registers have 2 ³²-1 state, it can not be divided exactly by 8, and therefore the cycle of 8 pseudo random numbers is 2 ³²-1.

The parallel organization feedback logic circuit of 31 longest linear feedback shift registers can be derived by identical method.To generate 8 pseudo random numbers, get primitive polynomial 1+x ³+ x ³¹, the circuit state of current time k is { Q [k] }, and its register value is Q ₃₀[k], Q ₂₉[k] ..., Q ₁[k], Q ₀[k], Q ₃₁[k] is

Q ₃₁[k]＝Q ₂₈[k]⊕Q ₀[k]

Then in stepping type, the circuit state { Q [k+8] } in k+8 moment is

Q ₀[k+8]＝Q ₈[k]

Q ₁[k+8]＝Q ₉[k]

...

Q ₂₂[k+8]＝Q ₃₀[k]

Q ₂₃[k+8]＝Q ₃₁[k]＝Q ₂₈[k]⊕Q ₀[k]

Q ₂₄[k+8]＝Q ₃₁[k+1]＝Q ₂₈[k+1]⊕Q ₀[k+1]

＝Q ₂₉[k]⊕Q ₁[k]

Q ₂₅[k+8]＝Q ₃₁[k+2]＝Q ₂₈[k+2]⊕Q ₀[k+2]

＝Q ₃₀[k]⊕Q ₂[k]

Q ₂₆[k+8]＝Q ₃₁[k+3]＝Q ₂₈[k+3]⊕Q ₀[k+3]

＝Q ₂₈[k]⊕Q ₃[k]⊕Q ₀[k]

Q ₂₇[k+8]＝Q ₃₁[k+4]＝Q ₂₈[k+4]⊕Q ₀[k+4]

＝Q ₃₁[k+1]⊕Q ₄[k]＝Q ₂₈[k+1]⊕Q ₀[k+1]⊕Q ₄[k]

＝Q ₂₉[k]⊕Q ₄[k]⊕Q ₁[k]

Q ₂₈[k+8]＝Q ₃₁[k+5]＝Q ₂₈[k+5]⊕Q ₀[k+5]

＝Q ₃₁[k+2]⊕Q ₅[k]＝Q ₂₈[k+2]⊕Q ₀[k+2]⊕Q ₅[k]

＝Q ₃₀[k]⊕Q ₅[k]⊕Q ₂[k]

Q ₂₉[k+8]＝Q ₃₁[k+6]＝Q ₂₈[k+6]⊕Q ₀[k+6]

＝Q ₃₁[k+3]⊕Q ₆[k]＝Q ₂₈[k+3]⊕Q ₀[k+3]⊕Q ₆[k]

＝Q ₂₈[k]⊕Q ₀[k]⊕Q ₃[k]⊕Q ₆[k]

＝Q ₂₈[k]⊕Q ₆[k]⊕Q ₃[k]⊕Q ₀[k]

Q ₃₀[k+8]＝Q ₃₁[k+7]＝Q ₂₈[k+7]⊕Q ₀[k+7]

＝Q ₃₁[k+4]⊕Q ₇[k]＝Q ₂₈[k+4]⊕Q ₀[k+4]⊕Q ₇[k]

＝Q ₃₁[k+1]⊕Q ₄[k]⊕Q ₇[k]＝Q ₂₈[k+1]⊕Q ₀[k+1]⊕Q ₄[k]⊕Q ₇[k]

＝Q ₂₉[k]⊕Q ₇[k]⊕Q ₄[k]⊕Q ₁[k]

Q ₃₁[k+8]＝Q ₂₈[k+8]⊕Q ₀[k+8]＝Q ₃₀[k]⊕Q ₈[k]⊕Q ₅[k]⊕Q ₂[k]

Derive above-mentioned various in, the circuit state in k+8 moment only depends on the circuit state in k moment.The parallel organization longest linear feedback shift register designed in this way often carrys out a clock, the internal state being just equivalent to original longest linear feedback shift register changes 8 times, the pseudo random number of 18 can be exported, improve the slow-footed shortcoming of Serial output method.Because 31 longest linear feedback shift registers have 2 ³¹-1 state, it can not be divided exactly by 8, and therefore the cycle of 8 pseudo random numbers is 2 ³¹-1.

Below for the pseudorandom number generator of two circuit units, illustrate that one of the present invention is specifically implemented.Circuit block diagram as shown in Figure 10.Pseudorandom number generator A is 32 bit parallel structure longest linear feedback shift registers, often carrys out a clock and exports one 8 pseudo random number A [k], selects primitive polynomial 1+x ²+ x ⁶+ x ⁷+ x ³², before its parallel organization feedback logic, did derivation.Pseudorandom number generator B is 31 bit parallel structure longest linear feedback shift registers, often carrys out a clock and exports one 8 pseudo random number B [k], selects primitive polynomial 1+x ³+ x ³¹, before its parallel organization feedback logic, did derivation.Pseudo random number A [k] and B [k] carry out XOR, generate pseudo random number D [k].The sequence period of pseudo random number A [k] is 2 ³²-1.The sequence period of pseudo random number B [k] is 2 ³¹-1, be a Mersenne Prime.The sequence period of pseudo random number D [k] is the lowest common multiple of the sequence period of pseudo random number A [k] and the sequence period of pseudo random number B [k], is (2 ³²-1) (2 ³¹-1), 2 are about ⁶³, greatly increase than the sequence period of A [k].The sequence period of pseudo random number is longer, and performance is more close to ideal random number.

Below for the pseudorandom number generator of three circuit units, illustrate that of the present invention another is specifically implemented.Circuit block diagram as shown in figure 11.Pseudorandom number generator A is 32 bit parallel structure longest linear feedback shift registers, often carrys out a clock and exports one 8 pseudo random number A [k], selects primitive polynomial 1+x ²+ x ⁶+ x ⁷+ x ³².Pseudorandom number generator B is 31 bit parallel structure longest linear feedback shift registers, and often carry out a clock and export one 8 pseudo random number B [k], its primitive polynomial is 1+x ³+ x ³¹.Pseudorandom number generator C is 19 bit parallel structure longest linear feedback shift registers, and often carry out a clock and export one 8 pseudo random number C [k], its primitive polynomial is 1+x+x ²+ x ⁵+ x ¹⁹, its parallel organization feedback logic can with reference to derivation method above.Pseudo random number A [k] carries out XOR with B [k] and C [k], generates 8 pseudo random number D [k].The sequence period of pseudo random number A [k] is 2 ³²-1.The sequence period of pseudo random number B [k] is 2 ³¹-1, be a Mersenne Prime.The sequence period of pseudo random number C [k] is 2 ¹⁹-1, be a Mersenne Prime.The sequence period of pseudo random number D [k] is pseudo random number A [k] and the lowest common multiple of B [k] with the sequence period of C [k], is (2 ³²-1) (2 ³¹-1) (2 ¹⁹-1), 2 are about ⁸², greatly increase than the sequence period of A [k].Should illustrate, in this example, the exponent number of pseudorandom number generator A and pseudorandom number generator B and pseudorandom number generator C is selected to be arbitrary, as long as three is uncorrelated mutually.

The present invention can produce and be uniformly distributed pseudo random number, Gaussian distribution pseudo random number, and also can produce other distribution pseudo random number, its average, variance are adjustable.

Produce the random number that probability density is f (x), its cumulative distribution function is F (x), has

$y=F\left(x\right)={\∫}_{-\mathrm{\∞}}^{x}f\left(u\right)du$

When y be between [0,1.0] be uniformly distributed pseudo-random number sequence time, x is the pseudo-random number sequence that probability density is f (x).

In engineering practice, the pseudo random number scope of generation is not from minus infinity to positive infinity, but a pseudo random number having figure place to limit.Therefore, the random number of actual certain distribution produced is similar to the one of the ideal random number of this distribution.Such as will produce the pseudo random number of 8, its numerical range is-128 ~ 127, produce the pseudo random number of 16, and its numerical range is-32768 ~ 32767.Obtain x value by y value to realize by a lut circuits.Look-up table is one and is searched the circuit obtaining exporting numerical value by input address values, generally realizes with RAM.

When generation is uniformly distributed pseudo random number, learnt by above method, the numerical curve stored in look-up table is a straight oblique line.

When producing Gaussian distribution pseudo random number, as shown in figure 12, as shown in figure 13, the numerical curve stored in look-up table as shown in figure 14 for its cumulative distribution function curve for its probability density curve.

In order to upper method, the pseudo random number of other distribution can be produced.Generate different pseudo random numbers, only need on request, calculate the numerical curve in look-up table, carry out loading.

The present invention can produce long sequence period pseudo random number, also can produce wide band digital white noise signal, and its Parameter adjustable such as average, variance saves.When producing pseudo random number, pseudo random number reads by reading interface circuit by outer CPU, often reads once, reads current pseudo-random number, and generates next pseudo random number.When producing digital white noise signal, needing a clock, under the excitation of clock, generating high-speed figure noise signal.

Below to produce 8 pseudo random numbers and digital noise signal, its principle of work is described.When pseudo random number circuit for generating represents with Figure 15, pseudo random number and digital noise signal generation control circuit are as shown in figure 16.In circuit, MODE_SEL is model selection input signal, selects to produce noise signal when being 0, selects to produce pseudo random number when being 1.CLK is input clock signal./ CS is that sheet selects input signal, when for 0 time, represent and this circuit operated./ RD is the read input signal that CPU sends, when for 0 time, represent carry out read operation.RNG [7..0] is pseudo random number input signal, from pseudo random number circuit for generating.RNGCLK is clock output signal, is connected to upper figure, as the clock of pseudo random number circuit for generating.Q [7..0] is digital noise output signal, and when selecting to produce noise signal pattern, the rising edge of each clock exports a digital noise signal, exports the maximum half being about clock frequency of bandwidth of digital white noise signal.DB [7..0] is pseudo random number output signal, and being connected on the data bus of CPU, is ternary signal, when selecting to produce pseudo-random number pattern, CPU often reads once this circuit, and pseudo random number circuit for generating exports a pseudo random number, produces next pseudo random number simultaneously.

Pseudo random number or digital noise signal are sampled, sample sequence is set to { x _i, the average u of N number of sample is:

$u=\frac{\underset{i=0}{\overset{N-1}{\Σ}}{x}_i}{N}$

Variances sigma ²be equivalent to the power asking signal communication part, formula is:

${\mathrm{\σ}}^2=\frac{\underset{i=0}{\overset{N-1}{\Σ}}{(x_i-u)}^2}{N}$

When N value is larger, the average u of sample sequence, variances sigma ²can as an estimation of the true average of this signal, true variance, its error is very little.

Average be u, variance is σ ²pseudo-random number sequence { x _ibe normalized into the pseudo-random number sequence { y that average is 0, variance is 1 _i, formula is:

$y_i=\frac{x_i-u}{\mathrm{\σ}}$

With average be 0, variance be 1 pseudo-random number sequence { x _istructure average is u, variance is σ ²pseudo-random number sequence { y _i, formula is:

y _i＝u+σ*x _i

If the bandwidth of the digital white noise signal of band limit is B, average is 0, variance is σ ², then its amplitude spectrum density is:

A(f)＝σ/B

Power spectrum density is:

P(f)＝σ ²/B

In order to upper method, the average, the variance that export pseudo random number can be controlled, and the average of digital white noise signal, variance, amplitude spectrum density or power spectrum density.

Use the method that high speed FPGA circuit realiration is discussed herein, clock frequency can reach 500MHz, can generation per second 500M pseudo random number, wideband digital noise signal more than exportable 200MHz bandwidth.Use superfast digital circuit, the digital noise signal of exportable more high bandwidth.

Be to be understood that example as herein described and embodiment only in order to illustrate, those skilled in the art can make various amendment or change according to it, when not departing from Spirit Essence of the present invention, all belong to protection scope of the present invention.

Claims (1)

1. a pseudo random number production method, is characterized in that: based on the N of parallel organization longest linear feedback shift register _aposition pseudorandom number generator A, what generate m position is uniformly distributed pseudo random number, is designated as A [k], take binary representation as A _m-1[k] A _m-2[k] ... A ₁[k] A ₀[k]; Based on the N of parallel organization _bthe pseudorandom number generator B of position longest linear feedback shift register, what generate m position is uniformly distributed pseudo random number, is designated as B [k], take binary representation as B _m-1[k] B _m-2[k] ... B ₁[k] B ₀[k]; Pseudo random number A [k] carries out XOR with corresponding data position in pseudo random number B [k], and generating pseudo random number D [k], take binary representation as D _m-1[k] D _m-2[k] ... D ₁[k] D ₀[k]; The pseudo random number B [k] that the pseudo random number A [k] requiring pseudorandom number generator A to generate and pseudorandom number generator B generate is uncorrelated, namely the primitive polynomial of pseudorandom number generator A and the primitive polynomial of pseudorandom number generator B can not be mirror image primitive polynomials, due to uncorrelated between pseudorandom number generator A and pseudorandom number generator B, each in the pseudo random number D [k] generated is equally distributed, and therefore D [k] is that m position is uniformly distributed pseudo random number.