Sequence with a low PAPR design method for wireless communication system

1. A computer-implemented method for providing low Peak to Average Power Ratio (PAPR) sequence design for a Orthogonal Frequency Division Multiplexing (OFDM) wireless communication system, the sequence with a low PAPR only contains elements −1 and +1, wherein the computer-implemented method comprises the following steps:

setting relevant parameters of a designed sequence at first, wherein multiple iterations are executed until conforming to a termination condition,

generating multiple length-designated sequences having elements of 0 and 1 and obeying the Bernoulli distribution of designated probability density parameters according to the parameters during primary iteration,

screening the generated sequences according to the PAPRs of the sequences, wherein a minimum PAPR is electronically selected, wherein a threshold of the PAPR is electronically set and is used for screening the generated sequences,

updating the parameters of the next iteration based on the screened sequences,

mapping the sequence having the minimum PAPR to obtain a sequence with a low PAPR with elements of −1 and 1 after terminating the iterations, and

transmitting or receiving wireless signals based on at least a portion of the sequence with the low PAPR via the OFDM wireless communication system.

2. The computer-implemented method of claim 1 , wherein the relevant parameters of the designed sequence comprise: a sequence length N; the number J of random sequences generated every time; a sampling coefficient S, 0<S<1; an initial probability density function parameter u={u n } n=1 N ; an iteration termination condition: iteration times T and/or a convergence condition threshold ε; and an initial PAPR value V PAPR old ;

the then carrying out multiple iterations until conforming to a termination condition, generating multiple length-designated sequences having elements of 0 and 1 and obeying the Bernoulli distribution of designated probability density parameters according to the parameters during primary iteration, screening the generated sequences according to the PAPRs of the sequences, updating the parameters of the next iteration based on the screened sequences, and mapping the sequence having the minimum PAPR to obtain a sequence with a low PAPR with elements of −1 and 1 after terminating the iterations, specifically comprise:

(2) generating J random sequences obeying the Bernoulli distribution of parameters u={u n } n=1 N by using the Monte Carlo method;

(3) calculating the PAPRs of mapping sequences Q j ϵ{−1,+1} N of the generated sequences P j ϵ{0,1} N , selecting the minimum PAPR from J PAPRs, marking the same as V PAPR new , and setting the threshold γ of the PAPR, wherein the threshold is used for screening the sequences participating in the calculation of updating iteration parameters;

(4) judging whether the iteration termination condition is satisfied, if so, executing step (6), and otherwise, executing step (5); in the case that the iteration times are set, the termination condition comprises reaching to the iteration times, and in the case that the convergence condition threshold is set, the termination condition comprises |V PAPR new −V PAPR old |≤ε;

(5) updating V PAPR old and u={u n } n=1 N , and transmitting the value of the V PAPR new to the V PAPR old , wherein u n is set according to the numerical value distribution of the n th sequence in all sequences conforming to the threshold conditions of the PAPR in step (3); and executing step (2) to enter the next iteration; and

(6) mapping the sequence ϵ{0,1} N corresponding to the minimum PAPR in step (3) to ϵ{−1,+1} N , wherein the obtained is the designed sequence.

3. The computer-implemented method of claim 2 , wherein the relevant parameters of the designed sequence further comprise: a limiting position domain C and a limiting position value W; and the sequences generated in step (2) are represented as follows:

P

j

=

{

P

j

,

n

}

n

=

1

N

=

{

P

j

,

n

∼

Ber

⁢

⁢

(

u

n

)

,

n

∉

C

P

j

,

n

=

w

n

,

n

∈

C

,

j

=

1

,

…

⁢

,

J

,

wherein w n ϵW represents the value of a limiting position element.

4. The computer-implemented method of claim 2 , wherein a mapping function of the mapping sequences Q j ϵ{−1,+1} N of the sequences P j ϵ{0,1} N in step (3) is Q j =1−2P j , P j Q j 1 all represent N-dimensional vectors; the formula for calculating the PAPRs of the mapping sequences Q j ϵ{−1,+1} N of the sequences P j ϵ{0,1} N in step (3) is as follows:

F

⁡

(

P

j

)

=

10

⁢

log

10

⁢

max

⁢

{



x

⁡

(

1

-

2

⁢

P

j

)



2

}

E

⁡

[



x

⁡

(

1

-

2

⁢

P

j

)



2

]

wherein, x( ) represents IFFT, E[ ] represents mathematical expectation, and max{ } represents taking the maximum value.

5. The computer-implemented method of claim 2 , wherein the specific steps of selecting the minimum PAPR from J PAPRs, marking the same as V PAPR new , and setting the threshold γ of the PAPR in step (3) comprise:

(3.1) carrying out ascending sorting on F(j), j=1, . . . , J to obtain {tilde over (F)}(j), wherein F(j) represents the PAPR of the sequence j;

(3.2) selecting the minimum PAPR V PAPR new ={tilde over (F)}(1); and

(3.3) setting the threshold of the PAPR as γ={tilde over (F)}(┌J·S┐), wherein ┌ ┐ represents an upward rounding function.

6. The computer-implemented method of claim 2 , wherein in step (5), the formula for setting u n according to the numerical value distribution condition of the n th sequence in all the sequences conforming to the threshold conditions of the PAPR in step (3) is as follows:

u

n

=

∑

j

=

1

J

⁢

⁢

(

F

⁡

(

P

j

)

≤

γ

)

⁢

P

j

,

n

∑

j

=

1

J

⁢

⁢

(

F

⁡

(

P

j

)

≤

γ

)

,

n

=

1

,

…

⁢

,

N

wherein, ( ) represents an indicating function: when and only when F(P j )≤γ, (F(P j )≤γ) is equal to 1, and otherwise is 0; and P j,n represents the value of the n th element of the generated j th sequence.