Orthogonal wavelet transform constant modulus blind equalization algorithm based on optimization of DAN genetic algorithm

1. A genetic optimization of DNA-based orthogonal small the wave is blind equalization method, characterized in that comprises the following steps:

Step 1, a signal (n) after the pulse in response to a channel h (n) then adding channel noise v (n), by orthogonal wavelet converter input signal y (n): y (n) = a (n) h (n) +v (n); wherein n is a positive integer and said time sequence, with;

Step 2, the step 1 the orthogonal wavelet converter input signal y (n) into the orthogonal wavelet converter performs orthogonal wavelet transform, orthogonal wavelet transformer to r output signal (n): r (n) =Vy (n); wherein V is orthogonal wavelet transform matrix;

Step 3, step 2 the orthogonal wavelet transformer r output signal (n) as the equalizer blind input signal, the output signal from the equalizer blind z (n): z (n) = w^H (n) r (n); wherein w (n) to the weight vector of the equalizer blind , superscripts H said conjugate transpose;

Step 4, step 2 the orthogonal wavelet transformer r output signal (n) as the input signal of the DNA genetic algorithm, the equalization method optimizes blindly DNA genetic algorithm w initial power vector of (0);

Wherein said method for DNA genetic algorithm balanced optimizes blindly w initial power vector of (0) process comprises the following steps:

Step 4-1, and setting initial stocks encoding DNA

DNA genetic algorithm is the original stocks Chrom= [w₁, w₂, …, w_M], wherein w_mthe mold is blind corresponding to the orthogonal small wave often WTCMA section of the equalizing method for a m vector, the 1 m≤M [...] , to stocks M number of individual scale; blind four base pairs in the equalizer vector w_m is encoded;

Step 4-2, determining fitness function

With the orthogonal small the wave is blind equalizing method for vector WTCMA w_m corresponding cost function defined as

J(wm)=Σi=1N(R-|zm(i)|2)2N

In the formula, N the length of the sequence of the received signal, an integer saw vertically from; z_m (i) blind the equalizer section m and a corresponding output signal to vector; is defined as DNA fitness function of the genetic algorithm for J (w_m) the reciprocal, that is,

F(wm)=bJ(wm)

In the formula, b of the proportional coefficient said; cost function J (w_m) the global minimum, that is the maximum value of the fitness function is to require an individual corresponding to the optimum individual;

Step 4-3, the stocks packet

The orthogonal wavelet converter output signal as the input signal of the DNA genetic algorithm, each individual in the population after decoding to the value of the fitness function in substitution, calculate the stocks of each individual in a numerical letter ; individual adaptation value according to the size of all individual sorted to, the front half-M/2 as an individual stocks of high quality, the rear half-M/2 inferior stocks individual as; in the high-quality stocks to the maximum value of the current in the individual as the most optimum individual stocks, and as the elite individual reservations;

Step 4-4, crossing operation quality of the stocks

The stocks for operating selected at random in the implementation of the cross-operation father body , father body to the selected of the displacement cross-operation and dislocation cross operation, the implementation of replacement cross-operation and position respectively as the probability of crossing operation p₁ and p₂; father body if the selected replacement are not implementation of the cross and an indexing cross operation, according to the reconstruction cross-probability p₃ crossing operation performing reconstruction; repeat the above-mentioned cross-operation until the produce M/2 a new individual, then the M/2 to a new individual is put in high-quality stocks and inferior stocks, with 3M/2 of the body of one mixed population;

Step 4-5, the variation of the mixed population of operation and league selection operation

By the high-quality stocks obtained after cross-operation with 3M/2 mixing stocks one implementation of mutation operation, mutation operation adopts the self-adaptive dynamic variation, the variation for the individual replacing the original individual, after the completion of the operation of variation, repeated M-1 league match selection operation, selected M-1 individual , stocks with the elite individual, the size of the new stocks M, stocks evolution algebraic adding 1;

Step 4-6, it is judged whether the termination condition for the evolution

Sets a maximum evolution algebraic to g_max and is a positive integer, if the evolution time reaches the most evolved algebra, the stocks in the largest value of the individual as the most optimum individual output, and the its decoding, the decoded value as the initial equalizer vector optimized power ; otherwise, return to step 4-3;

Step 5, from step 4 to obtain the initial optimized power vector w (0) the rear, the weight vector of the to the equalizer blind w (n) to update, updating formula is:

w(n+1)=w(n)+μR^-1(n)r(n)e*(n)z*(n).

2. DNA-based genetic optimization orthogonal small the wave is blind equalization method according to Claim 1, characterized in that the stated step 4-1 of the four DNA bases in the combination of the four digital form to represent, the four digital meet between a pair of complementary base pairing rules.

3. DNA-based genetic optimization orthogonal small the wave is blind equalization method according to Claim 2, characterized in that the " 0, 1, 2, 3 the of the four digital [...] arbitrary combined to represent the four DNA bases.

4. DNA-based genetic optimization orthogonal small the wave is blind equalization method according to Claim 3, characterized in that the digital sequence 0123 corresponding to the letter sequence CGAT, and 0 and 1 complementary mating, 2 and 3 complementary mating.

5. The arbitrary one of DNA-based genetic optimization of the orthogonal small the wave is blind equalization method according to Claim 1-4, characterized in that the stated step 4-3 in a decoding operation comprises the following steps:

Step 4-3-1, each individual DNA stocks will be decoded into a M_f-dimensional metric vector Wherein M_fblindthe power is long the equalizer, L blind equalizer that each of the vector in a tap coefficient used for coding the required an DNA, B (j) a coding section i the tap coefficients from left to right on the numeric section of the j-bit digital;

Step 4-3-2, through the following formula according to the proportion, the f_i (0) converted into vector solution;

wi(0)=fi(0)4l-1(dmaxi-dmini)+dmini,

In the formula, d_maxi and d_mini section i to a tapping coefficient updated weight vector the maximum value and the minimum value.

6. The arbitrary one of DNA-based genetic optimization of the orthogonal small the wave is blind equalization method according to Claim 1-4, characterized in that the stated step 4-4 high-quality crossing operation of the stocks comprises the following steps:

Step 4-4-1, replacement cross-operation: from the random choice in high-quality stocks as two individual father body and random produce a (0, 1) the random number between, the random number and the displacement cross-probability p₁ comparison, if the random number less than p₁, in each father body are respectively selected at random in a section of the base equals the number of gene sequence, a base sequence of the selected replacement cross-a-time, to obtain two new individual; otherwise, does not carry out replacement cross-operation;

Step 4-4-2, indexing cross-operation: re-random produce a (0, 1) the random number between, the random number with index cross-probability p₂ comparison, if the random number less than p₂, the step 4-4-1 obtained in the two individual base sequence selected at random and a section of the shear-down, a section is cut at the same time the individual base sequence of random choice in a new location of the individual and in the shear down from the base sequence is inserted to this new position, are respectively obtain two new individual; otherwise, does not carry out an indexing cross-operation;

Step 4-4-3, through steps 4-4-1 and step 4-4-2 the rear, if the selected two individual replacement has not been carried out both cross and an indexing cross operation, the random produce a (0, 1) the random number between, the random number and reconstruction cross-probability p₃ comparison, if the random number less than p₃, these two individual perform the reconstruction cross one time of operation, to obtain two new individual;

Step 4-4-4, each generation of populations to repeat steps 4-4-1 to step 4-4-3, until the new individual number is M/2 until one, then the new individual is placed in the original stocks.

7. The arbitrary one of DNA-based genetic optimization of the orthogonal small the wave is blind equalization method according to Claim 1-4, characterized in that the stated step 4-5 league in the selection operation comprises the following steps:

Step 4-5-1, from the execution of the mutation operation after the random choice in stocks of two individual compared to the size of the value, wherein the adaptive value will be the largest individual reservations in the next generation of groups;

Step 4-5-2, step 4-5-1 repeatedly performed M-1 time, can be obtained in the next generation M-1 groups of individuals.