Frequency-domain small wave blind equalization method based on united combining space-time diversity

Mode of execution

In conjuction with the following technical scheme of the invention to carry out a detailed description:

1 small the wave is blind method for frequency domain equalization

As shown in Figure 1, wt-CMA method to the input signal of the orthogonal wavelet conversion, the input signal is reduced the maximum autocorrelation matrix, the ratio of the minimum eigenvalue, the good styptics can be obtained. Still in the balancing process, however, the linear convolution method, the calculation amount is very large, is not conducive to engineering realization of the method. Reservations through FFT technology and overlap, wt-CMA in the calculation of the convolution, will greatly reduce the computational complexity of the algorithm, the frequency domain is obtained (FWTCMA) small the wave is blind balancing method.

Figure 1 in {a (n)} is an independent sequence of the transmitted signal with the distribution of the; c (n) is the impulse response of the channel ; {w (n)} is Gaussian white noise sequence; y (n) is the input signal of the wavelet transformer; r (n) = [r (n), r (n-1), …, r (n-M_f + 1)]^I by the wavelet is a time-domain in the output signal of the converter; Q= [G₀; G₁ H₀; G₂ H₁ H₀; G_J-1 G_J-2 … H₁ H₀; H_J-1 H_J-2 … H₁ H₀] to orthogonal wavelet transform matrix, wherein H_j and G_j are respectively formed by the coefficients of the wavelet filter h (n) filter coefficient and the dimension g (n) of the matrix a; F (N) updated weight vector is frequency domain equalizer, R (N) is the input signal of the frequency domain equalizer. According to the wavelet transformation theory

R (n) =Qy (n)

R will be (n) is divided into L long block, to r (n) of the blocks and N-1 N a block 2L point sequence, in N=1 time, in r (1) pre-acquire the L zero, if the set f (n) for each input block corresponding to the vector of time-domain equalizer, the following additional a-L 2L point sequence, use of fast FFT technology, using a cyclic convolution to calculate the linear convolution (overlapping reservations) is

R (N) =FFT {r (nL-L), r (nL-L + 1), ... (nL-1) r (nL) r, r (nL+ 1)... (nL+L-1) r] (1)

F (N) = FFT[f^T (n), 0, 0,     , 0]     (2)

Z (N) = R (N) F (N)     (3)

E (N) = Z (N)-R_F     (4)

In the formula, R (N) to r (n) after performing a Fourier transform of the signal; the Fourier transform FFT symbol; superscripts T transpose operation said; R_F modulus value of the signal in the frequency domain; Z (N) is the output signal of the frequency domain equalizer; E (N) into the frequency domain error. Based on wavelet transform that the equalizer blind , wavelet transform is combined with the CMA, adjusting the front to the right to vector normalization processing (see literature : han Yingge , guo Yecai , Wu afforestation, zhou Qiao hi. The orthogonal wavelet transform-based equalizer design adjust with the algorithm simulation study. Instrument Journal, 2008, 29 (7): 1441-1445). Still in the frequency domain using the same method, to construct the normalized matrix is

r(n)=[r1,0(n),r1,1(n)...rJ,kJ(n),sJ,0(n),...sJ,kJ(n)]T

Wherein

In the formula, For scale function, φ_jk (i) for small wavefunctions, r_j,k (n) small wave space in the section layer decomposes j signal k, s_j,k (n) expressed in the scale space section layer decomposes j signal k, k is a positive integer 0<k≤ K, K is the number of wavelet filter. Normalization matrix [R^(n)]-1=diag{[σj,0(n)]2,[σj,1(n)]2,...[σJ,kJ(n)]2,[σJ+1,0(n)]2,...,[σJ+1,kJ(n)]2};and Are respectively expressed The estimated average power, and can be held by the recursion is of the formula:

[σ^j,kJ(n+1)]2=β[σ^j,kJ(n)]2+(1-β)|rj,kJ(n)|2---(6a)

[σ^j+1,kJ(n+1)]2=β[σ^j+1,kJ(n)]2+(1-β)|sj,kJ(n)|2---(6b)

In the formula, | | the absolute value symbol. R^(N)=FFT[R^(n),0,0,...,0],In the frequency domain can be obtained on the basis of small the wave is blind equalizer for updating the weight vector of the formula

F(N+1)=F(n)+2μR^-1(N)E(N)sign(Z(N))R*(N)---(7)

In the formula, the symbols of the sign (·) function.

2 frequency domain based on the space-time diversity combining small the wave is blind balancing method

2.1 the collection is blind joint combined space-time hours equalizing method system model

As shown in Figure 2, time diversity refers to repeated more than channel coherence time interval for transmitting the same signal, making the receiving end obtain a plurality of the signal with independent fading environment; the space on the space diversity means through a plurality of transmission characteristics of the different channel, of if the time diversity signal to each path in the form of space diversity transmission, to form a kind of time division the technology.

Figure 2 in, T_c is time interval, time diversity is M the renumbers, z_l (n) l a to the output of the space diversity module (l=1, 2, the   M), z (n) is a space diversity module output of the merger of time the output of the diversity combiner. Figure 2 shows that, in the balanced the collection is blind time-space-time diversity method for each route different spatial diversity module, each space diversity through a certain post-merger integration manner the output of the diversity combiner as the input of the time, a joint. In the present invention, time diversity combined effect will be the best way the maximum ratio combining, the balanced the collection is blind method for space-time hours is the branch, a single consolidated manner and fading channel to reduce the effects of steady-state error is not obvious, therefore in space diversity combining mode using selected in the module, the merger of a balanced the collection is blind method for space-time hours, its resolution l space diversity module structure, as shown in Figure 3.

Figure 3 shows, a paragraph l heavy D space diversity module is composed of a space diversity branch, each branch circuit adopts FWTCMA method is equalized, the output signal enters the selection logic, selected by the selection logic baseband signal with the highest signal-to-noise ratio of the output of the module as the space.

2.2 method description

In the combined space-time diversity system model, each of the branches in the frequency domain of the equalizer updating small the wave is blind balancing method, the diversity path space in subsection l section of the module for example branches d, vector its power the update process is as follows

Z_ld (N) = R_ld (N) F_ld (N)   (8)

E_ld (N) = Z_ld (N)-R_F     (9)

Fld(N+1)=Fld(N)+2μR^ld-1(N)Eld(N)sign(Zld(N))Rld*(N)---(10)

Z_ld (N) l path space to section d of the module a diversity branch of the output signal of the frequency domain equalizer, its Fourier inverse transformation for z_ld (n); R_ld (N) section l path space for the diversity module section d wavelet transformer circuit output signal of frequency domain; E_ld (N) l diversity path space to section d of the module frequency domain of the error signal; the output of the arbiter s_ld (n); if the branch transfer section j characters recorded as the average measurement error

e_li (n-j)=z_ld (n-j)-s_ld (n-j)     (11)

The branch transfer N_B characters for the average measurement error E[!OverBar!]ld(n)=1NB(Σj=0NB-1|eld(k-j)|),At a certain moment to the subsection l space diversity module compares all branch, is selected as the minimum of the output of the space diversity module l z_l (n). To this completion of the selection combining. The remaining space diversity module also performs the same process. Each space diversity is a diagram of the output of the module 2 in the input of the combiner. Selection combining manner is easy to realize, but is not the best way, sometimes combined effect will be affected. Therefore, in Figure 2 the space-time diversity in the three combined effect in the best way the maximum ratio combining, to overcome this defect of a single consolidated manner. According to the principle of maximum ratio combining, each path the output of the space diversity module after chart 2 after the merger in the output of the combiner

z(n)=Σl=1DAlσl2zl(n)---(12)

wherein A_l section said supporting l the amplitude of the output signal of the time diversity, σ_l² section l that a noise variance of the branch of the time diversity. Type (8)-(12) of the joint is based on space-time diversity combining method for frequency domain equalization the wave is blind (JCTSD-FWTCMA) small.

The input signal to orthogonal wavelet transform, the sparse matrix Q, Q each row in the assumption of the number of nonzero element N₁, completed wavelet transform the multiplication of the number of required N₁ N₂. In the present invention the each of the branches in the orthogonal wavelet the frequency range is blind equalization method, method for the quadrature small compared with balanced the wave is blind , greatly reducing the amount of calculation thereof, its contrast analysis are as follows: the need for frequency domain equalization 3 time N₁ point FFT calculation and 2 times 2N₁ point complex multiplication, but for real input, because the symmetry can be used to calculate a a half power , and 2N₁ point FFT can be by 2N₁ point FFT and 2N₁ complex to realize. Each complex multiplication by 4 is a real multiplication to calculate 3N₁ log₂ (N₁/2) + 4N₁ + N₁ N₂ time, small wave often the number of digital-to-analog algorithm needs to be calculated for N₁ N₂ + N₁², reduce the computational complexity of each path for Δ=N₁ N₂ + N₁² -3Llog₂ (N₁/2) + 4N₁ + N₁ N₂, if heating N₁ = 32,     = 786, for reducing computational complexity is a total 786DM time, from this it can be seen, the branch the more the greater the reducing computational complexity.

Implementation examples

JCTSD-FWTCMA in order to verify the effectiveness of the method of the invention, using 16PSK signal simulation, emulation if assumptions M=D=2, instant space division centralized containing two space diversity module, and each space diversity module contains two branches, will need to be four underwater acoustic channel, are respectively the c₁ = [0.9656-0.09   060.0578   0.2368] and c₂ = [0.8264-0.1653   0.1653] as a 1st space module channel, c₃ = [0.35   0   0   1] and c₄ = [0.2   0.5   1   -0.1] as a 2nd space diversity module, the signal-to-noise ratio for 20dB, the equalizer the power is long 32 and the center tap initialization, each signal using DB2 wavelet decomposition, decomposition level is the 2 layer, power initial value is 4 ; β=0.999, the simulation step μ_wt-CMA = 0.00155; μ_FWTCMA = 0.015088; JCTSD-FWTCMA method in the, 1st module of two branches to step μ₁ = 0.007,₂ = 0.0073; 2nd module of two branches to step μ₃ = 0.15,₄ = 0.15; 1500 time Monte carlo simulation result, as shown in Figure 4.

Figure 4 shows, the method of the invention than the convergence speed JCTSD-FWTCMA wt-CMA and FWTCMA is improved for about 4500 step and 2500 step, the steady state error than wt-CMA and reduced respectively FWTCMA about 8dB and 3.5dB. Figure 4 (c, d, e) shows that, the output of the constellation clear FWTCMA, compact, but the method of the invention the output of the constellation JCTSD-FWTCMA the most clear.