LowComplexityMethodforSpreadingSequenceEstimationof.doc

精品论文low complexity method for spreading sequence estimation ofdsss signal in non-cooperative communication systemsliang chang, fuping wang, zanji wang(department of electrical engineering, tsinghua university, beijing 100084, peoples republic of china)abstract: it is a necessary step to estimate the spreading sequence of direct sequence spread spectrum (dsss) signal for blind despreading and demodulation in non-cooperative communications. the article proposes two innovative and effective detection statistics to implement the synchronization and spreading sequence estimation procedure. the proposed algorithm also has a low computational complexity with only linear additions and modifications. theoretical analysis and simulation results show that the algorithm performs quite well in low snr environment, and is much better than all the existing typical algorithms with a comprehensive consideration both in performance and computational complexity.keywords: dsss, detection statistic, low complexity1. introductionnon-cooperative communication systems are quite different from the cooperative communication systems. in non-cooperative communication systems, the receiver has minimum prior knowledge of the intercepted signal, such as frequency offset, baud rate, and modulation type. so in order to capture the transmitted information, the unknown parameters and modulation type should be obtained first by the family of blind signal processing methods, such as high-order or cyclostationary based methods.direct sequence spread-spectrum (dsss) signal has the characteristics of pseudorandom and correlation processing, which brings the advantages of anti-multipath fading, anti-narrowband interference, anti-noise, and cdma 1. but in non-cooperative communications, as the chip rate, baud rate, and spreading sequence isunknown to the receiver, the above characteristics of dsss signal makes the blind estimation of parameters andspreading sequence a crucial but also equally challenging problem to be solved in low snr environment.compared with the problem of spreading sequence estimation, the problem of parameters estimation is somewhat easier. numbers of robust algorithms 26 are proposed to finish the estimation of baud-rate, chip-rate,and frequency offset. with the knowledge of the above parameters, the spreading sequence can be extracted from the intercepted signal. so far there are several methods proposed to solve the problem. in 7 and 8, a subspacebased method is proposed to implement the sequence synchronization and spreading sequence estimation byextracting the two biggest eigenvalues and the corresponding eigenvector, but the estimation of thesynchronization parameter is not robust in low snr environment, and the procedure of eigenvalue decomposition has a very high computational complexity of o(n3). so a robust synchronization algorithm is proposed in 9 to solve the above problem. in 10, a constraint hebb rule based low-complexity method is proposed to estimate the spreading sequence, but the sequence synchronization, which is hard to estimate in low snr environment, should be a prior knowledge to this method. also the best choice of the step size relies on the training sequence, which is not practical in non-cooperative communcations. in 10, two detection statistics areproposed based on the intercepted signal to implement the sequence synchronization and sequence estimation, which also has low computational complexity. but it performs poorly in low snr environment compared with other existing algorithms. to robustly estimate the spreading sequence in lower snr environment is still a problem to be solved. by the way, all of the above literatures concentrated on the pure binary spreading code, however, three-value spreading code are widely used recently, such as las-cdma and ds-uwb systems, but the study of the blind estimation of the three-value spreading code has not been reported.by the anti-noise characteristic of correlation, the article proposes two simple detection statistics based on correlation matrix of the intercepted signal, which is robust and low computational complexity. the first detection statistic is for spreading sequence synchronization, which is implemented by calculating the statistic at every possible starting point, the maximum statistic gives the estimation of sequence synchronization. the second detection statistic implements the estimate of the spreading sequence chip-by-chip. with a little modification, the proposed statistic can be applied to estimate the three-value spreading code. the correct ratio with a given snr and symbol length is derived both in theoretical analysis and numerical illustration respectively, which manifest the effectiveness of the proposed algorithm and superiority against other existing typical algorithms.the article is organized as follows: section 2 gives the signal model and section 3 introduces the two detection statistics for sequence synchronization and sequence estimation respectively. section 4 provides the corresponding theoretical performance analysis, and in section 5 monte-carlo simulations are done to evaluate the performance and the superiority against other algorithms. section 6 concludes the article eventually.112 signal modelit is assumed that the symbol rate 1/ t0 , chip rate 1/ tcand frequency offset have been perfectly estimated.the spreading sequence is short code with period n, so t0 = ntc . after match-filtering and resampling by chiprate 1/ tc , the intercepted signal can be divided by symbol periodt0 , so every segment has n samples.consider the asynchronized circumstance, the m-th segment can be represented as follows:specialized research fund for the doctoral program of higher education (20060003032)精品论文22ym =s ( am h0 + am +1h1 ) + nm(2.1)where s is the signal power.ma is the m-th transmitted symbol, which can be mpsk modulation symbols2and i.i.d. nmis the m-th additive white gaussian noise (awgn) vector with dimension n and variance n , soh 2he nn= n i , where (i ) is the hermitian transposition. h0and h1include the latter n-n0 and the formern0 spreading codes respectively, can be represented as:h = p ,., p 0, ., 0h ,0 n0 +1 nn n0h = 0, .0, p , p , ., p h ;1 1 2 n0n0(2.2)wherepi 1for traditional binary spreading code, andpi 1, 0 for three-value spreading code.the goal of this article is to estimate the synchronization parameter n0 firstly, then estimate the spreading sequence p1 ,., pn from the intercepted signal.3proposed algorithm3.1 spreading sequence synchronizationthe correlation matrix of the intercepted signal from m divided segments can be estimated as follows:r m =1 y y h(3.1)m mm mdenoterk ,l as the matrixs element with index k and l standing for row and column respectively，therepresentation ofrk ,l in different position can be expanded as follows:k = l， rk ,l is a diagonal element： (am pk nm,k + am pk nm,k ) (nim ,k + nqm ,k )*22r= sp2 + m+ m ，( 1 k n )(3.2)k ,kkmmiwhere respectively.nandm ,k nare the in-phase and quadrature part of the k-th noise element in the m-th segmentqm ,k k l ,k , l 1, n n0 ork , l n n0 + 1, n ：(a p n*+ a* p n)nn*m k m,lm l m, k m,k m,l r = sp p + m + m （1 k n ，1 l n ）(3.3)k ,lk lmmk l , whenk 1, n n0 ,l n n0 + 1, n ; or whenk n n0 + 1, n , l 1, n n0 ：a a*(a p n*+ a* p n)nn* m m +1m k m,lm +1 l m,k m,k m +1,lr = p p m + m + m （1 k n ，1 l n ）(3.4)k ,lk lmmmwhen m ，based on equation (3.2)(3.4), the ideal correlation matrix can be expressed as followsm mr = e y y h sp2+ 2 sp p n0 +1n n0 +1 n #% #0 0n n spn pn +1= sp2 + 2sp2 + 2 sp p (3.5) 1 n1 n0 0 #% #2 sp p sp2 + 2 n0 1n0 n in 9, a detection statistic w.r.t the synchronization parameter n0is defined as follows:f (r ) =r( n n )(3.6)1n0 i , j , 10ijby exploiting the relationship between the eigenvalues and the elements of the correlation matrix, 9proves that the above defined statistic will reach the maximum when n0= n. but the imaginary part of theelement of the correlation matrix is only contributed by the noise, and the square law operation will enlarge thenoise. to avoid the above disadvantages, a modified detection statistic is defined as follows:330f1 (rn) = real ( ri , j )ij0(3.7)where real (.) is the real part of the signal. the above equation can be easily derived as:f (r) = ( n n )2 s + n2 s + n 21n000n, (1 n0 n )(3.8)00n= 2sn2 2n sn + n 2 s + n 2it can be seen clearly thatf1 (rn )reaches its maximum when n0= n 。son0 can be estimated by00searching the position corresponding tof1 (rn) s maximum. figure 1 shows the detection statisticf1 (rn )w.r.tn0 . the transmitted data has a modulation type of bpsk. the spreading sequence is a gold sequencegenerated by two characteristic polynomial f(x) = 1 + x2 + x3 + x4 + x5 and f(x) = 1 + x + x2 + x5 + x6respectively.hto avoid calculating the estimated correlation matrix rm at every start point from the first samples to the nth samples, which will increase the computational complexity, a vector of dimension 2n can be built asq = y hy h ， the corresponding correlation matrix can bem mm estimated as follows：1 mh10.9qm = qm qmm i =1(3.9)0.80.7the authors denote k with range from 1 to n, the k-th sub-matrix0.6with rows and column from k to k+n is denoted as r . so ncan be0.5estimated as follows:()k0f (r )/max(f (r )1 k1 kn0 = arg max fr(3.10)k1k0.10the above discussion is for pure binary spreading code. however, it can be directly extended to three-value spreading code. it is assumedthat the first and the last element should be non-zero. the condition10 20 30 40 50 60kfigure 1 detection statistic f1(rk)will be satisfied in most cases, so only the spreading code satisfying the above condition will be discussed. the performance will be evaluated by monte-carlo simulations in section 4.3.2 spreading sequence estimationafter the sequence synchronization is achieved, the sub-matrix corresponding to the maximum off1 (rk )can be extracted and denoted as r0 with the following form as:m mr = e y y h sp2 + 2sp p sp p 1 n 1 2 1 n (3.10)= sp2 p1 % # #%spn 1 pn sp psp p sp2 + 2 n 1n n 1n n so it is easy to construct a second detection statistic for spreading sequence as follows：f2 ( j ) = i ,i 1,i jreal (r ,1r (0)(0)i) real ( i , j )(3.11)where(0)ri , j is the element of matrixr0 . without loss of generality，the first element of spreadingsequence is assumed to be p1 = 1 ，so other spreading sequence element pj (2 j n )binary and three-value spreading code, it can be obtained as follows respectively:can be obtained. forp j = sgn f2 ( j ) ,(j=2,3,n)(3.12)sgn f2 ( j ),f2 ( j ) 0.5p j = 0,f2 ( j ) 0)(4.3)n kp( x ( d ) x (i ) )k ( n k )2(| y ( d ) | | z (i ) |)k ( k 1) / 22(| y ( d ) | | y (i ) |) 0 = i =1,i d j =1j j+j =1j j+j =1j j 2denote the mean and variance for random variable qifollows：as andqi , they can be calculated asqiqi= 2k ( n | d i |) ( |y | |z | ) ，(4.4.a)|y |z |y | x |() 2 = 4k ( n k ) 2 + 2 + 4k (k 1) 2 + 2k 2qi(4.4.b)= 2 | d i | 2+ 4 | d i | ( n 1) 2 + 4 | d i | ( n | d i |) 2| x |y |z |so the correct ratio can be represented by variableqi s mean and variance as follows：n 2 p= 1 erfc =qi (4.5)ct1 22 2 i =1,i d qi the theoretical correct ratio can be calculated from equation (5.1) to (5.5) with the knowledge ofthe spreading factor n, segment length m, and snr.654.2 spreading sequence estimationdenote the second and the third part ofr (0)as n, which0.80.7pdf(x)0.6( ( 24 ) i , j i , j + , then equation (3.8)has a distribution ofn 0, 22/ m0.5can be expressed as follows:0.4nf ( p ) =(sp + n)(sp + n )(2 j n )(4.6)0.30.22 j 1i =2,i jii ,1j ii , j00.1the authors firstly assume pi = p1 , the circumstance ofpi = p1willbediscussedlater.denote-8-6-4-202468xuii+ = s + n, v+= s + nwith mean and variance:iii , ji ,12 2 + 2 4figure 2 probability density function of wte u + = e v+ = s va