according to the present invention the exponent a ( k ) is calculated iteratively from a ( k − 1 ) and from the first and second differences between subsequent values of a ( k ): d ( 1 ) ( k )= a ( k )− a ( k − 1 )=−( 2 k + u − 1 )· 2 − 1 u − 1 ( 7 ) d ( 2 ) ( k )= d ( 1 )( k )− d ( 1 )( k − 1 )=− 2 · 2 − 1 u − 1 =− u − 1 ( 8 ) such an iterative calculation of the exponent is possible since a ( k ) is a quadratic polynomial in k . this is similar to the calculation of a quadratic permutation polynomial for interleavers given in [ 5 ]. the initial values a ( 0 ) and d ( 1 ) ( 0 ) are given by : a ( 0 )= 0 and d ( 1 ) ( 0 )=( 1 − u )· 2 − 1 u − 1 ( u − 1 − 1 )· 2 − 1 ( 9 ) from ( 7 ), ( 8 ), ( 9 ) and ( 10 ), the exponents a ( k ) are calculated iteratively for all values of k by the following procedure : note that the expression d ( 2 ) ( k ) is not explicitly involved in this procedure , since it is a constant that may be used directly . in an alternative embodiment the calculations modulo n in ( 11 ) can be simplified to give the following procedure : fig2 is a flow chart illustrating an embodiment of the method in accordance with the present invention for generating exponents of elements of a zadoff - chu sequence representing , in the frequency domain , a preamble for uplink synchronization of mobile stations . step s 1 obtains the preamble index u of the sequence to be generated . step s 2 inverts u modulo n . steps s 3 sets the initial value a ( 0 )= 0 and step s 4 determines d ( 1 ) ( 0 ) in accordance with the first parts of ( 11 ) and ( 12 ). step s 5 sets k = 1 . step s 6 tests whether k & lt ; n . if so , step s 7 updates d ( 1 ) ( k ) and step s 8 updates a ( k ). thereafter step s 9 increments k and the procedure returns to step s 6 . the procedure ends at step s 10 when k = n . steps s 5 - s 10 can , for example , be implemented by a for loop as in ( 11 ) or ( 12 ). fig3 is a block diagram of an embodiment of an apparatus in accordance with the present invention for generating exponents of elements of a zadoff - chu sequence representing , in the frequency domain , a preamble for uplink synchronization of mobile stations . the index u of the sequence to be generated is forwarded to a modulo n inverter 30 . the modulo n inverted value u − 1 is forwarded to an initial value provider 32 , which calculates d ( 1 ) ( 0 ) and a ( 0 ). the modulo n inverted value u − 1 is also forwarded to a sign inverter 34 , which stores the sign inverted value − u − 1 . the sign inverted value − u − 1 and the initial value d ( 1 ) ( 0 ) are forwarded to a modulo n adder 36 , which iteratively calculates successive values d ( 1 ) ( k ) in accordance with either : d ( 1 ) ( k )=( d ( 1 ) ( k − 1 )− u − 1 ) mod n ( 13 ) d ( 1 ) ( k )= d ( 1 ) ( k − 1 )− u − 1 if d ( 1 ) ( k )& lt ; 0 then d ( 1 ) ( k )=( k )+ n ( 14 ) this is represented by the indicated feedback loop to modulo n adder 36 , which includes a delay element d that introduces a delay corresponding to 1 iteration . similarly the initial value a ( 0 ) is used to start iterative calculations of successive values a ( k ) in a modulo n adder 38 using the calculated values d ( 1 ) ( k ) in accordance with either : a ( k )=( a ( k − 1 )+ d ( 1 ) ( k )) mod n ( 15 ) a ( k )= a ( k − 1 )+ d ( 1 ) ( k ) if a ( k )& gt ; n − 1 then a ( k )= a ( k )− n ( 16 ) this is represented by the indicated feedback loop to modulo n adder 38 , which includes a delay element d that introduces a delay corresponding to 1 iteration . the resulting exponents a ( k ) are forwarded to an exponentiating unit 40 which forms the elements w a ( k ) of the sequence using the value w = e − j2π / n stored in a memory cell 42 . due to the structure of ( 13 )-( 16 ) the iterations ( in the iteration unit iu including blocks 34 , 36 , 38 , d ) may be performed by first calculating all the values d ( 1 ) ( k ) and then using these values to calculate the values a ( k ). such a procedure , however , requires storing the values d ( 1 ) ( k ) until they are needed for calculating the values a ( k ). as an alternative , illustrated by ( 11 ) and ( 12 ), both iterations may be performed in parallel , which requires storing only the values of d ( 1 ) ( k ) and a ( k ) used in the next iteration . although the description has so far been restricted to generation of zadoff - chu sequences representing preambles in base station receivers for uplink synchronization of mobile stations , other applications where the same principles may be used are also feasible . one such application is generation of the preambles in the mobile station . another application is generation of reference signal sequences , which are also represented by zadoff - chu sequences , in mobile and base stations . it is also possible to generate zadoff - chu sequences representing preambles in the time domain instead of the frequency domain . for example , the mobile station may generate the preamble either in the time domain or the frequency domain . in the time domain the exponents a ( k )=− k ( k + u )· 2 − 1 u − 1 in ( 6 ) are replaced by the exponents a ( n )= un ( n + 1 )· 2 − 1 in ( 3 ). thus ( 7 ) and ( 8 ) will be replaced by d ( 1 ) ( n )= a ( n )− a ( n − 1 )= nu ( 17 ) d ( 2 ) ( n )= d ( 1 )( n )− d ( 1 ) ( n − 1 )= u , ( 18 ) d ( 1 ) ( n )=( d ( 1 ) ( n − 1 )+ u ) mod n a ( n )=( a ( n − 1 )+ d ( 1 ) ( n )) mod n if d ( 1 ) ( n )& lt ; 0 then d ( 1 ) ( n )=( n )+ n if a ( n )& gt ; n − 1 then a ( n )= a ( n )− n fig4 is a flow chart illustrating an embodiment of the method in accordance with the present invention for generating exponents of elements of a zadoff - chu sequence representing , in the time domain , a preamble for uplink synchronization of mobile stations . step s 11 obtains the preamble index u of the sequence to be generated . steps s 12 and s 3 set the initial values a ( 0 ) and d ( 1 ) ( 0 ), respectively , to 0 in accordance with the first parts of ( 19 ) and ( 20 ). step s 4 sets n = 1 . step s 15 tests whether n & lt ; n . if so , step s 16 updates d ( 1 ) ( n ) and step s 17 updates a ( n ). thereafter step s 18 increments n and the procedure returns to step s 15 . the procedure ends at step s 19 when n = n . steps s 14 - s 19 can , for example , be implemented by a for loop as in ( 19 ) or ( 20 ). fig5 is a block diagram of an embodiment of an apparatus in accordance with the present invention for generating exponents of elements of a zadoff - chu sequence representing , in the time domain , a preamble for uplink synchronization of mobile stations . the index u of the sequence to be generated is forwarded from a memory cell 44 to a modulo n adder 36 . modulo n adder 36 also receives the initial value d ( 1 ) ( 0 ) from an initial value provider 32 . modulo n adder 36 iteratively calculates successive values d ( 1 ) ( n ) in accordance with either : d ( 1 ) ( n )=( d ( 1 ) ( n − 1 )+ u ) mod n ( 21 ) d ( 1 ) ( n )= d ( 1 ) ( n − 1 )+ u if d ( 1 ) ( n )& lt ; 0 then d ( 1 ) ( n )= d ( 1 ) ( n )+ n ( 22 ) this is represented by the indicated feedback loop to modulo n adder 36 , which includes a delay element d that introduces a delay corresponding to 1 iteration . similarly the initial value a ( 0 ) is used to start iterative calculations of successive values a ( n ) in a modulo n adder 38 using the calculated values d ( 1 ) ( n ) in accordance with either : a ( n )=( a ( n − 1 )+ d ( 1 ) ( n )) modulo n ( 23 ) a ( n )= a ( n − 1 )+ d ( 1 ) ( n ) if a ( n )& gt ; n − 1 then a ( n )= a ( n )− n ( 24 ) this is represented by the indicated feedback loop to modulo n adder 38 , which includes a delay element d that introduces a delay corresponding to 1 iteration . the resulting exponents a ( n ) are forwarded to an exponentiating unit 40 which forms the elements w a ( n ) of the sequence using the value w = e − j2π / n stored in a memory cell 42 . due to the structure of ( 21 )-( 24 ) the iterations ( in the iteration unit iu including blocks 44 , 36 , 38 , d ) may be performed by first calculating all the values d ( 1 ) ( n ) and then using these values to calculate the values a ( n ). such a procedure , however , requires storing the values d ( 1 ) ( n ) until they are needed for calculating the values a ( n ). as an alternative , illustrated by ( 19 ) and ( 20 ), both iterations may be performed in parallel , which requires storing only the values of d ( 1 ) ( n ) and a ( n ) used in the next iteration . the principles described above for generating zadoff - chu sequences representing preambles in the time domain may also be used to generate reference signals in the frequency domain , both in mobile and base stations , if this is desirable . typically the various blocks in the described embodiments are implemented by one or several micro processors or micro / signal processor combinations and corresponding software . it is appreciated that the present invention provides a simple way to generate zadoff - chu sequences avoiding multiplications . an advantage is a complexity reduction in the implementation of the zadoff - chu sequence generation compared to the prior art . it will be understood by those skilled in the art that various modifications and changes may be made to the present invention without departure from the scope thereof , which is defined by the appended claims . b . popovic , “ generalized chirp - like polyphase sequences with optimum correlation properties ,” ieee trans . inform . theory , vol . 38 , no . 4 , pp . 1406 - 1409 , 1992 . 3gpp , ts 36 . 211 , “ physical channels and modulation ” v 8 . 2 . 0 , section 5 . 7 . 2 , march 2008 . 3gpp r1 - 071409 , huawei , “ efficient matched filters for paired root zadoff - chu sequences ,” march 2007 . d . v . sarwate , “ bounds on crosscorrelation and autocorrelation of sequences ,” ieee trans . inform . theory , vol . it - 25 , pp 720 - 724 , 1979 . m . k . cheng et al , “ an interleaver implementation for the serially concatenated pulse - position modulation decoder ,” in proc . ieee international symposium on circuits and systems , 2006 .