I METHOD, APPARATUS AND MOBILE COMMUNICATION SYSTEM OF FACILITATING COMMUNICATION FIELD OF THE INVENTION [0001] The present application is a divisional application from Australian patent Application No. 2011201802, the entire disclosure of which is incorporated herein by reference. [0001a] The invention relates to the technology of mobile communication, and more particularly, to a method, an apparatus and a mobile communication system of determining a set of Zero Correlation Zone lengths in the Random Access Preamble (RAP) technology. BACKGROUND [0002] In a mobile communication system, a Random Access Preamble is normally transmitted to a base station by a mobile terminal to initiate the random access procedure and to enable synchronization of the mobile terminal with the base station. [0003] There are 64 preambles in each cell in the document of "3GPP TS 36.211 vl.0.0 Physical Channels and Modulation" which was published in March 2007.When initiating a random access procedure, a mobile terminal transmits one of the 64 preambles. A message is transmitted to a base station by the mobile terminal selecting a particular preamble. [0004] Before transmitting the preamble, a mobile terminal must synchronize to the carrier frequency and the frame timing of a base station to become downlink synchronized. Although the mobile terminal is downlink synchronized, there is uncertainty when a signal transmitted by the mobile terminal arrives at the base station. This is because a mobile terminal far away from the base station will receive downlink signals with a larger delay than a mobile terminal close to the base station, and the transmitted signals in uplink will take longer time to propagate to the base station for a mobile terminal which is far away from the base station compared to the signals from a mobile terminal close to the base station. The uncertainty in round trip time causes interferences between uplink signals transmitted by different mobile terminals unless uplink synchronization is performed before data transmission in uplink. [0005] The transmission of any of the RAPs allows a base station to estimate the time of arrival of an uplink signal. The base station can then, based on the time of arrival estimate transmit a time advance command to a mobile terminal to ensure uplink synchronization. Hence, once a preamble is transmitted by a mobile terminal, the base station may detect which preamble has been transmitted and estimate the time of arrival.
2 [0006] To obtain good detection properties of the preambles, or to accurately estimate the time of arrival of the uplink signal, the set of preambles should be designed to have good autocorrelation and cross-correlation properties. [0007] The set of RAPs in Evolved UTRA (E-UTRA) is defined from one or several root sequences. A subset of the preambles xu,v(k)is generated from the uth order root Zadoff-Chu (ZC) sequence xu(k) by cyclic shifts of a plurality of the shift increments Ncs. Specifically, xu,v(k) may be generated according to the equation below: xuv(k) = xuv((k+ vNcs) mod Nzc), (1) where v is an integer, and Nzc is the length of the ZC sequence defined by: xu(k)=Wuk(k+1)/2, k--O,l,...,Nzc-l, W=e-j2rc/Nzc2) [0008] The number of preambles that may be generated from a single root sequence is Npe= LNzc /Ncs ], where Ln] denotes the largest integer not greater than n. If Npre < 64, then several preamble subsets generated from different root sequences are required to obtain 64 preambles in a cell. The cross-correlation between different root sequences is small but still larger than the cross-correlation between sequences generated by a single root sequence. Thus it is beneficial for the detection performance to have Npre = 64 if Npre could not be set greater. [0009] The number of ZC sequences contained in each set of ZC sequences with length of Nzc is Nzc- 1. If the number of root sequences for obtaining the 64 preambles of a cell is Nr, N, =F64 /Npre], where Fn] denotes the minimal integer not smaller than n, then the number of disjoint sets isND = (Nzc - 1)/N, ]. Different cells in a network should make use of preambles obtained from disjoint sets of root sequences, so that the base station knows whether a transmitted preamble is intended for a certain cell or not. The larger the number of root sequences N that is needed for obtaining 64 preambles in a cell, the smaller is the number of disjoint sets of RAPs ND. Thus, from network planning perspective it is desirable to have Npre = 64, and if that is not possible to have as high value as possible of Npre. [0010] A subset of preambles generated with equation (1) is a set of so-called Zero Correlation Zone (ZCZ) sequences. The definition for a set of ZCZ sequences is as follows: a set of M sequences {dv(k)}, v=0,1,..., M-1, k--O,1,..., N-1, of length N, is said to be a set of ZCZ sequences, if all the sequences in the set satisfy the following autocorrelation and cross correlation properties : 3 [0011] The periodic autocorrelation function Yd,(k)d*((k+p)modN) is zero for all p such that 0 < b| I T, and the periodic cross-correlation function kv d,(k)d* ((k + p) modN) is zero for all p such that b| < T (including p = 0), where T is the length of the ZCZ. [0012] A ZC sequence has ideal periodic autocorrelation, for example, lZkVx (k)x*((k + p)modN) is zero for all nonzero p. Thus the set of preambles defined as cyclic shifts of the root sequence according to equation (1) is a set of ZCZ sequences, where the ZCZ length is T= Ncs-1. [0013] Based on Npre=LNzc /Ncs ], Ncs should be as small as possible in order to make Npre be as great as possible. But the value of Ncs should not be too small. In a base station a bank of correlators are used when receiving RAPs, so that there is one correlator for each preamble. Each correlator outputs time of arrival from 0 to Tx Ts = (Ncs-1)x Ts, where Ts is the symbol period of the sequence. The ZCZ property of the set of preambles implies that the correlator for any preamble will give a zero output if any other preamble is transmitted as long as the sum of the round trip time and delay spread in the cell is less than or equal to the product of the length of ZCZ and T, (i.e., TxTs). The maximum round trip time T in a cell is given by the cell radius R: Tr = 2R/c, where c is the speed of light. Thus, the minimum value of the length of ZCZ and the minimum value of Ncs length for a certain cell increase with the cell radius. Therefore, the value of the selected Ncs should be large enough to ensure that the conditions mentioned above are satisfied. [0014] Since the cell radius to be supported in E-UTRA is from 1 km to 100 km, and since Ncs should be as small as possible for any given cell, there is a need for multiple values of Ncs. The value of an Ncs in a cell is broadcast to a mobile terminal by a base station. Of course, the base station may broadcast the length of ZCZ to the mobile terminal, so that the mobile terminal knows how to generate preambles. It is desirable to have as small amount of signaling as possible on the broadcast channel to save overload. Therefore, to achieve low signaling overload, there should be a limited predefined set of values of Ncs or a set of lengths of ZCZ. [0015] Currently, it is proposed in the 3GPP Tdoc "R1-071661-On construction and signaling of RACH preambles" disclosed in March 2007 that, the cyclic shift increment value Ncs in the cell was proposed to be signalled to the UE but there was no restriction on the 4 values of the cyclic shift increment, which would then give a substantial amount of signalling. An alternative proposal is given in the 3GPP Tdoc "R1-071471 -Outstanding issues in random access preamble design for E-UTRA" disclosed in March 2007, which is to have 11 values of Ncs without specification how to select the values. Of course, it is not described in these documents how to select the lengths of ZCZ either. Currently there is no feasible scheme for selecting an appropriate limited set of ZCZ lengths, in order to ensure a small and limited signaling overload. SUMMARY [0016] Embodiments of the invention provide a method, an apparatus and a mobile communication system of determining a set of ZCZ lengths, enabling the select of a limited set of ZCZ lengths good for enhancing the quality of random access of mobile terminals and for decreasing the overhead of signaling. [0017] An embodiment of the invention provides a method of determining a set of ZCZ lengths, the method comprises: determining a length of a root sequence; selecting such a set of ZCZ lengths that, for any cell radius, the maximum number of preambles determined from a ZCZ length selected from the selected set of ZCZ lengths, the ZCZ length being applicable to the cell and being capable of determining a maximum number of preambles, is closest to the maximum number of preambles determined from a ZCZ length selected from the set of all integers, the ZCZ length being applicable to the cell and being capable of determining a maximum number of preambles, wherein the maximum number of preambles is determined from the length of the root sequence and a ZCZ length selected. [0018] Another embodiment of the invention provides an apparatus of determining a set of ZCZ lengths, the apparatus comprises: a length determination unit, adapted to determine the length of a root sequence; and a set selection unit, adapted to select such a set of ZCZ lengths that, for any cell radius, the maximum number of preambles determined from a ZCZ length selected from the selected set of ZCZ length, the ZCZ length being applicable to the cell and being capable of determining a maximum number of preambles, is closest to the maximum number of preambles determined from a ZCZ length selected from the set of all integers, the ZCZ length being applicable to the cell and being capable of determining a maximum number of preambles, wherein the maximum number of preambles is determined from the length of the root sequence and a ZCZ length selected.
5 [0019] Another embodiment of the invention provides a base station, which includes: a length determination unit, adapted to determine a length of a root sequence; and a set selection unit, adapted to select such a set of ZCZ lengths that, for any cell radius, the maximum number of preambles determined from a ZCZ length selected from the selected set of ZCZ lengths, the ZCZ length being applicable to the cell and being capable of determining a maximum number of preambles, is closest to the maximum number of preambles determined from a ZCZ length selected from the set of all integers, being applicable to the cell and being capable of determining a maximum number of preambles, wherein the maximum number of preambles is determined from the length of the root sequence and a ZCZ length selected. [0020] Another embodiment of the invention provides a mobile communication system, the system comprises a base station and a mobile terminal, the base station is adapted to interact with the mobile terminal, and to specify a ZCZ length from a set of ZCZ lengths for the mobile terminal; the mobile terminal is adapted to generate a preamble according to the ZCZ length specified by the base station, and transmitting an uplink signal to the base station using the preamble; the set of ZCZ lengths is such a set of ZCZ lengths that, for any cell radius, the maximum number of preambles determined from a ZCZ length selected from the selected set of ZCZ lengths, the ZCZ length being applicable to the cell and capable of determining a maximum number of preambles, is closest to the maximum number of preambles determined from a ZCZ length selected from the set of all integers, the ZCZ length being applicable to the cell and capable of determining a maximum number of preambles, wherein the maximum number of preambles is determined from the length of the root sequence and a ZCZ length selected. [0021] In an embodiment of the invention, the limited set of ZCZ lengths being selected should satisfy a certain condition, providing a technical solution for selecting a limited set of ZCZ lengths which is relative good with decreased signaling overhead. BRIEF DESCRIPTION OF THE DRAWINGS [0022] Fig. 1 is a flow chart illustrating an method embodiment of the invention; [0023] Fig. 2 is a diagram illustrating the relationship between the maximum number of preambles and the cell radius according to an embodiment of the invention; [0024] Fig. 3 is a diagram illustrating the value of maximum relative difference in the cell radius interval k according to an embodiment of the invention; 6 [0025] Fig. 4 is a block diagram of the base station according to an embodiment of the invention; and [0026] Fig. 5 is a diagram illustrating the mobile communication system according to an embodiment of the invention. DETAILED DESCRIPTION [0027] The general solution of an embodiment of the invention is described first, incorporating Fig. 1. As illustrated in Fig. 1, the embodiment includes: [0028] Step 101: The length of the root sequence is determined; [0029] Step 102: A set of ZCZ lengths is selected so that, for any cell radius, the maximum number of preambles determined from a ZCZ length which is selected from the selected set of ZCZ lengths, and is applicable to the cell and capable of determining a maximum number of preambles, is closest to the maximum number of preambles obtained from a ZCZ length which is selected from the set of all integers, and is applicable to the cell and capable of determining a maximum number of preambles, wherein the maximum number of preambles is determined from the length of the root sequence and a ZCZ length selected. [0030] In an embodiment of the invention, it should be ensured that the product of a ZCZ length and the symbol period of the sequence is greater than the sum of the round trip time and the delay spread of a cell, i.e., Tx Ts> Tr+Td, in which, T is the length of ZCZ, Ts is the symbol period, Tr is the round trip time, and Td is the delay spread. [0031] Since the maximum round trip time Tr in a cell is determined by the cell radius R, i.e., T, = 2R/c, where c is the speed of light, TxTs> Tr+Td may be rewritten as TxTs>2R c+Td. [0032] Furthermore, since T=Ncs-1, Tx TS>2R c+Td may be rewritten as (Ncs 1)xTs>2R c+Td. Therefore, Ncs> 1+(2R c+ Td)/ Ts. [0033] Additionally, since Npre= LNzc /Ncs J, Npre< LNzc /(1 + (2R/c + Td) )]. Thus, Npre may be a function of the cell radius R. Of course, the cell radius may also be varying; and the value of Npre decreases as the value of Ncs increases. [0034] In an embodiment of the invention, a limited set of Ncs values is constructed, i.e., for a certain cell radius, the Npre corresponding to the minimum Ncs value which is selected from the limited set and is applicable to the cell, is closest to the Npre corresponding to the minimum Ncs value which is selected from the set of all integers and is applicable to the cell. Furthermore, a maximum relative difference may be constructed from Npre This maximum relative difference is between the Npre(R), which is determined from the minimum Ncs value 7 selected from the set of integers and is applicable to the cell, and the Npre(R), which is determined from the minimum Ncs value selected from the limited set and is applicable to the cell. If the finally determined or selected limited set is such a set that the maximum relative difference between the Npre(R), which is determined from the minimum Ncs value selected from the set of integers and is applicable to the cell, and the Npre(R), which is determined from the minimum Ncs value selected from the limited set and is applicable to the cell, is minimized in a cell of any radius, this limited set is a required one. [0035] As illustrated in Fig. 2, curve A indicates that for any one cell radius, an integer from the set of all integers may be selected as Ncs of the cell, wherein a maximum number of preamble sequences may be generated based on the integer selected, and the generated preamble sequences are applicable to the cell. Curve B indicates a set of Ncs including a limited number of Ncs. When the limited number of Ncs is applied in cells of all radii, within a certain interval of cell radii, a same Ncs will be used for all cell radii. Thus, the Ncs should be determined according to the maximum cell radius in the interval of cell radii. Compared with A, the preamble number generated according to B decreases. [0036] Under these conditions, if the selected limited set ensures that the maximum relative difference between the Npre(R) determined from a Ncs value selected from any integer and the Npre(R) determined from a Ncs value selected from the limited set is minimized, and it is assumed that the Npre(R) determined from a Ncs value selected from any integer is A(R) and the Npre(R) determined from a Ncs value selected from the limited set is B(R), and then A(R) and B(R) are respectively illustrated in Fig. 2. [0037] As seen from Fig. 2, there is a small deviation between A(R) and B(R). For a certain cell radius R, the deviation of B(R) from A(R) for some cell radius R may increase the number of required root sequences for that cell radius R. The increase of the number of root sequences becomes very important for large cell radii where Npre is small. For example, if A(R) = 3 and B(R) = 2, the number of root sequences increases significantly, from F64 / 37 = 22 to F64 /2 =32. An appropriate measure of the deviation of B from A should therefore weigh the difference A-B with higher weight for small Npre, e.g. by considering the maximum relative difference between A(R) and B(R), i.e., [A(R) - B(R)]/A(R). We will adopt the maximum relative difference between A(R) and B(R) over all cell radii as the measurement of the deviation of B(R) from A(R), and find a set of Ncs values that minimizes this measurement. This set may consist of one Ncs = 0 and K + 1 non-zero Ncs values. The total number of Ncs values in the set is K + 2.
8 [0038] For example, in a relatively small cell, it would be possible to generate 64 ZCZ preambles from a single root sequence if Ncs =LNzc / 64]. This value is the smallest value in the set Ncs(k). [0039] The maximum value, Ncs(K), is the one that allows for having 2 ZCZ sequences from a set single root sequence, so it is LNzc / 2]. [0040] For the largest cells there is only one RAP generated from each root sequence. Therefore, Ncs(K+1) = 0. [0041] The maximum relative difference between A(R) and B(R), i.e., [A(R) - B(R)]/A(R), is non-increasing with radius R within the interval of [(r(k-1), r(k)] and the interval being k, as illustrated in Fig. 2. In Fig. 2, r(k) denotes the kth cell radius arranged orderly from small ones to large ones. The reason is that B(R) is constant in the interval, whereas A is inversely proportional to the smallest possible Ncs for given R. This value of Ncs increases with the round trip time and hence with R. [0042] If it is assumed that the maximum number of preamble sequences of the set A(R) is Npre(k-1)-1 in the cell radius interval of [(r(k-1), r(k)], the maximum number of preamble sequences of the set B(R) generated in this interval associate with the cell radius r(k), i.e., the maximum number of preamble sequences is Npre(k). The maximum relative difference Dk in the interval k may be obtained from the following equation: Dk - N,,(k -1) -1- N ,(k) N ,(k -1) -1 [0043] If Dk and Npre(k - 1) are given, Npre(k) may be obtained by rearranging the above equation, i.e.: Npre (k) = (1 - Dk )(Npre (k - 1) - 1) [0044] The maximum relative difference Dmax for all cell radii may be given by Dmax max{Dk . [0045] For Npre(k), we will first allow Npre(k) to be a real number, and then round the result to the nearest integer. Additionally, Npre(O) and Npre(K) are fixed. [0046] Then Dmax is minimized if all Dk are equal, i.e. Dk = D, k = 1, 2, ... , K, as will be proved in the following. [0047] A set of values, {Ng (k) , is constructed with the constraint that NP (k) = N (k) for k = 0 and k = K, so that D = D, k--1, 2, ... , K. For this set, Dmax=D.
9 [0048] Next, another set of values, {N, (k)j , is constructed with the constraint that Np (k)= Npre(k) for k = 0 and k = K, so that Dmax<D, i.e. Dk 2 < D'), k--1, 2, ... , K. [0049] When k =1, since D <D" and Np 2 , (0)= N( (0), Ng (1) > N( (1) is obtained k1 k~ 2 pr and pre according to Np,, (k) = (1 - Dk)(Ne (k -1) - 1). [0050] When k =2, since D( 2 ) < D ( and Ng (1) > N( (1) , N( (2) > N( (2) is obtained according to Np,,(k)= (1 - Dk )(N, (k -1) - 1). [00511 Similarly, for all k, since N( (K) = N( (K) = Npr, (K), N ((k)> N( (k) is impossible. [00521 Thus, it is impossible to construct a set of values Npe(k) such that Dmax<D, which proves that Dmax is minimized if all Dk are equal, i.e. Dk = D, k = 1, 2, ... , K. [0053] In this way, the set of values {Npre(k)}ko which minimizes Dmax may be found. [0054] Replacing Dk by D in N, (k) =(1- Dk)(Np, (k -1) -1) and rearranging the equation, a linear difference equation is obtained as follows: NP,,(k) - aN (k -1) = -a, wherein a= (1-D). [0055] By recursion, it is obtained from the above equation: Npre (k) =Npre (0)ak + a (a- -1) (3) 1-a [0056] From the above equation and the boundary conditions Npre(O) and Npre(K), a may be determined numerically. [0057] For example, the maximum number of preambles generated from one root sequence is 64, i.e., N,,, (0) =64. The minimum number of preamble obtained by cyclic shift is 2, for example, N,, (14) = 2. Thus, a = 0.856 may be obtained from these two parameters, and all N,,r(k),k =1,2,... may further be obtained. [0058] The maximum relative difference is minimized through an approximate minimization by a sub-optimal algorithm, i.e., by minimizing the maximum relative difference for fictive real-valued maximum number of ZCZ RAPs, and the maximum number of the ZCZ RAPs is thereafter quantized. The method is specified below. [0059] By first rounding the fictive real-valued Npre(k) in Np,,(k) =Nre(0)ak + a (ak -1), the following equation is obtained: 1-a 10 Ncs(k) = LNc I[N ,(0) x ak + - a) X (ak - 1)] (4) where Lx] denotes the maximum integer not greater than x, Nzc is the length of the root sequence, N,,,(0) denotes the maximum number of preambles generated from the root sequence. [0060] Still taking the above example as an example, if N, (0)= 64 and N,,, (14)= 2, a = 0.856 is obtained based on equation (3). Next, when Nzc 839, Nj(k),k 0,1,2,...,14 obtained based on equation (4) is illustrated in table 1: Table 1 k Ncs(k) 0 13 1 15 2 18 3 22 4 26 5 32 6 38 7 46 8 59 9 76 10 93 11 119 12 167 13 279 14 419 [0061] If only one preamble sequence is obtained for a very large cell, which is the sequence itself, then Ncs = 0. Adding this value into the above table, table 2 is obtained: Table 2 k Ncs(k) 0 13 1 15 2 18 3 22 4 26 5 32 11 6 38 7 46 8 59 9 76 10 93 11 119 12 167 13 279 14 419 15 0 [0062] Finally, the true integer value of Npre(k) is obtained from Npre(k) =|LNzc /Ncs (k)] that for some values of k Nzc/Ncs(k) are greater than the rounded values Npre(k). As illustrated in Fig. 3, when K = 14, the value of Dk obtained from the real number value of Npre(k) is D = 0.144. It can be seen from Fig. 3 that the true integer values of Npre(k) will cause Dk to deviate from D. But the deviation is still very small for all cells except the two largest cells. Thus, the selected limited set of values of Ncs is applicable. [0063] It should be noted that if the limited set of values of Ncs is determined, the limited set of lengths of ZCZ may also be determined, for instance, according to T=Ncs-1. [0064] Correspondingly, the invention provides an embodiment of an apparatus of determining a set of ZCZ lengths. As illustrated in Fig. 4, the apparatus includes: a length determination unit 410, configured to determine a length of a root sequence; and a set selection unit 420, configured to select such a set of ZCZ lengths that, for any cell radius, the maximum number of preambles determined from a ZCZ length which is selected from the selected set of ZCZ lengths, and is applicable to the cell and capable of determining a maximum number of preambles, is closest to the maximum number of preambles determined from a ZCZ length which is selected from the set of all integers, and is applicable to the cell and capable of determining a maximum number of preambles, wherein the maximum number of preambles is determined by the length of the root sequence and a ZCZ length selected. [0065] The set selection unit 420 may include: a module 421 adapted for the selection of a set of cyclic shift increments, wherein, the module 421 is configured to select such a set of cyclic shift increments that, for any cell radius, the maximum number of preambles determined from a cyclic shift increment which is selected from the selected set of cyclic shift increments, and is applicable to the cell, is closest to the maximum number of preambles determined from a cyclic shift increment which is selected from the set of all integers and is applicable to the cell, wherein the maximum number of preambles is determined by the root sequence length and a cyclic shift increment selected; and a module 422 adapted to obtain a 12 set of ZCZ lengths, wherein the module is configured to obtain the set of ZCZ lengths according to the selected set of cyclic shift increments. [0066] In above apparatus embodiment, the cyclic shift increment selected from the selected set of cyclic shift increments is the minimum cyclic shift increment in the selected set of cyclic shift increments; and the cyclic shift increment selected from the set of all integers is the minimum cyclic shift increment in the set of all integers. [0067] The invention provides an embodiment of a base station, as illustrated in Fig. 4, which includes: a length determination unit 410, configured to determine a length of a root sequence; and a set selection unit 420, configured to select such a set of ZCZ lengths that, for any cell radius, the maximum number of preambles determined from a ZCZ length which is selected from the selected set of ZCZ lengths, and is applicable to the cell and capable of determining a maximum number of preambles, is closest to the maximum number of preambles determined from a ZCZ length which is selected from the set of all integers, and is applicable to the cell and capable of determining a maximum number of preambles, wherein the maximum number of preambles is determined from the length of the root sequence and a ZCZ length selected. [0068] The invention further provides an embodiment of a mobile communication system, as illustrated in Fig. 5. The system comprises a base station 400 and a mobile terminal 500. The base station 400 is configured to interact with the mobile terminal 500, and to specify a ZCZ length from a set of ZCZ lengths for the mobile terminal 500; the mobile terminal 500 is configured to generate a preamble according to the ZCZ length specified by the base station 400, and to transmit an uplink signal to the base station 400 using the preamble; the set of ZCZ lengths is such a set of ZCZ lengths that, for any cell radius, the maximum number of preambles determined from a ZCZ length which is selected from the selected set of ZCZ lengths, and is applicable to the cell and capable of determining a maximum number of preambles, is closest to the maximum number of preambles determined from a ZCZ length which is selected from the set of all integers, and is applicable to the cell and capable of determining a maximum number of preambles, wherein the maximum number of preambles is determined from the length of the root sequence and a ZCZ length selected. [0069] In above embodiment of the mobile communication system, the cyclic shift increment selected from the selected set of cyclic shift increments is the minimum cyclic shift increment applicable to the cell in the selected set of cyclic shift increments, the cyclic shift 13 increment selected from the set of all integers is the minimum cyclic shift increment applicable to the cell in the set of all integers. [0070] In general, in embodiments of the invention, the selected limited set of Ncs values should be such a set that, in a plurality of intervals of cell radii, the maximum relative difference between the maximum number of the ZCZ RAPs determined from the minimum Ncs value of the limited set, which is applicable to the plurality of cells, and the maximum number of the ZCZ RAPs determined from a plurality of Ncs values of a set of integers which are applicable to the plurality of cells is minimized. Furthermore, a limited set of ZCZ lengths may be selected. Of course, in a plurality of intervals of cell radii, the maximum relative difference between the maximum number of the ZCZ RAPs determined from the minimum ZCZ length of the limited set of ZCZ lengths, which is applicable to the plurality of cells, and the maximum number of the ZCZ RAPs determined from a plurality of ZCZ lengths of the set of all integers which are applicable to the plurality of cells is minimized. [0071] What are described above are only preferred embodiments of the invention. It should be noted that, for a person skilled in the art, variations and improvements may be made without deviating from the principle of the invention. Those variations and improvements are all regarded to be within the scope of the invention.