Method, apparatus and mobile communication system of determining a set of zero correlation zone lengths

FIELD OF THE INVENTION

0001The 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

0002In 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.

0003There are 64 preambles in each cell in the document of "<nplcit id="ncit0001" npl-type="s"><text>3GPP TS 36.211 v1.0.0 - Physical Channels and Modulation" which was published in March 2007</text></nplcit>.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.

0004Before 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.

0005The 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.

0006To 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.

0007The set of RAPs in Evolved UTRA (E-UTRA) is defined from one or several root sequences. A subset of the preambles <i>x</i>_u,v(<i>k</i>)is generated from the u^th order root Zadoff-Chu (ZC) sequence <i>x</i>_u(<i>k</i>) by cyclic shifts of a plurality of the shift increments <i>N</i>_CS. Specifically, <i>x</i>_u,v(<i>k</i>) may be generated according to the equation below: <maths id="math0001" num="(1)"><math display="block"><msub><mi>x</mi><mrow><mi mathvariant="normal">u</mi><mi>,v</mi></mrow></msub><mfenced><mi>k</mi></mfenced><mo>=</mo><msub><mi>x</mi><mrow><mi mathvariant="normal">u</mi><mi>,v</mi></mrow></msub><mfenced><mfenced><mi>k</mi><mo>+</mo><msub><mi mathvariant="italic">νN</mi><mi>CS</mi></msub></mfenced><mspace width="1ex" /><mi>mod</mi><mspace width="1ex" /><msub><mi>N</mi><mi>ZC</mi></msub></mfenced><mo>,</mo></math><img file="EP4064591B1_D0001.tif" /></maths> where v is an integer, and <i>N</i>_ZC is the length of the ZC sequence defined by: <maths id="math0002" num="(2)"><math display="block"><msub><mi>x</mi><mi mathvariant="normal">u</mi></msub><mfenced><mi>k</mi></mfenced><mo>=</mo><msup><mi>W</mi><mrow><mi mathvariant="italic">uk</mi><mfenced><mi>k</mi><mo>+</mo><mn>1</mn></mfenced><mo>/</mo><mn>2</mn></mrow></msup><mo>,</mo><mspace width="1ex" /><mi>k</mi><mo>=</mo><mn>0,1</mn><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>N</mi><mi>ZC</mi></msub><mo>−</mo><mn>1</mn><mo>,</mo><mspace width="1ex" /><mi>W</mi><mo>=</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>j</mi><mn>2</mn><mi>π</mi><mo>/</mo><msub><mi>N</mi><mi>ZC</mi></msub></mrow></msup><mo>,</mo><mi>j</mi><mo>=</mo><msqrt><mrow><mo>−</mo><mn>1</mn></mrow></msqrt></math><img file="EP4064591B1_D0002.tif" /></maths>

0008The number of preambles that may be generated from a single root sequence is <maths id="math0003"><math display="inline"><msub><mi>N</mi><mi>pre</mi></msub><mo>=</mo><mrow><mo>⌊</mo><mrow><msub><mi>N</mi><mi mathvariant="italic">ZC</mi></msub><mo>/</mo><msub><mi>N</mi><mi mathvariant="italic">CS</mi></msub></mrow><mo>⌋</mo></mrow></math><img file="EP4064591B1_D0003.tif" /></maths>, where <maths id="math0004"><math display="inline"><mo>⌊</mo><mi>n</mi><mo>⌋</mo></math><img file="EP4064591B1_D0004.tif" /></maths> denotes the largest integer not greater than <i>n.</i> If <i>N</i>_pre &lt; 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 <i>N</i>_pre = 64 if <i>N</i>_pre could not be set greater.

0009The number of ZC sequences contained in each set of ZC sequences with length of <i>N_ZC</i> is <i>N_ZC-</i> 1. If the number of root sequences for obtaining the 64 preambles of a cell is <i>N</i>_r, <maths id="math0005"><math display="inline"><msub><mi>N</mi><mi>r</mi></msub><mo>=</mo><mrow><mo>⌈</mo><mrow><mn>64</mn><mo>/</mo><mi mathvariant="italic">Npre</mi></mrow><mo>⌉</mo></mrow></math><img file="EP4064591B1_D0005.tif" /></maths>, where <maths id="math0006"><math display="inline"><mo>⌈</mo><mi>n</mi><mo>⌉</mo></math><img file="EP4064591B1_D0006.tif" /></maths> denotes the minimal integer not smaller than <i>n,</i> then the number of disjoint sets is <maths id="math0007"><math display="inline"><msub><mi>N</mi><mi>D</mi></msub><mo>=</mo><mrow><mo>⌊</mo><mrow><mfenced><msub><mi>N</mi><mi mathvariant="italic">ZC</mi></msub><mo>−</mo><mn>1</mn></mfenced><mo>/</mo><msub><mi>N</mi><mi>r</mi></msub></mrow><mo>⌋</mo></mrow></math><img file="EP4064591B1_D0007.tif" /></maths>. 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 <i>N</i>_r that is needed for obtaining 64 preambles in a cell, the smaller is the number of disjoint sets of RAPs <i>N</i>_D. Thus, from network planning perspective it is desirable to have <i>N</i>_pre = 64, and if that is not possible to have as high value as possible of <i>N</i>_pre.

0010A 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 {<i>d</i>_v(k)}, <i>v</i>=0,1,..., <i>M-</i>1, <i>k</i>=0,1,..., <i>N</i>-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:

0011The periodic autocorrelation function <maths id="math0008"><math display="inline"><mstyle displaystyle="true"><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></msubsup><mrow><msub><mi>d</mi><mi>ν</mi></msub><mfenced><mi>k</mi></mfenced><msubsup><mi>d</mi><mi>ν</mi><mo>∗</mo></msubsup><mfenced><mfenced><mi>k</mi><mo>+</mo><mi>p</mi></mfenced><mi>mod</mi><mspace width="1ex" /><mi>N</mi></mfenced></mrow></mstyle></math><img file="EP4064591B1_D0008.tif" /></maths> is zero for all <i>p</i> such that 0 &lt; |<i>p</i>| ≤ <i>T,</i> and the periodic cross-correlation function <maths id="math0009"><math display="inline"><mstyle displaystyle="true"><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></msubsup><mrow><msub><mi>d</mi><mi>ν</mi></msub><mfenced><mi>k</mi></mfenced><msubsup><mi>d</mi><mi>w</mi><mo>∗</mo></msubsup><mfenced><mfenced><mi>k</mi><mo>+</mo><mi>p</mi></mfenced><mi>mod</mi><mspace width="1ex" /><mi>N</mi></mfenced></mrow></mstyle></math><img file="EP4064591B1_D0009.tif" /></maths> is zero for all <i>p</i> such that |<i>p</i>| ≤ <i>T</i> (including <i>p</i> = 0), where <i>T</i> is the length of the ZCZ.

0012A ZC sequence has ideal periodic autocorrelation, for example, <maths id="math0010"><math display="inline"><mstyle displaystyle="true"><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></msubsup><mrow><msub><mi>x</mi><mi>u</mi></msub><mfenced><mi>k</mi></mfenced><msubsup><mi>x</mi><mi>u</mi><mo>∗</mo></msubsup><mfenced><mfenced><mi>k</mi><mo>+</mo><mi>p</mi></mfenced><mi>mod</mi><mspace width="1ex" /><mi>N</mi></mfenced></mrow></mstyle></math><img file="EP4064591B1_D0010.tif" /></maths> is zero for all nonzero <i>p</i>. 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 <i>T</i>= <i>N</i>_CS-1.

0013Based on <maths id="math0011"><math display="inline"><msub><mi>N</mi><mi>pre</mi></msub><mo>=</mo><mrow><mo>⌊</mo><mrow><msub><mi>N</mi><mi mathvariant="italic">ZC</mi></msub><mo>/</mo><msub><mi>N</mi><mi mathvariant="italic">CS</mi></msub></mrow><mo>⌋</mo></mrow></math><img file="EP4064591B1_D0011.tif" /></maths>, <i>N</i>_CS should be as small as possible in order to make <i>N</i>_pre be as great as possible. But the value of <i>N</i>_CS 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 <i>T</i>×<i>T_s</i> = (<i>N</i>_CS-1)×<i>T</i>_s, where <i>T</i>_s 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 <i>T</i>_s (i.e., <i>T</i>×<i>T</i>_s)<i>.</i> The maximum round trip time <i>T</i>_r in a cell is given by the cell radius R: <i>T</i>_r = 2<i>R</i>/<i>c</i>, where <i>c</i> is the speed of light. Thus, the minimum value of the length of ZCZ and the minimum value of <i>N</i>_CS length for a certain cell increase with the cell radius. Therefore, the value of the selected <i>N</i>_CS should be large enough to ensure that the conditions mentioned above are satisfied.

0014Since the cell radius to be supported in E-UTRA is from 1 km to 100 km, and since <i>N</i>_CS should be as small as possible for any given cell, there is a need for multiple values of <i>N</i>_CS. The value of an <i>N</i>_CS 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 <i>N</i>_CS or a set of lengths of ZCZ.

0015Currently, it is proposed in the 3GPP Tdoc "<nplcit id="ncit0002" npl-type="s"><text>R1-071661-On construction and signaling of RACH preambles" disclosed in March 2007</text></nplcit> that, the cyclic shift increment value <i>N</i>_CS in the cell was proposed to be signalled to the UE but there was no restriction on the values of the cyclic shift increment, which would then give a substantial amount of signalling. An alternative proposal is given in the 3GPP Tdoc "<nplcit id="ncit0003" npl-type="s"><text>R1-071471-Outstanding issues in random access preamble design for E-UTRA" disclosed in March 2007</text></nplcit>, which is to have 11 values of <i>N</i>_CS 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.

0016Other documents <nplcit id="ncit0004" npl-type="s"><text>LGE: "RACH Sequence Design Based on Repetition Method", 3GPP DRAFT; R1-062556, 3GPP, XP050103073 and QUALCOMM EUROPE: "RACH sequence structure and evaluation", 3GPP DRAFT; R1-062048, 3GPP, XP050102597</text></nplcit> relate to RACH sequence designs.

SUMMARY

0017One of the technical problems which the embodiment of the invention intends to solve is to 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.

0018The invention is defined in the appended independent claims while preferred embodiments of the invention are stipulated in the appended dependent claims.

BRIEF DESCRIPTION OF THE DRAWINGS

0019<ul id="ul0001" list-style="none" compact="compact"><li><figref idref="f0001">Fig. 1</figref> is a flow chart illustrating an method embodiment of the invention;</li><li><figref idref="f0002">Fig. 2</figref> is a diagram illustrating the relationship between the maximum number of preambles and the cell radius according to an embodiment of the invention;</li><li><figref idref="f0003">Fig. 3</figref> is a diagram illustrating the value of maximum relative difference in the cell radius interval k according to an embodiment of the invention;</li><li><figref idref="f0004">Fig. 4</figref> is a block diagram of the base station according to an embodiment of the invention; and</li><li><figref idref="f0004">Fig. 5</figref> is a diagram illustrating the mobile communication system according to an embodiment of the invention.</li></ul>

DETAILED DESCRIPTION

0020The general solution of an embodiment of the invention is described first, incorporating <figref idref="f0001">Fig. 1</figref>. As illustrated in <figref idref="f0001">Fig. 1</figref>, the embodiment includes: <ul id="ul0002" list-style="none" compact="compact"><li>Step 101: The length of the root sequence is determined;</li><li>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.</li></ul>

0021In 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., <i>T</i>×<i>T_s</i>> <i>T_r</i>+<i>T_d</i>, in which, <i>T</i> is the length of ZCZ, <i>T_s</i> is the symbol period, <i>T_r</i> is the round trip time, and <i>T_d</i> is the delay spread.

0022Since the maximum round trip time <i>T_r</i> in a cell is determined by the cell radius R, i.e., <i>T_r</i> = 2<i>R</i>/<i>c</i>, where <i>c</i> is the speed of light, <i>T</i>×<i>T_s</i>> <i>T_r</i>+<i>T_d</i> may be rewritten as <i>T</i>×<i>T_s</i>>2<i>R</i>/<i>c</i>+<i>T_d.</i>

0023Furthermore, since <i>T</i>=<i>N</i>_CS-1, <i>T</i>×<i>T_s</i>>2<i>R</i>/<i>c</i>+<i>T_d</i> may be rewritten as (<i>N</i>_CS-1)×<i>T_s</i>>2<i>R</i>/<i>c</i>+<i>T_d</i>. Therefore, <i>N_CS</i>> 1+(<i>2R</i>/<i>c</i>+ <i>T_d</i>)/ <i>T_s.</i>

0024Additionally, since <maths id="math0012"><math display="inline"><msub><mi>N</mi><mi>pre</mi></msub><mo>=</mo><mrow><mo>⌊</mo><mrow><msub><mi>N</mi><mi mathvariant="italic">ZC</mi></msub><mo>/</mo><msub><mi>N</mi><mi mathvariant="italic">CS</mi></msub></mrow><mo>⌋</mo></mrow><mo>,</mo><mspace width="1ex" /><msub><mi>N</mi><mi>pre</mi></msub><mo>&lt;</mo><mrow><mo>⌊</mo><mrow><msub><mi>N</mi><mi mathvariant="italic">ZC</mi></msub><mo>/</mo><mfenced><mn>1</mn><mo>+</mo><mfenced><mn>2</mn><mi>R</mi><mo>/</mo><mi>c</mi><mo>+</mo><msub><mi>T</mi><mi>d</mi></msub></mfenced><mo>/</mo><msub><mi>T</mi><mi>s</mi></msub></mfenced></mrow><mo>⌋</mo></mrow></math><img file="EP4064591B1_D0012.tif" /></maths>. Thus, <i>N</i>_pre may be a function of the cell radius <i>R</i>. Of course, the cell radius may also be varying; and the value of <i>N</i>_pre decreases as the value of <i>N</i>_CS increases.

0025In an embodiment of the invention, a limited set of <i>N</i>_CS values is constructed, i.e., for a certain cell radius, the <i>N</i>_pre corresponding to the minimum <i>N</i>_CS value which is selected from the limited set and is applicable to the cell, is closest to the <i>N</i>_pre corresponding to the minimum <i>N</i>_CS 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 <i>N</i>_pre This maximum relative difference is between the <i>N</i>_pre(<i>R</i>), which is determined from the minimum <i>N</i>_CS value selected from the set of integers and is applicable to the cell, and the <i>N</i>_pre(<i>R</i>), which is determined from the minimum <i>N</i>_CS 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 <i>N</i>_pre(<i>R</i>), which is determined from the minimum <i>N</i>_CS value selected from the set of integers and is applicable to the cell, and the <i>N</i>_pre(<i>R</i>), which is determined from the minimum <i>N</i>_CS 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.

0026As illustrated in <figref idref="f0002">Fig. 2</figref>, curve A indicates that for any one cell radius, an integer from the set of all integers may be selected as <i>N</i>_CS 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 <i>N</i>_CS including a limited number of <i>N</i>_CS. When the limited number of <i>N</i>_CS is applied in cells of all radii, within a certain interval of cell radii, a same <i>N</i>_CS will be used for all cell radii. Thus, the <i>N</i>_CS 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.

0027Under these conditions, if the selected limited set ensures that the maximum relative difference between the <i>N</i>_pre(<i>R</i>) determined from a <i>N</i>_CS value selected from any integer and the <i>N</i>_pre(<i>R</i>) determined from a <i>N</i>_CS value selected from the limited set is minimized, and it is assumed that the <i>N</i>_pre(<i>R</i>) determined from a <i>N</i>_CS value selected from any integer is <i>A</i>(<i>R</i>) and the <i>N</i>_pre(<i>R</i>) determined from a <i>N</i>_CS value selected from the limited set is <i>B(R),</i> and then <i>A</i>(<i>R</i>) and <i>B</i>(<i>R</i>) are respectively illustrated in <figref idref="f0002">Fig. 2</figref>.

0028As seen from <figref idref="f0002">Fig. 2</figref>, there is a small deviation between <i>A</i>(<i>R</i>) and <i>B</i>(<i>R</i>)<i>.</i> For a certain cell radius <i>R</i>, the deviation of <i>B</i>(<i>R</i>) from <i>A</i>(<i>R</i>) for some cell radius R may increase the number of required root sequences for that cell radius <i>R</i>. The increase of the number of root sequences becomes very important for large cell radii where <i>N</i>_pre is small. For example, if <i>A</i>(<i>R</i>) = 3 and <i>B</i>(<i>R</i>) = 2, the number of root sequences increases significantly, from <maths id="math0013"><math display="inline"><mrow><mo>⌈</mo><mrow><mn>64</mn><mo>/</mo><mn>3</mn></mrow><mo>⌉</mo></mrow><mo>=</mo><mn>22</mn></math><img file="EP4064591B1_D0013.tif" /></maths> to <maths id="math0014"><math display="inline"><mrow><mo>⌈</mo><mrow><mn>64</mn><mo>/</mo><mn>2</mn></mrow><mo>⌉</mo></mrow><mo>=</mo><mn>32</mn></math><img file="EP4064591B1_D0014.tif" /></maths>. An appropriate measure of the deviation of <i>B</i> from <i>A</i> should therefore weigh the difference <i>A</i>-<i>B</i> with higher weight for small <i>N</i>_pre, e.g. by considering the maximum relative difference between <i>A</i>(<i>R</i>) and <i>B</i>(<i>R</i>), i.e., [<i>A</i>(<i>R</i>) - <i>B</i>(<i>R</i>)]/<i>A</i>(<i>R</i>). We will adopt the maximum relative difference between <i>A</i>(<i>R</i>) and <i>B(R)</i> over all cell radii as the measurement of the deviation of <i>B</i>(<i>R</i>) from <i>A</i>(<i>R</i>), and find a set of <i>N</i>_CS values that minimizes this measurement. This set may consist of one <i>N</i>_CS = 0 and <i>K</i> + 1 non-zero <i>N</i>_CS values. The total number of <i>N</i>_CS values in the set is <i>K</i> + 2.

0029For example, in a relatively small cell, it would be possible to generate 64 ZCZ preambles from a single root sequence if <maths id="math0015"><math display="inline"><msub><mi>N</mi><mi>CS</mi></msub><mo>=</mo><mrow><mo>⌊</mo><mrow><msub><mi>N</mi><mi mathvariant="italic">ZC</mi></msub><mo>/</mo><mn>64</mn></mrow><mo>⌋</mo></mrow></math><img file="EP4064591B1_D0015.tif" /></maths>. This value is the smallest value in the set <i>N</i>_CS(<i>k</i>).

0030The maximum value, <i>N</i>_CS(<i>K</i>), is the one that allows for having 2 ZCZ sequences from a set single root sequence, so it is <maths id="math0016"><math display="inline"><mo>⌊</mo><mrow><msub><mi>N</mi><mi mathvariant="italic">ZC</mi></msub><mo>/</mo><mn>2</mn></mrow><mo>⌋</mo></math><img file="EP4064591B1_D0016.tif" /></maths>.

0031For the largest cells there is only one RAP generated from each root sequence. Therefore, <i>N</i>_CS(<i>K</i>+1) = 0.

0032The maximum relative difference between <i>A</i>(<i>R</i>) and <i>B</i>(<i>R</i>), i.e., [<i>A</i>(<i>R</i>) - <i>B</i>(<i>R</i>)]/<i>A</i>(<i>R</i>), is non-increasing with radius R within the interval of [(<i>r</i>(<i>k</i>-1), <i>r</i>(<i>k</i>)] and the interval being <i>k,</i> as illustrated in <figref idref="f0002">Fig. 2</figref>. In <figref idref="f0002">Fig. 2</figref>, <i>r</i>(<i>k</i>) denotes the <i>k</i>th cell radius arranged orderly from small ones to large ones. The reason is that <i>B(R)</i> is constant in the interval, whereas <i>A</i> is inversely proportional to the smallest possible <i>N</i>_CS for given <i>R.</i> This value of <i>N</i>_CS increases with the round trip time and hence with <i>R</i>.

0033If it is assumed that the maximum number of preamble sequences of the set <i>A</i>(<i>R</i>) is <i>N</i>_pre(<i>k</i>-1)-1 in the cell radius interval of [(<i>r</i>(<i>k</i>-1), <i>r</i>(<i>k</i>)], the maximum number of preamble sequences of the set <i>B</i>(<i>R</i>) generated in this interval associate only with the cell radius <i>r</i>(<i>k</i>), i.e., the maximum number of preamble sequences is <i>N</i>_pre(<i>k</i>). The maximum relative difference <i>D</i>_k in the interval <i>k</i> may be obtained from the following equation: <maths id="math0017"><math display="block"><msub><mi>D</mi><mi>k</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>k</mi><mo>−</mo><mn>1</mn></mfenced><mo>−</mo><mn>1</mn><mo>−</mo><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>k</mi></mfenced></mrow><mrow><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>k</mi><mo>−</mo><mn>1</mn></mfenced><mo>−</mo><mn>1</mn></mrow></mfrac></math><img file="EP4064591B1_D0017.tif" /></maths>

0034If <i>D</i>_k and <i>N</i>_pre(<i>k</i> - 1) are given, <i>N</i>_pre(<i>k</i>) may be obtained by rearranging the above equation, i.e.: <maths id="math0018"><math display="block"><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>k</mi></mfenced><mo>=</mo><mfenced><mn>1</mn><mo>−</mo><msub><mi>D</mi><mi>k</mi></msub></mfenced><mfenced><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>k</mi><mo>−</mo><mn>1</mn></mfenced><mo>−</mo><mn>1</mn></mfenced></math><img file="EP4064591B1_D0018.tif" /></maths>

0035The maximum relative difference <i>D</i>_max for all cell radii may be given by <maths id="math0019"><math display="inline"><msub><mi>D</mi><mi>max</mi></msub><mo>=</mo><mi>max</mi><msubsup><mfenced open="{" close="}"><msub><mi>D</mi><mi>k</mi></msub></mfenced><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>K</mi></msubsup></math><img file="EP4064591B1_D0019.tif" /></maths>.

0036For <i>N</i>_pre(<i>k</i>), we will first allow <i>N</i>_pre(<i>k</i>) to be a real number, and then round the result to the nearest integer. Additionally, <i>N</i>_pre(0) and <i>N</i>_pre(<i>K</i>) are fixed.

0037Then <i>D</i>_max is minimized if all <i>D</i>_k are equal, i.e. <i>D</i>_k = D, <i>k</i> = 1, 2, ..., <i>K,</i> as will be proved in the following.

0038A set of values, <maths id="math0020"><math display="inline"><msubsup><mfenced open="{" close="}"><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>1</mn></mfenced></msubsup><mfenced><mi>k</mi></mfenced></mfenced><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>K</mi></msubsup></math><img file="EP4064591B1_D0020.tif" /></maths>, is constructed with the constraint that <maths id="math0021"><math display="inline"><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>1</mn></mfenced></msubsup><mfenced><mi>k</mi></mfenced><mo>=</mo><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>k</mi></mfenced></math><img file="EP4064591B1_D0021.tif" /></maths> for <i>k</i> = 0 and <i>k</i> = <i>K</i>, so that <maths id="math0022"><math display="inline"><msubsup><mi>D</mi><mi>k</mi><mfenced><mn>1</mn></mfenced></msubsup><mo>=</mo><mi>D</mi></math><img file="EP4064591B1_D0022.tif" /></maths>, <i>k</i>=1<i>,</i> 2, ..., <i>K.</i> For this set, <i>D</i>_max=<i>D</i>.

0039Next, another set of values, <maths id="math0023"><math display="inline"><msubsup><mfenced open="{" close="}"><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>2</mn></mfenced></msubsup><mfenced><mi>k</mi></mfenced></mfenced><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>K</mi></msubsup></math><img file="EP4064591B1_D0023.tif" /></maths>, is constructed with the constraint that <maths id="math0024"><math display="inline"><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>2</mn></mfenced></msubsup><mfenced><mi>k</mi></mfenced><mo>=</mo><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>k</mi></mfenced></math><img file="EP4064591B1_D0024.tif" /></maths> for <i>k</i> = 0 and <i>k</i> = <i>K</i>, so that <i>D</i>_max&lt;<i>D,</i> i.e. <maths id="math0025"><math display="inline"><msubsup><mi>D</mi><mi>k</mi><mfenced><mn>2</mn></mfenced></msubsup><mo>&lt;</mo><msubsup><mi>D</mi><mi>k</mi><mfenced><mn>1</mn></mfenced></msubsup></math><img file="EP4064591B1_D0025.tif" /></maths>, <i>k</i>=1, 2, ..., <i>K.</i>

0040When <i>k</i> =1, since <maths id="math0026"><math display="inline"><msubsup><mi>D</mi><mi>k</mi><mfenced><mn>2</mn></mfenced></msubsup><mo><</mo><msubsup><mi>D</mi><mi>k</mi><mfenced><mn>1</mn></mfenced></msubsup></math><img file="EP4064591B1_D0026.tif" /></maths> and <maths id="math0027"><math display="inline"><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>2</mn></mfenced></msubsup><mfenced><mn>0</mn></mfenced><mo>=</mo><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>1</mn></mfenced></msubsup><mfenced><mn>0</mn></mfenced><mo>,</mo><mspace width="1ex" /><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>2</mn></mfenced></msubsup><mfenced><mn>1</mn></mfenced><mo>></mo><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>1</mn></mfenced></msubsup><mfenced><mn>1</mn></mfenced></math><img file="EP4064591B1_D0027.tif" /></maths> is obtained according to <i>N</i>_pre(<i>k</i>) = (1 - <i>D_k</i>)(<i>N</i>_pre(<i>k</i> - 1) - 1).

0041When <i>k</i> =2, since <maths id="math0028"><math display="inline"><msubsup><mi>D</mi><mn>2</mn><mfenced><mn>2</mn></mfenced></msubsup><mo><</mo><msubsup><mi>D</mi><mn>2</mn><mfenced><mn>1</mn></mfenced></msubsup></math><img file="EP4064591B1_D0028.tif" /></maths> and <maths id="math0029"><math display="inline"><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>2</mn></mfenced></msubsup><mfenced><mn>1</mn></mfenced><mo>></mo><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>1</mn></mfenced></msubsup><mfenced><mn>1</mn></mfenced><mo>,</mo><mspace width="1ex" /><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>2</mn></mfenced></msubsup><mfenced><mn>2</mn></mfenced><mo>></mo><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>1</mn></mfenced></msubsup><mfenced><mn>2</mn></mfenced></math><img file="EP4064591B1_D0029.tif" /></maths>, is obtained according to <i>N</i>_pre(<i>k</i>) = (1 - <i>D</i>_k)(<i>N</i>_pre(<i>k</i> - 1) -1).

0042Similarly, for all k, since <maths id="math0030"><math display="inline"><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>2</mn></mfenced></msubsup><mfenced><mi>K</mi></mfenced><mo>=</mo><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>1</mn></mfenced></msubsup><mfenced><mi>K</mi></mfenced><mo>=</mo><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>K</mi></mfenced><mo>,</mo><mspace width="1ex" /><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>2</mn></mfenced></msubsup><mfenced><mi>k</mi></mfenced><mo>></mo><msubsup><mi>N</mi><mi>pre</mi><mfenced><mn>1</mn></mfenced></msubsup><mfenced><mi>k</mi></mfenced></math><img file="EP4064591B1_D0030.tif" /></maths> is impossible.

0043Thus, it is impossible to construct a set of values <i>N</i>_pre(<i>k</i>) such that <i>D</i>_max&lt;<i>D</i>, which proves that <i>D</i>_max is minimized if all <i>D</i>_k are equal, i.e. <i>D</i>_k = D, <i>k</i> = 1, 2, ..., <i>K.</i>

0044In this way, the set of values <maths id="math0031"><math display="inline"><msubsup><mfenced open="{" close="}"><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>k</mi></mfenced></mfenced><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>K</mi></msubsup></math><img file="EP4064591B1_D0031.tif" /></maths> which minimizes <i>D</i>_max may be found.

0045Replacing <i>D</i>_k by <i>D</i> in <i>N</i>_pre(<i>k</i>) = (1 - <i>D_k</i>)(<i>N</i>_pre(<i>k</i> - 1) - 1) and rearranging the equation, a linear difference equation is obtained as follows: <maths id="math0032"><math display="block"><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>k</mi></mfenced><mo>−</mo><msub><mi mathvariant="italic">aN</mi><mi>pre</mi></msub><mfenced><mi>k</mi><mo>−</mo><mn>1</mn></mfenced><mo>=</mo><mo>−</mo><mi>a</mi><mo>,</mo></math><img file="EP4064591B1_D0032.tif" /></maths> wherein <i>a</i>= (1-<i>D</i>).

0046By recursion, it is obtained from the above equation: <maths id="math0033" num="(1)"><math display="block"><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>k</mi></mfenced><mo>=</mo><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mn>0</mn></mfenced><msup><mi>a</mi><mi>k</mi></msup><mo>+</mo><mfrac><mi>a</mi><mrow><mn>1</mn><mo>−</mo><mi>a</mi></mrow></mfrac><mfenced><msup><mi>a</mi><mi>k</mi></msup><mo>−</mo><mn>1</mn></mfenced></math><img file="EP4064591B1_D0033.tif" /></maths>

0047From the above equation and the boundary conditions <i>N</i>_pre(0) and <i>N</i>_pre(<i>K</i>), <i>a</i> may be determined numerically.

0048The maximum number of preambles generated from one root sequence is 64, i.e., <i>N_pre</i>(<i>0</i>) = 64. The minimum number of preamble obtained by cyclic shift is 2, for example, <i>N_pre</i>(14) = 2. Thus, <i>a</i> = 0.856 may be obtained from these two parameters, and all <i>N_pre</i>(<i>k</i>)<i>,k</i> = 1,2,... may further be obtained.

0049The 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.

0050By first rounding the maximum fictive real-valued <i>N</i>_pre(<i>k</i>) in <maths id="math0034"><math display="inline"><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>k</mi></mfenced><mo>=</mo><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mn>0</mn></mfenced><msup><mi>a</mi><mi>k</mi></msup><mo>+</mo><mfrac><mi>a</mi><mrow><mn>1</mn><mo>−</mo><mi>a</mi></mrow></mfrac><mfenced><msup><mi>a</mi><mi>k</mi></msup><mo>−</mo><mn>1</mn></mfenced></math><img file="EP4064591B1_D0034.tif" /></maths>, the following equation is obtained: <maths id="math0035" num="(2)"><math display="block"><msub><mi>N</mi><mi mathvariant="italic">CS</mi></msub><mfenced><mi>k</mi></mfenced><mo>=</mo><mrow><mo>⌊</mo><mrow><msub><mi>N</mi><mi mathvariant="italic">ZC</mi></msub><mo>/</mo><mfenced open="[" close="]"><msub><mi>N</mi><mi mathvariant="italic">pre</mi></msub><mfenced><mn>0</mn></mfenced><mo>×</mo><msup><mi>a</mi><mi>k</mi></msup><mo>+</mo><mi>a</mi><mo>/</mo><mfenced><mn>1</mn><mo>−</mo><mi>a</mi></mfenced><mo>×</mo><mfenced><msup><mi>a</mi><mi>k</mi></msup><mo>−</mo><mn>1</mn></mfenced></mfenced></mrow><mo>⌋</mo></mrow></math><img file="EP4064591B1_D0035.tif" /></maths> where <maths id="math0036"><math display="inline"><mo>⌊</mo><mi>x</mi><mo>⌋</mo></math><img file="EP4064591B1_D0036.tif" /></maths> denotes the maximum integer not greater than <i>x</i>, <i>N_ZC</i> is the length of the root sequence, <i>N_pre</i>(0) denotes the maximum number of preambles generated from the root sequence.

0051Still taking the above example as an example, if <i>N_pre</i>(0) = 64 and <i>N_pre</i>(14) = 2, <i>a</i> = 0.856 is obtained based on equation (1). Next, when <i>N_ZC</i> = 839 , <i>N_cs</i>(<i>k</i>), <i>k</i> = 0,1,2,...,14 obtained based on equation (2) is illustrated in table 1: <tables id="tabl0001" num="0001"><table frame="all"><title>Table 1</title><tgroup cols="2"><colspec colnum="1" colname="col1" colwidth="23mm" align="center" /><colspec colnum="2" colname="col2" colwidth="25mm" align="center" /><thead valign="middle"><row><entry><i>k</i></entry><entry><i>N</i>_CS(<i>k</i>)</entry></row></thead><tbody valign="middle"><row><entry>0</entry><entry>13</entry></row><row><entry>1</entry><entry>15</entry></row><row><entry>2</entry><entry>18</entry></row><row><entry>3</entry><entry>22</entry></row><row><entry>4</entry><entry>26</entry></row><row><entry>5</entry><entry>32</entry></row><row><entry>6</entry><entry>38</entry></row><row><entry>7</entry><entry>46</entry></row><row><entry>8</entry><entry>59</entry></row><row><entry>9</entry><entry>76</entry></row><row><entry>10</entry><entry>93</entry></row><row><entry>11</entry><entry>119</entry></row><row><entry>12</entry><entry>167</entry></row><row><entry>13</entry><entry>279</entry></row><row><entry>14</entry><entry>419</entry></row></tbody></tgroup></table></tables>

0052If only one preamble sequence is obtained for a very large cell, which is the sequence itself, then <i>N</i>_CS = 0. Adding this value into the above table, table 2 is obtained: <tables id="tabl0002" num="0002"><table frame="all"><title>Table 2</title><tgroup cols="2"><colspec colnum="1" colname="col1" colwidth="23mm" align="center" /><colspec colnum="2" colname="col2" colwidth="25mm" align="center" /><thead valign="middle"><row><entry><i>k</i></entry><entry><i>N</i>_CS(<i>k</i>)</entry></row></thead><tbody valign="middle"><row><entry>0</entry><entry>13</entry></row><row><entry>1</entry><entry>15</entry></row><row><entry>2</entry><entry>18</entry></row><row><entry>3</entry><entry>22</entry></row><row><entry>4</entry><entry>26</entry></row><row><entry>5</entry><entry>32</entry></row><row><entry>6</entry><entry>38</entry></row><row><entry>7</entry><entry>46</entry></row><row><entry>8</entry><entry>59</entry></row><row><entry>9</entry><entry>76</entry></row><row><entry>10</entry><entry>93</entry></row><row><entry>11</entry><entry>119</entry></row><row><entry>12</entry><entry>167</entry></row><row><entry>13</entry><entry>279</entry></row><row><entry>14</entry><entry>419</entry></row><row><entry>15</entry><entry>0</entry></row></tbody></tgroup></table></tables>

0053Finally, the true integer value of <i>N</i>_pre(<i>k</i>) is obtained from <maths id="math0037"><math display="inline"><msub><mi>N</mi><mi>pre</mi></msub><mfenced><mi>k</mi></mfenced><mo>=</mo><mrow><mo>⌊</mo><mrow><msub><mi>N</mi><mi mathvariant="italic">ZC</mi></msub><mo>/</mo><msub><mi>N</mi><mi mathvariant="italic">CS</mi></msub><mfenced><mi>k</mi></mfenced></mrow><mo>⌋</mo></mrow></math><img file="EP4064591B1_D0037.tif" /></maths> that for some values of <i>k</i> are greater than the rounded values. As illustrated in <figref idref="f0003">Fig. 3</figref>, when <i>K</i> = 14, the value of <i>D</i>_k obtained from the real integer value of <i>N</i>_pre(<i>k</i>) is <i>D</i> = 0.144. It can be seen from <figref idref="f0003">Fig. 3</figref> that the true integer values of <i>N</i>_pre(<i>k</i>) will cause <i>D</i>_k to deviate from <i>D.</i> But the deviation is still very small for all cells except the two largest cells. Thus, the selected limited set of values of <i>N</i>_CS is applicable.

0054It should be noted that if the limited set of values of <i>N</i>_CS is determined, the limited set of lengths of ZCZ may also be determined, for instance, according to <i>T</i>=<i>N</i>_CS-1.

0055Correspondingly, the invention provides an embodiment of an apparatus of determining a set of ZCZ lengths. As illustrated in <figref idref="f0004">Fig. 4</figref>, 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.

0056The 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 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.

0057In 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.

0058The invention provides an embodiment of a base station, as illustrated in <figref idref="f0004">Fig. 4</figref>, 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.

0059The invention further provides an embodiment of a mobile communication system, as illustrated in <figref idref="f0004">Fig. 5</figref>. The system comprises abase 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.

0060In 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 increment selected from the set of all integers is the minimum cyclic shift increment applicable to the cell in the set of all integers.

0061In general, in embodiments of the invention, the selected limited set of <i>N</i>_CS 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 <i>N</i>_CS 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 <i>N</i>_CS 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.

0062What 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. The scope of protection of the invention is defined by the appended claims.