# Patent

## Title
Method and apparatus for generating preamble using chaotic sequence

## Abstract

A preamble generating method which includes computing (N) chaotic samples; transforming the (N) chaotic samples into (N) binary values of certain bits, respectively, and computing a chaotic sequence bit successively using the (N) binary values; and generating a preamble based on the chaotic sequence bit. By using the sequence bit from the chaotic samples, a plurality of preambles with optimum auto-correlation and cross-correlation properties is generated.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application claims the benefit of U.S. Provisional Patent Application No. 60/479,220 filed Jun. 18, 2003 in the U.S. Patent and Trademark Office, and Korean Patent Application No. 2003-71618 filed Oct. 15, 2003, the disclosures of which are incorporated herein by reference.


BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method and an apparatus for generating a preamble, and more particularly, to a method and an apparatus for generating a preamble which is suitable for an ultra-wideband communication system supporting multi-piconet technology using a chaotic sequence.
2. Description of the Related Art
A preamble signal is used in the timing synchronization of signals transmitted between at least two systems. The preamble indicates that a certain system is about to transmit data, and is defined by a string of certain transmission pulses recognized by the communication systems. Reliable timing ensures correct translation of the beginning of information transmission of all the communication systems, and also ensures that all the receiving systems accurately understand when the data transmission begins. Pulses for a preamble vary depending on the network technologies adopted.
FIG. 1 shows the structure of a general preamble. As shown, a preamble generally includes a signal for synchronization, a signal for channel estimation and data for a physical sub-layer. In the communication system, the preamble synchronizes frames and estimates signal degradation in the channel used.
Generally, ‘ultra high frequency communication system’ refers to a system that supports ultra high frequency wireless communications services between a piconet coordinator (PNC) and a device (DEV). For synchronization between the PNC and DEV, a synchronous signal is periodically transmitted to indicate the beginning of the frames. The DEV receives the synchronous signal, synchronizes a frame to the PNC, and estimates signal degradation that may have occurred in the channel to utilize it in the wave detection of the data being received after the frame synchronization. As for the synchronous signal, it is common for a preamble signal agreed upon between the PNC and the DEV to be used.
The DEV receives the preamble signals which are periodically received from the PNC, and determines the frame synchronization in accordance with the strength of the signals being outputted through an internal correlator. The reception performance of the preamble signal depends on the auto-corrrelation property, and a higher auto-correlation property is required.
There are usually a plurality of piconets existing in the ultra-wideband communication system, and interference between neighboring piconets usually causes deterioration in wave detection. Interference with neighboring piconets can also occur in the reception of the preamble signal, which usually degrades the frame synchronization performance. A preamble signal has to be designed with the above-mentioned considered. Further, the preamble signal has to have a good cross-correlation property to support multiple piconets, which means the preamble signal requires a low cross-correlation property.
A similar use of the above-mentioned preamble is found in a UMTS (Universal Mobile Telecommunication System) of wideband CDMA. The UMTS has a plurality of slots in the frame, and a synchronous signal indicating the beginning of the slots. The frame synchronous signal is periodically transmitted between a base station and a terminal according to a predetermined sequence. However, because the UMTS is designed to operate optimally in a cellular communication environment, it is somewhat impractical to employ it in an ultra-wideband communication system. Accordingly, a preamble, which is optimum for use in ultra-wideband communication, is required.
SUMMARY OF THE INVENTION
The present invention has been developed in order to solve the above drawbacks and other problems associated with the conventional arrangement. An aspect of the present invention is to provide an apparatus and a method for generating a preamble suitable for use in an ultra-wideband communication system.
The above object and/or other aspects of the present invention can be substantially achieved by providing a preamble generating method, comprising: (a) computing (N) chaotic samples; (b) transforming (N) chaotic samples into (N) binary values of certain bits, respectively, and computing a chaotic sequence bit successively using the (N) binary values; and (c) generating a preamble based on the chaotic sequence bit.
In the transforming step, the (N) chaotic samples are represented by Xi, and are computed by using a chaotic mapping function (F) by periodic orbits, the chaotic mapping function (F) being expressed by, Xk+1=F(Xk), where, X0 is an initial value, and k=0, 1, 2, 3, . . . .
The chaotic mapping function (F) uses one of a Bernoulli shift map, a tent map, a twisted tent map, and a ship map.
Additionally, there are provided the steps of: computing an inverse mapping function of the chaotic mapping function (F), using the inverse mapping function with respect to (M) different chaotic samples by periodic orbits, and computing a plurality of initial values for the (M) chaotic samples, respectively; among the plurality of initial values computed for the (M) chaotic samples, selecting initial values which are at a maximum distance from each other; and generating (M) preambles with respect to the (M) selected initial values, by performing the steps (a) through (c), respectively. The preamble is used in an ultra-wideband communication system which supports multi-piconets, and the number of the multi-piconets is M.
The certain bits are 16 bits, and the number (N) comprises one of 4 and 8.
According to one aspect of the present invention, a preamble generating apparatus comprises a chaotic sample computing part to compute (N) chaotic samples; a chaotic sequence computing part to transform the (N) chaotic samples into (N) binary values of certain bits, respectively, and compute a chaotic sequence bit by successively using the (N) binary values; and a preamble generating part to generate a preamble based on the chaotic sequence bit.
The chaotic sample computing part comprises: a chaotic mapping function part to substitute an input value in a chaotic mapping function and output the result of operation; and a delay part to delay the output result of chaotic mapping function by a predetermined time, and provide the delayed values as the input value to the chaotic mapping function part.
The chaotic mapping function comprises one or more of a Bernoulli shift map, a tent map, a twisted tent map, and a ship map.
The certain bits are 16 bits. The number (N) comprises one of 4 and 8. The preamble is used in synchronization and channel estimation in an ultra-wideband communication system.



BRIEF DESCRIPTION OF THE DRAWINGS
The above aspects and features of the present invention will be more apparent by describing certain embodiments of the present invention with reference to the accompanying drawings, in which:
FIG. 1 illustrates the structure of a general preamble;
FIG. 2 illustrates one chaotic sample converted into a 16-bit length chaotic sequence bit;
FIG. 3 illustrates a 64-bit length chaotic sequence bit generated by using 4 chaotic samples;
FIG. 4 is a block diagram of one example of an apparatus which successively generates chaotic samples;
FIG. 5 illustrates one example of a chaotic mapping function, and attaining 4 chaotic samples using the same;
FIGS. 6A to 6D illustrate one example of an easily-achievable chaotic mapping function;
FIGS. 7A and 7B illustrate an asymmetric tent chaotic mapping function and an inverse mapping function;
FIG. 8 illustrates an initial value determination method for multiple piconets;
FIG. 9 illustrates a variety of initial values for 4 piconets;
FIG. 10 simulates the synchronization performance of the preamble which is generated by the preamble generating method using a chaotic sequence according to an embodiment of the present invention;
FIG. 11 illustrates an auto-correlation property of the 64-bit length chaotic sequence which is generated by the preamble generating method using a chaotic sequence according to an embodiment of the present invention;
FIG. 12 illustrates a cross-correlation property of the 64-bit length chaotic sequence which is generated by the preamble generating method using a chaotic sequence according to an embodiment of the present invention;
FIG. 13 illustrates the distance (DIST) of the preamble which is generated by the preamble generating method using a chaotic sequence according to an embodiment of the present invention versus bit error rate (BER) in the CM1 channel for performance comparison with other sequences;
FIG. 14 illustrates the distance (DIST) of the preamble which is generated by the preamble generating method using a chaotic sequence according to an embodiment of the present invention versus bit error rate (BER) in the CM2 channel for performance comparison with other sequences;
FIG. 15 illustrates the distance (DIST) of the preamble which is generated by the preamble generating method using a chaotic sequence according to an embodiment of the present invention versus bit error rate (BER) in the CM3 channel for performance comparison with other sequences; and
FIG. 16 illustrates the distance (DIST) of the preamble which is generated by the preamble generating method using a chaotic sequence according to an embodiment of the present invention versus bit error rate (BER) in the CM4 channel for performance comparison with other sequences.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Certain embodiments of the present invention will be described in greater detail with reference to the accompanying drawings.
In the following description, identical drawing reference numerals are used for the same elements even in different drawings. The matters defined in the description such as a detailed construction and elements are provided to assist in a comprehensive understanding of the invention. The present invention can be carried out without those defined matters. Also, well-known functions or constructions are not described in detail since they would obscure the invention in unnecessary detail.
FIG. 2 shows one chaotic sample transformed into a 16-bit length chaotic sequence bit. Referring to FIG. 2, a chaotic sample X0 of certain value is transformed by proper quantization into a 16-bit length binary value which is represented by fixed decimal. In order to generate a chaotic sequence bit of 64-bit or 128-bit length, 4 or 8 successive chaotic samples are generated and transformed into a 16-bit length binary value and used.
FIG. 3 illustrates the generation of a 64-bit length chaotic sequence bit by using 4 successive chaotic samples. Referring to FIG. 3, 4 chaotic samples X0, X1, X2, X3 are each transformed into a 16-bit binary value, and successively used for generating up to 64 bits of chaotic sequence bits. The chaotic sequence bits are used in the preamble.
Meanwhile, when the initial value X0 is determined, 4 chaotic samples can be generated using a proper chaotic mapping function. That is, by substituting the initial value X0 in a chaotic mapping function F, it is possible to obtain the next chaotic sample X1, and by substituting the next chaotic sample X1 in the chaotic mapping function F, it is possible to obtain the chaotic sample X2 next to the next chaotic sample X1. By several iterations, a desired number of chaotic samples are attained, and this can be expressed by the following function:

Xk+1=F(Xk)  [Function 1]

where, k=0, 1, 2, 3, . . .
By using chaotic samples X0, X1, X2, X3, a 64-bit length chaotic sequence as shown in FIG. 3 can be attained. In order to obtain a 128-bit length chaotic sequence bit, 8 chaotic samples are used.
FIG. 4 is a block diagram illustrating one example of an apparatus which can successively generate chaotic samples. The apparatus as shown in FIG. 4 comprises a chaotic mapping part 10 and a delay part 11. The chaotic mapping part 10 substitutes input Xi in a predetermined chaotic mapping function, to output a chaotic sample Xi+1. The delay part 11 delays the output value Xi+1 for a predetermined time and feeds back the same to the input of chaotic mapping part 10. By iterating this process a predetermined number of times, a desired number of chaotic samples are generated. The chaotic samples as generated are converted into chaotic sequence bits and used for the preamble. A variety of mathematical functions can be used as a chaotic mapping function in the chaotic mapping part 10, and simplicity and easy achievability of the algorithm are considered when selecting a chaotic mapping function.
FIG. 5 shows one example of a chaotic mapping function and the process of attaining 4 chaotic samples by using the chaotic mapping function. Referring to FIG. 5, an initial value X0 is substituted in the mapping function F(x) so that a value X1 is derived, and by substituting the value X1 in the mapping function F(x), a next value X2 is obtained. By the above iteration, the following values, X3 and X4, are obtained. For example, if X0=−0.9922, values X1, X2, X3 and corresponding binary values are:

    
    
        X0=−0.9922, 101001101100010
        X1=−0.4904, 100100110010100
        X2=0.7690, 000111100001010
        X3=−0.9800, 101001100100100
    
    


FIGS. 6A through 6D show an example of a chaotic mapping function which is simple to achieve. FIG. 6A shows a Bernoulli shift map, FIG. 6B a tent map, FIG. 6C a twisted tent map, and FIG. 6D is a ship map. As shown, a variety of maps can be used as a chaotic mapping function, according to which chaotic samples are obtained and chaotic sequence bits are obtained from the generated chaotic samples.
FIG. 7A shows an asymmetric tent chaotic mapping function, and FIG. 7B shows an inverse mapping function of the asymmetric chaotic mapping function of FIG. 7A. As shown in FIGS. 7A and 7B, an initial value can be determined by using the inverse mapping function of the chaotic mapping function. More specifically, an initial value Z0 can be determined by iterating an inverse mapping function F−1 of the chaotic mapping function.

Z2=F−1(Z3)

Z1=F−1(Z2)

Z0=F−1(Z1)  [Functions 2]

The above method can be used in determining an initial value of the piconet-supporting chaotic sequence bits. The last samples Z31=0.1, Z32=0.25 of the first piconet and the second piconet are substituted in the above functions 2 by periodic orbits, and the values as shown in FIG. 8 are obtained.
A value can be selected as an initial value among the chaotic sequence bits to obtain maximum distance as possible. In the same way, an initial value for 4 or more picoents can be obtained, and by using the selected initial value, a low cross-correlation property can be obtained.
FIG. 9 illustrates a variety of initial values for 4 piconets. As shown, by properly selecting initial values for the 4 piconets, a good preamble, that is, the preamble contributing to an improved cross-correlation property can be generated for use in the multi-piconet supporting communication system.
FIG. 10 simulates the synchronization performance with the preamble generated in accordance with the preamble generating method using a chaotic sequence according to one embodiment of the present invention. In the simulation, a preamble generated by 4 chaotic samples was used, and synchronization was attempted up to 1000 times. FIG. 10 shows the probability of synchronization failure vs. bit error rate (BER). More specifically, FIG. 10 shows the probability of the synchronization failure when the receptivity of the first bit of the preamble sequence was poorest, that is, the case when the probability of synchronization of the first bit was assumed to be 1⁄2.
FIGS. 11 and 12 illustrate auto-correlation and cross-correlation properties of a chaotic sequence which is generated by a preamble generating method using a chaotic sequence according to one embodiment of the present invention. As shown, the chaotic sequence generated in accordance with the present invention has a high auto-correlation coefficient and low cross-correlation coefficient.
FIGS. 13 through 16 illustrate distance vs. BER of a preamble by one embodiment of the present invention, respectively showing performance compared with other sequences in the channels of CM1, CM2, CM3 and CM4. In the example as shown in FIGS. 13 through 16, the sequence by the present invention was compared with a Gold sequence and a sequence proposed by TEXAS INSTRUMENTS (TI) (IEEE P802.15-3/142r0). As shown, the chaotic sequence according to the present invention provides superior performance to the other sequences as the channels degrade, such as in the channels of CM3 and CM4.
The following table lists results of a comparison between the chaotic sequence (CSS) by the preamble generating method according to one embodiment of the present invention, and the constant amplitude zero auto-correlation (CAZAC) sequence.










TABLE 1









CSS
CZACA









Processing technique
Subsequent processing of the
Correlation



input samples
technique





Length (bit)
64 (potential lt < 40)
128


Piconet identification
Yes
No


Number of available
Plural
1 (for BPSK


piconets

under UWB)


Implementation
Respectively simple


Channel characteristics
High SNR
SNR ~−10 dB


Stability
Yes
No



a) by choice unique map



b) by choice of unique map



parameters


External time
No
Yes


synchronization









As shown in the Table 1, it is simpler to generate preambles by using a chaotic sequence, and is also more feasible to generate preambles suitable for an ultra-wideband communication system which supports multi-piconets by using chaotic sequence.
As described above in a few exemplary embodiments of the present invention, a preamble of optimum auto-correlation and cross-correlation properties can be generated by using a sequence bit with a chaotic sample. By using the preamble generated according to the present invention, good data reception is guaranteed even under changes in channel environment and piconet environment.
The foregoing embodiments and advantages are merely exemplary and are not to be construed as limiting the present invention. The present teaching can be readily applied to other types of apparatuses. Also, the description of the embodiments of the present invention is intended to be illustrative, and not to limit the scope of the claims, and many alternatives, modifications, and variations will be apparent to those skilled in the art.

## Claims

1. A preamble generating method, comprising:
computing (N) chaotic samples by putting an initial value into a chaotic mapping function;
transforming the (N) chaotic samples into (N) binary values of certain bits, respectively, and computing a chaotic sequence bit successively using the (N) binary values; and
generating a preamble based on the chaotic sequence bit;
computing an inverse mapping function of the chaotic mapping function (F), using the inverse mapping function with respect to (M) different chaotic samples by periodic orbits, and computing a plurality of initial values for the (M) chaotic samples, respectively;
among the plurality of initial values computed for the (M) chaotic samples, selecting initial values which are at a maximum distance from each other; and
generating (M) preambles with respect to the (M) selected values.

2. The preamble generating method of claim 1, wherein the (N) chaotic samples are represented by Xi, and are computed by using the chaotic mapping function (F) by periodic orbits, the chaotic mapping function (F) being expressed by,
where, X0 is an initial value, and k=0, 1, 2, 3, . . .

3. The preamble generating method of claim 2, wherein the chaotic mapping function (F) uses one of a Bernoulli shift map, a tent map, a twisted tent map, and a ship map.

4. The preamble generating method of claim 1, wherein the preamble is used in an ultra-wideband communication system which supports multi-piconets, and the number of the multi-piconets is M.

5. The preamble generating method of claim 1, wherein the certain bits comprise 16 bits.

6. The preamble generating method of claim 1, wherein the number (N) comprises one of 4 and 8.

7. A preamble generating apparatus, comprising:
a chaotic sample computing part operable to compute (N) chaotic samples by putting an initial value into a chaotic mapping function;
a chaotic sequence computing part operable to transform the (N) chaotic samples into (N) binary values of certain bits, respectively, and compute a chaotic sequence bit by successively using (N) binary values; and
a preamble generating part operable to generate a preamble based on the chaotic sequence bit,
wherein an inverse mapping function of the chaotic mapping function is computed using the inverse mapping function with respect to (M) different chaotic samples by periodic orbits, and a plurality of initial values for the (M) chaotic samples are computed;
wherein, among the plurality of initial values computed for the (M) chaotic samples, initial values which are at a maximum distance from each other are selected; and
wherein (M) preambles with respect to the (M) selected values are generated.

8. The preamble generating apparatus of claim 7, wherein the chaotic sample computing part comprises:
a chaotic mapping function part operable to substitute an input value in the chaotic mapping function and output the result; and
a delay part operable to delay the output result of the chaotic mapping function by a predetermined time, and provide the delayed values as the input value to the chaotic mapping function part.

9. The preamble generating apparatus of claim 8, wherein the chaotic mapping function comprises one of at least a Bernoulli shift map, a tent map, a twisted tent map, and a ship map.

10. The preamble generating apparatus of claim 7, wherein the certain bits comprise 16 bits.

11. The preamble generating apparatus of claim 7, wherein the number (N) comprises one of 4 and 8.

12. The preamble generating apparatus of claim 7, wherein the preamble is used in synchronization and channel estimation in an ultra-wideband communication system.