KR20040034961A - DS/CDMA signature sequences based on PR-QMF coefficients - Google Patents

Abstract

PURPOSE: A method for realizing and optimizing a sequence using a PR-QMF and a method for applying the sequence in a CDMA system are provided to reduce interference between users and multi access interference. CONSTITUTION: According to the method, multi-valued sequences are made instead of a signature sequence used in the prior CDMA system and then is used as a signature sequence of the CDMA system. Two signature sequences are obtained on the base of filter coefficients of a perfect reconstruction quadrature mirror filter(PR-QMF). The first signature sequence has a perfect correlation feature in a synchronous DS/CDMA system, and the second signature sequence has a perfect correlation feature in a synchronous DS/CDMA system and has a better correlation feature in an asynchronous DS/CDMA system than other sequences. Thus, if the second signature sequence is used as a signature sequence of the DS/CDMA system, user interference and multi access interference can be reduced.

Description

Implementation method, optimization method, and method of applying the sequence to the CDM system using the Pr-MWF coefficients {DS / CDMA signature sequences based on PR-QMF coefficients}

The present invention relates to a method of implementing a sequence, an optimization method, and a method of applying the sequence to a CDMA system using the Pr-MWF coefficient, and more particularly, to create a new multi-valued sequence instead of the signature sequence used in the CDMA system. It is about using as a signature sequence.

The direct sequence code division multiple access (DS / CDMA) scheme allows a large number of users to assign a signature sequence appropriately for each user to multiply the information bits and widen the bandwidth. Allows you to use the same frequency band at the same time.

Therefore, in the DS / CDMA scheme, the signature sequence plays an important role in not only spreading and despreading but also selecting a desired user from among a plurality of users.

In particular, one of the methods of reducing multiple access interference, which is one of the main factors that reduce the capacity of the multi-access system by reducing the channel capacity, is to design a signature sequence with a low crosscorrelation value. It can be called a method.

Nowadays, a number of non-binary signature sequences have been proposed in order to get a better correlation.

One of them is a multi-valued signature sequence based on a perfect reconstruction quadrature mirror filter (PR-QMF).

See, for example, AN Akansu et al. (AN Akansu, MV Tazebay, and RA Haddad, "A new look at digital orthogonal transmultiplexers for CDMA communications," IEEE Tr. Signal Process. , Vol. 45, pp. 263-267, January 1997.) Considers a sequence based on a two-band full-reconstruction mirror filter, Q. Shi et al. (Q. Shi and S. Cheng, "Optimal spreading sequence design based on PR-QMF theory," Electronics Letters , vol. 35 , pp. 447-448, March 1999) considered a set of sequences based on multiple band full-reconstruction mirror filters.

However, the former sequence can be applied only when there are two users in the DS / CDMA system, the latter sequence can be used only in the synchronous DS / CSMA system and the phase is limited to two.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems, and an object of the present invention is to provide a good overall correlation property for a DS / CDMA communication system based on the filter coefficients of a full restore-angle mirror filter (PR-QMF). Implementing the sequence of value signatures, and applying the sequence to the CDMA system using the Pr-MWF coefficients that can greatly reduce interference between users and multi-way interference by implementing the set of signature sequences in DS / CDMA systems. To provide a way.

In order to achieve the above object, the present invention provides a method of implementing a sequence, an optimization method, and the sequence using the PR-MWF coefficients which are applied to the signature sequence of the direct-sequence code division multiple access method by making a multi-value sequence having excellent correlation properties. It is intended to provide a method applied to CDMA.

1A and 1B are structural diagrams of a transmitter and a receiver of a code division multiple access system.

2A to 2D are graphs showing the magnitude of the correlation function of gold, lattice-gold, the same odd gold, and lattice-even sequence when the sequence length is 127. FIG.

3 is a receiver model diagram of a desired user (index = 0) in a Rayleigh multipath attenuation channel.

4 is a length of a sequence of 127 in a Rayleigh multipath attenuation channel, Is a graph showing the bit error probability of the DS / CDMA system using gold, the same odd gold, and lattice sequences.

<Description of the symbols for the main parts of the drawings>

10a, 10b, 10c: Multiplier 12: Channel

14 Integrator 16: Switch

18: real output unit 20: judgment

Hereinafter, with reference to the accompanying drawings for the embodiment of the present invention will be described the specific configuration and operation.

First, a description will be given of a transmitter / receiver of a code division multiple access (CDMA) system for better understanding of the present invention.

In the transmitter of FIG. 1A, the multiplier 10a uses an information symbol ( ) Signature sequence ( Spreading the band by directly multiplying it, and the next multiplier 10b Modulate and output to channel 12.

In the receiver of FIG. 1B, the multiplier 10c receives the received signal ( Pairs of signature sequences () Despreading and demodulating the carrier frequency by multiplying

The next integrator 14 integrates the signal for one information symbol section T, and the switch 16 takes the output value of the integrator 14 when time t becomes a multiple of the information symbol section T. do.

The real output unit 18 takes only a real part (Re) of an input value and outputs it. When the output value is U, the decision stage 20 determines that the input value U is greater than zero. If the received information symbol is less than 0, it is determined as -1.

1. First Signature Sequence Set

Tree Band full-recovery in a rectangular mirror filter (PR-QMF) bundle The first subband filter The shock response Let's say

here, And depth silver Is an integer.

then, The degree of ego, Is the order of the prototype low and high frequency filters.

next, when, and Is applied to Equation 1 to obtain a first set of signature sequences according to the present invention.

here, to be.

This sequence is called tree ice sequence.

The length of the tree ring sequence is to be.

1B is a receiver model of a desired user (user index = 0) when using a tree-ear sequence.

here, Is the received signal, Is the symbol duration, Is the carrier frequency, Is Second signature waveform.

Also Is First signature sequence of Second chip value, Is the chip cycle, Is when , Elsewhere Square pulse.

size A full set of trees Say, Is the size Phosphorus subset and Can be divided into:

Subset The first filter of the sub- Defined as subsets of trees and subsets silver in Is a subset of.

Then, the correlation property of the tree-ear sequence is as follows.

i) chip-delay When autocorrelation and crosscorrelation are and to be.

ii) Non-chip delay When it is a multiple of, the size of autocorrelation and cross-correlation to be.

iii) With the sequence in The cross-correlation property between the sequences in is perfect.

iv) The maximum cross-correlation between two sequences in the same subset is very large.

According to properties (iii) and (iv), in the whole set of tree ice sequences Sequence pairs can be chosen to have perfect cross-correlation, but the rest The cross-correlation property of a sequence pair is not suitable for use in asynchronous multiple access systems.

Thus, the tree-earning sequences can only be used in synchronous DS / CDMA systems.

2. Second Signature Sequence Set

Another way to design a multiband full-reconstruction mirror filter (PR-QMF) is to use a lattice structure in series of factorized paraunitary transfer matrices.

Equation 2 below is a transfer matrix.

here, Is an identity matrix Is the size sign Is a column vector: If you write Im easy to see.

here, ego, and Denotes the conjugate and the conjugate transposition, respectively.

procession Can be implemented using a single delay, so order is one.

Degree In paraunitary matrix Can be expressed as in Equation 3.

here, Is a unitary matrix (i.e. ).

Then, as shown in Equation 4, the analysis filter bundle can be obtained.

here, ego to be.

Next, grid Create a signature sequence by changing the filter coefficients of the analysis side of the band full-reconstruction-square mirror filter (PR-QMF) bundle.

The length of the sequence When, the real part Imaginary , , This applies to Equation 1 above.

The defined sequence is called a lattice iris sequence, and the receiver as shown in FIG.

Vector of size 1 It can be seen from Equation 2-4 that the lattice sequence sequence characteristics can be changed when this is changed.

So that the correlation property of the next lattice How to optimize it.

Cascade depth for ease of calculation With 1 To optimize.

At this time, the length of the lattice to be.

first, of Redefine by.

here, to be.

then, procession Can be obtained as shown in Equation 5.

here Is Equation 6, Is equation (7).

Corresponding Full Band Restore-Square Mirror Filter (PR-QMF) Can be obtained as in Equation 8 using Equations 3 and 4.

Then, the size Grid lattice sequence assembly ( ) Can be obtained as shown in Equation 9.

here, to be.

Consider the correlation function in the following lattice sequence equation (9).

First, chip delay The function of Equation 10 is

ego Even autocorrelation,

ego Even crosscorrelation,

ego Od autocorrelation, when

ego Is called odd crosscorrelation.

The hole correlation function affects the output of the correlator when the information symbol changes within an integration period.

On the other hand, the pair correlation function affects the output when the information symbol is not changed.

Pairwise correlation function of the lattice sequence when the receiver model is shown in FIG. And hole correlation functions Can be written as in Equation 11.

here, Wow Are two sequences Wow Represents a pair correlation and a hole correlation between First base sequence Is equation (12).

Equation 11 means that the correlation function of the lattice sequence may be represented as the correlation function of the background sequence.

next When the pair cross-correlation function and the hole cross-correlation function of the base sequence are as shown in Equations 13 and 14, respectively.

here, Wow, Are as shown in Equations 15 and 16, respectively.

In Equation 13-16, when ego, Are each The even-magnitude and odd-magnetism correlation functions of, and the unit step function Is 1 when 0 when

Similarly, the mating autocorrelation function and the hole autocorrelation function of the base sequence are shown in Equations 17 and 18, respectively.

Vector in Equation 13, 14, 17, 18 Even-correlation function of And hole autocorrelation functions It can be seen that the smaller the is, the better the correlation properties of the background sequence can be.

Soon, the vector of good autocorrelation By using, we can improve the cross-correlation and auto-correlation property of lattice sequence.

Of all the conventional sequences (binary or polyphase sequences) proposed so far In this case, there is no sequence in which both the counter-correlation function and the hole auto-correlation function are both zero.

The Barker sequence is When autocorrelation function does not exceed 1 Useful as, but Barker sequences longer than 36 have not been found.

H. Fukumasa, R. Kohno, and H. Imai, "Design of pseudonoise sequences with goododd and even correlation properties for DS / CDMA," IEEE J. Sel. Areas Commun ., Vol. 12, pp. 828-836, June 1994.) proposed four-phase pseudonoise sequences with equal odd correlation and even correlation.

Among them, the same odd-numbered gold sequence has a good pair-correlation function and an odd magnetic correlation function. The maximum magnitude of the hole autocorrelation function is smaller than that in the Gold sequence.

Therefore, sipping gold sequences like gold sequences Suitable for writing

These two series of grid lattice The lattice gradation sequence using the same odd gold sequence as the gold sequence is referred to as lattice-gold sequence and lattice-even sequence.

2A-2D are correlation functions of gold (FIG. 2A), same odd gold (FIG. 2C), lattice-gold (FIG. 2B), lattice-odd (FIG. 2D) sequences when the sequence length is 127. FIG.

It can be seen that the lattice-gold sequence and the lattice-odd sequence are better correlated than the odd-numbered gold sequences, respectively.

In particular, it can be clearly seen in FIG. 2D that all four correlation properties in the lattice-odd sequence are better than in the odd-numbered gold sequence, such as the gold sequence.

When the maximum even autocorrelation function in the lattice-gold sequence is larger than in the Gold sequence, the cross-correlation and hole autocorrelation properties are much better.

In other words, the lattice-to-odd sequence has the best magnetic-correlation, even-cross correlation, and hole-cross correlation properties.

Next, we obtained the best and worst times among the highest correlation sizes of the sibling gold sequence, such as lattice-gold, lattice- sipping and gold.

Here, the best time and the bad time refer to the time when the highest size is the smallest and the big time for a set having the same sequence length.

The results when the sequence length is 127 are shown in Table 1.

condition relation Lattice-Gold Lattice-Toasting gold Sipping gold When it's best Co-correlation Hall Co-correlation Hall 0.01810.01710.01810.0171 0.01660.01660.01700.0156 0.00790.13390.12550.1654 0.12820.12820.14710.1471 At worst Co-correlation Hall Co-correlation Hall 0.02210.02080.02210.0208 0.01950.01950.01920.0156 0.00790.40160.12550.4646 0.40160.40160.35570.3557

As seen in Figure 2 The maximum size of the odd-magnitude-correlated, even-cross-correlation, and odd-cross correlation in the lattice-gold and lattice-evening sequence is much smaller than in the Gold or the same odd-numbered sequence.

In particular, the worst sized cross-correlation and hole cross-correlation of the lattice sequence in the worst case is It is only 12% -17% of, and only 12% -17% of the best cross-correlation of the best gold sequence or the same odd gold sequence.

Is the value in the gold sequence Although larger, the magneto-correlation properties of the lattice sequence are much better than the odd-numbered gold sequences such as the gold sequence.

3. Application method in DS / CDMA system

The user In a human and binary phase shift modulation (BPSK) transmitter, an asynchronous additive white light normal noise channel with frequency selective Rayleigh multipath attenuation, and a phase-locked rake receiver as shown in FIG. On the second road Size of the first user The probability density function is Equation 19 and is independent of each other.

here, ego, On the second road Phase of the first user silver Are independent of each other and are uniform random variables, silver Is the secondary moment of.

here Silver first road century Wow If you put a relationship The transmission signal of the first user may be written as in Equation 20.

here, , Is the average transmit power, Is Phase of the second carrier, Is the symbol duration.

Information symbol Are independent variables, all of the same distribution, to be.

At this time, the received signal is the same as Equation 21, and the extractor receiver output Is the same as (22).

The approximate bit mean error probability is given by Equation 23 (T. Eng and LB Milstein, "Coherent DS-CDMA performance in Nakagami multipath fading," IEEE Tr. Commun ., Vol. 43, pp. 1134-1143, February / March). April 1995.)

here, Branch number of extractor receivers,

,

,

,

,

,

,

,

,

to be.

Figure 4 shows the signal-to-noise ratio of the bit error probability in order to compare the performance of a direct sequence code division multiple access (DS / CDMA) system using gold, the same odd gold, and lattice sequences in a Rayleigh multipath attenuation channel. It is seen as a function of.

The length of the sequence is 127, And the number of users (K) is 50 and 100.

In Figure 4, it can be clearly seen that the performance of the grid-evened system is best in a Rayleigh multipath attenuation environment.

These observations mean that when using lattice sequence in DS / CDMA communication system, the bit error probability and channel capacity can be increased.

The method applied to CDMA in the present invention is a tree-array sequence set of size M implemented by the present invention in the transmitter / receiver of the code division multiple access system of FIGS. 1A and 1B. Set of lattice sequence of size or size M Is assigned to M users one by one and used as a signature sequence, a spreading sequence or a training sequence, and the receiver determines the sign of a symbol by taking only the real part of the output.

As described above, the first set of signature sequences obtained from the PR-QMF bundles show perfect correlation in the synchronous DS / CDMA system, and the lattice full recovery-right mirror filter (PR). The second set of signature sequences obtained from the QMF bundle is perfectly correlated in the synchronous DS / CMDA system, and is generally better correlated than the signature sequences in the asynchronous DS / CDMA system. In the case of using the signature sequence according to the present invention, the performance is superior to that of writing other sequences in the related art, and as the user increases, the performance difference becomes larger.

Claims (4)

Tree Band full-recovery in a rectangular mirror filter (PR-QMF) bundle The first subband filter That shock response This is called, when, and A method of implementing a sequence using a PR-FM coefficient, characterized in that to apply to the equation (24) to create a set of signature sequences. here, , depth silver Integer, The degree of , Is the order of the prototype low and high frequency filters, to be. Grid In the band full-reconstruction-square mirror filter (PR-QMF) bundle, the length of the sequence in the analysis-side filter bundle When, the real part Imaginary , , A method of implementing a sequence using the Pr-MWF coefficients, which is applied to Equation 26 to form a set of signature sequences. here, to be. Pairwise correlation function of the sequence obtained in claim 2 And hole correlation functions Representing as shown in Equation 28; here, Wow Are two sequences Wow Represents a pair correlation and a hole correlation between First base sequence Is to be. In Equation 27 When the cross-correlation function and hole cross-correlation function of the base sequence are represented by Equations 28 and 29, respectively; here, Wow, Are equations (30) and (31), respectively. here, when ego, Are each vector The even-magnitude and odd-magnetism correlation functions of, and the unit step function Is 1 when 0 when Representing the even-number autocorrelation function and the hole-magnetic correlation function of the base sequence in Equation 27 as Equations 32 and 33, respectively; Vector in the above equations 28, 29, 32, 33 Even-correlation function of And hole autocorrelation functions Minimizing to improve the correlation properties of the background sequence; Grid-line sequence optimization method using the Pr-MWF coefficient comprising a. In a transmitter / receiver of a code division multiple access system, a set of tree-array sequences of size M implemented in claim 1 or a set of lattice-array sequences of size M implemented in claim 2 are assigned to M users one by one, such as signature sequence, spreading sequence, or the like. 2. A method of applying a sequence using a PR-MWF coefficient to a CDMA system, characterized in that it is written as a training sequence and the receiver determines only the real part of the output to determine the sign of the symbol.