# Patent

## Title
Method for correlating chronologically discrete signal segments

## Abstract

The method determines the position of a predetermined known signal segment in a transmitted signal received in a receiver by means of a correlation between the received signal and a representation of the known signal segment stored in the receiver. The known signal segment is stored in the receiver as an erroned hierarchical sequence that is the sum of a hierarchical sequence and an error sequence. The correlation is formed as a sum of a correlation between the received signal and the stored hierarchical sequence and a correlation between the received signal end the stored error sequence.

## Background
BACKGROUND OF THE INVENTION
The present invention relates to a method for correlating discrete-time signal segments, wherein a predetermined signal section in a signal is determined by means of the correlation, in particular for a signal transmission system, wherein the system having the known signal segment is sent from a transmitter to a receiver, and the position of the known signal segment in the signal is determined in the receiver by means of the correlation between the received signal and the known signal segment.
Although usable in any digital message transmission system, the present invention as well as its underlying problems will be explained in relation to UMTS (Universal Mobile Telephone Systems) systems.
To detect a known signal segment (also referred to hereinafter as “test signal”) in a received signal, the correlation of the test signal that is known and stored there with the received signal is usually carried out in the receiver.
This position determination of the test signal serves, for example, to determine the starting instant of the test signal within the received signal, i.e., for purposes of synchronization.
Of particular interest hereby are test signals that have good autocorrelation properties that are noted for a high autocorrelation coefficient in the relative time shift zero and, additionally, for low values for the autocorrelation to time shifts different from zero.
Moreover, these test signals should have a systematic structure that makes it possible to carry out the necessary correlations with the fewest arithmetic operations possible. A special class of discrete-time test signals in this sense form “hierarchical codes” or sequences.
A hierarchical sequence h(k) of the nth order is formed systematically out of n not necessarily different short sequences

h1=(h1(0),h1(1), . . . ,h1(m1−1)),h2=(h2(0),h2(1), . . . ,h2(m2−1)), . . . ,hn=(hn(0),hn(1), . . . ,hn(mn−1))

having elements hi(k)ε{−1, +1}, according to the following construction scheme:

x1(k)=h1(k),k=0, . . . ,m1−1,  (1)

xi+1(k)=hi+1(k div mi+1)·xi(k mod mt),





  
    
      
        
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The expense to correlate such a hierarchical sequence with another signal or another sequence can be reduced considerably in known fashion by means of a rapid correlation in multiple steps, as compared to a direct realization. Moreover, hierarchical sequences can be found that have good correlation properties and are therefore well-suited in the sense mentioned initially as test signals for synchronization.
The mentioned procedure for the cost-efficient, rapid hierarchical correlation will be explained further hereinafter, because the method according to the invention described later is based on it. The received signal, with which the test signal is to be correlated in the receiver, is referred to as s(k). Without restricting the generality, it suffices to consider hierarchical sequences of the 2nd order (i.e., n=2), because hierarchical sequences having more than two hierarchical levels are always formed successively out of two subsequences, according to the above equations. The correlation should be carried out for each instant k.
The correlation result v(k) is thereby as follows:




  
    
      
        
          
            
              
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FIG. 2 illustrates the known hierarchical correlation procedure using the example of a hierarchical sequence of the 2nd order. The arithmetic steps are illustrated using lines.
The short subsequences are given by h1=(+1, +1, −1, +1) and h2=(+1, −1, +1, +1). The total sequence is therefore h=(+1, +1, −1, +1, −1, −1, +1, −1, +1, +1, −1, +1, +1, +1, −1, +1). In the first step or the first subcorrelation step TK1, the subcorrelation v1(k) is determined. In the second step or the second subcorrelation step TK2, the searched-for correlation v(k) is determined from this intermediate result. As time k continues, as indicated in FIG. 2 using the bold lines, three known results can be referred back to in each case, and only one new calculation need be carried out in the subcorrelation step TK1, namely for the most recent ones, by the sampling of received signal values of the signal s(k).
Further correlation steps result accordingly for n>2 subsequences according to the same basic principle.
SUMMARY OF THE INVENTION
The problem underlying the present invention is basically that the known method is to be expanded to non-hierarchical sequences without the computer power becoming too great for the correlation.
The basic idea underlying the present Invention is that the known rapid multi-level correlation procedure of the above-described kind, especially for representing signal segments of a mobile phone signal, using hierarchical sequences is expanded to include erroned hierarchical sequences.
An erroned hierarchical sequence {tilde over (h)} is to be described as a sequence, the construction of which is not immediately possible by means of decomposition into suitable subsequences, but a hierarchical sequence h can be found that is very similar to the sequence. The difference between h and {tilde over (h)} is described by a further sequence referred to hereinafter as error sequence he. The decomposition of {tilde over (h)} into h and he should be selected such that the necessary number of arithmetical operations for the correlation is reduced overall to the greatest extent possible.
In the method according to the invention, therefore, correcting expressions are also taken into consideration in addition to a hierarchical correlation to calculate the correlation v(k). The method according to the invention is therefore to be referred to as a “corrected hierarchical correlation”.
The method according to the invention of corrected hierarchical correlation is usable on sequences that cannot be decomposed themselves directly, but for which a suitable representation as sum of a hierarchical sequence and an error sequence can be found.
The sequence presented further below in the exemplary embodiment is usable as subsequence for generating a hierarchical sequence for the Universal Mobile Telecommunication System (UMTS) for purposes of synchronization. The method according to the invention now allows for the further decomposition of this subsequence according to a corrected hierarchical structure, so that the necessary computer power for determining the correlation can be reduced by a further 40% approximately. Since the numerical expense for the synchronization of a mobile station with a base station makes up a significant portion of the baseband computer power in the mobile station overall, the method according to the invention is very useful in reducing the computer power required.
Reduced computer power in the baseband signal processing means, on the one hand, lower costs for the baseband hardware (lower clock rate, fewer logic gates, etc.). On the other hand, lower computer power also leads to reduced power input of the baseband hardware, so that extended speech or stand-by times can be made possible for mobile stations in particular that are operated using storage cells.
Advantageous further developments and improvements of the method according to the invention are presented in the appended subclaims.
According to a preferred further development, the erroned hierarchical sequence {tilde over (h)} is representable as follows by the hierarchical sequence h and the error sequence he:

{tilde over (h)}(k)=h(k)+he(k),k=0, . . . ,m−1  (6)

wherein m is a natural number and describes the length of the sequences {tilde over (h)}, h and he, and wherein the elements of the sequences {tilde over (h)} and h are from the range of values {−1, +1} and the elements of he are from the range of values {−2, 0, +2}.

According to a further preferred further development, the correlation v(k) of {tilde over (h)} with the signal s(k) is described by:




  
    
      
        
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wherein u(k) is the correlation between the signal s(k) and the stored hierarchical sequence, and ue(k) is the correlation between the signal s(k) and the stored error sequence.

The first addend u(k) can be calculated directly using the rapid hierarchical correlation based on the hierarchical construction of h. For the second addend ue(k), the further procedure depends on the structure of he.
According to a further preferred further development, the decomposition into the sum of a hierarchical sequence and an error sequence is carried out in such a fashion that the error sequence contains elements that differ from zero as little as possible. Advantageously, a decomposition of {tilde over (h)} into h and he is such that he contains as few elements as possible that differ from zero.
For the case in which he contains, for example, only one element, he(K)=β, different from zero (βε{−2, +2}), the calculation of ue(k) simplies to ue(k)=β·s(k+K), so that this follows:

v(k)=u(k)+β·s(k+K)  (9)

If there is more than one element different from zero, correspondingly more correction terms are to be taken into consideration. In the general case, a method for calculating correlation expressions can also be used again to calculate the expression Ue(k).
According to a further preferred embodiment, the method is used in a mobile telephone system.



BRIEF DESCRIPTION OF THE DRAWING
An exemplary embodiment of the invention is presented in the drawings and described in greater detail in the subsequent description.
FIG. 1 shows an erroned hierarchical correlation procedure having a hierarchical sequence of the 2nd order and a simple error sequence as exemplary embodiment of the present invention; and
FIG. 2 shows the known hierarchical correlation procedure using the example of a hierarchical sequence of the 2nd order.



DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS
Referring to FIG. 1, an exemplary embodiment of the method according to the invention corresponding to an erroned hierarchical correlation procedure having a hierarchical sequence of the 2nd order and a simple error sequence is explained hereinafter.
The sequence presented in the exemplary embodiment has been proposed as a subsequence for generating a hierarchical sequence for the Universal Mobile Telecommunication System (UMTS) for purposes of synchronization.
The following Lindner sequence is considered (refer also to H. D. Lüke, Korrelationssignale [Correlation Signals], Springer Verlag, Berlin, Heidelberg, New York, 1992):

{tilde over (h)}=(+1, +1, −1, +1, −1, −1, +1, −1, +1, +1, −1, +1, +1, +1, −1, +1),

which apparently cannot be decomposed directly into suitable hierarchical subsequences so that the known hierarchical correlation—favorable in terms of expense—can be used. As an alternative, however, it can be represented using a hierarchical sequence and an error sequence according to

{tilde over (h)}(k)=h(k)+he(k),k=0, . . . ,m−1  (10)

with

    
    
        h=(+1, +1, −1, +1, −1, −1, +1, −1, +1, +1, −1, +1, +1, +1, −1, +1) and
        he=(0, 0, 0, −2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0).
    
    


A hierarchical decomposition of h is given by the subsequences h1=(+1, +1, −1, +1) and h2=(+1, −1, +1, +1).
The correlation procedure overall can therefore take place advantageously using the method according to the invention by means of the corrected hierarchical correlation.
FIG. 1 illustrates this procedure. In addition to the structure of the hierarchical correlation known from FIG. 2, combinations of received signal s(k) to the result of the second subcorrelation step TK2 are to be seen that represent the correction terms in the form of values of the input signal weighted with −2.
A consideration of the expense for the entire correlation is carried out hereinafter. A direct realization of the correlation of the sequence {tilde over (h)} (the length of m elements) using a sequence of, in general, complex variables s(k), requires a number of m complex additions for each correlation value v(k) to be determined. With m=16, that is 16 complex additions in this example.
The splitting into the hierarchical sequence and the error sequence reduces this number significantly. Four complex additions per correlation value v(k) are required for the hierarchical correlation in the first step, and 4 are also required in the second step. In addition, there is the multiplication of the value s(k+3) by the factor −2 and the addition of this correction value to the result of the hierarchical correlation, as indicated in FIG. 1. If one takes into consideration the fact that the multiplication by 2 corresponds to a bit shift of one place and therefore requires a negligibly small amount of computer power as compared to a “real” multiplication, the only thing remaining, notably, is to incorporate the one additional complex addition by the correction value into the correlation result. Using the corrected hierarchical correlation, therefore, the entire correlation procedure requires 9 complex additions per correlation value v(k) as compared to the 16 complex additions mentioned hereinabove in the direct realization of the correlation. This represents a savings of a good 40%.
The method presented has a very high level of actuality with regard for the current worldwide intensive research and development activities of all manufacturers of mobile radio equipment involving third-generation mobile radio systems (UMTS, etc.).
Although the present invention was described hereinabove using a preferred exemplary embodiment, it is not limited to that. Instead, it is modifiable in multiple fashions.
In particular, the invention is not limited to UMTS (Universal Mobile Telephone Systems) systems. Instead, it is usable with any digital, discrete-time signal processing system.

## Claims

1. A method of correlating discrete-time signal segments, said method comprising the steps of:
a) providing a signal for transmission from a transmitter to a receiver, said signal including a predetermined signal section; and
b) storing the predetermined signal section in the receiver as an erroned hierarchical sequence {tilde over (h)}, wherein said erroned hierarchical sequence {tilde over (h)} is represented by a hierarchical sequence h and an error sequence he as follows:


{tilde over (h)}(k)=h(k)+he(k),k=0, . . . ,m−1,


wherein m is a natural number and defines a length of the sequences, {tilde over (h)}, h and he, and wherein elements of {tilde over (h)} and h have a range of values: {−α, +α} and elements of he have a range of values: {−2α, 0, +2α}, wherein α represents any real or complex number;

c) correlating the erroned hierarchical sequence {tilde over (h)} stored in step b) with a received signal received in the receiver to determine a position of the predetermined signal section in the received signal, said correlating comprises forming a sum of a correlation between the received signal and said hierarchical sequence h and a correlation between the received signal and said error sequence he.

2. The method as defined in claim 1, further comprising decomposing the erroned hierarchical sequence {tilde over (h)} into a sum of the hierarchical sequence h and the error sequence he so that the error sequence he contains as few of said elements as possible that are different from zero.

3. A method of correlating discrete-time signal segments, said method comprising the steps of:
a) providing a signal for transmission from a transmitter to a receiver, said signal including a predetermined signal section; and
b) storing the predetermined signal section in the receiver as an erroned hierarchical sequence {tilde over (h)}, wherein said erroned hierarchical sequence {tilde over (h)} is represented by the hierarchical sequence h and the error sequence he as follows:


{tilde over (h)}(k)=h(k)+he(k),k=0, . . . ,m−1,


wherein m is a natural number and defines a length of the sequences, {tilde over (h)}, h and he and wherein elements of {tilde over (h)} and h have a range of values: {−α, +α} and elements of he have a range of values: {−α, +α}, wherein α represents any real or complex number;
c) correlating the erroned hierarchical sequence {tilde over (h)} stored in step b) with a received signal received in the receiver to determine a position of the predetermined signal section in the received signal, said correlating comprises forming a sum of a correlation between the received signal and said hierarchical sequence h and a correlation between the received signal and said error sequence he;
wherein a correlation v(k) of said erroned hierarchical sequence {tilde over (h)} with the received signal s(k) is given by





  
    
      
        
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wherein u(k)=the correlation between the hierarchical sequence h and the received signal s(k) and





  
    
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wherein ue(k)=the correlation between the error sequence he and the received signal s(k) and





  
    
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4. The method as defined in claim 3, further comprising decomposing the erroned hierarchical sequence {tilde over (h)} into a sum of the hierarchical sequence h and the error sequence he so that the error sequence he contains as few of said elements as possible that are different from zero.

5. The method as defined in claim 1 or 3, wherein said signal transmission system is a mobile telephone system.