Method for correlating chronologically discrete signal segments
View Patent ↗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.
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 h e as follows:
{tilde over (h)} (k) =h ( k )+ h e ( k ), k= 0 , . . . ,m− 1,
wherein m is a natural number and defines a length of the sequences, {tilde over (h)} , h and h e , and wherein elements of {tilde over (h)} and h have a range of values: {−α, +α} and elements of h e 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 h e .
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 h e so that the error sequence h e 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 h e as follows:
{tilde over (h)} ( k )= h ( k )+ h e ( k ), k= 0, . . . , m− 1,
wherein m is a natural number and defines a length of the sequences, {tilde over (h)} , h and h e and wherein elements of {tilde over (h)} and h have a range of values: {−α, +α} and elements of h e 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 h e ;
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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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 h e so that the error sequence h e 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.