Algebraic generators of sequences for communication signals
First Claim
1. A method of modulating a communication signal including:
- generating a family of shift sequences having lengths relatively prime using exponential, logarithmic or index functions and a polynomial or a rational function polynomial in iε
p−
1 for a finite field p of prime p;
substituting multiple columns of arrays having a relatively prime size with pseudo-noise sequences in a cyclic shift equal to the shift sequence for the respective column of the arrays to generate a substituted array;
unfolding sequences from the arrays using Chinese Remainder Theorem; and
applying the unfolded sequences to a carrier wave of the communication signal to generate a phase modulated communication signal;
wherein the family of shift sequences includes at least one of;
a (p−
1) ×
p array having (p−
1) columns each of length p;
a p×
(p−
1) array with p columns, each of length (p−
1) where the index function is used;
a p×
(p+1) array with p columns, each of length (p+1);
the family of shift sequences using a quadratic exponential map of Construction A1 or A2;
orthe family of shift sequences using a quadratic discrete logarithm map as an inverse of Construction A1 or A2.
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Accused Products
Abstract
A device for modulating communication signals comprises a transceiver for receiving and transmitting the signal, a storage medium storing computer implemented programme code components to generate sequences and a processor in communication with the storage medium and transceiver. The processor executes computer implemented programme code components to generate a family of shift sequences or arrays using exponential, logarithmic or index functions and a polynomial or a rational function polynomial in iεp−1 for a finite field p of prime p. Multiple columns of the arrays are substituted with pseudo-noise sequences or other suitable good correlation sequences in a cyclic shift equal to the shift sequence for the respective column to generate a substituted array. The substituted array, or a sequence unfolded using the CRT from the array when the array dimensions are relatively prime, is applied to a carrier wave of the communication signal to generate a modulated communication signal.
8 Citations
22 Claims
-
1. A method of modulating a communication signal including:
-
generating a family of shift sequences having lengths relatively prime using exponential, logarithmic or index functions and a polynomial or a rational function polynomial in iε
p−
1 for a finite field p of prime p;substituting multiple columns of arrays having a relatively prime size with pseudo-noise sequences in a cyclic shift equal to the shift sequence for the respective column of the arrays to generate a substituted array; unfolding sequences from the arrays using Chinese Remainder Theorem; and applying the unfolded sequences to a carrier wave of the communication signal to generate a phase modulated communication signal; wherein the family of shift sequences includes at least one of; a (p−
1) ×
p array having (p−
1) columns each of length p;a p×
(p−
1) array with p columns, each of length (p−
1) where the index function is used;a p×
(p+1) array with p columns, each of length (p+1);the family of shift sequences using a quadratic exponential map of Construction A1 or A2;
orthe family of shift sequences using a quadratic discrete logarithm map as an inverse of Construction A1 or A2. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)
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-
21. A device for modulating a communication signal, the device comprising:
-
a transceiver for receiving and transmitting the signal; a storage medium storing computer implemented programme code components to generate sequences; and a processor in communication with the storage medium and the transceiver to execute at least some of the computer implemented programme code components to cause; generating a family of shift sequences or arrays using exponential, logarithmic or index functions and a polynomial or a rational function polynomial in i ε
p−
1 for a finite field p of prime p;substituting multiple columns of the arrays with pseudo-noise sequences in a cyclic shift equal to the shift sequence for the respective column to generate a substituted array; and applying the substituted array, or a sequence unfolded from the array when the array dimensions are relatively prime, to a carrier wave of the communication signal to generate a modulated communication signal.
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22. A device for modulating a communication signal, the device comprising:
-
a transceiver for receiving and transmitting the signal; a storage medium storing computer implemented programme code components to generate sequences; and a processor in communication with the storage medium and the transceiver to execute at least some of the computer implemented programme code components to cause; generating a family of shift sequences having lengths relatively prime using exponential, logarithmic or index functions and a polynomial or a rational function polynomial in i ε
p−
1 for a finite field p of prime p;substituting multiple columns of arrays having a relatively prime size with pseudo-noise sequences in a cyclic shift equal to the shift sequence for the respective column of the arrays to generate a substituted array; unfolding sequences from the arrays using Chinese Remainder Theorem; applying the unfolded sequences to a carrier wave of the communication signal to generate a phase modulated communication signal; wherein the family of shift sequences includes at least one of; a (p−
1) ×
p array having (p−
1) columns each of length p;a p×
(p−
1) array with p columns, each of length (p−
1) where the index function is used;a p×
(p+1) array with p columns, each of length (p+1);the family of shift sequences using a quadratic exponential map of Construction A1 or A2;
orthe family of shift sequences using a quadratic discrete logarithm map as an inverse of Construction A1 or A2.
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Specification