Cell isolation through quasi-orthogonal sequences in a frequency hopping network

1. An advanced metering system frequency hopping network, comprising:

a central facility; and

a plurality of end devices, at least some of which end devices comprise metrology devices, with said central facility and said plurality of end devices being configured for bi-directional communications therebetween, and with each end device being associated with one of a plurality of cells each having a unique cell identifier;

wherein each end device within a given cell is configured for synchronized communications with each other end device in the given cell;

wherein communications among adjacent cells is substantially isolated; and

wherein communications effected by one or more end devices within a given cell are effected using a hopping pattern formed from a nested combination of two sequences, including an inner sequence generated with Galois field arithmetic and an outer sequence generated using the unique cell identifier for the given cell as a seed.

2. An advanced metering system as in claim 1 , wherein the hopping pattern is more

particularly formed by using the elements of the outer sequence to select a specific N-hop inner sequence, where integer N is the number of channels used by the advanced metering system frequency hopping network.

3. An advanced metering system as in claim 2 , wherein the outer sequence (OHS) is formed by:

breaking up the cell identifier for the given cell into a plurality of parts; and

generating a sequence starting with elements corresponding to respective selected ones of the plurality of parts of the cell identifier and forming subsequent elements in the sequence by repeatedly adding a plurality of prior sequence elements together.

4. An advanced metering system as in claim 1 , wherein the outer sequence (OHS) is constructed by breaking up the cell identifier for the given cell into at least two parts and combining the at least two parts in a Fibonacci sequence according to the following relationship:

OHS(0)=Cell Identifier(0)

OHS(1)=Cell Identifier(1);

OHS( n )=OHS( n− 1)+OHS( n− 2), n= 2, 3, 4 , . . . , M− 1;

where the integer M is the length of the outer sequence.

5. An advanced metering system as in claim 1 , wherein the outer sequence (OHS) is constructed by breaking up the cell identifier into at least four parts and combining the at least four parts in a Tetranacci sequence according to the following relationship:

OHS( n )=Cell Identifier( n ), n=0, 1, 2, 3

OHS( n )=OHS( n− 1)+OHS( n− 2)+OHS( n− 3)+OHS( n− 4), n= 4 , . . . , M− 1

where the integer M is the length of the outer sequence.

6. An advanced metering system as in claim 1 , wherein the inner sequence is calculated iteratively with knowledge of a previous hop and hopping sequence number.

7. An advanced metering system as in claim 2 , wherein the inner sequence is

generated with a Galois field of order p, where p is a prime number, and wherein the selected specific N-hop inner sequence is selected from a plurality of k different inner sequences, and wherein the k-th inner sequence (IHS) is generated by the k-th primitive element (α) and can be expressed as:

IHS( k )=(1,α k ,α k 2 ,α k 3 , . . . α k N−1 ).

8. An advanced metering system as in claim 3 , wherein the inner sequence (IHS) can be expressed as

IHS( k,n )=α k n , k= 0, 1, 2 , . . . K− 1 , n= 0, 1, 2 , . . . N− 1, where

IHS(k,n) is the channel number of the n-th hop of the k-th inner sequence and α k is the primitive element of the k-th inner sequence, and wherein the hopping pattern can be expressed as the following nested combination of inner and outer sequences:

{[IHS(OHS(0),0),IHS(OHS(0),1), . . . , IHS(OHS(0),N−1)],

[IHS(OHS(1),0),IHS(OHS(1),1), . . . , IHS(OHS(1),N−1)],

. . .

[IHS(OHS(M−1),0),IHS(OHS(M−1),1), . . . , IHS(OHS(M−1),N−1)]}.

9. A metrology device for use with an advanced metering system frequency hopping network, said metrology device characterized by a unique identifier, said metrology device comprising:

a metrology portion configured to measure consumption of a utility commodity;

a transmitter portion configured to transmit consumption information;

a receiver portion configured to receive information from other network devices; and

wherein said transmitter portion and said receiver portion are configured to communicate using a frequency hopping pattern formed from a nested combination of two sequences, including an inner hopping sequence generated with Galois field arithmetic and an outer hopping sequence generated using the unique identifier for the metrology device as a seed.

10. A metrology device as in claim 9 , wherein the hopping pattern is more

particularly formed by using the elements of the outer hopping sequence to select a specific N-hop inner hopping sequence, where integer N is the number of channels used by the advanced metering system frequency hopping network.

11. A metrology device as in claim 10 , wherein the outer hopping sequence (OHS) is formed by:

breaking up the unique identifier into a plurality of parts; and

generating a sequence starting with elements corresponding to respective selected ones of the plurality of parts of the unique identifier and forming subsequent elements in the sequence by repeatedly adding a plurality of prior sequence elements together.

12. A metrology device as in claim 9 , wherein the outer hopping sequence (OHS) is

constructed by breaking up the unique identifier into at least two parts and combining the at least two parts in a Fibonacci sequence according to the following relationship:

OHS(0)=Cell Identifier(0)

OHS(1)=Cell Identifier(1);

OHS( n )=OHS( n− 1)+OHS( n− 2), n= 2, 3, 4 , . . . , M− 1;

where the integer M is the length of the outer hopping sequence.

13. A metrology device as in claim 9 , wherein the outer hopping sequence (OHS) is

constructed by breaking up the unique identifier into at least four parts and combining the at least four parts in a Tetranacci sequence according to the following relationship:

OHS( n )=Cell Identifier( n ), n=0, 1, 2, 3

OHS( n )=OHS( n− 1)+OHS( n− 2)+OHS( n− 3)+OHS( n− 4), n= 4 , . . . , M− 1

where the integer M is the length of the outer hopping sequence.

14. A metrology device as in claim 9 , wherein the inner hopping sequence is calculated iteratively with knowledge of a previous hop and hopping sequence number.

15. A metrology device as in claim 10 , wherein the inner hopping sequence is

generated with a Galois field of order p, where p is a prime number, and wherein the selected specific N-hop inner hopping sequence is selected from a plurality of k different inner hopping sequences, and wherein the k-th inner hopping sequence (IHS) is generated by the k-th primitive element (α) and can be expressed as:

IHS( k )=(1,α k ,α k 2 ,α k 3 , . . . α k N−1 ).

16. A metrology device as in claim 10 , wherein the inner hopping sequence (IHS) can be expressed as IHS(k,n)=α k n , k=0, 1, 2, . . . K−1, n=0, 1, 2, . . . N−1,where IHS(k,n) is the channel number of the n-th hop of the k-th inner hopping sequence and α k is the primitive element of the k-th inner hopping sequence, and wherein the hopping pattern can be expressed as the following nested combination of inner and outer hopping sequences:

{[IHS(OHS(0),0),IHS(OHS(0),1), . . . , IHS(OHS(0),N−1)],

[IHS(OHS(1),0),IHS(OHS(1),1), . . . , IHS(OHS(1),N−1)],

. . .

[IHS(OHS(M−1),0),IHS(OHS(M−1),1), . . . , IHS(OHS(M−1),N−1)]}.