Frequency hopping sequence generation

1. A method, comprising:

generating a scrambling sequence using a sequence of pseudo random numbers;

mapping an unscrambled sequence of channels, using the scrambling sequence, to create a scrambled sequence of channels;

checking every other timeslot in the scrambled sequence of channels for a channel-repeat;

replacing a channel that is repeated in the scrambled sequence of channels with a pseudo random selection from among channels that would not result in a further instance of two adjacent timeslots using a same channel; and

operating a radio according to the scrambled sequence of channels.

2. The method of claim 1 , wherein:

a first integer number of timeslots fills a 24-hour day, each timeslot being assigned a channel of the scrambled sequence of channels; and

a second integer number of repetitions of the scrambling sequence is used to derive a channel for each timeslot of the first integer number of timeslots.

3. The method of claim 1 , wherein the scrambled sequence of channels is repeated in each of a plurality of days.

4. The method of claim 1 , wherein mapping the unscrambled sequence of channels to create the scrambled sequence of channels comprises:

selecting an element from the unscrambled sequence of channels indicated by a magnitude of an element of the scrambling sequence.

5. The method of claim 1 , additionally comprising:

generating the scrambling sequence, for use in a first network, using a first primitive element and a Galois field; and

generating a second scrambling sequence, for use in a second network, using a second primitive element and the Galois field.

6. The method of claim 1 , additionally comprising:

applying a circular shift to the scrambling sequence to obtain a shifted scrambling sequence;

utilizing the scrambling sequence in a first network; and

utilizing the shifted scrambling sequence in a second network.

7. The method of claim 1 , wherein the scrambled sequence of channels is whitened by modifying the unscrambled sequence of channels at intervals of time.

8. The method of claim 1 , wherein a channel-repeat comprises adjacent first and second timeslots, associated with either a same channel or two adjacent channels.

9. The method of claim 1 , wherein the scrambling sequence comprises a greater number of terms than there are available channels in a network used by the radio.

10. The method of claim 1 , wherein replacing the channel that is repeated comprises not using the same channel or a channel adjacent to the same channel.

11. A node in a network, the node comprising:

a processing unit;

a hopping sequence generator, operable by the processing unit, to generate a hopping sequence by operations comprising:

generating a first scrambling sequence, for use in a first network, using a first primitive element and a Galois field;

generating a second scrambling sequence, for use in a second network, using a second primitive element and the Galois field; and

mapping an unscrambled sequence of channels, using the first and second scrambling sequences, respectively, to create first and second scrambled sequences of channels, respectively; and

a radio to tune channels according to the first and second scrambled sequences of channels.

12. The node as recited in claim 11 , wherein the hopping sequence generator is also configured to perform operations comprising:

recognizing a channel-repeat in at least one of the first and second scrambled sequences of channels; and

changing a channel used by a timeslot to remove the channel-repeat.

13. The node as recited in claim 11 , wherein the hopping sequence generator is also configured to perform operations comprising:

calculating a timeslot and calculating an associated channel based on time information obtained from a clock of the node; and

tuning the radio of the node to the calculated channel.

14. The node as recited in claim 11 , wherein the hopping sequence generator is also configured to whiten at least one of the first and second scrambled sequences of channels by modifying the unscrambled sequence of channels at intervals.

15. The node as recited in claim 11 , wherein at least one of the first and second scrambling sequences comprises a greater number of terms than there are available channels in the network.

16. The node as recited in claim 11 , wherein:

the first scrambled sequence of channels and the second scrambled sequence of channels indicate a channel used in each of a plurality of timeslots of uniform length; and

there is an integer number of timeslots in one day.

17. The node as recited in claim 11 , wherein:

the radio tunes channels according to the first and second scrambled sequences of channels in the first and second networks, respectively.

18. One or more non-transitory computer-readable media storing computer-executable instructions that, when executed, cause one or more processors to perform operations comprising:

creating a first scrambling sequence from a first sequence of pseudo random numbers;

creating a first scrambled sequence of channels using the first scrambling sequence;

applying a circular shift to the first scrambling sequence to obtain a second scrambling sequence;

creating a second scrambled sequence of channels using the second scrambling sequence; and

providing the first scrambled sequence of channels and the second scrambled sequence of channels to a radio to enable the radio to tune to channels in a first network and a second network, respectively.

19. One or more non-transitory computer-readable media as recited in claim 18 , additionally comprising:

checking at least one of the first and second scrambled sequence of channels for a channel-repeat; and

replacing a channel to remove the channel-repeat, wherein a replacement channel is selected using at least one of the first and second scrambling sequence of channels.

20. One or more non-transitory computer-readable media as recited in claim 18 , wherein the first and second scrambling sequences are based on a Galois field having an order greater than a number of channels.