Orthogonal modulation using M-sequences and Hadamard transforms
Methods, systems, and devices are described for orthogonal modulation of signals using maximal length sequences and Hadamard transforms. Modulation symbols to be transmitted are arranged into sequences indexed from 1 to 2 n −1 for some integer n. A constant is added to the beginning of each sequence, which is then multiplied by a Hadamard matrix of size 2 n ×2 n . The resulting sequences will be orthogonal and will have a first value of zero. The first value is discarded, and the sequence are reordered and associated with m-sequences. The signal is then transmitted. A cyclic prefix may also be transmitted. Upon receiving the transmission, a receiver may discard the cyclic prefix or use it for channel equalization. The receiver may then reorder the received signal, insert a zero, apply the 2 n ×2 n Hadamard transform, discard the zero, and order the sequences again according to the index to retrieve the data.
1. A method of wireless communication using orthogonal modulation, comprising:
associating a set of data with an ordered set of sequences to produce a first set of modulation sequences for a wireless signal;
appending a constant to each sequence in the first set of modulation sequences to produce a second set of modulation sequences for the wireless signal;
associating each of the second set of modulation sequences with a set of orthogonal sequences to produce a third set of modulation sequences for the wireless signal;
discarding an element of each sequence in the third set of modulation sequences and associating the remaining elements of each sequence in the third set of modulation sequences with a sequence from a set of pseudorandom binary sequences to produce a fourth set of modulation sequences for the wireless signal; and
transmitting the wireless signal comprising the fourth set of modulation sequences.
2. The method of claim 1 , further comprising:
applying a Hadamard transform to each of the second set of modulation sequences to produce the third set of modulation sequences.
3. The method of claim 1 , wherein each sequence in the ordered set of sequences has a same number of elements.
4. The method of claim 1 , wherein the set of pseudorandom binary sequences comprises a set of cyclic shift invariant sequences.
5. The method of claim 1 , wherein the set of pseudorandom binary sequences comprises a set of maximal length sequences.
6. The method of claim 1 , wherein the transmitted wireless signal comprises at least one cyclic prefix.
7. The method of claim 1 , wherein the transmitted wireless signal comprises a pilot signal.
8. The method of claim 7 , further comprising:
transmitting the pilot signal at an offset for channel estimation.
9. The method of claim 1 , wherein each sequence in the ordered set of sequences comprises a number of elements equal to one less than a power of two.
10. The method of claim 1 , further comprising:
transmitting the wireless signal using more than one antenna.
11. The method of claim 1 , wherein the transmitted wireless signal is a broadcast signal.
12. An apparatus for wireless communication using orthogonal modulation, comprising:
means for associating a set of data with an ordered set of sequences to produce a first set of modulation sequences for a wireless signal;
means for appending a constant to each sequence in the first set of modulation sequences to produce a second set of modulation sequences for the wireless signal;
means for associating each of the second set of modulation sequences with a set of orthogonal sequences to produce a third set of modulation sequences for the wireless signal;
means for discarding an element of each sequence in the third set of modulation sequences and means for associating the remaining elements of each sequence in the third set of modulation sequences with a sequence from a set of pseudorandom binary sequences to produce a fourth set of modulation sequences for the wireless signal; and
means for transmitting the wireless signal comprising the fourth set of modulation sequences.
13. The apparatus of claim 12 , further comprising:
means for applying a Hadamard transform to each of the second set of modulation sequences to produce the third set of modulation sequences.
14. The apparatus of claim 12 , wherein each sequence in the ordered set of sequences has a same number of elements.
15. The apparatus of claim 12 , wherein the set of pseudorandom binary sequences comprises a set of cyclic shift invariant sequences.
16. An apparatus for wireless communication using orthogonal modulation, comprising:
a processor;
memory in electronic communication with the processor; and
instructions stored in the memory, the instructions being executable by the processor to:
associate a set of data with an ordered set of sequences to produce a first set of modulation sequences for a wireless signal;
append a constant to each sequence in the first set of modulation sequences to produce a second set of modulation sequences for the wireless signal;
associate each of the second set of modulation sequences with a set of orthogonal sequences to produce a third set of modulation sequences for the wireless signal;
discard an element of each sequence in the third set of modulation sequences and associate the remaining elements of each sequence in the third set of modulation sequences with a sequence from a set of pseudorandom binary sequences to produce a fourth set of modulation sequences for the wireless signal; and
transmit the wireless signal comprising the fourth set of modulation sequences.
17. The apparatus of claim 16 , further comprising instructions being executable to:
apply a Hadamard transform to each of the second set of modulation sequences to produce the third set of modulation sequences.
18. The apparatus of claim 16 , wherein the set of pseudorandom binary sequences comprises a set of maximal length sequences.