Efficient compressed sensing channel estimation for single-carrier communication systems
Methods and devices for receiving wireless signals employ compressed sensing-based estimation techniques to receive single-carrier transmissions, exploiting the common sparseness of the wireless channel, enabling signal reception in the presence of significant Delay and Doppler spreads. When implemented for an ATSC or ATSC-M/H mobile TV standard signal, the compressed sensing channel estimation algorithm enables data reception in Delay and Doppler spread conditions beyond the capabilities of conventional channel estimation methods.
1. A method for receiving a wireless signal transmitted over a single-carrier transmission, comprising:
deriving a channel impulse response using the wireless signal;
applying a compressed sensing algorithm, by one or more processors, to the derived channel impulse response to obtain a channel estimate; and
reconstructing the wireless signal using the channel estimate, wherein the wireless signal comprises predetermined randomly-generated training symbols transmitted in between a plurality of data symbol sets, and
wherein the compressed sensing algorithm comprises:
generating a sensing matrix, the sensing matrix being a partial Toeplitz matrix;
generating a circulant matrix from the generated sensing matrix;
generating a diagonal eigenvalue matrix from the generated circulant matrix; and
combining the predetermined randomly-generated training symbols with the generated diagonal eigenvalue matrix to obtain the channel estimate.
2. The method of claim 1 , wherein the compressed sensing algorithm comprises:
generating exactly one diagonal eigenvalue matrix from the generated circulant matrix.
3. The method of claim 1 , wherein the derived channel impulse response is approximately sparse.
4. The method of claim 1 , wherein the diagonal eigenvalue matrix is generated by executing a fast Fourier transform operation over a first column of the generated circulant matrix.
5. The method of claim 1 , wherein the compressed sensing algorithm is computationally comparable to that of a least squares or a correlation based channel estimation method.
6. A wireless receiver device for receiving a wireless signal transmitted over a single-carrier transmission, the wireless receiver device comprising:
means for deriving a channel impulse response using the wireless signal;
means for applying a compressed sensing algorithm to the derived channel impulse response to obtain a channel estimate; and
means for reconstructing the wireless signal using the channel estimate,
wherein the wireless signal comprises predetermined randomly-generated training symbols transmitted in between a plurality of data symbol sets, and wherein the means for applying a compressed sensing algorithm comprises:
means for generating a sensing matrix, the sensing matrix being a partial Toeplitz matrix;
means for generating a circulant matrix from the generated sensing matrix;
means for generating a diagonal eigenvalue matrix from the generated circulant matrix; and
means for combining the predetermined randomly-generated training symbols with the generated diagonal eigenvalue matrix to obtain the channel estimate.
7. The wireless receiver device of claim 6 , wherein the means for applying a compressed sensing algorithm comprises:
means for generating exactly one diagonal eigenvalue matrix from the generated circulant matrix.
8. The wireless receiver device of claim 6 , wherein the derived channel impulse response is approximately sparse.
9. The wireless receiver device of claim 6 , wherein means for generating a diagonal eigenvalue matrix comprises means for executing a fast Fourier transform operation over a first column of the generated circulant matrix.
10. The wireless receiver device of claim 6 , wherein the compressed sensing algorithm is computationally comparable to that of a least squares or a correlation based channel estimation method.
11. A wireless receiver device for receiving a wireless signal transmitted over a single-carrier transmission, comprising:
a memory; and
a processor coupled to the memory, wherein the processor is configured with processor-executable software instructions to perform operations comprising:
deriving a channel impulse response using the wireless signal;
applying a compressed sensing algorithm to the derived channel impulse response to obtain a channel estimate; and
reconstructing the wireless signal using the channel estimate,
wherein the processor is configured with processor-executable software instructions to perform operations such that the channel impulse response is derived from a wireless signal including predetermined randomly-generated training symbols transmitted in between a plurality of data symbol sets, and with processor-executable software instructions to perform operations such that the compressed sensing algorithm comprises:
generating a sensing matrix, the sensing matrix being a partial Toeplitz matrix;
generating a circulant matrix from the generated sensing matrix;
generating a diagonal eigenvalue matrix from the generated circulant matrix; and
combining the predetermined randomly-generated training symbols with the generated diagonal eigenvalue matrix to obtain the channel estimate.
12. The wireless receiver device of claim 11 , wherein the processor is configured with processor-executable software instructions to perform operations such that the compressed sensing algorithm comprises: generating exactly one diagonal eigenvalue matrix from the generated circulant matrix.
13. The wireless receiver device of claim 11 , wherein the processor is configured with processor-executable software instructions to perform operations such that the derived channel impulse response is approximately sparse.
14. The wireless receiver device of claim 11 , wherein the processor is configured with processor-executable software instructions to perform operations such that the diagonal eigenvalue matrix is generated by executing a fast Fourier transform operation over a first column of the generated circulant matrix.
15. The wireless receiver device of claim 11 , wherein the processor is configured with processor-executable software instructions to perform operations such that the compressed sensing algorithm is computationally comparable to that of a least squares or a correlation based channel estimation method.
16. A non-transitory processor-readable storage medium having stored thereon processor-executable software instructions configured to cause a wireless receiver device processor to perform operations comprising:
deriving a channel impulse response using the wireless signal;
applying a compressed sensing algorithm to the derived channel impulse response to obtain a channel estimate; and
reconstructing the wireless signal using the channel estimate,
wherein the stored processor-executable software instructions are further configured to cause the processor to perform operations such that the channel impulse response is derived from a single-carrier wireless signal including predetermined randomly-generated training symbols transmitted in between a plurality of data symbol sets, and to cause the processor to perform operations such that the compressed sensing algorithm comprises:
generating a sensing matrix, the sensing matrix being a partial Toeplitz matrix;
generating a circulant matrix from the generated sensing matrix; and
generating a diagonal eigenvalue matrix from the generated circulant matrix; and
combining the predetermined randomly-generated training symbols with the generated diagonal eigenvalue matrix to obtain the channel estimate.
17. The non-transitory processor-readable storage medium of claim 16 , wherein the stored processor-executable software instructions are configured to cause the processor to perform operations such that the compressed sensing algorithm comprises:
generating exactly one diagonal eigenvalue matrix from the generated circulant matrix.
18. The non-transitory processor-readable storage medium of claim 16 , wherein the stored processor-executable software instructions are configured to cause the processor to perform operations such that the derived channel impulse response is approximately sparse.
19. The non-transitory processor-readable storage medium of claim 16 , wherein the stored processor-executable software instructions are further configured to cause the processor to perform operations such that the diagonal eigenvalue matrix is generated by executing a fast Fourier transform operation over a first column of the generated circulant matrix.
20. The non-transitory processor-readable storage medium of claim 16 , wherein the stored processor-executable software instructions are configured to cause the processor to perform operations such that the compressed sensing algorithm is computationally comparable to that of a least squares or a correlation based channel estimation method.