Distributed radio system

1. A method of wireless communication, comprising:

generating a base expanded matrix having a plurality of rows and a plurality of columns, wherein a sum of values in each row produces a base signal vector;

updating values in at least one column of the base expanded matrix to produce an updated expanded matrix;

summing values in each row of the updated expanded matrix to produce an updated signal vector; and

transmitting the updated signal vector over a wireless channel.

2. The method of claim 1 , wherein the updating comprises an operation wherein a data matrix and a weight matrix are configured to commute under multiplication, thereby removing the data matrix and an inverse of the data matrix from the operation.

3. The method of claim 2 , further comprising removing the inverse of a base weight matrix in the operation by setting an initial weight matrix to an Identity matrix or by setting the data matrix equal to a product of a previous weight matrix with a previous data matrix or by setting the base expanded matrix equal to a previous updated expanded matrix.

4. The method of claim 1 , further comprising selecting the updated expanded matrix for further updating or for transmission over the wireless channel based on at least one of peak-to-average-power ratio (PAPR) and multiple-input multiple-output (MIMO) performance of at least the updated expanded matrix.

5. The method of claim 1 , wherein the updating values in at least one column of the base expanded matrix comprises at least one of multiplying the base expanded matrix with a weight matrix, changing a sign of a selected value in the base expanded matrix, deleting selected values in the base expanded matrix, phase-shifting selected values in the base expanded matrix, performing bit operations on selected values of the base expanded matrix, performing an additive update to the base expanded matrix, and performing an additive update to the base signal vector.

6. The method of claim 1 , wherein the updating values in at least one column of the base expanded matrix changes at least one signal parameter in the base signal vector, the at least one signal parameter comprising a data symbol value, a resource unit mapping, a layer mapping, an antenna selection, a spreading code, a selective mapping weight, a dummy symbol value, a precoding weight, a pulse shape, a mixing matrix, sparsity pattern, or order of data symbols in a data sequence.

7. The method of claim 1 , wherein the updating comprises an application of a machine learning algorithm to at least one of the base expanded matrix, the base signal vector, the updated expanded matrix, and the updated signal vector; and wherein the machine learning algorithm comprises an association-rule machine learning algorithm, a clustering algorithm, a k-means algorithm, a collaborative filtering algorithm, an artificial intelligence algorithm, an artificial neural network algorithm, a filter-generating network, a dynamic filtering layer, or a prediction network.

8. The method of claim 1 , wherein generating the base expanded matrix comprises performing at least one of a matrix multiplication and an invertible transform operation on a matrix expansion of data symbols.

9. A network device, comprising:

a non-transitory computer-readable memory; and

at least one processor in communication with the non-transitory computer-readable memory and configured for:

generating a base expanded matrix having a plurality of rows and a plurality of columns, wherein a sum of values in each row produces a base signal vector;

updating values in at least one column of the base expanded matrix to produce an updated expanded matrix;

summing values in each row of the updated expanded matrix to produce an updated signal vector; and

transmitting the updated signal vector over a wireless channel.

10. The network device of claim 9 , wherein the updating comprises an operation wherein a data matrix and a weight matrix are configured to commute under multiplication, thereby removing the data matrix and an inverse of the data matrix from the operation.

11. The network device of claim 10 , further comprising removing the inverse of a base weight matrix in the operation by setting an initial weight matrix to an Identity matrix or by setting the data matrix equal to a product of a previous weight matrix with a previous data matrix or by setting the base expanded matrix equal to a previous updated expanded matrix.

12. The network device of claim 9 , wherein the processor is further configured for selecting the updated expanded matrix for further updating or for transmission over the wireless channel based on at least one of peak-to-average-power ratio (PAPR) and multiple-input multiple-output (MIMO) performance of at least the updated expanded matrix.

13. The network device of claim 9 , wherein updating values in at least one column of the base expanded matrix comprises at least one of multiplying the base expanded matrix with a weight matrix, changing a sign of a selected value in the base expanded matrix, deleting selected values in the base expanded matrix, phase-shifting selected values in the base expanded matrix, performing bit operations on selected values of the base expanded matrix, performing an additive update to the base expanded matrix, and performing an additive update to the base signal vector.

14. The network device of claim 9 , wherein updating values in at least one column of the base expanded matrix changes at least one signal parameter in the base signal vector, the at least one signal parameter comprising a data symbol value, a resource unit mapping, a layer mapping, an antenna selection, a spreading code, a selective mapping weight, a dummy symbol value, a precoding weight, a pulse shape, a mixing matrix, sparsity pattern, or order of data symbols in a data sequence.

15. The network device of claim 9 , wherein the updating comprises an application of a machine learning algorithm to at least one of the base expanded matrix, the base signal vector, the updated expanded matrix, and the updated signal vector; and wherein the machine learning algorithm comprises an association-rule machine learning algorithm, a clustering algorithm, a k-means algorithm, a collaborative filtering algorithm, an artificial intelligence algorithm, an artificial neural network algorithm, a filter-generating network, a dynamic filtering layer, or a prediction network.

16. The network device of claim 9 , wherein generating the base expanded matrix comprises performing at least one of a matrix multiplication and an invertible transform operation on a matrix expansion of data symbols.

17. A computer program product, comprising a non-transitory computer-readable memory having computer-readable program code stored thereon, the computer-readable program code containing instructions executable by one or more processors to implement a method comprising:

generating a base expanded matrix having a plurality of rows and a plurality of columns, wherein a sum of values in each row produces a base signal vector;

updating values in at least one column of the base expanded matrix to produce an updated expanded matrix;

summing values in each row of the updated expanded matrix to produce an updated signal vector; and

transmitting the updated signal vector over a wireless channel.

18. The computer program product of claim 17 , wherein the updating comprises an operation wherein a data matrix and a weight matrix are configured to commute under multiplication, thereby removing the data matrix and an inverse of the data matrix from the operation.

19. The computer program product of claim 18 , further comprising removing the inverse of a base weight matrix in the operation by setting an initial weight matrix to an Identity matrix or by setting the data matrix equal to a product of a previous weight matrix with a previous data matrix or by setting the base expanded matrix equal to a previous updated expanded matrix.

20. The computer program product of claim 18 , wherein the method further comprises selecting the updated expanded matrix for further updating or for transmission over the wireless channel based on at least one of peak-to-average-power ratio (PAPR) and multiple-input multiple-output (MIMO) performance of at least the updated expanded matrix.

21. The computer program product of claim 18 , wherein updating values in at least one column of the base expanded matrix comprises at least one of multiplying the base expanded matrix with a weight matrix, changing a sign of a selected value in the base expanded matrix, deleting selected values in the base expanded matrix, phase-shifting selected values in the base expanded matrix, performing bit operations on selected values of the base expanded matrix, performing an additive update to the base expanded matrix, and performing an additive update to the base signal vector.

22. The computer program product of claim 18 , wherein updating values in at least one column of the base expanded matrix changes at least one signal parameter in the base signal vector, the at least one signal parameter comprising a data symbol value, a resource unit mapping, a layer mapping, an antenna selection, a spreading code, a selective mapping weight, a dummy symbol value, a precoding weight, a pulse shape, a mixing matrix, sparsity pattern, or order of data symbols in a data sequence.

23. The computer program product of claim 18 , wherein the updating comprises an application of a machine learning algorithm to at least one of the base expanded matrix, the base signal vector, the updated expanded matrix, and the updated signal vector; and wherein the machine learning algorithm comprises an association-rule machine learning algorithm, a clustering algorithm, a k-means algorithm, a collaborative filtering algorithm, an artificial intelligence algorithm, an artificial neural network algorithm, a filter-generating network, a dynamic filtering layer, or a prediction network.

24. The computer program product of claim 18 , wherein generating the base expanded matrix comprises performing at least one of a matrix multiplication and an invertible transform operation on a matrix expansion of data symbols.