Determining a precoder for wireless communications

1. A method, comprising:

determining a precoder for a set of modulation symbols, the precoder comprising a plurality of codewords and configured to reduce an ensemble interference and a pairwise interference for the plurality of codewords;

precoding the set of modulation symbols based on the precoder;

in response to the precoding, mapping the set of modulation symbols to a set of resources for a transmission layer, wherein a number of modulation symbols of the set of modulation symbols is greater than a number of resources in the set of resources;

generating a non-orthogonal multiplexed channel for the resources by overloading the set of modulation symbols at a transmission rate that is greater than a Nyquist rate; and

transmitting an indication of the precoder and the set of resources.

2. The method of claim 1 , wherein the precoder compresses the set of modulation symbols, superpositions the set of modulation symbols, or combines the set of modulation symbols, or a combination thereof.

3. The method of claim 1 , wherein the precoder comprises a codebook of N codewords selected on a surface of a complex unit M-sphere, where M is the number of resources and M<N.

4. The method of claim 3 , wherein the codebook is based on a set of discrete harmonics on the sphere surface given by an N-th root of unity and the codebook comprises an M×N truncated N-Discrete Fourier Transform (N-DFT) linear codebook.

5. The method of claim 4 , further comprising:

selecting M harmonics of the set of discrete harmonics for a compressed representation of a precoded signal space of the set of modulation symbols based on a criteria, wherein the criteria comprise at least one of:

an ensemble interference magnitude and a pairwise interference magnitude for an entire search space of available discrete set of N harmonics;

partially to the ensemble interference magnitude upon the selection of any M harmonics out of the available discrete set of N harmonics; or

the ensemble interference magnitude and the pairwise interference magnitude for all possible harmonic and non-harmonic spherical codebook realizations by selecting any M harmonics of an available set of N=M+1 harmonics.

6. The method of claim 4 , wherein a configuration of the codebook is based on a dimensionality and indices of at least one of the selected M harmonics and a pruned N−M set of discrete harmonics.

7. The method of claim 6 , further comprising:

determining the M×N truncated N-DFT linear codebook based on storage of a tabulated codebook entry comprising the set of M harmonics and at least two codebook dimension parameters selected from the group comprising M, N,

N

M

,

 N−M, or any combination thereof; and

transmitting a second indication of a codebook index corresponding to the tabulated codebook entry of the precoder.

8. The method of claim 6 , wherein determining the precoder configuration is based on at least one of:

a rate, a latency, and a reliability of at least a portion of the set of modulation symbols;

channel state information (“CSI”) comprising at least a channel quality indicator (“CQI”); or

a channel coder type and a modulation and coding scheme (“MCS”).

9. The method of claim 1 , wherein the precoder comprises a codebook of N codewords based on complex-valued approximate spherical codes that reduce the ensemble interference and pairwise codeword interference magnitude yielding an M×N linear precoding codebook, the N codewords positioned on the unit M-sphere.

10. The method of claim 9 , further comprising determining an M×N configuration of the M×N linear precoding codebook based on an indexed codebook entry, the indexed codebook entry derived on at least one of a non-decreasing index counter and a hash function representation of the M×N linear precoding codebook.

11. The method of claim 9 , wherein determining the configuration is based on at least one of:

a rate, a latency, and a reliability of at least a portion of the set of modulation symbols;

channel state information (“CSI”) comprising at least a channel quality indicator (“CQI”); or

a channel coder type and a modulation and coding scheme (“MCS”).

12. The method of claim 1 , wherein the set of modulation symbols comprises an information stream comprising at least one of:

a fixed coding rate and a modulation configuration across a transmission block (“TB”);

a dynamic coding rate and a modulation configuration across the TB; or

an additional non-negative number of information streams with distinct coding rates and modulation configurations for unequal error protection.

13. The method of claim 1 , wherein the set of modulation symbols represent at least two distinct non-orthogonal and synchronous multiplexed streams of information.

14. The method of claim 13 , wherein the at least two non-orthogonal and synchronous multiplexed information streams comprise heterogeneous requirements to associated with at least one of a rate, a latency, or a reliability.

15. The method of claim 1 , further comprising transmitting the indication of the precoder based on one or more reference signals over one or more control channels or data channels.

16. The method of claim 1 , further comprising transmitting at least a portion of a precoder codebook information corresponding to the indicated determined precoder in response to receiving a second indication of at least one of an unknown or an unverified precoder corresponding to the indicated precoder.

17. The method of claim 1 , further comprising using one of:

a layer-common precoding with a same determined precoder for each transmission layer; and

a layer-independent precoding with different precoders determined for each transmission layer.

18. An apparatus, comprising:

a processor; and

a memory coupled to the processor, the memory comprising instructions that are executable by the processor to cause the apparatus to:

determine a precoder for a set of modulation symbols, the precoder comprising a plurality of codewords and configured to reduce an ensemble interference and a pairwise interference for the plurality of codewords;

precode the set of modulation symbols based on the precoder;

in response to the precoding, map the set of modulation symbols to a set of resources for a transmission layer, wherein a number of modulation symbols of the set of modulation symbols is greater than a number of resources in the set of resources;

generate a non-orthogonal multiplexed channel for the resources by overloading the set of modulation symbols at a transmission rate that is greater than a Nyquist rate; and

transmit an indication of the precoder and the set of resources.

19. The apparatus of claim 18 , wherein the precoder compresses the set of modulation symbols, superpositions the set of modulation symbols, or combines the set of modulation symbols, or a combination thereof.

20. An apparatus, comprising:

a processor; and

a memory coupled to the processor, the memory comprising instructions that are executable by the processor to cause the apparatus to:

receive an indication of a precoder;

receive a set of resources, the resources mapped to a set of modulation symbols that are precoded using the precoder, the set of modulation symbols overloaded at a rate that is greater than a Nyquist rate based at least in part on the precoder generating a non-orthogonal multiplexed channel for the resources; and

use the precoder and the set of resources for transmissions.