System and method for transmitting a sub-space selection

A method for receiving channel state information, comprising:

• receiving, by a base station, a first group index from a user equipment (UE), the first group index including bits identifying a first group of beams selected from a codebook of beams, a number of bits in the first group index being equal to ceiling (log2(MN)), where N is a number of beams in the codebook of beams and M is a number of beams in the first group of beams, and the first group index set in accordance with
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• where x0, x1, . . . , xM-1 are M beam indices being identified by the first group index;
• and
• communicating, by the base station, a signal with the UE in accordance with one or more beams from the first group of beams identified by the first group index.

A method for receiving a channel state information, comprising:

• transmitting, by a base station, one or more reference signals to a user equipment (UE);
• receiving, by the base station, a first group index from the UE, the first group index identifying a first group of beams based on the first group of beams, a number of beams in a codebook of beams (N), and a number of beams in the first group of beams (M), a number of bits used to indicate the first group index being equal to ceiling (log2(MN));
• identifying, by the base station, from the received first group index, the beams in the first group of beams, wherein the beams in the first group of beams are identified in accordance with
• ∑
• n
• =
• 1
• x
• 0
• ⁢
• (
• N
• -
• n
• M
• -
• 1
• )
• +
• [
• ∑
• i
• =
• 0
• M
• -
• 3
• ⁢
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• ∑
• n
• =
• x
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• i
• )
• +
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• i
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• N
• -
• n
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• )
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• +
• x
• M
• -
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• -
• x
• M
• -
• 2
• -
• 1
• where x0, x1, . . . , xM-1 are M beam indices corresponding to the first group of beams;
• and
• communicating, by the base station, a signal with the UE in accordance with one or more beams based on the identified beams in the first group of beams.

A base station comprising:

• a non-transitory memory storage comprising instructions;
• and
• a processor in communication with the non-transitory memory storage, wherein the processor executes the instructions to:
• transmit one or more reference signals to a user equipment (UE);
• receive a first group index from the UE, the first group index identifying a first group of beams based on the first group of beams, a number of beams in a codebook of beams (N), and a number of beams in the first group of beams (M), a number of bits used to indicate the first group index being equal to ceiling(log2(MN));
• identify from the received first group index, the beams in the first group of beams wherein the beams in the first group of beams are identified in accordance with
• ∑
• n
• =
• 1
• x
• 0
• ⁢
• (
• N
• -
• n
• M
• -
• 1
• )
• +
• [
• ∑
• i
• =
• 0
• M
• -
• 3
• ⁢
• ⁢
• ∑
• n
• =
• x
• (
• i
• )
• +
• 2
• x
• (
• i
• +
• 1
• )
• ⁢
• ⁢
• (
• N
• -
• n
• M
• -
• 2
• -
• i
• )
• ]
• +
• x
• M
• -
• 1
• -
• x
• M
• -
• 2
• -
• 1
• where x0, x1, . . ., xM-1 are M beam indices corresponding to the first group of beams;
• and
• communicate a signal with the UE in accordance with one or more beams based on the identified beams in the first group of beams.