SYSTEMS AND METHODS FOR IMPROVING REFERENCE SIGNALS FOR SPATIALLY MULTIPLEXED CELLULAR SYSTEMS
A method for using a numerical method to design reference signals for multiple input multiple output (MIMO) systems is described. An input multiple input multiple output signal is determined. A nearest tight frame to one or more given structured vectors is obtained. One or more structured vectors from the nearest tight frame are obtained. The one or more structured vectors are projected onto the space of circulant matrices. One or more classes of matrices associated with reference signals are outputted.
1 . A method for using a numerical method to design reference signals for multiple input multiple output (MIMO) systems, the method comprising:
determining an input multiple input multiple output signal;
obtaining a nearest tight frame to one or more given structured vectors; obtaining one or more structured vectors from the nearest tight frame;
projecting the one or more structured vectors onto the space of circulant matrices; and outputting one or more classes of matrices associated with reference signals.
2 . The method of claim 1 , further comprising providing a set of reference signals to cover three sectors of a cell.
3 . The method of claim 2 , wherein at least two reference signals per sector are provided.
4 . The method of claim 2 , wherein the set of reference signals is orthogonal in each sector of a given cell.
5 . The method of claim 2 , wherein the set of reference signals is orthogonal in sectors adjacent to a given cell.
6 . The method of claim 2 , further comprising minimally correlating reference signals not in adjacent sectors.
7 . The method of claim 2 , wherein the set of reference signals comprise a Peak to Average Power Ratio that approximates the value of one.
8 . The method of claim 1 , wherein multiple bandwidths are employed simultaneously.
9 . The method of claim 8 , wherein a set of sequences are recursively generated from a base sequence.
10 . The method of claim 1 , further comprising providing a matrix on the unit hyper-sphere with non-zero components.
11 . The method of claim 1 , further comprising outputting the correlation between each of the one or more structured vectors.
12 . The method of claim 1 , further comprising projecting a sequence set to a nearest tight frame.
13 . The method of claim 1 , further comprising projecting subsets of a nearest tight frame to one or more orthogonal matrices.
14 . The method of claim 1 , further comprising projecting one or more orthogonal matrices to a nearest circulant matrix.
15 . The method of claim 1 , further comprising projecting each sequence onto a minimum Peak to Average Power Ratio vector.
16 . A transmitter that is configured to use a numerical method to design reference signals for multiple input multiple output (MIMO) systems, the transmitter comprising:
a processor;
memory in electronic communication with the processor;
instructions stored in the memory, the instructions being executable to:
determine an input multiple input multiple output signal;
obtain a nearest tight frame to one or more given structured vectors;
obtain one or more structured vectors from the nearest tight frame;
project the one or more structured vectors onto the space of circulant matrices; and
output one or more classes of matrices associated with reference signals.
17 . The transmitter of claim 16 , wherein the instructions are further executable to provide a matrix on the unit hyper-sphere with non-zero components.
18 . The transmitter of claim 16 , wherein the instructions are further executable to output the correlation between each of the one or more structured vectors.
19 . The transmitter of claim 16 , wherein the instructions are further executable to provide a set of reference signals to cover three sectors of a cell.
20 . The transmitter of claim 19 , wherein at least two reference signals per sector are provided.
21 . The transmitter of claim 19 , wherein the set of reference signals is orthogonal in each sector of a given cell.
22 . The transmitter of claim 19 , wherein the set of reference signals is orthogonal in sectors adjacent to a given cell.
23 . The transmitter of claim 19 , wherein the instructions are further executable to minimally correlate reference signals not in adjacent sectors.
24 . A computer-readable medium comprising executable instructions for:
determining an input multiple input multiple output signal;
obtaining a nearest tight frame to one or more given structured vectors;
obtaining one or more structured vectors from the nearest tight frame;
projecting the one or more structured vectors onto the space of circulant matrices; and
outputting one or more classes of matrices associated with reference signals.
25 . The method of claim 1 , further comprising providing a numerical method to design reference signals for a spatially multiplexed cellular system, wherein the numerical method comprises:
executing a numerical algorithm, wherein the numerical algorithm is executed by a computing device.
26 . The method of claim 25 , further comprising projecting each sequence onto a minimum Peak to Average Power Ratio vector.
27 . The method of claim 25 , further comprising projecting a discrete Fourier transform of each sequence onto a minimum Peak to Average Power Ratio vector and performing an inverse discrete Fourier transform.
28 . The method of claim 1 , further comprising projecting a discrete Fourier transform of each sequence onto a minimum Peak to Average Power Ratio vector and performing an inverse discrete Fourier transform.
29 . The transmitter of clam 16 , wherein in the instructions are further executable to execute a numerical algorithm to design reference signals for a spatially multiplexed cellular system.