Method for computing a downlink beamforming weighting vector based on up link channel information
Described herein is a method for obtaining a downlink beamforming weighting vector in a wireless communications system based on channel information about an uplink channel. The method comprises obtaining the channel information about the uplink channel by a means selected from the group comprising of training signals, pilot signals, and data signals, wherein the uplink channel comprises a set of uplink sub-channels, calculating a spatial signature of the uplink channel with the channel information, and computing a downlink beamforming weighting vector of a downlink channel with the spatial signature of the uplink channel, wherein the downlink channel comprises a set of downlink sub-channels that share few or no sub-carriers with the set of uplink sub-channels.
1. A method comprising:
receiving at a plurality of antennas of an antenna array of a base station an uplink transmission that is transmitted from a mobile station, wherein the uplink transmission is transmitted in an uplink channel that comprises a plurality of sub-channels, each of which comprises a plurality of subcarriers;
computing uplink channel coefficients for the uplink channel from the received uplink transmission at the base station;
computing for each antenna in the antenna array of the base station, one or more coefficients for a time-domain channel impulse response function from the uplink channel coefficients;
computing a frequency response of the uplink channel from the time-domain channel impulse response function for each antenna;
calculating a spatial signature of the uplink channel from the frequency response; and
computing a downlink beamforming weighting vector for use when making a downlink transmission via the antenna array of the base station on a downlink channel to the mobile station from the spatial signature of the uplink channel, wherein the downlink channel comprises a plurality of downlink sub-channels that share few or no frequency sub-carriers with the plurality of uplink sub-channels.
2. The method of claim 1 , wherein computing the frequency response of the uplink channel comprises computing a
Fast Fourier Transform of the time-domain channel impulse response function for each antenna described by the one or more coefficients for a pre-determined number of sub-channels of a frequency band in which the uplink channel and downlink channel reside.
3. The method of claim 2 , wherein computing the
uplink channel coefficients uses covariance method based on the uplink transmission received at the plurality of antennas; and
computing the one or more coefficients of the time-domain channel impulse response function for each antenna from the uplink channel coefficients according to a predetermined equation.
4. The method of claim 3 , wherein computing the one or more coefficients of the time-domain channel impulse response function comprises computing the one or more coefficients according to the predetermined equation defined as:
(
r
g
1
r
g
2
⋮
r
g
W
)
=
(
1
exp
(
-
j2π
g
1
F
)
exp
(
-
j2π
2
g
1
F
)
⋯
exp
(
-
j2π
(
M
-
1
)
g
1
F
)
1
exp
(
-
j2π
g
2
F
)
exp
(
-
j2π
2
g
2
F
)
⋯
exp
(
-
j2π
(
M
-
1
)
g
2
F
)
⋮
⋮
⋮
⋮
1
exp
(
-
j2π
g
W
F
)
exp
(
-
j2π
g
W
F
)
⋯
exp
(
-
j2π
(
M
-
1
)
g
W
F
)
)
(
a
1
a
2
⋮
⋮
a
M
)
,
where
r gi is a received signal at a given antenna at frequency g i , F is the size of the Fast Fourier Transform (FFT) and a i is the coefficient of an i-th multi-path component of the time-domain channel impulse response function at the given antenna.
5. The method of claim 4 , wherein computing the one or more coefficients of the time-domain channel impulse response function comprises computing a solution to the predetermined equation using by matrix operations comprising at least one of inverse and pseudo-inverse matrix operations.
6. The method of claim 4 , wherein computing the one or more coefficients of the time-domain channel impulse response function comprises computing a solution to the predetermined equation using by estimation techniques comprising at least one of a maximum likelihood method, a minimum mean square error method, and a maximum a posteriori method.
7. A method comprising:
receiving at a plurality of antennas of an antenna array of a base station an uplink transmission that is transmitted from a mobile station, wherein the uplink transmission is transmitted in an uplink channel that comprises a plurality of sub-channels, each of which is composed of a plurality of subcarriers;
computing uplink channel coefficients for the uplink channel from the received uplink transmission at the base station;
calculating a spatial signature of the uplink channel from the uplink channel coefficients; and
computing a downlink beamforming weighting vector for use when making a downlink transmission via the antenna array of the base station in a downlink channel to the mobile station from the spatial signature of the uplink channel, wherein the downlink channel comprises a set of downlink sub-channels of frequency subcarriers that fall within neighborhoods of one or more uplink sub-channels of frequency subcarriers.
8. The method of claim 7 , wherein computing the downlink beamforming weight vector comprises computing the downlink beamforming weight vector such that a predetermined uplink sub-channel is at a center of the neighborhood.
9. The method of claim 8 , wherein computing the downlink beamforming weight vector comprises computing the downlink beamforming weight vector such that the neighborhood of one or more frequency subcarriers in an uplink sub-channel overlaps with the neighborhood of one or more frequency subcarriers in another uplink sub-channel.
10. The method of claim 7 , wherein computing the downlink beamforming weighting vector comprises:
computing the downlink beamforming weighting vector for the downlink sub-channels from the uplink channel coefficients under the condition that the subcarriers in the downlink sub-channels fall within one or more neighborhoods of the uplink sub-channels; and
constructing the downlink beamforming weighting vector for the downlink sub-channels from the uplink channel coefficients with respect to immediate neighborhoods of the uplink sub-channels for the subcarriers in the downlink sub-channels which fall outside one or more neighborhoods with respect to the uplink sub-channels.
11. The method of claim 10 , wherein constructing the downlink beamforming weighting vector uses at least one of interpolation and extrapolation based on the immediate neighboring uplink subchannels.
12. The method of claim 3 , wherein computing the one or more coefficients of the time-domain channel impulse response function is based on a channel impulse response function of the form
h
(
t
)
=
a
1
δ
(
t
-
τ
1
)
+
a
2
δ
(
t
-
τ
2
)
+
…
+
a
M
δ
(
t
-
τ
M
)
=
∑
¨
M
a
l
δ
(
t
-
τ
1
)
,
where τ i is a delay of the i-th multi-path component and coefficient a i is a complex number representing an amplitude of the i-th multi-path component.
13. The method of claim 12 , wherein computing the one or more coefficients of the time-domain channel impulse response from the uplink channel coefficients is based on a relationship between the frequency response of the uplink channel and the time-domain channel impulse response function h(t).
14. The method of claim 7 , and further comprising computing for each antenna in the antenna array of the base station, one or more coefficients for a time-domain channel impulse response function from the uplink channel coefficients; computing a frequency response of the uplink channel from the time-domain channel impulse response function for each antenna described by the one or more coefficients, wherein computing the spatial signature is based on frequency response.