Apparatus and method for estimation of frequency offset in wireless communications
A method and apparatus for estimation of frequency offset in wireless communications. Symbols to be transmitted are arranged in blocks of K symbols. The symbol blocks and their replicas are interleaved and then encoded into K sequences of coded symbols in space and time domains. The K coded symbol sequences are transmitted from K transmit antennas, while baseband signals carrying the coded symbols are received via J receive antennas and converted into J groups of intermediate signals. Thereafter, an interlaced operation and coherent combination is performed on each of the J intermediate signal groups. J sets of computed signals are thus generated and then combined in the space and time domains to develop a set of combined signals. Consequently, a frequency offset is estimated on the basis of this combined signal set.
1. An apparatus for wireless reception of signals via multiple antennas, comprising:
J distributors receiving respective discrete baseband signals from corresponding antennas where J is an integer greater than zero, and each distributor is configured to collet the received discrete baseband signal within a time interval to form a group of intermediate signals;
J block processors, each coupled to a respective one of said J distributors and is configured to perform a coherent combination by complex conjugate operation, inter-signal multiplication and addition an the corresponding group of intermediate signals to generate a set of computed signals;
a space-time combiner for combining J sets of computed signals from the J block processors in space and time domains to generate a set of combined signals; and
an estimator for estimating a frequency offset based on the set of combined signals.
2. The apparatus for wireless reception according to claim 1 , wherein each of the distributors develops the respective group of intermediate signals group as
y i (j) ( m )= x (j) (4( m− 1)+ i ), for i= 1,2,3,4 and jεJ
where y (j) (m) is the jth group of intermediate signals output by the jth distributor at a given time interval m, x (j) (n) is the received baseband signal via the jth antenna and n=4m.
3. The apparatus for wireless reception according to claim 2 , wherein the received baseband signal x (j) (n) comprises a symbol block and a replica thereof in which the symbol block is made up of symbols S 2(m−1)+1 and S 2(m−1)+2 .
4. The apparatus for wireless reception according to claim 3 , wherein the intermediate signals y i (j) (m) converted by the jth distributor at the given time interval m correspond to
y 1 (j) ( m )= x (j) (4 m− 3)=( S 2(m−1)+1 ·h 1,j +S 2(m−1)+2 ·h 2,j )· e j2π·Δf·t 0 +N 1
y 2 (j) ( m )= x (j) (4 m− 2)=( −S 2(m−1)+2 * ·h 1,j +S 2(m−1)+1 * ·h 2,j )· e j2π·Δf·(t 0 +T) +N 2
y 3 (j) ( m )= x (j) (4 m− 1)=( S 2(m−1)+1 ·h 1,j +S 2(m−1)+2 ·h 2,j )· e j2π·Δf·(t 0 +2T) +N 3
y 4 (j) ( m )= x (j) (4 m )=( −S 2(m−1)+2 * ·h 1,j +S 2(m−1)+1 * ·h 2,j )· e j2π·Δf·(t 0 +3T) +N 4
where Δf is an actual frequency offset, t 0 is an initial time, T is a symbol period for every symbols S 2(m−1)+1 and S 2(m−1)+2 , N 1 to N 4 represent additive white Gaussian noise, h 1,j and h 2,j represent a first and second channel with respect to the jth antenna, respectively, and * appended to the symbol S 2(m−1)+1 or S 2(m−1)+2 represents the complex conjugate of that symbol.
5. The apparatus for wireless reception according to claim 4 , wherein the jth block processor obtains the jth set of computed signals by performing a coherent combination on the jth group of intermediate signals y i (j) (m) as follows:
r 1 (j) ( m )= Re[y 1 (j) ( m )· y 3 (j)* ( m )+ y 2 (j)* ( m )· y 4 (j) ( m )]
r 2 (j) ( m )= Im[y 1 (j) ( m )· y 3 (j)* ( m )− y 2 (j)* ( m )· y 4 (j) ( m )]
where Re[ ] and Im[ ] represent the real and imaginary part of complex numbers, respectively, y 2 (j)* (m) is the complex conjugate of y 2 (j) (m), y 3 (j)* (m) is the complex conjugate of y 3 (j) (m), and r 1 (j) (m) and r 2 (j) (m) form the jth set of computed signals at the given time interval m.
6. The apparatus for wireless reception according to claim 5 , wherein the space-time combiner combines the J sets of computed signals from the J block processors by taking double summations over a J-dimensional space domain and an M-dimensional time domain:
z
1
=
∑
m
=
1
M
∑
j
=
1
J
r
1
(
j
)
(
m
)
z
2
=
∑
m
=
1
M
∑
j
=
1
J
r
2
(
j
)
(
m
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where z 1 and z 2 form the set of combined signals.
7. The apparatus for wireless reception according to claim 6 , wherein the estimator obtains the estimated frequency offset by calculating:
Δ
f
^
=
1
2
π
·
2
T
tan
-
1
(
-
z
2
z
1
)
where Δ{circumflex over (f)} is the estimated frequency offset.
8. A method for estimation of frequency offset in wireless communications, comprising the steps of:
arranging symbols to be transmitted in blocks of K symbols and interleaving each symbol block and a replica thereof, where K is a first integer greater than one;
encoding each symbol block and the replica thereof in space as well as time domains into K sequences of coded symbols;
separately transmitting the K coded symbol sequences from K transmit antennas;
separately receiving baseband signals including the coded symbols via J receive antennas, where J is a second integer greater than zero;
respectively converting the received baseband signals within a time interval as J groups of intermediate signals;
respectively performing a coherent combination on each of the J intermediate signal groups by complex conjugate operation, inter-signal multiplication and addition to generate J sets of computed signals;
combining the J computed signal sets in the space and time domains to generate a set of combined signals; and
estimating a frequency offset based on the set of combined signals.
9. The method for estimation of frequency offset in wireless communications according to claim 8 , wherein the symbols to be transmitted are arranged in blocks of two adjacent symbols {S i ,S j } and each symbol block and the replica thereof are interleaved as {S i ,S j ,S i ,S j } when K=2.
10. The method for estimation of frequency offset in wireless communications according to claim 9 , wherein the encoding step encodes the symbol block {S i ,S j } and the replica thereof into a first sequence of coded symbols {S i ,−S j *,S i ,−S j *} and a second sequence of coded symbols {S j ,S i *,S j ,S i *}, where * appended to the symbol S i or S j represents the complex conjugate of that symbol.
11. The method for estimation of frequency offset in wireless communications according to claim 10 , wherein the transmitting step transmits the first coded symbol sequence {S i −S j *,S i ,−S j *} from a first transmit antenna and transmits the second code symbol {S j ,S i *,S j ,S i *} from a second transmit antenna, separately.
12. The method for estimation of frequency offset in wireless communications according to claim 8 , wherein the converting step develops the J groups of intermediate signals as
y i (j) ( m )= x (j) (4( m− 1)+ i ), for i= 1,2,3,4 and jεJ
where y i (j) (m) is the jth group of intermediate signals at a given time interval m, x (j) (n) is the jth received baseband signal via the jth receive antenna and n=4m.
13. The method for estimation of frequency offset in wireless communications according to claim 12 , wherein the intermediate signals y i (j) (m) at the given time interval m correspond to
y 1 (j) ( m )= x (j) (4 m− 3)=( S 2(m−1)+1 ·h 1,j +S 2(m−1)+2 ·h 2,j )· e j2π·Δf·t 0 +N 1
y 2 (j) ( m )= x (j) (4 m− 2)=( −S* 2(m−1)+2 ·h 1,j +S* 2(m−1)+1 ·h 2,j )· e j2π·Δf·(t 0 +T) +N 2
y 3 (j) ( m )= x (j) (4 m− 1)=( S 2(m−1)+1 ·h 1,j +S 2(m−1)+2 ·h 2,j )· e j2π·Δf·(t 0 +2T) +N 3
y 4 (j) ( m )= x (j) (4 m )=( −S* 2(m−1)+2 ·h 1,j +S* 2(m−1)+1 ·h 2,j )· e j2π·Δf·(t 0 +3T) +N 4
where S 2(m−1)+1 , S 2(m−1)+2 , S (m−1)+1 * and S 2(m−1)+2 * are constituents of the coded symbols in which * appended to the symbol S 2(m−1)+1 or S 2(m−1)+2 represents the complex conjugate of that symbol, Δf is an actual frequency offset, t 0 is an initial time, T is a symbol period for every symbol S 2(m−1)+1 and S 2(m−1)+2 , N 1 to N 4 represent additive white Gaussian noise, and when K=2, h 1,j represents a first channel between a first transmit antenna and the jth receive antenna, h 2,j represents a second channel between a second transmit antenna and the jth receive antenna.
14. The method for estimation of frequency offset in wireless communications according to claim 12 , wherein the jth set of computed signals obtained by performing the a coherent combination on the jth group of intermediate signals y i (j) (m) are
r 1 (j) ( m )= Re[y 1 (j) ( m )· y 3 (j)* ( m )+ y 2 (j)* ( m )· y 4 (j) ( m )]
r 2 (j) ( m )= Im[y 1 (j) ( m )· y 3 (j)* ( m )− y 2 (j)* ( m )· y 4 (j) ( m )]
where Re[ ] and Im[ ] represent the real and imaginary part of complex numbers, respectively, y 2 (j)* (m) is the complex conjugate of y 2 (j) (m), y 3 (j)* (m) is the complex conjugate of y 3 (j) (m), and r 1 (j) (m) and r 2 (j) (m) form the jth set of computed signals at the given time interval m.
15. The method for estimation of frequency offset in wireless communications according to claim 14 , wherein the combining step combines the J sets of computed signals by taking double summations over a J-dimensional space domain and an M-dimensional time domain:
z
1
=
∑
m
=
1
M
∑
j
=
1
J
r
1
(
j
)
(
m
)
z
2
=
∑
m
=
1
M
∑
j
=
1
J
r
2
(
j
)
(
m
)
where z 1 and z 2 form the set of combined signals.
16. The method for estimation of frequency offset in wireless communications according to claim 15 , wherein the estimating step is performed by calculating:
Δ
f
^
=
1
2
π
·
2
T
tan
-
1
(
-
z
2
z
1
)
where Δ{circumflex over (f)} is the estimated frequency offset.