Wideband codebook construction and applications
View Patent ↗A precoding scheme in which the downlink channel is estimated and an optimal precoding matrix to be used by the multi antenna transmitter is determined accordingly. The optimal precoding matrix is selected from a codebook of matrices that includes matrices having a structure matched to that of the eigenvectors of the spatial covariance matrix, wherein the spatial covariance matrix is modeled as a Hermitian and Toeplitz matrix parameterized by a single complex-valued scalar.
1. A method of operating a precoding system comprising:
modulating a data signal to generate modulated symbols;
precoding the modulated symbols using a precoder matrix drawn from a plurality of precoder matrices; and
transmitting the precoded modulated symbols using eight transmit antennas, wherein the plurality of precoder matrices include:
8×1 vectors having the form
[1, e jv , e j2v , e j3v , e jΘ , e jΘ e jv , e jΘ e j2v , e jΘ e j3v ] T /2√{square root over (2)}, where (.) T denotes the transpose operation, j=√{square root over (−1)} and v,Θ are real-valued scalars lying in the interval [0,2π) and drawn from a finite set;
8×2 matrices having the form
[
1
,
ⅇ
j
v
,
ⅇ
j
2
v
,
ⅇ
j
3
v
,
ⅇ
j
ϑ
,
ⅇ
j
ϑ
,
ⅇ
j
v
,
ⅇ
j
ϑ
ⅇ
j
2
v
,
ⅇ
j
ϑ
ⅇ
j
3
v
1
,
ⅇ
j
v
,
ⅇ
j
2
v
,
ⅇ
j
3
v
,
-
ⅇ
j
ϑ
,
-
ⅇ
jϑ
ⅇ
j
v
,
-
ⅇ
j
ϑ
ⅇ
j
2
v
,
-
ⅇ
j
ϑ
ⅇ
j
3
v
]
T
/
2
2
and 8×k matrices for 3≦k≦8, whose k columns are mutually orthogonal and have the form [x T ,e jΘ x T ] T where x is a column of a 4×4 matrix E that can be expanded as E=D p (H⊕Q), where ⊕ denotes the Hadamard product of matrices, H is a 4×4 real-valued Hadamard matrix, D p is a 4×4 diagonal matrix of the form
D
p
=
[
1
0
0
0
0
ⅇ
j
v
0
0
0
0
ⅇ
j
2
v
0
0
0
0
ⅇ
j
3
v
]
and Q is a real-valued 4×4 matrix of the form
Q
=
[
p
r
q
s
q
s
p
r
q
s
p
r
p
r
q
s
]
such that p, q, r, s are real-valued scalars satisfying p 2 +q 2 =r 2 +s 2 =1/2.
2. The method of claim 1 , wherein said H is a 4×4 complex-valued Hadamard matrix.