A Joint Real Grassmannian Quantization Strategy
for SISO IA with Limited Feedback
Wen Wu
1
,XuLi
1
, Huarui Yin
1
, Chen Zhang
2
and Guo Wei
1
1
Dept. of Electronic Engineering and Information Science
University of Science and Technology of China, Hefei, China
Email: {wuwen854,lixu}@mail.ustc.edu.cn, {yhr,wei}@ustc.edu.cn
2
Nanjing Research Institute of Electronic Technology Email: zhangzc@mail.ustc.edu.cn
Abstract—Interference alignment (IA) is a scheme to achieve
degrees of freedom (DOF) of interference network at high signal-
to-noise ratio (SNR). In order to implement IA scheme in
frequency-division duplexing (FDD) system, receivers feedback
channel state information to transmitters. The key problem is to
acquire accurate transmitter channel state information (CSIT)
in the presence of the quantization error. In this paper, a joint
real Grassmannian quantization strategy is proposed to reduce
codebook size in single-input single-output (SISO) frequency-
selective channel with K user. More concretely, this strategy
quantizes the real part and imaginary part of channel vector
respectively to reduce the chordal distance. Meanwhile, a noise-
limited criterion is assumed that interference leakage is smaller
than thermal noise. Under this criterion, the codebook size using
the proposed strategy is much smaller than the codebook size
using conventional complex Grassmannian quantization strategy.
With the same codebook size, simulations show a significant sum
rate gain at high SNR compared with the conventional strategy.
I. INTRODUCTION
Interference alignment (IA) demonstrates that the capacity
of interference network can be much higher than previous
thought [1]. To implement IA, transmitter channel state infor-
mation (CSIT) is required to compute precoders at transmitter.
However, the performance of IA is sensitive to the accuracy
of CSIT.
In frequency-division duplexing (FDD) system, CSIT is
measured at the receiver and fed back to the transmitter.
However, quantization error and delay are two sources of
inaccurate CSIT [2]. In time-varying channel, delay of feed-
back channel makes CSIT outdated, and quantization error
contributes to CSIT distortion. In addition, high resolution
CSIT incurs significant overhead and increases codebook size.
In this paper, we only consider quantization error problem.
Using Grassmannian codebook, the work in [3] clarifies the
lower bound of the number of feedback bits to achieve the
total degrees of freedom (DOF) in single-input single-output
(SISO) channel with frequency extensions. Then this work is
extended to MIMO frequency selectively channel in [4]. In [5],
the upper bound of mean loss in sum rate is addressed and
analog CSIT feedback is considered to decrease the overhead.
By exploiting channel’s temporary correlation, a differential
quantization strategy is proposed to reduce further overhead in
[6]. However, at high SNR, conventional quantization strategy
requires a huge codebook which is impractical. Codebook size
is the bottleneck of the performance of IA. In this paper,
we propose a joint real Grassmannian quantization strategy
to reduce codebook size.
IA scheme tries to mitigate interference to a low level.
However, with limited codebook, the achieved CSIT is in-
accurate which causes interference leakage. Even with limited
codebook, quality of service (QoS) could be satisfied when
the interference leakage is weak. In this paper, we raise the
question: how large should the codebook be to ensure the QoS
of interference network?
The contribution of this paper is presented in two part-
s. First, the noise-limited criterion is proposed to ensure
QoS, and a joint real Grassmannian quantization strategy is
proposed in this paper. In SISO interference network with
frequency extensions, we analyze the average interference
leakage through chordal distance. Results indicate that inter-
ference leakage depends on the chordal distance. Then, by
analyzing the chordal distance of conventional strategy and
our proposed strategy, a key observation is achieved that our
proposed strategy has a smaller chordal distance. Second,
under the noise-limited criterion, the codebook size using our
proposed strategy is much smaller than that of the conventional
strategy.
Notation: Capital and small bold letters represent matri-
ces and vectors; A
H
and A
T
stand for conjugate trans-
pose and transpose of A respectively; a
∗
represents the
conjugate of vector a; tr (A) is the trace of matrix A;
A ◦ B is the Hadamard product of the matrices A and
B; F
N
(x)=
N
n=1
x (n) e
−j2πnk/N
is the N -point discrete
Fourier transform (DFT) of vector x; C
M×N
and R
M×N
are the set of complex and real matrices with M rows and
N columns respectively; C
N
is the N dimensional complex
space; E[x] stands for the expectation of x; diag (x) is the
diagonal matrix with diagonal vector x; I
N
is identity matrix.
II. S
YSTEM MODEL
Throughout the paper, we make such four assumptions:
• Each receiver has error-free feedback links to transmit-
ters.
• Perfect channel estimation at receivers.
• Perfect time and frequency synchronization, and cyclic
prefix is long enough to accommodate the impulse re-
sponse of any channels.
2014 IEEE 25th International Symposium on Personal, Indoor and Mobile Radio Communications
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