IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 11, NO. 2, FEBRUARY 2012 703
A New Design of Polar-Cap Differential Codebook
for Temporally/Spatially Correlated MISO Channels
Junil Choi, Bruno Clerckx, Namyoon Lee, and Gil Kim
Abstract—Accurate channel direction information is essential
to achieve considerable capacity gains in multiple-input multiple-
output (MIMO) wireless communication systems. Limited feed-
back using a polar-cap differential codebook which utilizes
the temporal correlation in multiple-input single-output (MISO)
channels is presented in this paper. We first describe the
general properties of the polar -cap differential codebook and
then explain the design methodology of the size of the polar-
cap given the temporal correlation coefficient. We also propose
an enhancement of the polar-cap differential codebook which
is suitable for a spatially correlated channel. We compare the
polar-cap differential codebook with a rotation-based differential
codebook in terms of the chordal distance to demonstrate the
superiority of the polar-cap differential codebook. Monte Carlo
simulation results show that the polar-cap differential codebook
facilitates a significant performance gain in both temporally and
spatially correlated channels.
Index Terms—Temporally/spatially correlated multiple-input
single-output (MISO) channel, limited feedback, differential
codebook.
I. INT RODUCTION
M
ULTIPLE-INPUT multiple-output (MIMO) systems
have drawn a considerable amount of attention over
the past few decad es owing to their ability to enhance capacity
using the spatial dimension to transmit multiple data streams
simultaneously [1]. In single-user (SU) MIMO systems, while
channel direction information (CDI) at the base-station (BS)
side is not necessary to achieve a multiplexing gain, the
beamforming gain is highly affected by the accuracy of CDI,
especially in the low-rank transmission case. Contrary to SU-
MIMO, the BS should h ave CDI to achieve a multiplexing gain
in multiple-user (MU) MIMO broadcasting systems. In MU-
MIMO, it is well known that the capacity increases linearly
with the minimum number of transmit antenna and users [2].
The optimal transmit scheme for MU-MIMO is Dirty-Paper-
Coding (DPC) [3], but this type of non-linear precoding is
difficult to implement in practice. A practical linear precoding
scheme, known as Zero-Forcing Beamforming (ZFBF) has
been shown to achieve the optimal sum-rate of MU-MIMO as
Manuscript receive d February 18, 2011; revised June 21, September 7
and November 3, 2011; accepted November 13, 2011. The associate editor
coordinating the review of this paper and approving it for publication was
Prof. H. Nguyen.
J. Choi is with the Department of Electronic and Computer Engineering,
Purdue University, West Lafayette, IN (e-mail: junil.choi@gmail.com).
B. Clerckx is with the Department of Electrical and Electronic Engineering,
Imperial College London (e-mail: b.clerckx@imperial.ac.uk).
N. Lee is with the Department of Electronic and Computer Engineering,
Uni versity of Texas at Austin (e-mail: namyoon.lee@gmail.com).
G. Kim is with the DMC R&D Center , Samsung Electronics (e-mail:
giil.kim@samsung.com).
Digital Object Identifier 10.1109/TWC.2011.122211.110313
the number of users increases [4]. However, the gain is only
possible when the BS has perfect CDI, which is unrealistic
in practice because conventional wireless communication sys-
tems employ limited feedback at the BS to acquir e CDI. With
limited feedback, ZFBF MU-MIMO becomes interference-
limited due to the inter-user interference caused by channel
quantization errors [5].
Therefore, the p erformance of SU/MU-MIMO systems are
sensitive to the codebook which is used to quantize the
channel. An appropriate codebook design depends greatly on
the channel statistics. The Grassmannian-Line-Packing (GLP)
codebook is known to be optimal for an independent and
identically distributed (i.i.d.) Rayleigh fading channel [6],
[7]. Channel-statistic-based codebook adaptation methods for
a spatially correlated channel have been investigated with
several studies appearing in the literature [8]–[12]. Other
advanced feedback schemes utilizing a temporally correlated
channel have also been investigated [13]–[19] and [12]. Espe-
cially, [13] and [15] have proposed a transmission subspace
tracking method, while other schemes have attempted to
track the channel itself or the CDI. There are also other
approaches to enhance the performance of MU-MIMO such as
transmission mode selection [20] and feedback bit allocation
approach [21], [22].
Unlike these academic works, 3GPP LTE Rel.8 relies on
a single-fixed codebook which is stored at both the user
terminal and the BS. Common reference signal (CRS) in LTE
prevents the use of an advanced precoding scheme at the
BS. However, IEEE 802.16m and LTE-Adv. have introduced
a user-specific reference signal, also known as a d edicated
pilot, which enables non-codebook based precoding at the
BS. To benefit fully from advanced precoding, 802.16m has
adopted a Differential codebook and a Transformation code-
book, also known as an Adaptive codebook, to reduce quanti-
zation error. Recently, LTE-Adv. has adopted a dual-codebook
structure of 𝑊 = 𝑊
1
𝑊
2
where 𝑊
1
and 𝑊
2
represent the
wideband and subband channel information respectively [23].
The dual-codebook structure has some similarities with the
differential and adaptive codebook for better channel quan-
tization. In IEEE 802.16m, two types of differential code-
books, i.e., a Rotation-based differential codebook [24],[25],
and a Transformation-based (Polar-Cap) differential codebook
[26],[27] have been thoroughly discussed. The rotation-based
differential codebook was closely investigated in earlier re-
search [19]; h owever, there is no analytical explanation of the
polar-cap differential codebook in the literature thus far. Only
the structure of the polar-cap codebook has been introduced
for a spatially correlated channel [11] and for a temporally
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2012 IEEE