IEEE Signal Processing - May 2018 - 53

is determined, the training symbols can be designed by using
the channel common and/or individual sparsity in the systems.
Besides using the common support, the work in [50] proposed
a new pilot structure with joint common and dedicated sup-
port, where the common one is used to estimate the common
channel parameters of the related users in multiuser massive
MIMO systems, while the dedicated support is used to esti-
mate the individual channel parameters of each user.
Besides the general massive MIMO systems, Alkhateeb
et al. designed a compressed hierarchical multiresolution
codebook specially for mm-wave massive MIMO systems to
construct training beamforming vectors [51]. Based on this
idea, others have proposed many different hierarchical multi-
resolution codebooks from different angles. For example, the
research in [52] produced a design of a compressive beacon
codebook with different sets of pseudorandom phases. The
authors of [53] proposed a common codebook satisfying the
conflicting design requirements as well as validating practical
mm-wave systems through utilizing the strong directivity of
mm-wave channels. Wang et al. [54] proposed a multireso-
lution uniform-weighting-based codebook, similar to a nor-
malized discrete FT matrix, to reduce the implementation
complexity, where the estimation of the angle of arrival and
angle of departure will have a much lower training overhead.
Therefore, the codebook-based beamforming training proce-
dure can achieve a good balance between complexity and high
performance for practical systems.

Scatters for User 1
at BS Side

Compressive channel estimation and feedback
CS can be used to reduce the cost of channel estimation and
feedback by exploiting the channel sparsity. The existing
CS-based channel estimation and feedback schemes can be
divided into the following three categories according to the
exploiting of sparsity in different domains.

With time-domain sparsity
Work has shown that the channel slowly varies in a number of
applications so that the prior channel estimation result can still
be used to reconstruct subsequent channels, as illustrated in
Figure 8. By using the structure in the figure, investigators
have proposed several CS algorithms [8], [55], [56] to recover
massive MIMO channels.
Exploiting the common time-domain support, Shen et al.
proposed a CS-enabled differential CSI estimation and feed-
back scheme [55]. The approach in [56] further combines LS
and CS techniques to improve estimation performance. Here,
the LS and CS techniques can be used to, respectively, esti-
mate a dense vector obtained by projecting into the previous
support and a sparse vector obtained by projecting into the
null space of the previous support. Since the current channel
vector has only a small number of nonzero elements outside
the support of the previous channel, the proposed scheme
can reduce the pilot overhead and improve the tracking per-
formance of the channel subspace. Since the quality of the
prior support information will affect the estimation accuracy,

Local Scatters for
User 1

Initial Channel Hk

Sparsity
ω
Representation Hk

H1 = AH1

Common Scatters
for All Users

BS with
Large-Scale
Antennas

Individual Parameters

Local Scatters for
User K

Common Parameters

Scatters for User
K at BS Side
ω

HK = AHK

Nonzero Elements

Zero Elements

FIGURE 7. A channel model with limited scatters, where A is the spatial correlation matrix.
IEEE Signal Processing Magazine

May 2018

Table of Contents for the Digital Edition of IEEE Signal Processing - May 2018