Downlink and Uplink Transmissions in Distributed
Large-Scale MIMO Systems for BD Precoding with
Partial Calibration
Hao Wei, Dongming Wang, and Xiaohu You
National Mobile Communications Research Lab., Southeast University, China; wangdm@seu.edu.cn
Abstract—When both access points (APs) and user equipments
(UEs) have multiple antennas, the block diagonalization (BD)
precoding is preferred for the distributed large-scale multiple-
input multiple-output (MIMO) systems. In time division du-
plexing (TDD) operation, the APs can exploit the estimated
uplink channel for downlink joint precoding transmission to
simultaneously serve multiple UEs, due to the principle of
channel reciprocity. However, the non-symmetric hardware radio
frequency (RF) circuits at both sides of the link disable the
channel reciprocity and result in a system performance loss.
Based on a low complex BD precoding method, this paper designs
a scheme for both the downlink and the uplink transmissions
with the partial calibration. Theoretical analysis and simulation
results show that the inter-stream interference (ISI) can be
canceled out at the UEs through the minimum mean square
error (MMSE) receiver in the downlink transmission. While in
the uplink transmission, the APs can distinguish each data stream
of every UE via the maximal ratio combining (MRC) receiver.
Besides, the interference suppression precoding matrix at the APs
can be used for both the downlink and uplink transmissions,
which need to be calculated only once.
Index Terms—large-scale MIMO, reciprocity calibration, time
division duplexing, block diagonalization
I. INTRODUCTION
Massive multiple-input multiple-output (MIMO), also
named as large-scale MIMO has been becoming a promising
technique for the next generation of wireless communication
systems, because its significant ability to improve the spectral
efficiency and reduce the radiated power [1]. As an effective
deployment pattern, distributed large-scale MIMO systems
has drawn much attention in the past few years, where the
antennas are located at several access points (APs) which are
distributively deployed and connected to the central processing
unit by the high-bandwidth optical fibers [2]–[6]. In time di-
vision duplexing (TDD) operation, the transmitter can exploit
the estimated uplink channel for downlink joint precoding
transmission to simultaneously serve multiple users, due to the
principle of channel reciprocity [1]. However, the hardware
radio frequency (RF) circuits at both sides of the link are
usually not symmetric [7]. The RF mismatches disable the
channel reciprocity and result in a system performance loss.
Recently, many researches have been focused on the cali-
bration methods. In [8], total least square (TLS) method was
proposed for MIMO systems. Although this full calibration
method can compensate for the RF mismatches at both the
transmitters and receivers [9], the large feedback overhead
from the UEs will be unacceptable in large-scale MIMO
systems. While, according to the analysis in [10] [11], the RF
mismatches at the UEs have a negligible impact on the system
performance. Thus, it seems enough to only calibrate the RF
mismatches at the transmitters, which is called the partial
calibration [9]. To avoid involving UEs into the calibration
process, the Argos method [12] and the least squares (LS)
method [13] were proposed, where the transmitters exchange
calibration signals only with themselves.
However, most papers about the partial calibration only
investigated the zero-forcing (ZF) precoding, and just con-
sidered the special case for single-antenna UEs. Although
ZF scheme is one of the simplest precoding techniques for
this case, its performance is rather poor due to a transmit
power boost issue and it is still confined to a single receive
antenna case [14]. When the UEs have multiple antennas, the
block diagonalization (BD) is a well-known precoding scheme
[15]. As a generalization of the ZF for multi-user MIMO
systems, the BD attempts to completely eliminate the inter-
user interference (IUI) without any consideration on the noise
[14]. Nevertheless, with BD precoding, although performing
the perfect partial calibration, the RF mismatches at the UEs
still cause the inter-stream interference (ISI) and lead to a
performance degradation [16]. Therefore, it is essential to
investigate the calibration problem for the BD precoding.
This paper is focused on the performance analysis for
distributed large-scale MIMO systems with BD precoding.
To reduce the high complexity of the singular value de-
composition (SVD) for large matrix, we use a low complex
BD precoding method which only computes a simple matrix
inversion [14]. To the best knowledge of the authors, most
papers only investigated the downlink transmission, while the
uplink transmission is not yet considered. Thus, we design a
scheme for both the downlink and the uplink transmissions
with the partial calibration. By this transmission scheme, the
ISI can be canceled out at the UEs through the minimum mean
square error (MMSE) receiver in the downlink transmission.
While in the uplink transmission, the APs can distinguish each
data stream of every UE via the maximal ratio combining
(MRC) receiver. Furthermore, the interference suppression
precoding matrix at the APs can be used for both the downlink
and uplink transmission, which need to be calculated only
once.
The notation adopted in this paper conforms to the fol-
lowing convention. Vectors are denoted in lower case bold:
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