User Loading in Downlink Multiuser Massive
MIMO with 1-bit DAC and Quantized Receiver
Jindan Xu, Wei Xu, Fengfeng Shi, and Hua Zhang
National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China.
Email: {jdxu, wxu, sff, zhanghua}@seu.edu.cn
Abstract—One-bit digital-to-analog converter (DAC) has been
a promising potential for both cost- and power-efficient massive
multiple-input multiple-output (MIMO) implementation. We in-
vestigate the performance of a downlink massive MIMO with
the 1-bit DAC using regularized zero-forcing (RZF) precoding
serving quantized receivers. By taking the quantization errors
at both transmitter and receivers, regularization parameter for
the RZF is optimized with closed-form solution by applying
asymptotic random matrix theory. The optimal parameter is
discovered as linearly increasing w.r.t. the user loading ratio.
Furthermore, asymptotic sum rate performance is derived and
a closed-form expression of the optimal user loading ratio is
achieved specifically for low SNR. The optimal user loading is
found decreasing with increasing receiver quantization resolu-
tions. Numerical simulations verify our observations.
I. INTRODUCTION
Massive multiple-input multiple-output (MIMO) has gained
significant attentions as a candidate technique for the next
generation wireless communication system [1]. In massive
MIMO, a large amount of antennas equipped at base station
(BS) can provide high spectral and energy efficiency [2]. Re-
cently, low-resolution digital-to-analog converter (DAC) and
analog-to-digital converter (ADC) are considered for serving
each antenna in order to reduce hardware cost and power
consumption. Since the power dissipation of both DAC and
ADC grows exponentially with converter resolutions, few-bit,
or even 1-bit, DAC/ADC can significantly mitigate the power
usage in massive MIMO.
The replacement of low-resolution quantization, however,
inevitably causes performance degradation under various sys-
tem setups. In particular, [3] presented a mathematical perfor-
mance analysis for multiuser massive MIMO downlink using
zero-forcing (ZF) precoder and 1-bit DACs. Few-bit DACs and
two other percoders, i.e., regularized zero-forcing (RZF) and
maximal ratio transmission (MRT), were further discussed in
[4]. As for uplink channels, [5] considered the effects of 1-bit
ADC on channel estimation and revealed satisfactory system
performance in terms of symbol error rate (SER) and mutual
information. The performance analysis was then extended in
[6] for a multiuser relay network using mixed ADCs. Most of
the existing studies focused only on low-resolution converters
at BS side, i.e., few-bit DACs for downlink or ADCs for
uplink. However, the joint effect of finite-bit ADCs at users,
which is in fact even the case in current applications, along
with low-resolution DACs at BS, remains undiscovered.
Moreover, the ability of serving multiple users efficiently,
e.g., in terms of multiuser beamforming implementation, is
an essential advantage of massive MIMO. Therefore, user
loading, namely the ratio of the number of users simultane-
ously served over antenna number, has been recognized as
a cited parameter in system design. It was revealed in [7]
that the user number is optimized as a function of signal-to-
noise ratio (SNR) and other system parameters. Specifically
for a large-antenna system, the optimal user loading ratio
was obtained in [8]. Furthermore, user clustering due to
different path gains was considered in [9] and a group loading
scheme was proposed. While for a massive MIMO with signal
quantization at both sides, however, few has discussed the
nature and optimization of user loading ratio for performance
enhancement.
In this paper, we consider a downlink multiuser massive
MIMO system where efficient 1-bit DACs and finite-bit ADCs
are equipped at BS and user sides, respectively. RZF precoder
is considered in the system. For performance enhancement,
we first optimize the regularization parameter in the RZF
design using the asymptotic random matrix theory [10]. Given
the optimized RZF, we then analyze the asymptotic sum
rate performance of the massive MIMO system. Further by
maximizing the sum rate, the optimal user loading can be
achieved. Especially for low SNRs which is deemed as an im-
portant scenario for massive MIMO, we obtain an asymptotic
closed-form solution to the optimal user loading ratio. Some
design insights for the optimal user loading are accordingly
concluded.
The rest of this paper is structured as follows. System model
is introduced in Section II. In Section III, we derive the
optimal regularization parameter, asymptotic achievable rate
and optimal user loading ratio. Section IV presents simulation
results and conclusions are drawn in Section V.
Notations: A
T
, A
∗
and A
H
represent the transpose, con-
jugate and conjugate transpose of A, respectively. Tr{A}
denotes the trace of A and diag(A) keeps only the diagonal
entries of A. E{·} is the expectation operator.
a.s.
−−→ denotes
the almost sure convergence.
II. SYSTEM MODEL
We consider a multiuser massive MIMO downlink. The
BS has N antennas and simultaneously serves M users each
equipped with a single antenna. In order to reduce power
consumption of driving the massive antenna array, each an-
tenna at BS equips with a 1-bit DAC while each user equips