Spatial Cross-Correlation Properties of MmWave
Massive MIMO Channels
(Invited Paper)
Rui Feng
1
, Jie Huang
1
, Jian Sun
1,2
, Yi Tan
3
, Cheng-Xiang Wang
3
, and Shidong Zhou
4
1
Shandong Provincial Key Lab of Wireless Communication Technologies, Shandong University, Jinan, Shandong, 250100, China.
2
State Key Lab. of Millimeter Waves, Southeast University, Nanjing, 210096, China.
3
Institute of Sensors, Signals and Systems, School of Engineering & Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, U.K.
4
Department of Electronic Enjineering, Tsinghua University, Beijing, 100084, China.
Email: fengxiurui604@163.com, hj 1204@sina.cn, sunjian@sdu.edu.cn, yi.tan@hw.ac.uk, cheng-xiang.wang@hw.ac.uk, zhousd@tsinghua.edu.cn
Abstract—To analyze the propagation characteristics of mil-
limeter wave (mmWave) massive multiple-input multiple-output
(MIMO) channels, channel measurements in an office envi-
ronment using a vector network analyzer (VNA) are carried
out. Detailed parameter settings of the measurement system
and configuration of the large receiver (Rx) antenna array are
introduced. Through dividing the Rx array into several sub-
arrays, characteristics like spherical wavefront, non-stationarity,
and cluster evolution over the array can be found with parameter
estimation using the space alternating generalized expectation-
maximization (SAGE) algorithm. For signals received by the
virtual horizontal planar array, it is shown that the spatial cross-
correlation functions (SCCFs) exhibit significant changes along
different dimensions of the Rx horizontal planar array. Thus, it is
worth taking the relative angle between transmitter (Tx) pointing
direction and Rx array location into consideration while carrying
out channel measurements. It is also verified that the SCCFs can
be influenced by the measurement environment, the coordinates
of antenna elements in the large array, as well as the operated
frequencies.
Index Terms—Massive MIMO, millimeter wave, 5G, planar
array, spatial cross-correlation function.
I. INTRODUCTION
Increasing demands of high capacity, energy efficiency,
spectral efficiency, and reliability have expedited the research
of the fifth generation (5G) communication systems. New tech-
nologies such as mmWave and massive MIMO have been pro-
posed and widely studied to enable a dramatic improvement of
channel capacity and spectrum limitation [1]. The combination
of several techniques also has significant contribution to the
system performance [2]. For example, mmWave and massive
MIMO can be complement regarding the antenna array size
and cell coverage.
MmWave massive MIMO channels show some new charac-
teristics and researchers have carried out many channel mea-
surements to study the propagation channel characteristics. It
was introduced in [3] that, massive MIMO channels exhibited
characteristics such as spherical wavefront and spatial non-
stationarity as the array size is much larger than conventional
MIMO channels. Power imbalance on the antenna array and
statistical properties like spatial-temporal-frequency correla-
tion function (STFCF) were investigated. Lund University
conducted many massive MIMO channel measurements using
128-element uniform linear array (ULA) and cylindrical array,
respectively. The sum-rate capacity and condition number to
separate closely spaced users were investigated [4], and it
was pointed out that the non-stationarity and near field effect
can help decorrelating channels for different users [5]. In [6],
channel measurements carried out at four mmWave frequency
bands with large uniform virtual planar arrays were introduced
to validate the spherical wavefront, cluster birth-death, and
non-stationarity properties. In this paper, we divide the large
antenna array into several sub-arrays and extract channel pa-
rameters for each sub-array using the SAGE algorithm. Thus,
those characteristics can be simply validated by analyzing the
estimated parameters.
However, we find that channel statistical properties like
SCCFs in different dimension of a planar array have never
been analyzed or compared before. This paper focuses on
the discussion of SCCFs along two distinct dimensions of
a horizontal large planar array and impacts of Tx locations
and the operated mmWave frequencies on spatial correlation
properties. We find that SCCF is not only a very useful term
to check the correctness of measurement data, but also able to
show how the channel properties change at different antenna
positions and frequency bands. The correlation coefficient is
verified to be affected by the measurement environment, oper-
ated frequency, relative locations of Tx and Rx, and the angle
between the Tx pointing direction and Rx array. Furthermore,
the difference of SCCFs along different dimensions of the
large array should be taken into consideration while proposing
massive MIMO channel models.
The remainder of this paper is organized as follows. The
signal model is introduced in Section II. Channel measurement
environment and system setups are described in Section III. In
Section IV, the measurement results are given and the SCCFs
are analyzed. Finally, conclusions are drawn in Section V.