In this paper, we present the biterror rate (BER) performance of quasiorthogonal spacetime block code (QOSTBC) massive multipleinput multipleoutput (MIMO) system employing up to 32 transmit and receive antennas. The QOSTBC, due to its advantages in transmission rate and decoding complexity, is an important transmit diversity scheme for more than 2 transmit antennas. As massive MIMO implies very large number of antennas, practically at least more than 15 antennas, a different number of transmit and receive antennas (i.e. 2×2, 4×4, 8×8, 16×16 and 32×32) using QOSTBC for the massive MIMO system are considered. The BER performance of the massive MIMO with antennas up to 32×32 using BPSK modulation scheme is analyzed. Simulation results show that the fullrate massive MIMO systems with QOSTBC give a significant performance improvement due to increasing diversity effect, compared with previously considered massive MIMO systems.
Ⅰ. Introduction
As mobile communication systems evolve, higher transmission data rate, higher spectral efficiency and higher reliability requirements have been an important issue. To meet these requirements, massive multipleinput multipleoutput (MIMO) technology has become an attractive field of research and massive MIMO can be built with inexpensive, lowpower components
[1]
. Massive MIMO communication is widely considered to be an appropriate to achieve much higher bandwidth efficiency and improve the performance reliability of modern wireless communication
[2]
. The massive MIMO transmission of signal processing is performed in time and spatial dimensions by utilizing multiple, spatially distributed antennas at both transmitting and receiving sides.
In addition, combining with spacetime codes (STC)
[3]
, the usage of multiple antennas offers not only enormous spectral efficiencies but also a significant improvement in system performance. STC techniques such as Alamouti’s spacetime block code (STBC) that combine coding, modulation and signal processing in wireless communication, have been used to achieve spatial diversity and improve the biterror rate (BER) performance
[4

6]
. The transmit diversity scheme proposed by Alamouti
[7]
is a simple and effective orthogonal spacetime block codes (OSTBCs or STBCs) of the full rate with two transmit antennas for the system. OSTBCs
[8]
based on orthogonal design are the most interesting schemes among spacetime codes. They can significantly improve signal quality in quasistatic MIMO channel due to their fulldiversity property.
Unfortunately, for more than 2 transmit antennas, the rate of the OSTBC
[9]
, defined by the number of symbols transmitted divided by the number of time slots used by the OSTBC, cannot be larger than 3/4 [10]. However, we can achieve the rate larger than 3/4 for more than 2 transmit antennas using QuasiOrthogonal STBC (QOSTBC) methods
[11]
. The QOSTBC is a very attractive transmit diversity scheme in terms of rate and decoding complexity. In
[12]
, however, the number of transmit antennas for a rateone QOSTBC was limited to 8. For massive MIMO systems, however, the number of antennas must be larger than at least 15. Therefore, a more thorough investigation in a true massive MIMO configuration with a large number of antennas still needs to be reported.
In this paper, we present a true massive MIMO with a large number of transmit and receive antennas up to 32 and perform comparative evaluation over different configurations. The main idea of increasing antennas is to increase the capacity with increasing error performance, i.e. decreasing BER. Therefore, we focus on BER reduction with full rate for a large number of antennas.
The rest of the paper is organized as follows. We explain about the massive MIMO system model in Section 2. The spacetime block code is discussed in Section 3. Section 4 describes quasiorthogonal spacetime block code. In Section 5, simulation results are presented. Finally, conclusions are drawn in Section 6.
Ⅱ. Massive MIMO System Model
Recently, massive MIMO systems, or largescale antenna systems, have been investigated as new cellular network architecture for next generation highspeech wireless communications with several attractive characteristics. Massive MIMO can improve spectrum efficiency (SE), energy efficiency (EE) and reliability just by configuration massive antenna arrays at the existing base stations (BSs), which has been seen as a promising technology for future wireless communication systems
[13]
. This great potential of massive MIMO has stimulated great interest from both academics and industry.
Let N
_{t}
denote the number of antenna elements at the transmitter, and N
_{r}
the number of antenna elements at the receiver. The channel with N
_{r}
outputs and N
_{t}
inputs is referred to a N
_{r}
×N
_{t}
matrix. The MIMO system model can be represented as
where
Z
∈
C^{Nr}
^{x1}
denote the received complex vector,
ω
∈
C^{Nt}
^{x1}
is the complex vector representing the transmitted signal.
H
∈
C^{Nr}
^{x}
^{Nt}
is the complex channel matrix and
υ
∈
C^{Nr}
^{x1}
is the noise vector, whose components are complex circular symmetric Gaussian with zero mean and unit variance, where
σ_{v}
is the standard deviation of the noise at that receiver, given by
for unit signal power. The signaltonoise ratio (SNR) is defined as SNR=E
_{b}
/N
_{o}
when BPSK is employed.
Fig. 1
depicts such MIMO system block diagram.
대규모 MIMO 블럭도 Fig. 1 Block diagram of massive MIMO system
Ⅲ. SpaceTime Block Code
The term STBC, in general, is used to describe transmission schemes capturing these high data rates attainable by MIMO channels
[14]
. The STBC matrix has columns equal to the number of the transmit antennas and rows equal to the number of the time slots required to transmit the data. The STBC is represented by a matrix, where
T
denotes the number of time slots
[15]
and
k
refers to the number of independent complex information symbols in the codeword which are transmitted per time slot
T
. The code rate of STBC is defined as
k/T
. The channel with N
_{r}
receiver antenna and N
_{t}
transmitter antenna is modeled by a matrix.
where u
_{ij}
denotes information data symbol transmitted at time slot
i
and from
j
th transmit antenna. The orthogonal code was shown in
[8]
that rate1 generalized real orthogonal designs (ODs) and rate3/4 generalized complex orthogonal designs exist for any dimension. In addition, rate3/4 complex orthogonal designs were provided for the specific dimensions of two, three, and four. For real ODs, every entry of the code matrix is a linear combination of the information symbols. For example, the codeword matrices of the 2×2 and 4×4 real orthogonal designs are given by
In complex ODs, both the information symbols and their conjugates are utilized. The ith column of the code matrix can contain either the information symbols u
_{1}
,⋯, u
_{T}
, or their conjugates u
_{1}
^{*}
, ⋯, u
_{T}
^{*}
only. The spacetime block code proposed by Alamouti
[7]
uses the complex orthogonal design. Orthogonal structure of code matrix of Alamouti scheme expressed in (5) achieves fullrate and full diversity.
Here, two time slots are required to transmit two symbols. Thus,
k
=2 and
T
=2. The Alamouti code is the first STBC that provides full diversity at full data rate when transmitter has two antennas and simple linear processing under the assumption of no channel state information at the transmitter (CSIT) but perfect channel state information at the receiver (CSIR)
[8]
. It has been generalized for four transmit antennas as given in equation (6)
Ⅳ. QuasiOrthogonal SpaceTime Block Code
Alamouti code provides the full rate with full diversity for two antennas. Although Alamouti code can be further generalized for more than two antennas by using the concept of orthogonal designs, unfortunately, it does not provide any coding gain nor achieve a rate larger than 3/4
[16]
. It is also proved in
[17]
that a complex orthogonal design and corresponding STBC which provide full diversity and full transmission rate is not possible for more than two antennas. Alamouti scheme is the only example of a fullrate fulldiversity complex STBC using orthogonal designs.
QOSTBC is a full rate STBC for more than two transmit antennas. To design full rate codes with complex constellation, we consider codes with a decoding pair of symbols
[17]
. Such nonorthogonal codes for the 4 transmit antennas given in equation (7) are called QOSTBC.
In this code matrix column 1 and 2 as well as columns 3 and 4 are orthogonal to each other. We represent the ith column of above matrix by z
_{i}
. Then, for any intermediate variable u
_{1}
, u
_{2}
, u
_{3}
, u
_{4}
, we have
In (8), subspace created by
z
_{1}
and
z
_{4}
is nonorthogonal to the subspace created by
z
_{2}
and
z
_{3}
. This is why they are called quasiorthogonal STBC codes.
Although Jafarkhani
[17]
built the transmission matrix for 8 transmit antennas from 4 antennas, the 8x8 matrix cannot provide more than
rate code. For example, we compare two quasiorthogonal STBCs with different rates for eight transmit antennas. The Jafarkhani QOSTBC for 8 transmit antennas (N
_{t}
) to send 6 information symbols (
k
) in 8 time slots that use
T
time slots is shown in (10)
[17]
.
The rate R of this QOSTBC code is,
The proposed design of transmission matrix for the same transmit antennas is shown in (12). This matrix is clearly a QOSTBC and sends
k
=8 information symbols in 8 time slots. Therefore, the rate of this QOSTBC code is
The BER performance of QOSTBC in massive MIMO is evaluated through simulations and the results are discussed in the next section.
Ⅴ. Simulation Results
In this section, computer simulations are conducted to investigate the BER performance of the massive MIMO system. When we increase the QOSTBC matrix size (see in (12)), we evaluate the BER performance according to the matrix size (i.e., the number of antennas). It should be noted that for increasing the number of antennas, the STBC code should be matched to the antenna number. In the simulation, we increased the number of antennas up to 32, by designing the QOSTBC code into the size of 32×32. In order to examine the BER performance, the massive MIMO system using QOSTBC with 1×1, 2×2, 4×4, 8×8, 16×16 and up to 32×32 number of antennas is implemented and the results are shown in
Figs. 2
and
3
.
1×1, 2×2, 4×4 및 8×8 대규모 MIMO 성능 Fig. 2 Performance of massive MIMO system with1×1, 2×2, 4×4 and 8×8 antennas
32×32, 16×16, 8×8 및 4×4 대규모 MIMO 성능 Fig. 3 Performance of massive MIMO system with32×32, 16×16, 8×8 and 4×4 antennas
In this simulation, the modulation used is BPSK and the total transmit signal power was equally divided by the number of antennas. The channel is assumed to be an Additive White Gaussian Noise (AWGN) channel. The results are observed with the assumption that the channel state information is perfectly known to the receiver. The parameters used in the simulation are shown in
Table 1
.
시뮬레이션 파라미터Table. 1 Parameters of the Simulation
시뮬레이션 파라미터 Table. 1 Parameters of the Simulation
Simulations are carried out for evaluating performances with different SNR values.
Figs. 2
and
3
show a significant performance improvement when the number of transmit and receive antennas increases. Also, a greater performance improvement is observed with increased SNR.
Fig. 2
shows BER performance of the massive MIMO using QOSTBC with 1×1, 2×2, 4×4 and 8×8 number of antennas. As can be seen in
Fig. 2
, increasing the number of antennas results in significant BER performance. In case of higher SNRs, BER decreases drastically. It is important to note that the performances of massive MIMO increase with a higher number of transmit and receive antennas. This is due to diversity from a large number of transmission paths deliberately created. In the 8×8 configuration, the BER performance shows nearly 10
^{4}
at a SNR value of 0dB.
Fig. 3
illustrates the comparison of the BER performances of massive MIMO with 4×4, 8×8, 16×16 and 32×32 number of transmit and receive antennas using QOSTBC. The BER performances increase as more antennas at both sides are employed. The best BER performance is achieved with the 32×32 configuration as expected. Therefore, it can be said that an increasing number of antennas in massive MIMO provide significant increase in diversity gain and subsequently BER improvement.
Ⅵ. Conclusions
We have presented the BER performance of massive MIMO systems with up to 32×32 antenna configuration using QOSTBC. The performances are compared with a different number of transmit and receive antennas under the BPSK modulation scheme. Simulation results for QOSTBC in massive MIMO show a consistent performance improvement with increasing number of transmit and receive antennas.
It is concluded that QOSTBC shows full rate and is an adequate modulation format for massive MIMO. The work for massive MIMO performance evaluation under fading conditions as well as with imperfect channel state information can be undertaken. In addition, a field test of the proposed system could be of interest as future works.
Acknowledgements
This work was supported by a Research Grant of Brain Busan (BB) 21 Project (2014 year)
BIO
킨자치윈 (Khin Zar Chi Winn)
2011년 Department of Information Technology, Technological University (Thanlyin), Myanmar (공학사)
2015년 부경대학교 정보통신공학과 (공학석사)
※관심분야 : OFDM, MIMO, massive MIMO
정연호(Yeon‑ho Chung)
1984년 경북대학교 전자공학과 (공학사)
1992년 영국 Imperial College London (공학석사)
1996년 영국 Liverpool University (공학박사)
2006년 미국 Pennsylvania State University 객원교수
2001년 ~ 현재 부경대학교 정보통신공학과 교수
※관심분야 : 가시광통신 기술, 적응 변복조, OFDM
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